atmosphere. A plasma-induced nonequilibrium electrochemistry system was employed for the functionalization of the CNT ribbons, utilizing direct-current microplasma generated in helium between a nickel capillary tube and the electrolyte surface. The CNT ribbons underwent treatment at a constant current for 15 min and two distinct plasma–liquid treatments were investigated: one consisting of a 1:9 ethanol:water ratio and another containing 10% ethylenediamine in the same stock solution. Following plasma treatments, the ribbons were rinsed in distilled water and disentangled by sonication to form NFs. Yu et al. [66] prepared carbon-based nanofluids using a modified vortex trap method, which utilizes water mist to collect carbon NPs produced by oxygen–acetylene combustion, equipped with an external circulation device that improved carbon NP collection efficiency and production rate. In a separate study, Chen et al. [68] prepared carbon quantum dots and dispersed them in PEG-200 using a microwave heating method. They employed a 700 W home-used microwave oven to heat 5 mL of PEG-200. This heating process led to the breakdown of PEG chains, which subsequently oxidized into various fragments in the presence of oxygen, ultimately forming a surface passivation layer. The degree of carbonization was controlled by adjusting the microwave heating duration. Guo et al. [69] prepared three NFs of graphene oxide (GO), multiwalled CNTs, and Ti3C2 in 1-Butyl-3-methylimidazolium tetrafluoroborate. Commercial samples of GO and CNTs were used, while Ti3C2 was synthesized using a solvent etching method. Briefly, they dissolved 8 g of lithium fluoride in 100 mL of HCl solution (10 M) and added 5 g of Ti3AlC2 MAX to polyethylene while stirring in a water bath. The final suspension was stirred for two days and washed with water, and a thin layer of Ti3C2Tx was collected after multiple centrifugations and ultrasonication steps. In an extensive study on CNTs, Mesgari et al. [70] chemically functionalized single-, double-, and multiwalled CNTs and produced three different NFs with water, propylene glycol (PG), and Therminol. The NFs were prepared using probe-type sonication in a water–ice bath.

#### *2.4. Metal Oxide Nanoparticles*

Metal oxides, including copper oxide, zinc oxide, titanium dioxide, and iron oxide, can absorb solar radiation with limitations imposed by their bandgap. Upon light absorption, electrons are excited from the valence band to the conduction band, generating electronhole pairs [71]. The relaxation from excited states releases energy in the form of heat [72]. The efficiency of light-to-heat conversion in metal oxides is highly dependent on factors such as material composition, crystal structure, and surface properties.

Copper oxide NPs have emerged as a prominent material in solar thermal conversion research due to their unique properties. In a recent study conducted by Moghaieb et al. [29], the authors synthesized surfactant-free CuOx NPs by plasma-induced nonequilibrium electrochemistry, which featured a sacrificial copper foil anode and a capillary tube cathode. The researchers prepared a 6 mL electrolyte solution by combining equal parts of sodium chloride, sodium nitrate, and sodium hydroxide, without the addition of reducing, capping, or stabilizing agents. They maintained atmospheric-pressure microplasma for 30 min at the electrolyte surface, leading to a visible colour change from transparent to orange. Following centrifugation, heat drying, and annealing at 400 ◦C for 6 h, a completely black powder was obtained, suggesting a phase transformation due to thermal oxidation. Both annealed and nonannealed CuOx NP powders were then separately re-dispersed in ethylene glycol (EG) at different volume fractions and subjected to sonication to achieve homogenous dispersions. In an extensive study by Milanese et al. [73], the researchers investigated a broad array of metal oxide water-based NFs, encompassing commercially available Al2O3, CuO, and TiO2, as well as CeO2, ZnO, and Fe2O3, prepared via the hydrolytic synthesis method. For instance, the CeO2 NPs were synthesized by dissolving 2.6 mmol Ce(NO3)3·6H2O in methanol, followed by the addition of acetylacetone. Subsequently, a 30 wt% ammonia solution in water was introduced to the mixture, which was then vigorously stirred for 24 h. The final suspensions of CeO2, ZnO, and Fe2O3 NPs were acquired after centrifugation, ensuring optimal particle collection. Moreover, magnetic metal oxides have gained considerable interest due to their unique magnetic properties. In a study by Balakin et al. [74], the authors prepared a magnetic Fe2O3/water NF by mechanically stirring Fe2O3 NPs in distilled water and subjecting the suspension to bathtype sonication at 130 W for 30 min. They refrained from using surfactants to avoid potential electromagnetic and rheological impacts on the solar thermal conversion process. In a related study, Hosseini and Dehaj [75] prepared Fe2O3/water and Fe3O4/water NFs by employing more powerful sonication (probe ultrasonicator at 300 W) and incorporating the surfactant sodium dodecylbenzene sulfonate (SDBS) with a neutral pH to improve colloidal behaviour. Afterwards, the mixture was re-sonicated using a bath-type sonicator. They ultimately obtained two NFs at volume fractions of 0.005%, 0.01%, and 0.02%, further expanding the range of potential applications in solar thermal conversion processes.

Considering the plasmonic absorption properties of Ag NPs and antimony-doped tin oxide (ATO) NPs in the visible and near-infrared spectra, Sreekumar et al. [76] developed a multicomponent ATO–Ag/water NF to enable broader absorption across these regions and potentially enhance STC efficiency. They prepared the mixture through a reduction reaction involving Sb2O5, SnCl2, HCl, AgNO3, and ATO NPs. Following the chemical reduction process, the ATO–Ag NP solution was washed and dried in a hot air oven at 60 ◦C. The ATO–Ag NPs were finally re-dispersed in distilled water and sodium dodecyl sulfate (SDS) surfactant was added to improve the stability of the NFs. As an example of a semiconducting nitride, titanium nitride (TiN), which exhibits strong plasmonic absorption, can be highlighted. Wang et al. [77] prepared TiN NPs/EG by dispersing 0.1135 g of TiN NPs in 1000 mL of EG, followed by simultaneous stirring and ultrasonication for 30 min, resulting in a concentration of 0.01 wt.%. Further dilutions using ultrasonication yielded concentrations of 0.001 wt.%, 0.003 wt.%, 0.005 wt.%, and 0.007 wt.%.

*Nanomaterials* **2023**, *13*, 1232

*Nanomaterials* **2023**, *13*, 1232

#### **3. Energy Flow in Solar Thermal Nanofluids Used in DASCs**

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 13 of 32

Light interaction with an NF can give rise to several physical and chemical phenomena (Figure 3), establishing a flow pattern for the energy originating from solar photons. Here we consider phenomena taking place within the NF, as interface interactions such as reflection, etc., at the front- and back-end of the NF can be discussed under textbook optics. The extent of energy exchange and the mechanisms involved strongly depends on the material characteristics of the NP in the NFs [91–96] as well as the size/shape of the NPs and their concentration in the NF. With reference to Figure 3, heating of the working fluid, hence its temperature increase, is ultimately the desired 'finish-line' for the energy flow. Note that the temperature of the NPs may not be at equilibrium with the fluid temperature under solar irradiation, hence the NPs and the working fluid should be considered separately. the NFs and can represent a form of energy loss that has received little attention so far. Localized heating can result in the degradation of NPs and agglomeration over time under several operating conditions such as high solar and thermal loadings as well as solar and thermal cycling. This type of energy loss to chemical energy (transformation of matter) is extremely important not only because it reduces the STC efficiency but also because it can impact the chemical/physical stability of the NFs, hence their long-term applicability. As NPs exhibit temperature values that are higher than the working fluid, heat conduction occurs only in one direction, i.e., from the NPs to the working fluid. While NP IR emissions can be significant in some cases, this can be often re-absorbed directly by the working fluid and should not represent a major loss mechanism.

**Figure 3.** Energy flow in solar thermal nanofluids (nanoparticles and base fluid). **Figure 3.** Energy flow in solar thermal nanofluids (nanoparticles and base fluid).

**4. Fundamental Optical Characterisation of Nanofluids for DASCs**  Conventional base fluids used in DASCs are strong absorbers in the UV and IR regions, which represents 57% of the total solar energy; however, they are transparent in the Vis part, meaning that 43% is mostly lost as transmitted light [20]. Figure 4a reports the solar irradiance together with the transmittance spectra for four relevant working fluids used in DASCs. The optical characteristics of the working fluids result in power absorbed (Figure 4b), which clearly shows that very little solar irradiance is used up to ~900 nm. The main functionality in adding NPs to these base fluids is, therefore, to compensate for this by absorbing the solar energy present in the Vis region. In this view, studying the absorption and scattering behaviours of NFs is essential in evaluating their potential as working media in DASCs since this determines to what extent the NF can effectively uti-Transmission, scattering, and absorption are the three main light–matter interaction events to be considered. As illustrated in Figure 3, the two components of NFs, i.e., the NPs and the base fluid, interact differently with light. While both can absorb light to varying degrees with different patterns over the solar spectrum, only NPs can scatter light. Transmitted light is lost energy with no possibility of being recovered. Light that is scattered when travelling through the NF [96] can be in part 'recycled' with chances of being completely lost through transmission, scattered again, or eventually absorbed. Hence, scattering can only lead to partial light re-absorption and should be minimized in favour of direct absorption. Absorbed light, either by the working fluid or the NPs, is energy that becomes available for conversion into heat; however, several energy-loss paths are still possible, especially after absorption by the NPs.

lize solar radiation energy [99,100]. For the performance improvement of DASCs, it is ultimately desirable to increase absorption, which can be impacted by the shape, size, material type, and concentration of the NPs, as well as the type of base fluid [101]. Direct light absorption by the working fluid is a very efficient energy conversion process as the only loss mechanism after absorption is represented by the fluid IR emission if the NF is adequately insulated. NP light absorption initially produces an excited state for electrons and the subsequent decay is highly dependent upon the material characteristics and composition. For instance, metallic NPs generally exhibit fast phonon emissions [97,98], hence increasing the NP temperature very quickly before any other loss mechanism can take place. Some metals or materials with high carrier concentrations can exhibit plasmonic absorption, i.e., enhanced absorption at specific wavelength ranges. This can be beneficial if the absorption range is within the visible and still relatively broad. However, plasmonic electronic excitation is often abrupt and generates high electric fields at the NP surface, which could result in cavitation (in extreme cases) or sudden temperature changes at the NP–fluid interface that could be detrimental to the chemical stability of the NFs.

In nonmetallic NPs that feature an energy bandgap, such as metal oxide or semiconducting NPs, electrons decay through phonon emissions down to the bandgap edge; there, phonon emission is either prohibited or sufficiently slow for other mechanisms to take

place. A similar process can take place due to surface states, where electron relaxation through phonon emission can be prevented. For instance, photoluminescence (PL), i.e., the re-emission of a photon of a lower wavelength than the one that was absorbed, can occur in these cases. Similar to scattering, PL can recycle the light, and minimizing this phenomenon in the UV–Vis range in favour of direct absorption is preferred. Slow electron decay, especially due to surface states can also enhance NP–fluid chemical reactions and possibly pose a challenge to NF stability through its degradation. Hence fast phonon emission is the preferred channel also for metal oxide and semiconducting NPs, where a higher bandgap generally reduces heating and increases energy losses.

Upon heating the NP and a temperature rise, heat conduction from the NPs to the working fluid takes place. Stabilizers or surfactants that are often used in chemical synthesis introduce an additional thermal resistance which could locally increase the temperature at the interface between the NPs and the working fluid. Localized heating due to surfactants or via plasmonic absorption may have an impact on the chemical stability of the NFs and can represent a form of energy loss that has received little attention so far. Localized heating can result in the degradation of NPs and agglomeration over time under several operating conditions such as high solar and thermal loadings as well as solar and thermal cycling. This type of energy loss to chemical energy (transformation of matter) is extremely important not only because it reduces the STC efficiency but also because it can impact the chemical/physical stability of the NFs, hence their long-term applicability.

As NPs exhibit temperature values that are higher than the working fluid, heat conduction occurs only in one direction, i.e., from the NPs to the working fluid. While NP IR emissions can be significant in some cases, this can be often re-absorbed directly by the working fluid and should not represent a major loss mechanism.

#### **4. Fundamental Optical Characterisation of Nanofluids for DASCs**

Conventional base fluids used in DASCs are strong absorbers in the UV and IR regions, which represents 57% of the total solar energy; however, they are transparent in the Vis part, meaning that 43% is mostly lost as transmitted light [20]. Figure 4a reports the solar irradiance together with the transmittance spectra for four relevant working fluids used in DASCs. The optical characteristics of the working fluids result in power absorbed (Figure 4b), which clearly shows that very little solar irradiance is used up to ~900 nm. The main functionality in adding NPs to these base fluids is, therefore, to compensate for this by absorbing the solar energy present in the Vis region. In this view, studying the absorption and scattering behaviours of NFs is essential in evaluating their potential as working media in DASCs since this determines to what extent the NF can effectively utilize solar radiation energy [99,100]. For the performance improvement of DASCs, it is ultimately desirable to increase absorption, which can be impacted by the shape, size, material type, and concentration of the NPs, as well as the type of base fluid [101].

Experimentally, when taking measurements in the lab, the light interaction with an NF sample is characterized by the transmittance (*T*(*λ*) = *Itr*(*λ*)/*Iinc*(*λ*)), absorptance (*Abs*(*λ*) = *Iabs*(*λ*)/*Iinc*(*λ*)), and scattering (*S*(*λ*) = *Isct*(*λ*)/*Iinc*(*λ*)), which correspond to fractions, with values from 0 to 1, of the incident light intensity (*Iinc*(*λ*)), hence

$$T(\lambda) + Abs(\lambda) + S(\lambda) = 1\tag{1}$$

All the optical quantities are wavelength-dependent (*λ*); however, here below we have omitted this dependence for simplicity. Furthermore, the interaction of light with an NF sample is three-dimensional in nature; however, a one-dimensional analysis is applicable for the measurements of the fundamental physical NF properties where the sample size can be minimized in two of the three dimensions and ensuring re-absorption is negligible. The light that is not transmitted (i.e., *Abs* + *S* or 1−*T*) is also referred to as attenuated light. From a practical point of view, both scattered and transmitted light represents the light that has escaped the sample, the latter without any change in the direction of the propagation. However, experimental measurements of *S* and *T* include more than purely

scattering and transmission phenomena and their values result from the sum of all of the light exiting the sample. If, for example, samples exhibit strong PL or IR emissions (Figure 3), the corresponding light emission is measured as either scattering or transmission. As previously discussed, PL and IR emissions should be generally considered losses to be minimized and should be expected to be negligible. Optical measurements of NF samples then allow the extraction of fundamental physical NF properties such as extinction (*µext*), absorption (*µabs*), and scattering (*µsct*) coefficients measured in m−1 , which can then be used, for instance, to simulate full DASC system performance in three dimensions [29]. *Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 14 of 32

**Figure 4.** (**a**) Spectral solar irradiance at Earth's level (air mass of 1.5, AM1.5) [102] and (**b**) transmittance of common base fluids used in DASCs for a one cm sample thickness (transmittance for Terminol VP-1 is taken from [29]). **Figure 4.** (**a**) Spectral solar irradiance at Earth's level (air mass of 1.5, AM1.5) [102] and (**b**) transmittance of common base fluids used in DASCs for a one cm sample thickness (transmittance for Terminol VP-1 is taken from [29]).

Experimentally, when taking measurements in the lab, the light interaction with an NF sample is characterized by the transmittance (() = ௧()/() ), absorptance (() = ௦()/() ), and scattering (() = ௦௧()/() ), which correspond to fractions, with values from 0 to 1, of the incident light intensity (()), hence () + () + () = 1 (1) All the optical quantities are wavelength-dependent (); however, here below we have omitted this dependence for simplicity. Furthermore, the interaction of light with an NF sample is three-dimensional in nature; however, a one-dimensional analysis is applicable for the measurements of the fundamental physical NF properties where the sample size can be minimized in two of the three dimensions and ensuring re-absorption is negligible. The light that is not transmitted (i.e., *Abs* + *S* or 1—− *T*) is also referred to as attenuated light. From a practical point of view, both scattered and transmitted light represents the light that has escaped the sample, the latter without any change in the direction of the propagation. However, experimental measurements of *S* and *T* include more than purely scattering and transmission phenomena and their values result from the sum of all of the light exiting the sample. If, for example, samples exhibit strong PL or IR emissions (Figure The total attenuation of light while travelling through an NF sample with a given depth (or thickness, *L*) can be evaluated by measuring the transmittance using a spectrophotometer. Most conventional spectrophotometers can cover electromagnetic spectral ranges between 300 nm and 900 nm, including the ultraviolet and visible regions, as well as part of the near-infrared, and this can extend into higher wavelengths depending on the type of the instrument used, e.g., up to 3000 nm. The transmittance is determined by the ratio of the light intensity transmitted through the NF sample (*Itr*), and collected by the detector to the intensity of the incident light, i.e., the intensity of the light source incident on the sample and prior to interacting with the sample (*Iinc*), see Figure 5A. The latter needs to be measured with an appropriate reference sample, which can take into account instrumental losses including those due to the cuvette absorption and reflection at the interfaces. As most working fluids have negligible attenuation in relevant UV and Vis ranges, in order to evaluate the impact of NFs, it is convenient to use a reference with just the working fluid (i.e., without NPs). This will, however, limit the validity of the NF optical properties to these ranges where the working fluid has little interaction with the light (e.g., <900 nm). In order to further extend the validity of the measurements to the IR, more complex calculations and verifications would need to be introduced.

3), the corresponding light emission is measured as either scattering or transmission. As The extinction coefficient of the NF can be calculated from the Beer–Lambert law [96]:

absorption (௦), and scattering (௦௧) coefficients measured in m−1, which can then be used, for instance, to simulate full DASC system performance in three dimensions [29].

depth (or thickness, *L*) can be evaluated by measuring the transmittance using a spectrophotometer. Most conventional spectrophotometers can cover electromagnetic spectral ranges between 300 nm and 900 nm, including the ultraviolet and visible regions, as well as part of the near-infrared, and this can extend into higher wavelengths depending on the type of the instrument used, e.g., up to 3000 nm. The transmittance is determined by

$$T(L) = \frac{I\_{lr}}{I\_{inc}} = e^{-\mu\_{cat}L} \tag{2}$$

$$
\mu\_{\rm ext} = -\frac{\ln T}{L} \tag{3}
$$

= ିఓೣ (2)

Attenuation is due to both absorption as well as scattering, hence the extinction coefficient is the sum of the corresponding coefficients: Attenuation is due to both absorption as well as scattering, hence the extinction coefficient is the sum of the corresponding coefficients:

The extinction coefficient of the NF can be calculated from the Beer–Lambert law [96]:

() = ௧

the ratio of the light intensity transmitted through the NF sample (௧), and collected by the detector to the intensity of the incident light, i.e., the intensity of the light source incident on the sample and prior to interacting with the sample (), see Figure 5A. The latter needs to be measured with an appropriate reference sample, which can take into account instrumental losses including those due to the cuvette absorption and reflection at the interfaces. As most working fluids have negligible attenuation in relevant UV and Vis ranges, in order to evaluate the impact of NFs, it is convenient to use a reference with just the working fluid (i.e., without NPs). This will, however, limit the validity of the NF optical properties to these ranges where the working fluid has little interaction with the light (e.g., <900 nm). In order to further extend the validity of the measurements to the IR, more

$$
\mu\_{\rm ext} = \mu\_{\rm abs} + \mu\_{\rm sct} \tag{4}
$$

The contribution of scattering can be neglected in some conditions, e.g., for NPs with sizes much smaller than the incident wavelength [103–105] and at low particle concentrations with no agglomeration (<0.01% volume fraction) [104]. In this case, the extinction coefficient can be representative of the absorption coefficient (*µext* ≈ *µabs*) [96]. Larger particles, high particle concentrations and/or the presence of agglomeration can lead to significant scattering, which requires the spectrophotometer instrument to be equipped with an integrating sphere system (Figure 5B) to yield transmittance and scattering separately. Depending on the spectrometer and integrating sphere, separate measurements of *T* and *S* may not be possible, so scattering is calculated from the measurements of *T* and (*T* + *S*), by difference. In general, it is difficult to have a priori knowledge of the light–NF interactions and the general case where both absorption and scattering coefficients are not negligible should be assumed. The contribution of scattering can be neglected in some conditions, e.g., for NPs with sizes much smaller than the incident wavelength [103–105] and at low particle concentrations with no agglomeration (<0.01% volume fraction) [104]. In this case, the extinction coefficient can be representative of the absorption coefficient (௫௧ ≈ ௦) [96]. Larger particles, high particle concentrations and/or the presence of agglomeration can lead to significant scattering, which requires the spectrophotometer instrument to be equipped with an integrating sphere system (Figure 5B) to yield transmittance and scattering separately. Depending on the spectrometer and integrating sphere, separate measurements of *T* and *S* may not be possible, so scattering is calculated from the measurements of *T* and (*T* + *S*), by difference. In general, it is difficult to have a priori knowledge of the light–NF interactions and the general case where both absorption and scattering coefficients are not negligible should be assumed.

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 15 of 32

complex calculations and verifications would need to be introduced.

**Figure 5.** Schematic shows methods of direct measurements of (**A**) transmittance using the transmission port and (**B**) transmittance and scattering combined in the integrating sphere compartment **Figure 5.** Schematic shows methods of direct measurements of (**A**) transmittance using the transmission port and (**B**) transmittance and scattering combined in the integrating sphere compartment [106].

[106]. The light absorbed (*Iabs*) by an NF sample of depth *L* can be described in terms of the transmitted light intensity *Itr* at depth , multiplied by the absorption coefficient, and The light absorbed (*Iabs*) by an NF sample of depth *L* can be described in terms of the transmitted light intensity *Itr* at depth *x*, multiplied by the absorption coefficient, and where Equation (2) has been used:

$$I\_{\rm abs} = \int\_0^L \mu\_{\rm abs} I\_{\rm lr}(\mathbf{x}) \cdot d\mathbf{x} = \mu\_{\rm abs} I\_{\rm inc} \int\_0^L e^{-\mu\_{\rm ext} \mathbf{x}} \cdot d\mathbf{x} = \mu\_{\rm abs} I\_{\rm inc} \left(\frac{1 - e^{-\mu\_{\rm ext} L}}{\mu\_{\rm ext}}\right) = \mu\_{\rm abs} \frac{I\_{\rm inc} (1 - T)}{\mu\_{\rm ext}} \tag{5}$$

The absorption coefficient can be then determined by rearranging Equation (5) and substituting the values produced by the measurements of *T* and (*T* + *S*) as follows:

$$\mu\_{\rm abs} = I\_{\rm abs} \frac{\mu\_{\rm ext}}{I\_{\rm inc}(1-T)} = \frac{I\_{\rm abs}}{I\_{\rm inc}} \frac{\mu\_{\rm ext}}{(1-T)} = [1 - (S+T)] \frac{\mu\_{\rm ext}}{(1-T)} = -\frac{[1-(S+T)]}{(1-T)} \frac{\ln T}{L} \tag{6}$$

Consequently, the scattering coefficient can be simply determined by subtracting the absorption coefficient in Equation (6) from the extinction coefficient in Equation (4).

$$\mu\_{\rm scf} = -\frac{\ln T}{L} - \left\{ -\frac{[1 - (S + T)]}{(1 - T)} \frac{\ln T}{L} \right\} = \frac{\ln T}{L} \left\{ \frac{[1 - (S + T)]}{(1 - T)} - 1 \right\} \tag{7}$$

This approach was used, for instance, to evaluate the properties of surfactant-free Au NPs prepared by McGlynn et al. [61], which exhibited a variety of shapes and sizes, with most particles consisting of small spherical NPs with an average diameter of 27 nm. ௦ =න ௦௧()

௦ = ௦

௫௧ (1−) = ௦

They evaluated the absorption and scattering behaviours of their NF (Au NPs in ethylene glycol) across the wavelength range of 300–900 nm, and the results revealed that both absorption and scattering coefficients increased with the NP concentrations, as expected. In addition, the absorption coefficient is dominated by the plasmonic absorption between 540 nm and 560 nm (red in Figure 6b), which is much higher than the corresponding scattering coefficient (red in Figure 6c) for most of the spectral range. evaluated the absorption and scattering behaviours of their NF (Au NPs in ethylene glycol) across the wavelength range of 300–900 nm, and the results revealed that both absorption and scattering coefficients increased with the NP concentrations, as expected. In addition, the absorption coefficient is dominated by the plasmonic absorption between 540 nm and 560 nm (red in Figure 6b), which is much higher than the corresponding scattering coefficient (red in Figure 6c) for most of the spectral range.

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 16 of 32

∙ = ௦ ቆ

(1−) = ሾ1 − (+)ሿ ௫௧

ቊ

substituting the values produced by the measurements of *T* and (+) as follows:

absorption coefficient in Equation (6) from the extinction coefficient in Equation (4).

ሾ1 − (+)ሿ

1−ିఓೣ

The absorption coefficient can be then determined by rearranging Equation (5) and

Consequently, the scattering coefficient can be simply determined by subtracting the

This approach was used, for instance, to evaluate the properties of surfactant-free Au NPs prepared by McGlynn et al. [61], which exhibited a variety of shapes and sizes, with most particles consisting of small spherical NPs with an average diameter of 27 nm. They

௫௧ ቇ=௦

(1−) = − ሾ1 − (+)ሿ

(1−)

(1−) − 1ቋ (7)

(1−) ௫௧

(6)

(5)

∙ = ௦ න ିఓೣ௫

௫௧

௦௧ = −— =

**Figure 6.** (**a**) Extinction, (**b**) absorption, and (**c**) scattering coefficients for gold (red) and copper oxide (blue) NPs in an ethylene glycol base fluid. Adapted with permission from [61]. **Figure 6.** (**a**) Extinction, (**b**) absorption, and (**c**) scattering coefficients for gold (red) and copper oxide (blue) NPs in an ethylene glycol base fluid. Adapted with permission from [61].

Many reports use absorbance to characterize NFs; however, this parameter does not allow for a direct comparison with other NFs and cannot be used directly in simulations [58,78]. The transmittance of the water-based metal oxide NFs of Al2O3, CuO, TiO2, ZnO, CeO2, and Fe2O3 prepared by Milanese et al. [73] at 0.05–1 vol% were measured over 200– 1300 nm using a 3 mm path-length quartz cuvette. As depicted in Figure 7a, at 0.05 vol%, the six materials exhibited three transmittance patterns where CuO and Fe2O3 transmitted light only in the near-IR region at wavelengths above 800 nm and 600 nm, respectively, while TiO2, ZnO, and CeO2 transmitted more in the Vis and near-IR region at wavelengths above ~380 nm; the last material, Al2O3, had the lowest performance with most of the light transmitted. In Figure 7b, the distance at which all incident light was attenuated was calculated at different concentrations for the six materials and showed that Al2O3 is the worst material while the other five materials have much higher attenuation rates within short distances of less than 0.02 m at a concentration as low as 0.05 vol%. The extinction Many reports use absorbance to characterize NFs; however, this parameter does not allowfor a direct comparison with other NFs and cannot be used directly in simulations [58,78]. The transmittance of the water-based metal oxide NFs of Al2O3, CuO, TiO2, ZnO, CeO2, and Fe2O3 prepared by Milanese et al. [73] at 0.05–1 vol% were measured over 200–1300 nm using a 3 mm path-length quartz cuvette. As depicted in Figure 7a, at 0.05 vol%, the six materials exhibited three transmittance patterns where CuO and Fe2O3 transmitted light only in the near-IR region at wavelengths above 800 nm and 600 nm, respectively, while TiO2, ZnO, and CeO2 transmitted more in the Vis and near-IR region at wavelengths above ~380 nm; the last material, Al2O3, had the lowest performance with most of the light transmitted. In Figure 7b, the distance at which all incident light was attenuated was calculated at different concentrations for the six materials and showed that Al2O3 is the worst material while the other five materials have much higher attenuation rates within short distances of less than 0.02 m at a concentration as low as 0.05 vol%. The extinction coefficient of ATO–Ag NPs [76] with an average particle size of 40 nm and dispersed in water at 0.01–0.2 wt% was calculated over 300–900 nm, and its peak was 8.2 cm−1 at 300 nm at 0.2 wt% and dropped to 3.7 cm−1 at 900 nm. It was also observed that the extinction coefficient exhibited approximately a linear function with the mass fraction. By dispersing graphene nanoplates with a thickness of 2 nm and diameter of less than 2 µm in deionized water at 0.00025–0.005 wt% [82], the NFs demonstrated a strong absorption band in the range of 250–300 nm, with complete absorption across the range of 1400–1550 and above 1850 nm. In addition, the NF with the highest concentration of 0.005 wt% exhibited the highest extinction coefficient with a peak of 6.5 cm−1 at 300 nm, which decreased gradually to below 4.5 cm−1 at wavelengths above 700 nm. Milanese et al. [73] studied the effect of temperature change within a range of 100–500 ◦C in 100 ◦C steps on the optical properties of ZnO, CeO2 (~4.3 nm in diameter), and Fe2O3 (~3.0 nm in diameter) in chloroform solution at 3 mg/mL and 5 mg/mL for Fe2O3 and CeO2 NPs, respectively.

tion at 3 mg/mL and 5 mg/mL for Fe2O3 and CeO2 NPs, respectively.

**Figure 7.** (**a**) Comparison between the transmittance of several NFs as a function of wavelength. (**b**) The extinction distance for investigated NFs as a function of NP concentration, in the case of wavelength equal to 1300 nm. Adapted from [73]. **Figure 7.** (**a**) Comparison between the transmittance of several NFs as a function of wavelength. (**b**) The extinction distance for investigated NFs as a function of NP concentration, in the case of wavelength equal to 1300 nm. Adapted from [73].

coefficient of ATO–Ag NPs [76] with an average particle size of 40 nm and dispersed in water at 0.01–0.2 wt% was calculated over 300–900 nm, and its peak was 8.2 cm−1 at 300 nm at 0.2 wt% and dropped to 3.7 cm−1 at 900 nm. It was also observed that the extinction coefficient exhibited approximately a linear function with the mass fraction. By dispersing graphene nanoplates with a thickness of 2 nm and diameter of less than 2 µm in deionized water at 0.00025–0.005 wt% [82], the NFs demonstrated a strong absorption band in the range of 250–300 nm, with complete absorption across the range of 1400–1550 and above 1850 nm. In addition, the NF with the highest concentration of 0.005 wt% exhibited the highest extinction coefficient with a peak of 6.5 cm−1 at 300 nm, which decreased gradually to below 4.5 cm−1 at wavelengths above 700 nm. Milanese et al. [73] studied the effect of temperature change within a range of 100–500 °C in 100 °C steps on the optical properties of ZnO, CeO2 (~4.3 nm in diameter), and Fe2O3 (~3.0 nm in diameter) in chloroform solu-

Similar to absorbance, the use of attenuation or extinction coefficients, or transmission only, cannot differentiate between absorbed and scattered light, hence the results can be misinterpreted. In general, assessing the optical properties of NFs using transmittance or absorbance or extinction coefficient only can be misleading. For instance, we have produced NFs from three different types of CuO particles. We have used quantum dots (QDs) [107], commercially available NPs and microparticles (MPs) (Sigma Aldrich with CAS numbers of 1317-38-0 and 1317-38-0, respectively), and each sample of the three CuO particles was dispersed in 10 mL of ethylene glycol (Sigma, CAS number 107-21-1) at a volume fraction of 0.005%. The re-dispersion process was performed for 1 h in a bath-type sonicator (VWR USC300TH, 230 V, 50 Hz, 370 VA) and then for 3 min in a probe-type sonicator (VCX-130PB ultrasonic processor, Sonics Materials) at 80% (104 W) for high dispersion homogeneity. The impact of the different sizes on the scattering is immediately Similar to absorbance, the use of attenuation or extinction coefficients, or transmission only, cannot differentiate between absorbed and scattered light, hence the results can be misinterpreted. In general, assessing the optical properties of NFs using transmittance or absorbance or extinction coefficient only can be misleading. For instance, we have produced NFs from three different types of CuO particles. We have used quantum dots (QDs) [107], commercially available NPs and microparticles (MPs) (Sigma Aldrich with CAS numbers of 1317-38-0 and 1317-38-0, respectively), and each sample of the three CuO particles was dispersed in 10 mL of ethylene glycol (Sigma, CAS number 107-21-1) at a volume fraction of 0.005%. The re-dispersion process was performed for 1 h in a bath-type sonicator (VWR USC300TH, 230 V, 50 Hz, 370 VA) and then for 3 min in a probe-type sonicator (VCX-130PB ultrasonic processor, Sonics Materials) at 80% (104 W) for high dispersion homogeneity. The impact of the different sizes on the scattering is immediately clear in Figure 8c.

clear in Figure 8c. In this case, using the extinction coefficient to characterize the optical behaviour of QDs (red in Figure 8a) is a suitable approach for the part of the wavelength range under analysis as scattering (red in Figure 8c) is very low in comparison to the absorption coefficient (red in Figure 8b). However, the scattering coefficient of NPs (blue in Figure 8c) is comparable to the absorption coefficient (blue in Figure 8b), hence the first cannot be neglected. This is even more obvious for MPs where the extinction coefficient (green in Figure 8a) is very high throughout the full wavelength range. However, the analysis of absorption and scattering separately (green in Figure 8b,c, respectively) shows that much of the extinction is due to scattering in the range 800–900 nm. In this specific case, the higher scattering is most likely all due to the relationship between incident wavelength and particle size as per Mie's theory. However, we should note that scattering can take over the absorption also due to other light–NP interaction phenomena, such as is the case for NPs with plasmonic properties (e.g., red in Figure 6c) as plasmon resonance enhances scattering above the plasmonic peak wavelength. It is therefore important to evaluate NF properties appropriately for these to be used in assessing NF performance and in more complex analytical and simulation efforts.

**Figure 8.** Coefficients of (**a**) extinction, (**b**) absorption, and (**c**) scattering of three different types of CuO at different sizes dispersed in ethylene glycol (mean diameter: ~3.5 nm QDs, ~50 nm NPs, ~3– 10 µm MPs). **Figure 8.** Coefficients of (**a**) extinction, (**b**) absorption, and (**c**) scattering of three different types of CuO at different sizes dispersed in ethylene glycol (mean diameter: ~3.5 nm QDs, ~50 nm NPs, ~3–10 µm MPs).

#### In this case, using the extinction coefficient to characterize the optical behaviour of **5. Characterization of the Stability of Nanofluids for DASC Applications**

QDs (red in Figure 8a) is a suitable approach for the part of the wavelength range under analysis as scattering (red in Figure 8c) is very low in comparison to the absorption coefficient (red in Figure 8b). However, the scattering coefficient of NPs (blue in Figure 8c) is comparable to the absorption coefficient (blue in Figure 8b), hence the first cannot be neglected. This is even more obvious for MPs where the extinction coefficient (green in Figure 8a) is very high throughout the full wavelength range. However, the analysis of absorption and scattering separately (green in Figure 8b and 8c, respectively) shows that much of the extinction is due to scattering in the range 800–900 nm. In this specific case, the higher scattering is most likely all due to the relationship between incident wavelength and particle size as per Mie's theory. However, we should note that scattering can take over the absorption also due to other light–NP interaction phenomena, such as is the case for NPs with plasmonic properties (e.g., red in Figure 6c) as plasmon resonance enhances scattering above the plasmonic peak wavelength. It is therefore important to evaluate NF Nanofluids are colloids of nanoparticles within base fluids and it is critical for the performance of NF-based DASCs to address the long-term stability under various thermal and solar radiation operating conditions. Dispersed particles are prone to destabilization under the effect of forces, such as Van der Waal and gravity, which can induce agglomeration leading to the formation of larger particles/agglomerates and enhancing sedimentation. Other forces, such as buoyancy, steric, and electrostatic forces, can play opposite roles in improving particle stability, and nanofluid stability is dependent on which group of forces dominates. The formation of large agglomerates leads to a sequence of operational issues and contributes to the deterioration of the thermal and optical properties of NFs, affecting the overall performance of DASCs. Such destabilization/stabilization forces are highly affected by the operating conditions (temperatures, particle loading, and incident solar radiation). In addition, the chemical stability of NFs and the NPs or working fluid separately is important to maintain NF properties across operational conditions.

properties appropriately for these to be used in assessing NF performance and in more complex analytical and simulation efforts. **5. Characterization of the Stability of Nanofluids for DASC Applications**  Nanofluids are colloids of nanoparticles within base fluids and it is critical for the performance of NF-based DASCs to address the long-term stability under various thermal and solar radiation operating conditions. Dispersed particles are prone to destabilization under the effect of forces, such as Van der Waal and gravity, which can induce agglomeration leading to the formation of larger particles/agglomerates and enhancing sedimentation. Other forces, such as buoyancy, steric, and electrostatic forces, can play opposite roles in improving particle stability, and nanofluid stability is dependent on which group of forces dominates. The formation of large agglomerates leads to a sequence of operational issues and contributes to the deterioration of the thermal and optical properties of NFs, affecting the overall performance of DASCs. Such destabilization/stabilization forces are highly affected by the operating conditions (temperatures, particle loading, and incident solar radiation). In addition, the chemical stability of NFs and the NPs or working fluid separately is important to maintain NF properties across operational conditions. High operating temperatures increase Brownian motion leading to higher particle collision frequencies, also enhanced by a reduction in viscosity of the base fluid at higher temperatures. Temperature change also has an impact on the surface charge and zeta potential of the particles [108]. In addition, an increase in temperature can lead to the degradation of surfactants in the case of steric-stabilized NPs [109]. Direct exposure of the NFs to concentrated radiation (intensity higher than one sun) can cause the chemical deterioration of surfactants and functional groups and even of the chemical composition or phase of the NPs, particularly from UV radiation [110]. Furthermore, medium- and hightemperature DASCs operate at high solar radiation intensity, which requires relatively high particle loadings, i.e., more particles per unit volume and consequently shorter interparticle distance, which induce agglomeration of particles at higher rates compared to low particle loadings. Moreover, due to heating during exposure to sunlight in the daytime and cooling during nighttime, this daily cyclic heating/cooling impacts several parameters, including changes in the morphology of the NPs that could promote agglomeration and chemical reactions such as oxidation [83,111] as well as a reduction in thermophysical properties [112]. For these reasons, the chemical stability of NPs needs to be assessed in the specific working fluid as several chemical reactions could be taking place at the NP–fluid solid–liquid interface that would not normally take place in other environmental conditions.

High operating temperatures increase Brownian motion leading to higher particle collision frequencies, also enhanced by a reduction in viscosity of the base fluid at higher temperatures. Temperature change also has an impact on the surface charge and zeta po-The stability of NFs can be assessed following various methodologies, which can produce operational stability parameters and an understanding of relevant underlying mechanisms. The observation of discolouration and/or particle sedimentation of the NFs

tential of the particles [108]. In addition, an increase in temperature can lead to the

is perhaps one of the simplest and most direct assessment methods. However, seldom can it provide quantifiable operational measures and scientific insights. On the other hand, measuring the changes in the optical properties, morphology, surface chemical composition, etc., of the NPs can be more helpful in analysing and understanding stability.

Sharaf et al. [78] extensively investigated the stability of polymer-coated Au NPs/water against several destabilization factors, including ambient storage for 16 months, elevated temperature, continuous and cyclic modes of solar radiation, and intensified UV radiation. In their work, they tested four samples: CIT–Au NPs and CIT–Au NPs coated using three different polymers to give BSA–AuNPs, PVP–AuNPs, and PEG–AuNPs. The results revealed that the ambient dark storage for three years did not affect the stability and PEG–AuNPs demonstrated the best long-term stability. The absorbance measurements showed that no plasmonic wavelength shifts or shoulder evolutions took place in all four NFs. The absorbance peak intensity, however, increased for PVP– and BSA–Au NPs by 9.0% and 9.5%, and this was attributed to changes in the thickness of the adsorbed polymer coating over time, while the peak intensity of CIT–Au NPs dropped by 9.6% due to sedimentation. In addition, after the samples were exposed to broadband solar radiation at different intensities for 12 h, CIT–Au NPs resulted to be the most stable with no changes in absorbance intensity, while both PEG– and PVP–Au NPs showed a drop in absorbance and the hydrodynamic diameter under radiation exposure. However, no shifting or broadening in the absorbance peaks of PEG– and PVP–Au NPs were observed, indicating that they experienced no agglomeration after being exposed to radiation. Furthermore, cyclic radiation for 20 cycles at one-sun intensity for 8 h followed by 16 h in the dark produced more significant changes in absorbance and hydrodynamic diameter compared to exposure to continuous radiation, with the CIT–Au NPs less impacted than the polymer-coated samples. Moreover, they tested the NFs at elevated temperatures of 55 ◦C, 70 ◦C, and 85 ◦C for 12 h, and all NFs showed excellent thermal stability confirmed by their absorbance measurements. The stability of the same NFs (aqueous NFs with Au NPs coated by CIT, PEG, PVP, and BSA) was then investigated for a much longer period [60]. Over three years of ambient storage, continuous irradiation at varying intensity for 12 h and 20 consecutive cycles of one-sun illumination (8 h under light, followed by 16 h in the dark), the NFs exhibited no shifts in their plasmonic absorption peak wavelength and insignificant changes in the hydrodynamic diameter. They also reported that CIT-coated AuNPs were the most stable under continuous solar radiation. The effect of ambient storage on the stability of CTAC surfactant-based Au NPs/water was investigated by Chen et al. [58] and they found that the NFs were stable after days but the increase in temperature up to 90 ◦C worsened the stability and rapid sedimentation appeared several hours after the experiments. They attributed the post-experiment instability to agglomeration induced by Brownian motion and surfactant degradation at high temperatures.

Gorji and Ranjbar [80] measured the zeta potential of three different types of materials (Ag NPs, Fe3O4 NPs, and graphite) in water and found that the graphite/water exhibited the highest value of 45.1 mV compared to 41.3 mV and 38.7 mV for Fe3O4/water and Ag NPs/water, respectively, all at a pH of 9.5–10. Coating Ag NPs with SiO2 and then dispersing them in water to form Ag NPs@SiO2/water NFs resulted in better stability when compared with uncoated Ag NPs in the same base fluid, which exhibited poor stability under both heating and UV radiation cycles [83]. Kimpton et al. [62] investigated the stability of both Ag NPs/water with and without coating with SiO2. They monitored the stability of both NFs over three weeks of ambient storage, as well as under exposure for a period of two weeks to simulated and natural solar radiation, the latter during the first half of June 2018 in the UK. As shown in Figure 9, they assessed the impacts of destabilization factors by studying the UV–Vis spectra and the morphology of the particles via transmission electron microscopy (TEM). Their results revealed a lot of interesting points when comparing bare Ag NPs and SiO2-coated Ag NPs, as well as differences due to the use of simulated and natural light. For instance, SiO2-coated Ag NPs showed less stability than the uncoated Ag NPs, as the former showed a higher reduction and position

shifting in the absorption peak after ambient dark storage and upon exposure to simulated light. This lack of stability was explained by the changes in the morphology of the SiO2@Ag NPs samples verified by TEM. They found a reduction in the size of Ag NPs inside SiO2 shells by about 10 nm suggesting that the silver was being etched inside the coating. In addition, they found degradation of the SiO2 shell, since it had reduced in size, and some Ag NPs were found no longer coated. Based on these results, they carried out further modifications by using thicker SiO2 coatings to improve stability. However, they found that increasing the coating thickness accelerated the change in morphology of Ag NPs under exposure to light. On the other side, exposure to natural sunlight revealed similar results to that obtained under exposure to simulated light in terms of the shift of the absorbance peak position, but different in the reduction in the peak values. They attributed this to a faster change in the morphology of the particles. that increasing the coating thickness accelerated the change in morphology of Ag NPs under exposure to light. On the other side, exposure to natural sunlight revealed similar results to that obtained under exposure to simulated light in terms of the shift of the absorbance peak position, but different in the reduction in the peak values. They attributed this to a faster change in the morphology of the particles. Zheng et al. [79] studied the dispersion stability of CTAB surfactant-based NFs of CNT/water and CNT–TiN/water over ambient storage of one week. At different mass fractions of up to 30 ppm, they found no precipitation after the one-week test, and to confirm this, they recorded the time-dependent absorbance spectra of the single- and multicomponent NFs. At low concentrations, they found overlapping in the spectra between the asprepared samples and the same samples after seven days, while samples with higher concentrations exhibited some changes in absorbance.

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 20 of 32

the experiments. They attributed the post-experiment instability to agglomeration in-

Gorji and Ranjbar [80] measured the zeta potential of three different types of materials (Ag NPs, Fe3O4 NPs, and graphite) in water and found that the graphite/water exhibited the highest value of 45.1 mV compared to 41.3 mV and 38.7 mV for Fe3O4/water and Ag NPs/water, respectively, all at a pH of 9.5–10. Coating Ag NPs with SiO2 and then dispersing them in water to form Ag NPs@SiO2/water NFs resulted in better stability when compared with uncoated Ag NPs in the same base fluid, which exhibited poor stability under both heating and UV radiation cycles [83]. Kimpton et al. [62] investigated the stability of both Ag NPs/water with and without coating with SiO2. They monitored the stability of both NFs over three weeks of ambient storage, as well as under exposure for a period of two weeks to simulated and natural solar radiation, the latter during the first half of June 2018 in the UK. As shown in Figure 9, they assessed the impacts of destabilization factors by studying the UV–Vis spectra and the morphology of the particles via transmission electron microscopy (TEM). Their results revealed a lot of interesting points when comparing bare Ag NPs and SiO2-coated Ag NPs, as well as differences due to the use of simulated and natural light. For instance, SiO2-coated Ag NPs showed less stability than the uncoated Ag NPs, as the former showed a higher reduction and position shifting in the absorption peak after ambient dark storage and upon exposure to simulated light. This lack of stability was explained by the changes in the morphology of the SiO2@Ag NPs samples verified by TEM. They found a reduction in the size of Ag NPs inside SiO2 shells by about 10 nm suggesting that the silver was being etched inside the coating. In addition, they found degradation of the SiO2 shell, since it had reduced in size, and some Ag NPs were found no longer coated. Based on these results, they carried out further modifications by using thicker SiO2 coatings to improve stability. However, they found

duced by Brownian motion and surfactant degradation at high temperatures.

**Figure 9.** UV–Vis spectra of Ag NPs and SiO2@Ag NPs in water: (**a**) after exposure to stimulated solar light, (**b**) after exposure to natural solar light for two weeks, and (**c**) after storage in the dark for three weeks (adapted from [62]). **Figure 9.** UV–Vis spectra of Ag NPs and SiO2@Ag NPs in water: (**a**) after exposure to stimulated solar light, (**b**) after exposure to natural solar light for two weeks, and (**c**) after storage in the dark for three weeks (adapted from [62]).

Chen et al. [68] found that CQDs/PEG-200 prepared by microwave heating are stable over 30 days of ambient storage. They observed light sedimentation from optical images and very small changes in transmittance spectra. GO/water–EG NFs with GO of 0.06 wt% were irradiated with an ultraviolet lamp for 240–615 s to obtain a series of GO//water–EG Zheng et al. [79] studied the dispersion stability of CTAB surfactant-based NFs of CNT/water and CNT–TiN/water over ambient storage of one week. At different mass fractions of up to 30 ppm, they found no precipitation after the one-week test, and to confirm this, they recorded the time-dependent absorbance spectra of the single- and multicomponent NFs. At low concentrations, they found overlapping in the spectra between the as-prepared samples and the same samples after seven days, while samples with higher concentrations exhibited some changes in absorbance.

Chen et al. [68] found that CQDs/PEG-200 prepared by microwave heating are stable over 30 days of ambient storage. They observed light sedimentation from optical images and very small changes in transmittance spectra. GO/water–EG NFs with GO of 0.06 wt% were irradiated with an ultraviolet lamp for 240–615 s to obtain a series of GO//water–EG NFs [88]. For comparison purposes, a reduced GO/water NF was also prepared at 0.02 wt% using PVP surfactant followed by UV irradiation for 340 s. After two months of ambient storage, GO/water–EG NFs obtained under irradiation durations of ≤465 s exhibited no sedimentation, while some sediments were observed at longer duration. When the temperature changed from 30 ◦C to 70 ◦C, GO/water–EG NFs at 0.06 wt% showed an increase in zeta potential, while the water-based GO NFs at 0.02 wt% showed the opposite, highlighting the effect of the base fluid used on the stability of NFs.

In a study on NF samples of two metal oxides of spherical Al2O3 NPs of 40 nm diameter and spherical CuO NPs of 100 nm diameter, as well as the combination of both (Al2O3-CuO NPs) in EG [85], the stability of the samples was tested over two weeks of ambient storage. NFs based on metal oxides offer interesting features for DASC applications due to their chemical inertness and thermal stability. Whilst many stoichiometric oxides exhibit very large bandgap values and low or no absorption in the solar spectral range, it is possible to produce metal oxide NPs with strong absorption also in the visible [29]. Pure CuO, for instance, deviating from the characteristics of most oxides, has a relatively low bandgap (~1.2 eV [113]), which is suitable for absorbing solar energy. However, the bandgap is impacted by quantum confinement and given the relatively large CuO Bohr radius (~28.27 nm [114,115]), the size of CuO NPs should be sufficiently large not to

experience significant bandgap widening. Adversely, larger NPs will tend to affect the NF stability. This can be shown again by comparing the stability of the same CuO QDs, NPs, and MPs that we reported in Figure 8. In order to assess the long-term static stability of NFs, we have monitored the transmittance over days (Figure 10a–c), with the NF stored in a dark space at room temperature without any form of mixing or shaking ('static stability'). The results show that while QDs (Figure 10c) exhibit superior stability compared to MPs (Figure 10a) or NPs (Figure 10b), their transmittance is relatively high, a consequence of quantum confinement and widening of the bandgap (to 2.2 eV [116,117]). As the cumulative transmittance increases with the size of the CuO particles, the static stability worsens and the best compromise between optical performance and stability should be found. However, static stability tests can be viewed as too severe for DASC applications, considering that NFs are generally in some form of motion when used in DASCs. Here, we show that after a simple manual shaking ("after shaking" in Figure 10a–c), the transmittance of all different types of CuO particles return to the values measured at the start (D0). *Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 22 of 32

**Figure 10.** Transmittance variation in (**a**) CuO MPs, (**b**) CuO NPs, and (**c**) CuO QDs in addition to (**d**) ZnO NPs in EG across a wavelength range of 300–1500 nm. The transmittance measurements were performed in a static mode, i.e., without shaking, and were then manually shaken before the last measurement "After shaking". **Figure 10.** Transmittance variation in (**a**) CuO MPs, (**b**) CuO NPs, and (**c**) CuO QDs in addition to (**d**) ZnO NPs in EG across a wavelength range of 300–1500 nm. The transmittance measurements were performed in a static mode, i.e., without shaking, and were then manually shaken before the last measurement "After shaking".

*Performance Of Nanofluid-Based DASCs*  DASCs are used in solar thermal systems, as illustrated in Figure 11a. The overall performance of DASC systems is impacted by various losses. Before reaching the nanofluid surface, the incident solar radiation intensity () is reduced by reflection at the surface of the transparent glass layer (௦௦) as well as absorption through it (௦௦௦). The manipulation of the morphology or chemical composition of metal oxide NPs also offers other opportunities to enhance the combined optical-stability performance of NFs. In Figure 10d, we report the stability of NFs produced with oxygen-deficient ZnO NPs. The results show substantial improvements in the optical properties with very low cumulativetransmittance at day 0 (D0) compared to the expected high transparency of ZnO NPs, due

It is worth mentioning that despite this loss in incident radiation intensity, the glass layer plays an important role in improving the overall performance of the DASCs by reducing the thermal energy loss to the surrounding, which is relatively high compared to the loss

goes an STC process through which the solar radiation is absorbed and scattered while travelling through the NF, as shown in Figure 11c (see also Figure 3). Here, we refer to the total radiation absorbed as ௦, while we use ௦ to refer to the amount of light that is scattered or that escaped the NF without re-absorption. Furthermore, thermal energy is then generated () from the absorbed radiation via an STC process. With the increase in the NF temperature above the surrounding temperature, a portion of the generated thermal energy is lost to the surrounding, as shown in Figure 11b, by convection (௦௦௩) and radiation (௦௦ௗ). Thus, the thermal energy gain within the NF, i.e., the net thermal

௧ = − ቂቀ௦௦ + ௦௦௦ቁ + ௦ + ൫௦௦௩ + ௦௦ௗ൯ቃ (8)

energy (௧), can be obtained using the energy balance as follows:

to the very high ZnO bandgap. While the stability of these NFs with ZnO NPs requires some optimization, these still outperform other CuO-based NFs after 20 days.

#### *Performance of Nanofluid-Based DASCs*

DASCs are used in solar thermal systems, as illustrated in Figure 11a. The overall performance of DASC systems is impacted by various losses. Before reaching the nanofluid surface, the incident solar radiation intensity (*Io*) is reduced by reflection at the surface of the transparent glass layer (*Ire f glass*) as well as absorption through it (*Iabsglass*). It is worth mentioning that despite this loss in incident radiation intensity, the glass layer plays an important role in improving the overall performance of the DASCs by reducing the thermal energy loss to the surrounding, which is relatively high compared to the loss in radiation intensity. The amount of solar radiation reaching the nanofluid (*In f*) undergoes an STC process through which the solar radiation is absorbed and scattered while travelling through the NF, as shown in Figure 11c (see also Figure 3). Here, we refer to the total radiation absorbed as *Iabsn f* , while we use *Iscn f* to refer to the amount of light that is scattered or that escaped the NF without re-absorption. Furthermore, thermal energy is then generated (*Qgen*) from the absorbed radiation via an STC process. With the increase in the NF temperature above the surrounding temperature, a portion of the generated thermal energy is lost to the surrounding, as shown in Figure 11b, by convection (*Qlossconv*) and radiation (*Qlossrad*). Thus, the thermal energy gain within the NF, i.e., the net thermal energy (*Qnetn f*), can be obtained using the energy balance as follows: *Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 23 of 32 The net thermal energy can be also determined at a given mass flow rate (ሶ), specific heat capacity (), and temperature rise (∆) of the NF: ௧ = ሶ ൈ ൈ ∆ (9) The overall efficiency of a DASC system, (ௌ), can be determined from the ratio of the net thermal energy stored by the nanofluid and the incident solar radiation, as follows: ௌ =௧ (10) Other aspects to be considered when evaluating the overall efficiency of a DASC sys-

$$Q\_{\text{net}nf} = I\_0 - \left[ \left( I\_{\text{ref}\,g\,\text{las}} + I\_{\text{abs}\,\text{glass}} \right) + I\_{\text{scnf}} + \left( Q\_{\text{lossconv}} + Q\_{\text{lossrad}} \right) \right] \tag{8}$$

the NF, and the variation in the ambient temperature.

**Figure 11.** DASC schematics; (**a**) simplified closed-loop system for heat transfer. Adapted from [24], (**b**) irradiation and heat loss sources. Adapted from [118], (**c**) nanoparticle and solar irradiation interaction. **Figure 11.** DASC schematics; (**a**) simplified closed-loop system for heat transfer. Adapted from [24], (**b**) irradiation and heat loss sources. Adapted from [118], (**c**) nanoparticle and solar irradiation interaction.

DASCs can take a variety of geometries/shapes to achieve the desired performance within a defined range of operating temperatures. For instance, Chen et al. [58] described the effect of DASC design on the plasmonic absorption-induced STC of Au NPs/water NFs The net thermal energy can be also determined at a given mass flow rate ( . *m*), specific heat capacity (*cp*), and temperature rise (∆*T*) of the NF:

$$Q\_{\text{net}\,\text{nf}} = \dot{m} \times c\_p \times \Delta T \tag{9}$$

DASCs made of polymethyl methacrylate (PMMA). The flat- and cubic-shaped DASCs were designed with inner dimensions of 100 mm × 100 mm × 6 mm and 50 mm × 50 mm × 48 mm, respectively, and both were thermally insulated. As depicted in Figure 12, they The overall efficiency of a DASC system, (*ηDASC*), can be determined from the ratio of the net thermal energy stored by the nanofluid and the incident solar radiation, as follows:

tion in the size of Au NPs (25 nm, 33 nm, and 40 nm) to see if this can alter the performance results of both shapes. The STC efficiency in the flat DASC increased by reducing the NP size, while this size reduction did not influence the cube-shaped DASC. However, the cube-shaped DASC exhibited higher overall efficiency since the flat-shaped DASC exhib-

$$
\eta\_{\text{DASC}} = \frac{Q\_{\text{netnf}}}{I\_0} \tag{10}
$$

Other aspects to be considered when evaluating the overall efficiency of a DASC system include the diffraction and reflection of light at the outer and inner surfaces of the glass layer, as well as at the interfaces between the NF and the DASC walls that contain the NF, and the variation in the ambient temperature.

DASCs can take a variety of geometries/shapes to achieve the desired performance within a defined range of operating temperatures. For instance, Chen et al. [58] described the effect of DASC design on the plasmonic absorption-induced STC of Au NPs/water NFs in a static mode under simulated solar radiation of 450 W/m2 . They tested flat and cubic DASCs made of polymethyl methacrylate (PMMA). The flat- and cubic-shaped DASCs were designed with inner dimensions of 100 mm × 100 mm × 6 mm and 50 mm × 50 mm × 48 mm, respectively, and both were thermally insulated. As depicted in Figure 12, they found that at a concentration of Au NPs of as low as 0.000008 wt%, the flat-shaped DASC system improved the STC efficiency by 21.3%, which was higher than that of the cube-shaped DASC (19.9%) at the same concentration. They also included the impact of variation in the size of Au NPs (25 nm, 33 nm, and 40 nm) to see if this can alter the performance results of both shapes. The STC efficiency in the flat DASC increased by reducing the NP size, while this size reduction did not influence the cube-shaped DASC. However, the cube-shaped DASC exhibited higher overall efficiency since the flat-shaped DASC exhibited higher heat loss. From this, we can see that the performance of DASC systems can be tuned by their size and shape. *Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 24 of 32

**Figure 12.** Photo-thermal and collector efficiencies as well as the heat loss of different NFs in (**A**) cube-shaped and (**B**) flat DASCs (adapted from [58]). **Figure 12.** Photo-thermal and collector efficiencies as well as the heat loss of different NFs in (**A**) cubeshaped and (**B**) flat DASCs (adapted from [58]).

The effect of NP concentration and solar radiation intensity were studied by Wang et al.[77]. They investigated the effect of these parameters on the absorption and STC performance of EG-based TiN NFs. They used TiN NPs at various concentrations (0.001–0.01 wt.%) in static mode in a thermally insulated (with aerogel) DASC made of quartz with a radius and height of 1.75 cm and 4 cm, respectively. They irradiated the samples with solar radiation of intensity up to two suns (2000 W/m2) and studied the effect of two different directions of the radiation on the DASC performance: side and bottom. The absorption performance of the NFs increased by ~50% with the increase in temperature from 0 °C to 60 °C. At a concentration of 0.003 wt.%, the bottom irradiation mode achieved a conversion efficiency of 45% higher than that of side irradiation. However, the latter saved nearly 40% of the time required to reach steady-state temperature when compared with the side radiation mode. In addition, both radiation direction modes exhibited uniform temperatures over the NF depth of 1 cm. Ag/water, Fe3O4/water and graphite/water were tested in a dynamic mode (fluid circulation) [80] in a rectangular channel made of stainless steel (12 mm × 5 mm × 2 mm), with the top glazing made of low-reflectance borosilicate glass of 4 mm and the inner surface of the bottom wall covered with reflective steel. The The effect of NP concentration and solar radiation intensity were studied byWang et al. [77]. They investigated the effect of these parameters on the absorption and STC performance of EG-based TiN NFs. They used TiN NPs at various concentrations (0.001–0.01 wt.%) in static mode in a thermally insulated (with aerogel) DASC made of quartz with a radius and height of 1.75 cm and 4 cm, respectively. They irradiated the samples with solar radiation of intensity up to two suns (2000 W/m2 ) and studied the effect of two different directions of the radiation on the DASC performance: side and bottom. The absorption performance of the NFs increased by ~50% with the increase in temperature from 0 ◦C to 60 ◦C. At a concentration of 0.003 wt.%, the bottom irradiation mode achieved a conversion efficiency of 45% higher than that of side irradiation. However, the latter saved nearly 40% of the time required to reach steady-state temperature when compared with the side radiation mode. In addition, both radiation direction modes exhibited uniform temperatures over the NF depth of 1 cm. Ag/water, Fe3O4/water and graphite/water were tested in a dynamic mode (fluid circulation) [80] in a rectangular channel made of stainless steel (12 mm × 5 mm × 2 mm), with the top glazing made of low-reflectance borosilicate glass of 4 mm and the inner surface of the bottom wall covered with reflective steel. The DASC was thermally insulated

DASC was thermally insulated by a 3 cm thick Styrofoam with a thermal conductivity of 0.03 W/m K. At varying simulated solar radiation of 600 W/m2, 800 W/m2 and 1000 W/m2,

Fe2O3/water NFs at two concentrations of 0.5 wt% and 2 wt% were investigated by Balakin et al. [74] in a dynamic mode with Reynolds numbers up to 1000 in a DASC of 400 mm long transparent glass tube with an internal diameter of 4 mm. The NFs reached a maximum thermal efficiency of 65% at the highest concentration of 2 wt%, while the lowest concentration of 0.5 wt% achieved 8%. In another similar work [75] Fe2O3/water NFs were used in an evacuated tubular DASC made of a borosilicate glass tube of 140 cm in length and containing a smaller glass tube of 2.5 cm and 4 cm inner and outer diameters, respectively. The flow rate was 400 mL/min (Reynold number of 340) and a surface area of 0.055 cm2 was exposed to solar radiation. At a 4 cm sample depth, Fe2O3/water at 0.02 vol% absorbed all incident radiation while the other NF absorbed 17% less at the same volume fraction. In terms of STC efficiency, Fe2O3/water confirmed its better performance over Fe3O4/water by a maximum efficiency of 73%, which is higher by 22% than the maximum efficiency reached by Fe2O3 NF at 0.02 vol%. CQDs of less than 10 nm in diameter prepared by microwave heating [68] were dispersed in PEG-200 and investigated in a static mode under simulated solar radiation of 1–4 sun for 60 min under continuous magnetic stirring in a DASC made from a quartz vessel of 3 cm × 3 cm × 3 cm with a sponge plate on the top to reduce sample evaporation. The results revealed that extending the by a 3 cm thick Styrofoam with a thermal conductivity of 0.03 W/m K. At varying simulated solar radiation of 600 W/m2 , 800 W/m2 and 1000 W/m2 , Fe3O4/water showed the highest outlet temperature and collector efficiency at all radiation flux values followed by graphite/water, with Ag/water being the lowest.

Fe2O3/water NFs at two concentrations of 0.5 wt% and 2 wt% were investigated by Balakin et al. [74] in a dynamic mode with Reynolds numbers up to 1000 in a DASC of 400 mm long transparent glass tube with an internal diameter of 4 mm. The NFs reached a maximum thermal efficiency of 65% at the highest concentration of 2 wt%, while the lowest concentration of 0.5 wt% achieved 8%. In another similar work [75] Fe2O3/water NFs were used in an evacuated tubular DASC made of a borosilicate glass tube of 140 cm in length and containing a smaller glass tube of 2.5 cm and 4 cm inner and outer diameters, respectively. The flow rate was 400 mL/min (Reynold number of 340) and a surface area of 0.055 cm2 was exposed to solar radiation. At a 4 cm sample depth, Fe2O3/water at 0.02 vol% absorbed all incident radiation while the other NF absorbed 17% less at the same volume fraction. In terms of STC efficiency, Fe2O3/water confirmed its better performance over Fe3O4/water by a maximum efficiency of 73%, which is higher by 22% than the maximum efficiency reached by Fe2O3 NF at 0.02 vol%. CQDs of less than 10 nm in diameter prepared by microwave heating [68] were dispersed in PEG-200 and investigated in a static mode under simulated solar radiation of 1–4 sun for 60 min under continuous magnetic stirring in a DASC made from a quartz vessel of 3 cm × 3 cm × 3 cm with a sponge plate on the top to reduce sample evaporation. The results revealed that extending the microwave heating duration has an advantageous impact on STC efficiency. In addition, the efficiency reached its maximum of 81% when exposed to 1 sun and microwave heating was 24 min, which is triple the efficiency of the base fluid PEG-200 (27%).

Guo et al. [50] produced NFs with GO (0.5–5 µm diameter), CNTs (−5 nm and 8–15 nm inner and outer diameters), and Ti3C2 at concentrations from 0.001 wt% to 0.04 wt% for investigating their STC performance in a static mode in a quartz DASC of 2.5–4 cm height. The collector was covered with a sponge, except for the top part, and it was exposed to varying solar concentrations from 1 sun to 2.5 suns. Ti3C2 outperformed both GO and CNTs by achieving an STC efficiency of 20% and 29% higher. The STC efficiency of the 0.04 wt% Ti3C2 NF was 2.7 times that of the pure working fluid when irradiated for 6500 s at a solar concentration ratio of 2.5 with a DASC height of 2.5 cm. In terms of concentration effect, they found that 0.02 wt% was the optimal particle concentration since no significant enhancement in performance was found at higher concentrations. Zheng et al. [79] studied the solar absorption and STC efficiency of a single-component NF of CNT/water (5–10 nm and 20–30 nm inner and outer diameters and 10–30 µm length) and a muti-component NF of CNT–TiN/water (TiN NPs are 20 nm in diameter) at mass fractions of 10 ppm, 20 ppm, and 30 ppm. The DASC that they used for this work was a cylinder made of acrylic with a 15 mm height, 26.4 mm inner diameter and 2 mm wall thickness. To reduce heat losses, they covered the DASC top with a 1 mm quartz glass of over 90% light transmittance and they also used an aluminium mirror at the bottom to reflect transmitted light back to the NFs. In a static mode and under one sun radiation intensity, the STC efficiency of the singleand multicomponent NF reached 25% and 26%, respectively, which is higher by 8.7% and 13.0%, respectively, compared to that of the base fluid. The increase in STC efficiency by the CNT–TiN/water over the single-component NF was attributed to the plasmonic absorption of TiN NPs. The increase in mass fraction above 10 ppm increased scattering by TiN NPs, which negatively impacted the efficiency.

The physical shape of NPs plays a crucial role in determining the performance of NFs. Nanoparticles with different shapes have distinct physicochemical properties, such as surface area, surface energy, and surface charge. These properties affect the absorption, stability, and thermal conductivity of NFs. Maheshwary et al. [119] explored the impact of NP shapes on the thermal conductivity and stability enhancement of NFs. The study investigated the thermal conductivity and stability of five different water-based NFs, CuO, MgO, TiO2, ZrO2, and Al2O3, with different shapes of spherical, cubic, and rod-shaped NPs.

All NFs were prepared with the same concentration of 2.5 wt%. It was revealed that the NF of cubic Al2O3 showed the highest thermal conductivity over the base fluid by 3.13 times. However, the cubic-shaped NPs exhibited lower stability compared to spherical and rod shapes. Chen et al. [120] reported that cubic Au NPs produce higher solar heating and higher absorption than spherical and cylindrical NPs, as shown in Figure 13. Additionally, Wang et al. [121] indicated that the absorption, in terms of both magnitude and bandwidth, of the cubic core–shell carbon Au NPs was better than spherical NPs. *Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 26 of 32

**Figure 13.** Optical properties of different Au nanostructures; (**A**) absorption section, and (**B**) scattering section. Adapted from [120]. **Figure 13.** Optical properties of different Au nanostructures; (**A**) absorption section, and (**B**) scattering section. Adapted from [120].

NFs have shown promising potential in the performance enhancement of DASCs by increasing the heat transfer rate and increasing the absorption of the solar spectrum. However, there are some limitations and disadvantages that need to be considered before implementing NFs in DASCs. One of the primary concerns is the stability of NFs since NPs tend to agglomerate and settle down over time and negatively affect the homogeneity of the fluid properties. Consequently, the usability of NFs will be limited for some applications, especially those that demand a higher concentration of NPs [63,123]. Corrosion is also another challenge, as some NPs can corrode the components of the solar collector, leading to material degradation and reduced efficiency [92]. The viscosity of NFs is also a problem, as NFs have higher viscosities compared to traditional heat transfer fluids, Using mixed NP morphologies can enhance the performance of NFs in terms of absorption and thermal conductivity. Mixed Au NPs with different shapes were used by Duan et al. [122] to prepare a plasmonic water-based NF and study this for DASC applications. A plasmonic-blended NF was created by mixing Au NPs of three distinct shapes (spherical, rod, and star-shaped) in water. Both experimental and numerical studies showed that the optical and thermal properties of blended NFs indicate that the extinction spectra of Au blended NFs were wider in comparison to single-component nanofluids. Moreover, the photothermal properties of these three mixed shapes of NPs showed a higher temperature rise and higher heat collection ability, and the experimental results aligned with the numerical analysis findings.

which means that they encounter greater resistance when flowing through a system. As a result, the pressure drop in the system increases and more power is needed to maintain the flow rate [124]. Overall, while the deployment of NFs for DASCs still presents some challenges, scientific and technological progress has shown that these can be overcome in the future. **6. Conclusions: Challenges, Research Gaps and Future Perspectives**  From the literature reviewed above, researchers have clearly made commendable progress in the development of efficient and stable NFs for DASCs. However, research work is still required to bring this new technology from lab experiments to large-scale production and attract investments from the industrial sector. The commercialization of NF-based DASCs will depend on completely resolving issues such as the instability of NFs, high costs and the synthesis complexity of nanomaterials [125], increased pumping power and the appearance of mechanical erosion and chemical corrosion due to deposi-NFs have shown promising potential in the performance enhancement of DASCs by increasing the heat transfer rate and increasing the absorption of the solar spectrum. However, there are some limitations and disadvantages that need to be considered before implementing NFs in DASCs. One of the primary concerns is the stability of NFs since NPs tend to agglomerate and settle down over time and negatively affect the homogeneity of the fluid properties. Consequently, the usability of NFs will be limited for some applications, especially those that demand a higher concentration of NPs [63,123]. Corrosion is also another challenge, as some NPs can corrode the components of the solar collector, leading to material degradation and reduced efficiency [92]. The viscosity of NFs is also a problem, as NFs have higher viscosities compared to traditional heat transfer fluids, which means that they encounter greater resistance when flowing through a system. As a result, the pressure drop in the system increases and more power is needed to maintain the flow rate [124]. Overall, while the deployment of NFs for DASCs still presents some challenges, scientific and technological progress has shown that these can be overcome in the future.

#### tion of NPs on the inner surfaces of flow channels [126], in addition to possible environmental concerns [127,128]. An in-depth understanding is required for sedimentation, ag-**6. Conclusions: Challenges, Research Gaps and Future Perspectives**

can all be studied and optimized to overcome the current challenges.

glomeration, morphological transformations, and the chemical deterioration of NPs in base fluids over long periods of operation, at elevated temperatures, and under thermal and solar cycling processes, as these factors are all critical to the optical, thermal, and rheological properties of NFs. Many optimization avenues are available and, for instance, NP From the literature reviewed above, researchers have clearly made commendable progress in the development of efficient and stable NFs for DASCs. However, research work is still required to bring this new technology from lab experiments to large-scale production and attract investments from the industrial sector. The commercialization of

loading, flow conditions, DASC system geometry, and NP chemical/structural properties

due to the overheating of the NF surface [128]. At very low NP loadings, e.g., less than 0.1 vol%, such limitations may not affect the applicability of NFs in DASCs. Another benefit of using very low particle loadings in DASCs is that it alleviates the problem of nanomaterials synthesis, which can be costly and sophisticated in some cases [129]. However, NF-based DASCs will depend on completely resolving issues such as the instability of NFs, high costs and the synthesis complexity of nanomaterials [125], increased pumping power and the appearance of mechanical erosion and chemical corrosion due to deposition of NPs on the inner surfaces of flow channels [126], in addition to possible environmental concerns [127,128]. An in-depth understanding is required for sedimentation, agglomeration, morphological transformations, and the chemical deterioration of NPs in base fluids over long periods of operation, at elevated temperatures, and under thermal and solar cycling processes, as these factors are all critical to the optical, thermal, and rheological properties of NFs. Many optimization avenues are available and, for instance, NP loading, flow conditions, DASC system geometry, and NP chemical/structural properties can all be studied and optimized to overcome the current challenges.

High concentrations of NPs increase scattering at the surface, increasing radiative losses, which further increase with particles of large sizes, as well as higher heat losses due to the overheating of the NF surface [128]. At very low NP loadings, e.g., less than 0.1 vol%, such limitations may not affect the applicability of NFs in DASCs. Another benefit of using very low particle loadings in DASCs is that it alleviates the problem of nanomaterials synthesis, which can be costly and sophisticated in some cases [129]. However, because low particle loading may compromise the ability of NFs to maintain high solar absorption and thermal conduction of the NFs, further research work is still needed to develop innovative solutions for simple and cost-effective techniques for both the synthesis of nanomaterials and the preparation of stable NFs. Since DASCs are a green technology that depends on solar energy, it is highly important to use NFs with no environmental impacts. In some cases, NFs may have environmental and toxicological effects [130–132], hence the selection of appropriate size, surface properties, and chemical composition is also important.

Solar thermal energy conversion technologies can greatly benefit from ongoing and future NF research. NF fundamental and physical properties can be reliably assessed in a laboratory setting and can provide valuable information in the development of full DASC systems aided by computer simulations. The availability of sophisticated synthesis methodologies in combination with fundamental materials science investigations can produce very high specification NFs at sufficiently low costs for the full deployment of NF-based DASCs.

**Author Contributions:** Conceptualization, H.S.M. and D.M.; methodology, H.S.M., V.A. and D.M.; validation, H.S.M. and V.A.; formal analysis, H.S.M., S.K., S.C., P.M. and D.M.; investigation, H.S.M. and V.A.; resources, V.A., S.C., P.M. and D.M.; data curation, H.S.M., S.K., S.C. and D.M.; writing—original draft preparation, H.S.M., S.K., S.C. and D.M.; writing—review and editing, H.S.M., V.A., S.K., S.C., P.M. and D.M.; visualization, H.S.M., S.K., S.C., P.M. and D.M.; supervision, S.C. and D.M.; project administration, V.A., S.C. and D.M.; funding acquisition, V.A., S.C., P.M. and D.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EPSRC grant number EP/V055232/1 and EP/M024938/1 and the Department for Economy-Northern Ireland grant number USI160.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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## *Review* **A Comprehensive Review of Nanofluid Heat Transfer in Porous Media**

**Hossam A. Nabwey 1,2,\* , Taher Armaghani 3 , Behzad Azizimehr 3 , Ahmed M. Rashad 4 and Ali J. Chamkha 5**

**Abstract:** In the present paper, recent advances in the application of nanofluids in heat transfer in porous materials are reviewed. Efforts have been made to take a positive step in this field by scrutinizing the top papers published between 2018 and 2020. For that purpose, the various analytical methods used to describe the flow and heat transfer in different types of porous media are first thoroughly reviewed. In addition, the various models used to model nanofluids are described in detail. After reviewing these analysis methods, papers concerned with the natural convection heat transfer of nanofluids in porous media are evaluated first, followed by papers on the subject of forced convection heat transfer. Finally, we discuss articles related to mixed convection. Statistical results from the reviewed research regarding the representation of various parameters, such as the nanofluid type and the flow domain geometry, are analyzed, and directions for future research are finally suggested. The results reveal some precious facts. For instance, a change in the height of the solid and porous medium results in a change in the flow regime within the chamber; as a dimensionless permeability, the effect of Darcy's number on heat transfer is direct; and the effect of the porosity coefficient has a direct relationship with heat transfer: when the porosity coefficient is increased or decreased, the heat transfer will also increase or decrease. Additionally, a comprehensive review of nanofluid heat transfer in porous media and the relevant statical analysis are presented for the first time. The results show that Al2O3 nanoparticles in a base fluid of water with a proportion of 33.9% have the highest representation in the papers. Regarding the geometries studied, a square geometry accounted for 54% of the studies.

**Keywords:** porous media; heat transfer; Darcy–Brinkman–Forchheimer; MHD

#### **1. Introduction**

A porous medium or a porous material is a solid material that contains pores. Depending on the ability of the porous medium to allow fluids to pass through it under the influence of external forces, it is classified as a permeable or a nonpermeable porous medium. Porous media may be non-dispersed or post-dispersed, homogeneous or heterogeneous, and multi-structure or the result of a combination of different structures [1]. Porosity, the main characteristic property of a porous medium, is a measure of the empty spaces in a material and is a fraction of the volume of the empty spaces over the total volume between 0 and 1. Most natural porous materials have a porosity of 0.6 (excluding hair). However, manufactured materials, such as metal foams, can have a porosity of up to 0.99. Table 1 shows the porosity value for different materials [2].

**Citation:** Nabwey, H.A.; Armaghani, T.; Azizimehr, B.; Rashad, A.M.; Chamkha, A.J. A Comprehensive Review of Nanofluid Heat Transfer in Porous Media. *Nanomaterials* **2023**, *13*, 937. https://doi.org/10.3390/ nano13050937

Academic Editors: M. M. Bhatti, Kambiz Vafai and Sara I. Abdelsalam

Received: 17 January 2023 Revised: 26 February 2023 Accepted: 2 March 2023 Published: 4 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Table 1.** The porosity of various materials [2].

Investigating heat transfer characteristics in porous media is of great interest in various industries and engineering domains such as heat exchangers, heat storage, geothermal systems, and drying techniques. Including a porous material in a mechanical system can be considered a passive method for heat transfer enhancement. Indeed, the presence of a porous material alters the flow patterns and improves the overall thermal conductivity of the system [3–7].

A further improvement in heat transfer can be achieved by adding conductive nanoparticles to the base fluid. The working fluid is then considered a nanofluid. The added nanoparticles can be metallic and made of metals such as aluminum and copper, among others, or metal oxides, or non-metallic materials such as carbon. Hybrid nanofluids refer to the fluids in which two or more types of nanoparticles are dispersed. The main objective of dispersing nanoparticles in the fluid is to increase its thermal conductivity [8]. Nonetheless, adding nanoparticles to a fluid presents a drawback that should be avoided. Increasing the volume fraction of the nanoparticles above a certain level increases the fluid viscosity and may, as a result, hinder heat transfer.

Due to the double importance of nanofluids and porous materials in heat transfer enhancement, significant research has been performed to study the thermal characteristics of nanofluid flow in porous media. The present paper summarizes the recent papers dealing with this topic. Considering the large number of articles published since the last review article (2017 to the present) and their analytical complexities, the authors divide the articles into two parts: 2018–2020 and 2020 until the present. These parts are presented in two articles. The paper is organized as follows: in Section 2, the various models of fluid flow and heat transfer in porous media are recalled and the classifications of the nanofluids are presented. In Section 3, the works dealing with heat transfer in porous media are presented and are classified into free convection and forced convection. Finally, Section 4 presents a general conclusion.

#### **2. Methods and Materials**

#### *2.1. Methods of Analysis of Porous Material*

In this section, the various analytical methods used to describe porous media are presented based on the scale length of the medium.

#### 2.1.1. Microporous Medium

Microporous media are at the size scale of the nanometer. Examples of such media include activated carbon, silica gels, carbon molecular sieves, and some crystalline structures such as zeolites.

#### 2.1.2. Mesoporous Media

The pore size of mesoporous media is between 2 and 50 nm. This size applies to non-organic jellies such as alumina, silica powders, porous glass, and columnar or noncolumnar bricks [2]. Since this review considers the heat transfer of nanofluids in porous media and nanofluids have particles with a diameter of more than 10 nm, the two methods described above cannot be used for this purpose. Therefore, we describe the macroscopic method in the following sections.

#### 2.1.3. Macroporous Media

Macroporous media have a size scale of greater than 50 nanometers. Macroporous media are widely found in nature, such in soil, broken rocks, sandstones, wood materials, and various types of food. Foods are generally macroporous but have different porosity size properties in some cases. This feature is indicated by the distribution of pore size, which indicates two or more sizes. Manufactured materials such as thermal insulation materials, silicate, ceramics, cement, synthetic resins, and many other artificial materials are also macroporous materials. They have many applications, such as in fluid filters, electronic components, complex fiber structures, bioceramics, fluid chromatography, and biotechnology [2].

#### 2.1.4. Macroscopic Governing Equations

The macroscopic equation is written as follows [2]:

$$
\vec{\nabla}.\mathbf{v} = \mathbf{0} \tag{1}
$$

Considering the Boussinesq assumption, the macroscopic momentum is as follows:

$$\rho\_f \left[ \frac{\partial v}{\partial t} + \heartsuit . \left( \frac{vv}{\mathcal{Q}} \right) \right] = -\heartsuit \rho\_p + \mu\_f \heartsuit^2 v + \mathcal{B} - \rho\_f \varpi \mathcal{B} \left( \dot{\Upsilon}\_f - \dot{\Upsilon}\_\infty \right) \mathbf{g} \tag{2}$$

where

$$B = -\frac{1}{v} \int\_{A\_{fs}} p\_f dS + \frac{\mu\_f}{v} \int\_{A\_{fs}} \left(\nabla v\_f\right) dS \tag{3}$$

and

$$
\mathfrak{p} = \mathfrak{Q}\hat{\mathfrak{p}}\_f \tag{4}
$$

In these formulas *p*, ∅, ρ, and µ are the pressure, porosity, density, and viscosity, respectively. The subscripts s and f are related to the solid and fluid.

The macroscopic energy equations for the fluid and solid are as follows: ̂

∅ (

) [ ̂

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 4 of 28

$$\mathcal{D}\left(\rho \mathbb{C}\_{p}\right)\_{f} \left[\frac{\partial \hat{\mathcal{T}}\_{f}}{\partial t} + \nabla \cdot \left(\mathbb{s}\_{f} \hat{\mathcal{T}}\_{f}\right)\right] = \mathcal{D}\bar{\mathcal{T}} \cdot \left[\left(k\_{f} + k'\right)\hat{\nabla}T\_{f}\right] + q\_{sf} \tag{5}$$

+ ∇̂. (̂

$$(\mathbf{1} - \boldsymbol{\varpi}) \left( \rho \mathbf{C}\_p \right)\_s \frac{\partial \hat{\mathbf{T}}\_s}{\partial t} = (\mathbf{1} - \boldsymbol{\varpi}) \left[ \boldsymbol{\nabla}. (k\_s \boldsymbol{\nabla} \hat{\mathbf{T}}\_s) \right] - q\_{sf} \tag{6}$$

̂  )] = ∅∇̂.[( +

′ )∇̂

] + (5)

(6)

In these formulas, *qs f* is the heat transfer between the solid matrix and fluid flow, and k represents the conductivity. *2.2. Nanofluid* Generally, a nanofluid is obtained by dispersing a certain volume fraction of nano-

#### *2.2. Nanofluid* particles in a base fluid. Nanoparticles are produced at different sizes from 10 nm to 100

Generally, a nanofluid is obtained by dispersing a certain volume fraction of nanoparticles in a base fluid. Nanoparticles are produced at different sizes from 10 nm to 100 nm, depending on their application. Since most of the fluids used for heat transfer have a low conductivity, heat transfer can be significantly improved with a uniform distribution of nanoparticles within the base fluid. Therefore, the typical size of nanofluid particles is greater than the typical pore size of microporous media and of the same order of magnitude as the typical pore size of mesoporous media. Therefore, nanofluids can only be used in macroporous media. Figure 1 shows a picture of the Titania nanoparticles [4]. nm, depending on their application. Since most of the fluids used for heat transfer have a low conductivity, heat transfer can be significantly improved with a uniform distribution of nanoparticles within the base fluid. Therefore, the typical size of nanofluid particles is greater than the typical pore size of microporous media and of the same order of magnitude as the typical pore size of mesoporous media. Therefore, nanofluids can only be used in macroporous media. Figure 1 shows a picture of the Titania nanoparticles [4].

**Figure 1.** Titania nanoparticles (30 nm). **Figure 1.** Titania nanoparticles (30 nm).

conductivity;

Some of the exceptional properties of nanoparticles include their non-linear relationship between the conductivity and the concentration of solids, the low momentum of the particles, a higher mobility than microparticles, the strong dependence of conductivity on temperature, a strong increase in heat flux in the boiling region, and acceptable viscosity. Some of the exceptional properties of nanoparticles include their non-linear relationship between the conductivity and the concentration of solids, the low momentum of the particles, a higher mobility than microparticles, the strong dependence of conductivity on temperature, a strong increase in heat flux in the boiling region, and acceptable viscosity. These properties, provided to the fluids, are considered some of the most suitable and strongest choices.

These properties, provided to the fluids, are considered some of the most suitable and strongest choices. • Thermal conductivity: the coefficient of the thermal conductivity of nanofluids depends on parameters such as the composition of the chemical percentage of nanoparticles, the volume percentage of nanoparticles, the surface-active substances, and the • Thermal conductivity: the coefficient of the thermal conductivity of nanofluids depends on parameters such as the composition of the chemical percentage of nanoparticles, the volume percentage of nanoparticles, the surface-active substances, and the temperature. The coefficient of thermal conductivity is also influenced by mechanisms such as the Brownian motion of nanoparticles in the fluid, which increases mixing in the fluid, facilitates heat transfer and increases the coefficient of thermal conductivity;

erosion of parts such as heat exchangers, pipelines, and pumps;

temperature. The coefficient of thermal conductivity is also influenced by mechanisms such as the Brownian motion of nanoparticles in the fluid, which increases mixing in the fluid, facilitates heat transfer and increases the coefficient of thermal

• Size reduction: the small size of the nanoparticles reduces their motion and contact

• Stability: nanoparticles are less likely to be precipitated due to their low weight and

with the solid wall, reduces momentum, and ultimately reduces the possibility of

small size, which prevents the problem of nanoparticle suspension caused by sedimentation. Presently, the instability of nanofluids hinders the application of

	- Adding a surfactant;
	- Controlling the pH of the nanofluid;
	- Ultrasonic vibration.

#### 2.2.1. Nanofluid Evaluation Methods

Researchers use different perspectives to analyze nanoscale behavior. Therefore, the modeling and formulation of nanoscale behavior also differs based on these perspectives. From one point of view, a certain volume fraction of nanoparticles is combined with the base fluid, but the nanofluid concentration does not change with respect to the initial concentration. The concentration of the nanofluid remains constant in different areas, but the newly formed fluid (nanofluid) has improved thermophysical properties compared to the base fluid. On the other hand, the movement of nanoparticles relative to the base fluid is not considered. Hence, this method or perspective is called a homogeneous or single-phase method. In the homogeneous method, three equations of mass conservation, momentum conservation, and energy conservation form the main structure of the model, and the thermophysical properties of the nano-fluid are substituted in conservation equations. The second method of analyzing nanoscale behavior is somewhat different from the homogeneous method. In this method, the movement of the nanoparticles changes the volume fraction of the nanoparticles (relative to the initial concentration) in different areas of the flow domain. Therefore, this method is called a non-homogeneous or pseudo-two-phase method. Several factors, such as gravitational force, Brownian forces, and thermophoresis forces, affect the heat transfer in this model. However, the Brownian and thermophoresis forces are dominant forces, according to ref. [8]. Because nanofluids consist of solid particles and a base fluid, one of the modeling approaches is to solve the conservation equations for the base fluid and the nanoparticles separately and is called the two-phase model.

#### 2.2.2. Hybrid Nanofluid

Another type of nanofluid in which two or more nanoparticles exist within the base fluid is called a hybrid nanofluid [6]. When one nanoparticle type is dispersed in a combination of two or more fluids it is also called a hybrid nanofluid. The heat conductivity is improved significantly when using this type of nanofluid. For example, although the addition of aluminum oxide nanoparticles to water increases the conductivity, the addition of copper nanoparticles to the aluminum–water nanofluid can further increase the conductivity relative to the base fluid. Figure 2 shows the aluminum and copper hybrid nanofluid presented in ref. [9].

**Figure 2.** Aluminum and copper hybrid nanofluid. **Figure 2.** Aluminum and copper hybrid nanofluid.

#### *2.3. Fluid Flow Models 2.3. Fluid Flow Models*

#### 2.3.1. Darcy's Equation

2.3.1. Darcy's Equation Based on the experimental data, Darcy's equation provides a linear proportion between the fluid's volumetric average velocity () and its pressure difference (∆) in addition to a porous media. Based on the experimental data, Darcy's equation provides a linear proportion between the fluid's volumetric average velocity (*v*) and its pressure difference (∆*p*) in addition to a porous media.

$$v = k \frac{\Delta p}{\Delta x} \tag{7}$$

 = ∆ (7) In this formula, ∆ ∆ is the pressure gradient. Hydraulic conductivity is an expression of how easily a fluid can flow throughout the hollows of a medium. Darcy's equation is In this formula, ∆*p* ∆*x* is the pressure gradient. Hydraulic conductivity is an expression of how easily a fluid can flow throughout the hollows of a medium.  Hazen–Darcy Equation

[2]. 2.3.2. Hazen–Darcy Equation Darcy's experiments were performed with a single-type fluid at a constant tempera-Darcy's experiments were performed with a single-type fluid at a constant temperature; therefore, Darcy's equation did not include the fluid's viscosity, *µ*. By providing a specific permeability relation, *K* = *kµ*, Darcy's equation is redefined in a viscosity-dependent form as follows:

$$v = \left(\frac{K}{\mu}\right) \frac{\Delta p}{\Delta x} \tag{8}$$

pendent form as follows: = ( ) ∆ ∆ (8) The specific permeability *K* is considered a hydraulic parameter and is independent of the fluid's characteristics. The above-mentioned formula is the Hazen–Darcy equation, which is known as Darcy's law [2].

#### The specific permeability is considered a hydraulic parameter and is independent 2.3.3. Hazen–Dupuit–Darcy Equation

of the fluid's characteristics. The above-mentioned formula is the Hazen–Darcy equation, which is known as Darcy's law [2]. The quadratic Hazen–Dupuit–Darcy equation is derived from the analysis of steadystate, open-channel flows. The equation is defined based on an equilibrium state between the gravitational force and the shearing resistance as follows:

$$0 = \frac{\partial p}{\partial \mathbf{x}} + \frac{\mu}{K} \mathbf{v} - \mathbb{C}\rho v^2 \tag{9}$$

state, open-channel flows. The equation is defined based on an equilibrium state between the gravitational force and the shearing resistance as follows: 0 = + − 2 (9) The second and third terms on the right-hand side express the viscous drag and geometrical drag, respectively. It is worthwhile to mention that the equation is only valid for steady-state and one-dimensional flows [2].

#### 2.3.4. Brinkman–Hazen–Dupuit–Darcy Equation

Brinkman realized that when the permeability is low, the shearing tension of the fluid's viscosity can be negligible in comparison to the viscous drag. Therefore, by adding the shearing tension term (a Laplacian one), the Brinkman–Hazen–Dupuit–Darcy equation is derived.

$$0 = -\nabla p + \mu \nabla^2 v - \frac{\mu}{K} \phi v + \frac{\mathcal{C}\_F}{K^{1/2}} \rho \phi^2 |v| v \tag{10}$$

where |*v*| is the magnitude of the velocity. The fluid is capable of transforming the viscous shearing tension independent of the viscous drag. Both the K and CF parameters have a wide variety in porous media in the engineering paradigms; for example, as packed beds, windowing environments, metal foams, and aerodynamic gels [2].

#### 2.3.5. Brinkman–Forchheimer Equation

The modified equation is as follows.

$$
\rho \left[ \frac{1}{\varphi} \frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\varphi^2} (\mathbf{v} \cdot \nabla v) \right] = -\nabla p + \mu\_\varepsilon \nabla^2 \mathbf{v} - \frac{\mu}{K} \mathbf{v} - \frac{c\_F \rho}{K^{1/2}} \mathbf{v} \mathbf{v} \tag{11}
$$

The equation is applied for an incompressible fluid. The inertia term on the left-hand side is calculated by conventional averaging. The first viscosity term in the Brinkman equation and the last term in Forchheimer's equation, the *CF*, is the Forchheimercoefficient. For more information about the mentioned formula, please see ref. [2].

#### *2.4. Heat Transfer Models*

Generally, there are two heat transfer models based on the volumetric averaging method: the single-equation model, which is based on the LTE (local thermal equilibrium) assumption, and the two-equation model, which is based on the LNTE (the local, nonthermal equilibrium) assumption. The two models will be discussed separately in terms of their assumptions and their application limitations [2].

#### 2.4.1. LTE

By distinguishing the gradient operator in the microscopic and macroscopic coordinates, a simple form of the volumetric average is provided. By averaging the microscopic equations on a representative elementary volume (REV), the macroscopic equations for the mandatory relocation of an incompressible flow in a variant porous medium are derived.

$$\left(\rho \mathbb{C}\_p\right)\_m \frac{\partial \hat{\mathcal{T}}}{\partial t} + \overline{\nabla} \cdot \left[v \hat{\mathcal{T}}\right] = a\_f \left(\frac{k\_m}{k\_f} + \frac{k'}{k\_f}\right) \nabla^2 \hat{\mathcal{T}} \tag{12}$$

According to the LTE assumptions, the single-equation model regarding the energy equation is highly capable of saving calculation time. The LTE assumption is that the temperature difference between the solid object and the fluid is negligible or is very small in comparison to the whole system's temperature difference. This hypothesis can describe the inaccuracies in the energy transfer model.

#### 2.4.2. LNTE

If the heat transfer between the solid object and the liquid is permissible, it leads to:

$$(1 - \varphi)(\rho c)\_s \frac{\partial T\_s}{\partial t} = (1 - \varphi) \nabla.(k\_s \nabla T\_s) + (1 - \varphi)q\_s''' + h\left(T\_f - T\_s\right) \tag{13}$$

$$
\rho \boldsymbol{\varrho} (\rho \boldsymbol{c}\_P)\_f \frac{\partial T\_f}{\partial t} + (\rho \boldsymbol{c}\_P) \boldsymbol{v} \cdot \nabla T\_f = \boldsymbol{\varrho} \nabla \left( k\_f \nabla T\_f \right) + \boldsymbol{\varrho} \boldsymbol{q}\_f''' + h \left( T\_s - T\_f \right) \tag{14}
$$

In these formulas, *q* 000 represents the volumetric heat generation, and h represents the convection heat transfer coefficient between the solid matrix and fluid flow.

#### 2.4.3. Buongiorno's Heterogeneous Model

Heat transfer among nanoparticles due to the effects of two phenomena, the thermophoresis sliding velocity and Brownian motion, results in a kind of heterogeneity in the nanofluid which is known for transfer or as Buongiorno's model. In Buongiorno's heterogeneous model, the thermophoresis and Brownian forces are the dominant forces exerted on the nanoparticles.

The thermophoresis force acts against the temperature gradient and tends to carry the nanoparticles from warm regions to cold ones. In contrast, the Brownian motion tends to transfer the nanoparticles from high-concentration regions to low-concentration regions. Due to the movement of nanoparticles in the base fluid, two important effects appear. The first is that the nanofluid in the low-concentration regions is lightweight and tends to move upward, while the nanofluid in the high-concentration regions is heavy and tends to move downward. The second is that the movements of the nanoparticles lead to energy transfer due to mass transfer [10].

The continuity equation, or the concentration of the particles using Buongiorno's model in dimensional form, is as follows:

$$\frac{1}{\varepsilon}V.\nabla\varphi = \nabla.[D\_B\nabla\varphi + \frac{D\_T}{T}\nabla\varphi] \tag{15}$$

*DB* and *DT* are the Brownian motion and thermophoresis coefficient, respectively:

$$D\_B = \frac{k\_B T}{3\pi \mu d\_{np}}\tag{16}$$

$$D\_T = (\frac{0.26k}{2k + k\_{np}})(\frac{\mu}{\rho})\varphi \tag{17}$$

where kB and dnp are the Boltzmann constant and the particle diameter, respectively.

For LTE, the energy equation in porous media is:

$$
\rho c\_p V.\nabla T = \nabla.k\_m \nabla T + \epsilon \rho\_{np} c\_{p,np} [D\_B \nabla \rho.\nabla T + D\_T \frac{\nabla T.\nabla T}{T}] \tag{18}
$$

where *km* is the effective thermal conductivity of the porous medium.

#### **3. Results and Discussion**

#### *3.1. Free Convection Heat Transfer*

When there is a temperature difference between a hot source and its surrounding fluid, the fluid's density varies in terms of the temperature variation and the buoyancy forces come into play. Therefore, the fluid begins to flow on the solid's surface in accordance with the temperature difference. In this case, heat transfer that occurs without any external stimulus and is completely autonomous is called free or natural convectional heat transfer.

Considering the importance of heat transfer, all its aspects and solutions should be taken into account to maximize the heat transfer speed. Natural heat transfer happens through the random motions of the molecules and the bulk motion of the fluid. Therefore, utilizing compounds with high heat conduction ratios in comparison to the fluids is useful. In this regard, using tiny particles with high heat conduction is considered. Studies showed that the smaller the size and dimension of the particles, the greater the effect on heat transfer rate [9–13].

#### *3.2. Integrated Free Convectional Heat Transfer*

Integrated free convectional heat transfer makes sense when two phenomena are combined: first, heat transfer due to the fluid's displacement, and conduction heat transfer due to the contact between the fluid and the solid object. The type of medium that can host the integrated free convectional heat transfer phenomenon is a porous medium containing a fluid and nanoparticles. The integrated free convectional heat transfer phenomenon has several industrial applications, such as for particle storage, filtering, gas drying, underground pollution, maintaining cooling radioactive waste containers, soil cleaning by steam injection, heat insulation for buildings, solar collector technologies, electronic cooling, and many more [14].

Yekani-Motlagh et al. [15] investigated the free convection of a two-phase nanofluid in an inclined, porous, semi-annulus enclosure. They used Fe3O4-water as their magnetic nanofluid and used Darcy and Boungiorno's models. They concluded that the Nusselt number increases when the nanoparticle volume fraction is increased.

The characteristics of the research papers related to free convection heat transfer and their results are summarized in Table 2.

**Table 2.** Research paper characteristics related to the free convection heat transfer.

[20] Inverse T-shaped cavity

[19]

Square cavity and linearly heated left wall with composite nanofluid–porous layers

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 10 of 28

Free convection, Galerkin finite element method, Darcy–Brinkmann model

Free convection MHD, extended Darcy– Brinkman– Forchheimer model

 = 0.1; 10−7 ≤ Da ≤ 1; 103 ≤ Ra ≤ 10

0 ≤ magnetic field viscosity parameter ≤ 1; 0.7 ≤ porosity ratio ≤ 1.4; 0 ≤ magnetic field inclination angle ≤ ; 0 ≤ ratio of dimensionless convection coefficient ≤ 10; Ha = 20; Ra = 10 5

7

#### **Table 2.** *Cont*.

Cu-water

MWCN T– Fe3O4/w ater

#### **Table 2.** *Cont*.

#### **Table 2.** *Cont*.

#### *3.3. Forced Convection Heat Transfer*

Forced convection occurs when the fluid motion is generated by an external source and not only by the density difference inside the fluid.

Sheikholeslami et al. [43] performed analyses on the effects of Reynolds number, the volumetric quotient of the water–calcium oxide nanofluid, and the Hartmann and Darcy numbers on the forced convectional heat transfer in a container of a hot liquid. They realized that the heat profile decreases with the increase of the voltage, but heat conduction is improved by an increase in the Darcy and Reynolds numbers. In addition, the studies indicate that there is an inverse relationship between the temperature gradient and the Hartmann number.

Furthermore, Sheikholeslami et al. [44] evaluated the forced convectional heat transfer of water–aluminum oxide in the presence of a magnetic field and realized that the nanofluid velocity profile is in direct relation to the Reynolds number of the volumetric quotient of aluminum oxide but in an inverse relation to the Hartmann number. In addition, by the increase in the Lorentz force, the convectional heat transfer decreases. It was also revealed that the temperature gradient on the moving surface increases as the hot surface velocity and the volumetric aluminum oxide quotient increase. They reported that increasing the Reynold number resulted in the Nusselt number increasing. In addition, increasing the Hartmann number augmented heat transfer.

Ferdows and Alzahrani [45] numerically investigated the possibility of similar solutions as well as dual-branch solutions to evaluate the performance of nanoparticles associated with water: the base water. A steady-state condition was considered through a moving, flat, porous plate in the presence of magnetic fields. They concluded that the largest velocity profile and the smallest temperature distribution refer to the Cu-water nanofluid.

Table 3 summarizes several studies dealing with the forced convection of nanofluids.

**Table 3.** Research paper characteristics related to the forced convection heat transfer.

#### **Table 3.** *Cont*.

#### *3.4. Mixed Convection*

Khademi et al. studied the mixed convection of nanofluids on a sloped, flat surface in a porous medium with the presence of a magnetic field. The boundary layer equations were solved numerically using the DQM method. This research identified a decrease in the Nusselt number [53].

Bondarenko et al. evaluated the mixed convection heat transfer of a nanofluid in a square container with insulated lateral walls and cold top and bottom walls. The boundary layer equations were solved using the FDM method [54]. Various research papers that considered the mixed convection of nanofluids are presented in Table 4.

**Table 4.** Research paper characteristics related to the mixed convection heat transfer.

#### **Table 4.** *Cont*.

[64] Vertical surface

*Nanomaterials* **2023**, *13*, x FOR PEER REVIEW 18 of 28

Mixed convection, Laplace transform technique Crank Nicolson method

Mixed convection, incompress-

Cuwater

Cu-

Magnetic parameter; porosity parameter; thermal and solute Grashof number; nanoparticle volume fraction parameter; time; Schmidt number; chemical reaction parameter; Prandtl number

0.001 < Ri < 100;

#### **Table 4.** *Cont*.

#### *3.5. Overall Review of Papers*

Considering that the most important purpose of adding nanoparticles to a base fluid is the possibility of increasing the heat transfer, in the following section and in Table 5, the selected articles presented in Tables 2–4 in the previous section were examined and studied based on the increase or decrease of the Nusselt number, and a report of the increase or decrease in the Nusselt number is presented as a percentage. In addition, due to the importance of the size of nanoparticles, their sizes are presented in a separate column.

number, and for a

In most articles about the natural and mixed convection of a nanofluid in porous media, the Nusselt number is increased by adding the volume fraction of nanoparticles; however, some articles also reported a decrease. When nanoparticles are added to the base fluid, the conductivity definitely increases. Viscosity also increases; therefore, in low-velocity flows, such as free displacement heat transfer, the decrease in speed due to the increase in viscosity is quite evident and effective and it can dominate the increase in conductivity, causing a decrease in displacement heat transfer. The same applies to a low-speed combined heat transfer. In forced heat transfer, the increase in nanoparticles increases the heat transfer. Additionally, in some cases in which an increase in the nanoparticle diameter is observed, the natural convection heat transfer rate is increased by more than 5%. By increasing the nanoparticle diameter in the articles, the forced convection heat transfer rate was decreased.

**Table 5.** Nu changes with nanofluid concentration and size.

#### *3.6. Statistical Results*

In this section, the statistical distribution of different parameters in the published papers on nanofluids in porous materials is presented. By reviewing the published research, it was revealed that Al2O3 nanoparticles in a base fluid of water with a proportion of 33.9% have the highest representation in the papers. Copper nanomaterials and Fe3O4-water, with a representation of 32.14% and 12.5%, respectively, occupy the second and third ranks. The share of each nanofluid is depicted in Table 6.

pers.

**Without MHD 70%**

magnetic field.

**Table 6.** The share of each nanoparticle in published studies.

In general, it can be said that the most popular nanoparticle is the alumina nanoparticle due to its very good dispersion in the base fluid. Of course, the role of the stability of the nanofluid in the porous media is more important. Metal oxide nanoparticles have shown a dual behavior in free convection heat transfer which has been reported to increase in some cases and decrease in some cases. However, in forced convection heat transfer, the increase of any type of nanoparticle increases the heat transfer.

Regarding the studied geometries, a square geometry accounted for 54% of the studies. Hole and circular geometries were represented with a share of 17% and 13%, respectively, and occupy the next ranks. The details are depicted in Table 7.

**Table 7.** The share of each of the studied geometries in published papers.

Figure 3 illustrates the proportion of the models that were used for evaluation. Based on the figure, Darcy–Brinkman–Forchheimer has the most share at 16%, followed by the Darcy–Brinkman and Darcy models, with shares of 6% and 2%, respectively. Figure 3 illustrates the proportion of the models that were used for evaluation. Based on the figure, Darcy–Brinkman–Forchheimer has the most share at 16%, followed by the Darcy–Brinkman and Darcy models, with shares of 6% and 2%, respectively.

Darcy Darcy-Brinkman Darcy-Brinkman-Forchheimer

**Figure 3.** The contribution of each of the models used to model the system in the published pa-**Figure 3.** The contribution of each of the models used to model the system in the published papers.

Figure 4 illustrates the share of the models used in the presence and absence of a Figure 4 illustrates the share of the models used in the presence and absence of a magnetic field.

> **MHD 18%**

**FHD 12%**

**Figure 4.** The presence or absence of magnetic fields to model the system in published papers.

**MHD FHD Without MHD**

Figure 5 depicts the contribution of scientific publishers Science Direct, Springer, Tandf Online, John Wiley, and ASME in published papers related to this specific topic.

pers.

magnetic field.

**MHD FHD Without MHD**

Other shapes 16

2%

6%

Darcy–Brinkman and Darcy models, with shares of 6% and 2%, respectively.

0

16%

**Figure 3.** The contribution of each of the models used to model the system in the published pa-

Darcy Darcy-Brinkman Darcy-Brinkman-Forchheimer

Figure 4 illustrates the share of the models used in the presence and absence of a

Figure 3 illustrates the proportion of the models that were used for evaluation. Based on the figure, Darcy–Brinkman–Forchheimer has the most share at 16%, followed by the

Figure 5 depicts the contribution of scientific publishers Science Direct, Springer, Tandf Online, John Wiley, and ASME in published papers related to this specific topic. Figure 5 depicts the contribution of scientific publishers Science Direct, Springer, Tandf Online, John Wiley, and ASME in published papers related to this specific topic. According to this figure, the highest share of the studies was indexed in Science Direct at 56%. According to this figure, the highest share of the studies was indexed in Science Direct at 56%.

**Figure 5.** The contribution of each publisher of the published papers related to nanofluids in a porous material. **Figure 5.** The contribution of each publisher of the published papers related to nanofluids in a porous material.

In the statistical analysis section, the items that are important for heat transfer, according to the authors, were examined: In the statistical analysis section, the items that are important for heat transfer, according to the authors, were examined:

• The type of nanoparticle; • The type of nanoparticle;

This has not been done before.

ity coefficient;

**4. Conclusion**

follows:

• The geometry under consideration. • The geometry under consideration.

Additionally, considering that the major contribution of the articles was related to numerical modeling, the model selected for investigating the flow in the porous medium was analyzed. It may be said that the last two forms are not directly related to the subject; Additionally, considering that the major contribution of the articles was related to numerical modeling, the model selected for investigating the flow in the porous medium was analyzed. It may be said that the last two forms are not directly related to the subject;

however, as we know, external forces, including the magnetic force, have an effect on heat

In this paper, works published between 2018 and 2020 that concern nanofluid heat transfer within porous media are reviewed. As the latest review in this field was published at 2017, it can be found at ref. [69]. Additionally, a good book was published in this field [70]. However, in this article, a statistical analysis of the published articles was performed.

The results showed that heat transfer is improved by adding nanoparticles to the base fluid. On the contrary, by increasing the volume concentration of nanoparticles, the viscosity effect overcomes the thermal conductivity and hinders the heat transfer. The heat transfer is also reduced with an increase in the nanoscale conductivity relative to the porous matrix, and heat transfer is enhanced with the rise of the Darcy number and the porosity coefficient. Some important results emerged from this study. They are presented as

1. As a dimensionless permeability, hte effect of the Darcy number on heat transfer is direct. Therefore, as the Darcy number increases, the heat transfer increases. As the

2. The effect of the porosity coefficient has a direct relationship with the heat transfer, and the heat transfer will increase or decrease by increasing or decreasing the poros-

Darcy number decreases, the heat transfer decreases;

transfer, and approximately 30% of the subject articles dealt with it.

however, as we know, external forces, including the magnetic force, have an effect on heat transfer, and approximately 30% of the subject articles dealt with it.

#### **4. Conclusions**

In this paper, works published between 2018 and 2020 that concern nanofluid heat transfer within porous media are reviewed. As the latest review in this field was published at 2017, it can be found at ref. [69]. Additionally, a good book was published in this field [70]. However, in this article, a statistical analysis of the published articles was performed. This has not been done before.

The results showed that heat transfer is improved by adding nanoparticles to the base fluid. On the contrary, by increasing the volume concentration of nanoparticles, the viscosity effect overcomes the thermal conductivity and hinders the heat transfer. The heat transfer is also reduced with an increase in the nanoscale conductivity relative to the porous matrix, and heat transfer is enhanced with the rise of the Darcy number and the porosity coefficient. Some important results emerged from this study. They are presented as follows: