**Abstract**

A one-dimensional transient heat conduction equation is solved using analytical and numerical methods. An iterative technique is employed which estimates unknown boundary conditions from the measured temperature time history. The focus of the present chapter is to investigate effects of input parameters such as time delay, thermocouple cavity, error in the location of thermocouple position and time- and temperature-dependent thermophysical properties. Inverse heat conduction problem IHCP is solved with and without material conduction. A two-time level implicit finite difference numerical method is used to solve nonlinear heat conduction problem. Effects of uniform, nonuniform and deforming computational grids on the estimated convective heat transfer are investigated in a nozzle of solid rocket motor. A unified heat transfer analysis is presented to obtain wall heat flux and convective heat transfer coefficient in a rocket nozzle. A two-node exact solution technique is applied to estimate aerodynamic heating in a free flight of a sounding rocket. The stability of the solution of the inverse heat conduction problem is sensitive to the spatial and temporal discretization.

**Keywords:** analytical solution, inverse heat conduction problem, numerical analysis, deforming grid, heat transfer coefficient, heat flux, random search method

### **1. Introduction**

The basic theory of heat and structure of solid body is associated with the internal energy of matter which in the first law of thermodynamics is referred to as the internal energy concerned with the physical state of the material. The first law of thermodynamics defines that the flowing heat energy is conserved in the absence of heat sources and sinks. It is, therefore, important to study the influence of thermocouple lead wires and distortion due to the thermocouple cavity in solution of the inverse heat conduction problem. According to the second law of thermodynamics, the heat will be transferred from one body to another body only when the bodies are at two different temperatures level and the heat will flow from the point of higher to the point of lower temperature.

A direct solution of transient heat conduction equation with prescribed initial and boundary conditions yields temperature distribution inside a slab of finite thickness. The direct solution is mathematically considered as well-posed because the solution exists, unique and continuously depends on input data. The estimation of unknown parameters from the measured temperature history is called as inverse problem of heat conduction. It is mathematically known as an ill-posed problem since the solution now does not continuously depend on the input data. Measurement data error in temperature, thermal lagging, thermocouple's cavity, signal noise, etc. makes stability problem in the estimation of unknown parameters.

Numerical inversion of the integral solution [1], exact solution [2], numerical techniques [3], least-squares method [4], transform methods [5], different series approach [6], variable time-step size [7] have been applied to solve inverse heat conduction problems. Solutions of the ill-posed inverse heat conduction problem have been presented in detail by Beck et al. [8] and Özisik et al. [9]. Tikhonov regularization method [10] has been described for cross-validation criterion for selecting the regularization parameter to obtain a stable approximation to the solution. Kurpisz et al. [11] have presented series with derivatives with temperature to solve inverse thermal problem. Hensel [12] has described space marching numerical methods to solve inverse heat transfer problem. Various mathematical methods and numerical algorithms for solving inverse heat conduction problems are described and compared by Alifanov [13]. Taler and Duda [14] have presented solutions of direct and inverse heat conduction problems.

Inverse heat conduction analysis provides an efficient tool for estimating the thermophysical properties of materials, the boundary conditions, or the initial conditions. Estimation of surface heat flux has been carried out without [15] and with [16] heat conduction and comparison between them shows discrepancies as high as about 27% [17]. Moving window optimization method [18] has been applied to predict the aerodynamic heating in a free-flight of sounding rocket by comparing numerically calculated and measured temperature history. Howard [19] developed a numerical procedure for estimating the heat flux with variable thermal properties using a single embedded thermocouple. Simultaneous identification of the temperature-dependent thermal conductivity and the asymmetry parameter of the Henyey-Greenstein scattering phase function have been shown by Zmywaczyk and Koniorczyk [20].

flux history has been analyzed with simulated data in a one-dimensional domain by

*Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem*

*DOI: http://dx.doi.org/10.5772/intechopen.91000*

Chen and Danh [27] have carried out experimental studies to obtain transient temperature distortion and thermal delay in a slab due to presence of thermocouple cavity. The distortion of temperature profiles inside the slab may be influenced by the dissimilar thermophysical properties of thermocouple and surrounding materials and by the diameter and depth of the cavity. The temperature distortion [28] inside a slab is a function of the thermocouple cavity diameter *d* and location *xm*. Standard statistical analysis consists of error in the measurement as an additive of true plus random, in zero mean, in constant variance, uncorrelated, normal, bell shaped probability density function, constant variance known, errors in the dependent variables and no-prior information about the parameters. The error in mea-

*E* ¼ cosð Þ *x=L* ð Þ cos *ε* � 1 *e*

*E* ¼ sin ð Þ *x=L* ð Þ cos *ε* � 1 *e*

where *ε* and *δτ* refer to error in measurement of thermocouple location and in time recording, respectively. One of the important points that must be mentioned, here, is the use of a starting solution. In the case of a solid rocket motor where boundary conditions are suddenly imposed by a wall, there will be high intensity of heat flux on cold wall, and the heat flux during the first few steps in time may not be very accurate. The numerical solution is initiated using an exact analytical solution instead of starting from the initial constant condition. Such solutions can be obtained from to exact analytical solution [30] of transient heat conduction equation. Heat transfer rates to the calorimetric probe are estimated from measurements of temperature and rate of temperature change using energy conservation considerations [31].

�*δτ* (1)

�*δτ* (2)

surement can be obtain using exact analytical solution [29] as

Woodbury [26].

*Geometry of the specimen.*

**Figure 1.**

**165**

The conjugate gradient method with adjoint problem for function estimation iterative technique is used to solve IHCP to estimate heat flux and internal wall temperature of the throat section of the rocket nozzle [21]. Heisler [22] have reported supplementary "short-time" temperature-time charts for the center, midlocation and surface of large plates, long cylinders and spheres for the dimensionless time sub-domain. Convective heat transfer coefficient and combustion temperature in a rocket nozzle is determined using transient-temperature response chart [23].

The solution of transient IHCP can be obtained using analytical or numerical schemes in conjunction with measured temperature-time history. The estimation of the unknown parameters can be carried out by employing gradient or non-gradient methods to predict the unknown parameters in a prescribed tolerance limit. The focus of the present work is to investigate the influence of various parameters on the solution of inverse heat conduction problem.

#### **2. Measurement errors**

Experimental difficulties [24] are noticed in implanting thermocouples at the surface for temperature measurements. Temperature response delays have been studied to solve IHCP applied to cooled rocket thrust chamber [25]. The temperature measured inside the slab may delay and damp depending on *xm* as illustrated in **Figure 1**. A thermocouple indicates temperature lag behind the actual temperature. The effect of the thermocouple sensor dynamics on prediction of a triangular heat

*Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem DOI: http://dx.doi.org/10.5772/intechopen.91000*

**Figure 1.** *Geometry of the specimen.*

of unknown parameters from the measured temperature history is called as inverse problem of heat conduction. It is mathematically known as an ill-posed problem since the solution now does not continuously depend on the input data. Measurement data error in temperature, thermal lagging, thermocouple's cavity, signal noise, etc. makes stability problem in the estimation of unknown parameters. Numerical inversion of the integral solution [1], exact solution [2], numerical techniques [3], least-squares method [4], transform methods [5], different series approach [6], variable time-step size [7] have been applied to solve inverse heat conduction problems. Solutions of the ill-posed inverse heat conduction problem have been presented in detail by Beck et al. [8] and Özisik et al. [9]. Tikhonov regularization method [10] has been described for cross-validation criterion for selecting the regularization parameter to obtain a stable approximation to the solution. Kurpisz et al. [11] have presented series with derivatives with temperature to solve inverse thermal problem. Hensel [12] has described space marching numerical methods to solve inverse heat transfer problem. Various mathematical methods and numerical algorithms for solving inverse heat conduction problems are described and compared by Alifanov [13]. Taler and Duda [14] have presented solutions of

Inverse heat conduction analysis provides an efficient tool for estimating the thermophysical properties of materials, the boundary conditions, or the initial conditions. Estimation of surface heat flux has been carried out without [15] and with [16] heat conduction and comparison between them shows discrepancies as high as about 27% [17]. Moving window optimization method [18] has been applied to predict the aerodynamic heating in a free-flight of sounding rocket by comparing numerically calculated and measured temperature history. Howard [19] developed a numerical procedure for estimating the heat flux with variable thermal properties

using a single embedded thermocouple. Simultaneous identification of the

temperature-dependent thermal conductivity and the asymmetry parameter of the Henyey-Greenstein scattering phase function have been shown by Zmywaczyk and

The conjugate gradient method with adjoint problem for function estimation iterative technique is used to solve IHCP to estimate heat flux and internal wall temperature of the throat section of the rocket nozzle [21]. Heisler [22] have reported supplementary "short-time" temperature-time charts for the center, midlocation and surface of large plates, long cylinders and spheres for the dimensionless time sub-domain. Convective heat transfer coefficient and combustion temperature in a rocket nozzle is determined using transient-temperature response chart [23]. The solution of transient IHCP can be obtained using analytical or numerical schemes in conjunction with measured temperature-time history. The estimation of the unknown parameters can be carried out by employing gradient or non-gradient methods to predict the unknown parameters in a prescribed tolerance limit. The focus of the present work is to investigate the influence of various parameters on

Experimental difficulties [24] are noticed in implanting thermocouples at the surface for temperature measurements. Temperature response delays have been studied to solve IHCP applied to cooled rocket thrust chamber [25]. The temperature measured inside the slab may delay and damp depending on *xm* as illustrated in **Figure 1**. A thermocouple indicates temperature lag behind the actual temperature. The effect of the thermocouple sensor dynamics on prediction of a triangular heat

direct and inverse heat conduction problems.

*Inverse Heat Conduction and Heat Exchangers*

the solution of inverse heat conduction problem.

**2. Measurement errors**

**164**

Koniorczyk [20].

flux history has been analyzed with simulated data in a one-dimensional domain by Woodbury [26].

Chen and Danh [27] have carried out experimental studies to obtain transient temperature distortion and thermal delay in a slab due to presence of thermocouple cavity. The distortion of temperature profiles inside the slab may be influenced by the dissimilar thermophysical properties of thermocouple and surrounding materials and by the diameter and depth of the cavity. The temperature distortion [28] inside a slab is a function of the thermocouple cavity diameter *d* and location *xm*.

Standard statistical analysis consists of error in the measurement as an additive of true plus random, in zero mean, in constant variance, uncorrelated, normal, bell shaped probability density function, constant variance known, errors in the dependent variables and no-prior information about the parameters. The error in measurement can be obtain using exact analytical solution [29] as

$$E = \cos\left(\mathbf{x}/L\right) (\cos\varepsilon - \mathbf{1})e^{-\delta\tau} \tag{1}$$

$$E = \sin\left(\pi/L\right) (\cos\varepsilon - \mathbf{1})e^{-\delta\mathbf{r}}\tag{2}$$

where *ε* and *δτ* refer to error in measurement of thermocouple location and in time recording, respectively. One of the important points that must be mentioned, here, is the use of a starting solution. In the case of a solid rocket motor where boundary conditions are suddenly imposed by a wall, there will be high intensity of heat flux on cold wall, and the heat flux during the first few steps in time may not be very accurate. The numerical solution is initiated using an exact analytical solution instead of starting from the initial constant condition. Such solutions can be obtained from to exact analytical solution [30] of transient heat conduction equation. Heat transfer rates to the calorimetric probe are estimated from measurements of temperature and rate of temperature change using energy conservation considerations [31].

An optimization method based on a direct and systematic search region reduction optimization method [32] can be employed to estimate the unknown convective heat transfer coefficient in a typical rocket nozzle. The most attractive feature of the direct search scheme is the simplicity of computer programming. The pseudo-random algorithm, an effective tool for optimization, does not require computation of derivatives but depends only on function evaluation. It works even when the differentiability requirements cannot be ensured in the feasible domain. For initiating the search only an estimate of the feasible domain is needed. Therefore, another advantage of the method is that the starting condition is not crucial; any reasonable value will do.

*F qw*

*DOI: http://dx.doi.org/10.5772/intechopen.91000*

*Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem*

iteration procedure will continue until j*F*(*qw*)j ≤ 10�4

Newton-Raphson to obtain the estimate value.

method.

**3.3 Numerical methods**

equations:

**167**

where *θc* and *θm* are the calculated and measured temperatures at (*Xm*, *τ*), respectively. The computed temperature is a nonlinear function of unknown parameters such as wall heat flux or convective heat transfer coefficient. Temperature is calculated using Eq. (6) and compared with the measured temperature as expressed in Eq. (7). The inverse problem starts with initial guess value of the unknown parameter. The second step is to correct the previous guessed unknown parameter using the Newton-Raphson method. The sensitivity coefficient can be obtained by differentiating temperature with respect to wall heat flux *qw*. The

mates the component of the *qw* at a time and thus may be considered on-line

initial guess value of *qw*, satisfy the convergence criterion, and implement the

*Bi* ¼ *Lqw*

criterion for the iterative scheme remains same as mentioned above.

method to consider the radiation boundary condition.

delay in the measurement of back wall temperature.

*dθ*0 *dτ* ¼ 1

**3.4 Two-nodes system of transient heat conduction equation**

*dθ*1 *dτ* ¼ 1

two-node finite-difference approximation to the original problem.

The inverse method for solving a value of *qw*(*0*, *τ*) is as follows. Initiate with an

Now, it is possible to estimate convective heat transfer coefficient and combustion gas temperature in conjunction with measured temperature history [35]. The equation for converting the calculated heat flux to the heat transfer coefficient is

*K*ð Þ*θ Tg* � *Ti*

In the foregoing equation,*T*g is an unknown quantity and can be estimated using again the above-mentioned minimization and iteration methods. The convergence

It is not always feasible to obtain analytical solution of temperature-dependent thermal conductivity and radiation boundary condition. The Crank-Nicolson finite difference method with two-time level implicit numerical scheme [36] has been employed to solve the nonlinear conduction problem with the Newton-Raphson

Deforming or moving finite elements method [37] is used to solve linear heat conduction equation. The moving finite element [38] is used to consider the time

For only two nodes the system of [39] equations reduce to the following pair of

where 0 and 1 represent node in a slab of finite thickness. These are the exact solutions to the system of two ordinary differential equations which resulted from a

ð Þ Δ*X* 2 ½ � �2ð Þ *θ*1 þ *Bi*Δ*X θ*0 þ 2*θ*1 (9)

ð Þ Δ*X* 2 ½ � 2*θ*0 � 2*θ*1 (10)

≈j j *θc*ð Þ� *Xm*, *τ θm*ð Þ *Xm*, *τ* (7)

. This iterative scheme esti-

(8)


**1. Introduction**

Marine animals, especially marine invertebrates, contain various carotenoids, with structural diversity [1–4]. Interesting structural carotenoids are still being found in marine animals [4]. In general, animals do not synthesize carotenoids *de novo*, and so those found in animals are either directly accumulated from food or partly modified through metabolic reactions [2]. The major metabolic conversions of carotenoids found in marine animals are oxidation, reduction, transformation of double bonds, oxidative cleavage of double bonds, and cleavage of epoxy bonds [2,3]. Therefore, various structural varieties are found in carotenoids of marine animals [4].

We have studied carotenoids in several marine invertebrates from chemical and comparative biochemical points of view [4]. In the present study, we focused on carotenoids of the corals *Acropora japonica*, *A. secale*, and *A. hyacinthus*, the tridacnid clam (elongate giant clam) *Tridacna squamosa*, crown-of-thorns starfish *Acanthaster planci*, and small sea snail *Drupella fragum*, inhabiting the Kuroshio current coast. These animals are closely associated within the food chain. Corals and the tridacnid clam are filter feeders and are associated with symbiotic zooxanthellae (dinoflagellate algae). On the other hand, the crown-of-thorns starfish and small sea snail *D. fragum* are carnivorous and mainly prey upon corals. Therefore, carotenoids that originated from zooxanthellae are passed to starfish and small sea snails through this food chain. In the present paper, we describe the carotenoids of these marine invertebrates.

## **2. Results and Discussion**

Structural formulae of carotenoids identified from *Acropora* corals, the tridacnid clam *T. squamosa*, starfish *A. planci*, and sea snail *D. fragum* are shown in Figure 1.


*2.4. Temperature Distibution in the Cannon Barrel for a Series of Sixty Shots*

Thermophysical properties, i.e., thermal conductivity, specific heat and density as a function of temperature in the range of 1000 ◦C to 1300 ◦C, were obtained by the linear extrapolation of experimental data of the selected steels in the RT range up to 1000 ◦C. For the selected steels, temperature distributions *Ti*(*t*,*r*, *z*) of the barrels inner surface and along the barrel thickness for a sequence of sixty shots in each zone S1 to S6 (*z* in the middle of each zone) are shown in Figure 12 for 30HN2MFA steel and Figure 13 for DUPLEX steel. The results for the 38HMJ steel are very similar to the results for the 30HN2MFA steel, therefore they are not shown in a separate drawing.

**Figure 12.** Temperature distribution *Ti*(*t*,*rw*, *z*) along the barrel thickness at the zones S1 to S6 (*z* in the middle of each zone) for the sequence of sixty shots, for the 30HN2MFA steel: black line—on the inner surface of the barrel, red line—0.1 mm below the inside surface, blue line—0.5 mm below the inside surface, green line—1 mm below the inside surface, violet line—2 mm under the inner surface, yellow line—5 mm under the inner surface, light blue line—on the outer surface of the barrel. The signs: P1.5—in the middle of the S1 zone, P2.5—in the middle of the S2 zone, etc.

**Figure 13.** Temperature distribution *Ti*(*t*,*rw*, *z*) along the barrel thickness at the zones S1 to S6 (*z* in the middle of each zone) for the sequence of sixty shots, for the DUPLEX steel: black line—on the inner surface of the barrel, red line—0.1 mm below the inside surface, blue line—0.5 mm below the inside surface, green line—1 mm below the inside surface, violet line—2 mm under the inner surface, yellow line—5 mm under the inner surface, light blue line—on the outer surface of the barrel. The signs: P1.5—in the middle of the S1 zone, P2.5—in the middle of the S2 zone, etc.

Figure 14 shows the envelopes of the so-called highest peak temperatures and lowest peak base temperatures for 60 shots for all selected steels. For 38HMJ and 30HN2MFA steels, the lines match blue.

**Figure 14.** Envelope of the lowest and the highest temperature of the inner surface at the zones S1 to S6 (*z* in the middle of each zone) for the sequence of sixty shots, for chosen steels: 30HN2MFA, 38HMJ, DUPLEX. The signs: P1.5—in the middle of the S1 zone, P2.5—in the middle of the S2 zone, etc.

#### **3. Discussion**

The results of numerical tests of the heat transfer in the barrel of the 35 mm anti-aircraft gun made of three selected steel grades showed a similar nature of heat transfer in the 38HMJ and 30HN2MFA steels, but a different one in the Duplex steel. The heat transfer model is relatively simple and the obtained values of temperature fields on the inner surface of the barrel were not overestimated, as they were in the paper [24]. The division of the cannon into six zones S1 to S6 was agreed with the Polish weapons manufacturer. As numerical tests of heat transfer in the barrel are very time-consuming, such a division method reduces the calculation time to several hours for one steel.

In the case of a single shot—the temperature on the inner surface of the barrel:

In DUPLEX steel, the maximum temperature of the inner surface of the barrel, i.e., socalled highest peak temperature was about 87 ◦C higher than for the other two steels, and it dropped less than the other two. It results from a lower value of thermal diffusivity coefficient as a function of the Duplex steel temperature in relation to the other two. In each of the three selected steels, the maximum temperature of the inner surface of the barrel occurred in the third zone, S3. In the second, S2, and fourth, S4, zones, the temperatures were not much lower. In addition, the maximum temperatures on the inner surface of the barrel in the first four zones, S1 to S4, occurred before the exit of the bullet from the barrel, while the maximum temperatures in the fifth zone, S5, and the sixth zone, S6, occurred after the bullet exited the barrel.

In the case of the sequence of seven shots—temperature on the inner surface of the barrel:

In DUPLEX steel in the S3 zone, the highest temperature and the lowest temperature of the inner surface, i.e., the so-called highest peak temperature and lowest temperature of the peak base after the seven shots reached the values of 1088 ◦C and 462 ◦C, respectively— Figure 9. The difference between the highest and lowest inner surface temperature was maximum and equal to 626 ◦C in the S3 zone and minimum and equal to 468 ◦C in the S6 zone—Figure 9. In the 38HMJ and 30HN2MFA steels in the S3 zone, the lowest and the highest temperature of the inner surface after seven shots reached the values of 345 ◦C and 1039 ◦C for 30HN2MFA steel, and 355 ◦C and 991 ◦C for 38HMJ steel, respectively. The difference between the highest and lowest inner surface temperature for these steels was maximum and equal to 694 ◦C for 30HN2MFA steel and 636 ◦C for 38HMJ steel in the S3 zone and the minimum and equal to 552 ◦C for 30HN2MFA steel and 507 ◦C for 38HMJ steel in the S6 zone. For each of the selected steels, the lowest temperature reached its maximum in the S6 zone, and the increase in the lower internal surface temperature, i.e., in the lowest temperature of the peak base became an almost linear function of the number of shots.

In the case of the sequence of seven shots—the calculation of heat transfer along the barrel thickness:

On each curve of increasing temperature of the inner surface of the barrel during the shot, we could distinguish the so-called highest peak temperature and the lowest base temperature, which was in fact the temperature of the inner wall of the barrel. This temperature was practically identical to the temperature of the barrel wall at a depth of 0.5 mm below its inner surface—Figure 10. Therefore, it can be assumed that the temperature of the inner surface of the barrel during a series of shots is equal to the barrel temperature at a depth of 0.5 mm below its surface. Temperature distributions *Ti*(*t*,*r*, *z*) along the barrel thickness for selected steels for the first, fourth and seventh shots are shown in Figure 11. At a depth of 0.5 mm, the greatest temperature difference occurred between 30HN2MFA, 38HMJ steels and DUPLEX steel. The difference increased with subsequent shots and after the seventh shot in the zone S6 it was about 86 ◦C—Figure 11 (lower drawing).

In the case of the sequence of sixty shots—the temperature along the barrel thickness:

After sixty shots, the highest internal surface temperature of the barrel occurred in the S3 zone and for all three steel grades, i.e., 30HN2MFA, 38 HMJ and DUPLEX steel, it was similar and amounted to approx. 1363 ◦C for 30HN2MFA and 38 HMJ steels, and 1348 ◦C for DUPLEX steel—Figures 12–14.

The lowest temperature of the internal surface in DUPLEX steel occurred in zones S1 and S2, i.e., around 849 ◦C in zone S1 and 916 ◦C in zone S2. For the remaining steels, the lowest temperature also occurred in zones S1 and S2, i.e., about 748 ◦C for 30HN2MFA and 38 HMJ steels in zone S1 and 827 ◦C for 30HN2MFA and 38 HMJ steels in zone S2. This is due to the fact that DUPLEX steel heats up to a higher temperature and cools down slowly as it has a lower thermal diffusivity coefficient than 30HN2MFA and 38HMJ steels. As it cools more slowly, the highest internal surface temperature after sixty shots is also lower than it would have been if this shielding effect, which is associated with an increase in inner wall temperature after each shot, was not observed in the heat flux density calculation. It should also be remembered that for 38HMJ and 30HN2MFA steels there is a shrinkage of the material and a phase change at a temperature of about 800 ◦C. The internal surface temperature of about 800 ◦C was achieved in 30HN2MFA and 38HMJ steels after about thirty shots in zone S5 (after 3.0 s) and S6 (after 2.9 s) and after about sixty shots in zone S1 (after 5.9 s)—Figure 12. It also means that the inner surface of the barrel in zones S5 and S6 will wear out the fastest. Due to the integral heat propagation effect in the steel, no changes were observed in the highest or lowest temperature of the inner surface of the barrel in the case of 30HN2MFA or 38HMJ steels specifically related to this shrinkage effect. After sixty shots, the maximum temperature of 30HN2MFA and 38HMJ steels and Duplex steel in the S2 to S4 zones was practically the same and was about 1363 ◦C for 30HN2MFA and 38 HMJ steels and 1348 ◦C for DUPLEX steel, while the lowest temperature in the 30HN2MFA and 38HMJ steels in the S5 and S6 zones was about 892◦, and in DUPLEX steel it was about 955 ◦C in zone S5 and 944 ◦C in zone S6. After sixty shots, the outer surface of the barrel in zone S6 heated up to a temperature of about 226 ◦C for 30HN2MFA steel and 230 ◦C for 38 HMJ steel, and to 103 ◦C for DUPLEX steel–Figures 12 and 13. For selected steels, the envelopes of the highest and the lowest temperatures are shown in Figure 14. There were only differences between DUPLEX steel and the other steels, i.e., 30HN2MFA and 38HMJ.

#### **4. Conclusions**

The calculations of the heat transfer in the barrel of the 35 mm anti-aircraft gun were made for the temperature-dependent thermophysical parameters, i.e., thermal conductivity, specific heat and thermal expansion (in the RT range up to 1000 ◦C) of the selected barrel steels. The paper indicates that the energy of the phase transformation should not be taken into account multiple times, e.g., both in terms of thermal conductivity and specific heat.

The results of the numerical simulation of the heat transfer in the barrel of the 35 mm anti-aircraft cannon are summarized as follows:

(1) After the first shot, the maximum temperature on the inner surface of the barrel, the so-called highest temperature is the highest in DUPLEX steel—Figure 7. The temperature difference in relation to the other two steels is about 87 ◦C in zone S3 and decreases with successive shots, and after about 4 s and about 40 shots it is similar to the temperature of DUPLEX steel (in zone S3)—Figure 14. After sixty shots, the highest temperature of the 30HN2MFA and 38HMJ steels begins to exceed the highest temperature of the DUPLEX steel by about 15 ◦C, mostly in zone S3 and S4—Figure 14;

(2) After the first and subsequent shots, when the projectile leaves the barrel, instability appears in the calculations of *Ti*(*t*,*rin*, *z*) in zones S5 and S6—Figure 8. This is related to a sharp drop in the heat transfer coefficient *hi*(*t*) in these zones, much greater than in other zones—Figure 2;

(3) In Figure 9, for a series of 7 shots, it can be seen that the shape of *Ti*(*t*,*rin*, *z*) is the same in all zones from S1 to S6—Figure 9. In all zones, the so-called lowest temperature is highest for DUPLEX steels in each zone;

(4) The so-called lowest temperature on the inner surface of the barrel *Ti*(*t*,*rin*, *z*) plays a very important role in the analysis of heat transfer in the barrel, because it is related to the phase transition of the steel from which the barrel is made. It can be assumed that the temperature of the inner surface of the barrel during a series of shots is equal to the barrel temperature at a depth of 0.5 mm below its surface, i.e., *Ti*(*t*,*r* = *rin* − 0.5 mm, *z*) —Figures 10 and 11;

(5) For the 30HN2MFA and 38HMJ steels, for which the phase transition takes place, the temperature of 800 ◦C appears in different zones at different times, the fastest in zones S5 and S6. This means that zones S5 and S6 of the barrel will be exposed to the greatest wear. Already after about 3 s, i.e., after about thirty shots, these parts of the barrel will exceed the phase transition temperature—Figure 12;

(6) The so-called lowest temperature on the inner surface of the barrel *Ti*(*t*,*rin*, *z*) made of DUPLEX steel is always higher than the same temperature for a barrel made of 30HN2MFA or 38HMJ steel—Figure 14. In 2 s, i.e., after twenty-five shots, the difference between them in zones S2 and S3 is greatest at about 136 ◦C, after sixty shots it will drop in zone S6 to about 52 ◦C;

(7) Due to the lack of a phase transition, the DUPLEX steel can operate above the temperature of 800 ◦C. This steel does not have the material shrinkage effect and therefore repeatedly exceeding this temperature in the process of heating and cooling the barrel has no effect on the formation of cracks on the inner surface of the barrel.

**Author Contributions:** Conceptualization, M.Z., P.K. and Z.S.; methodology, P.K., M.Z. and Z.S.; software, M.Z., Z.S.; validation, J.Z. and M.P.; formal analysis, P.K., M.Z. and Z.S.; writing—original draft preparation, P.K., M.Z. and Z.S.; writing—review and editing, P.K., M.Z. and J.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research results reported in this work were obtained thanks to funding from the Polish National Centre for Research and Development 2012–2016 Scientific Fund, Project no. O ROB 0046 03 001.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

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


**4. Risk study in warehouse by scenarios**

Within the framework of scenarios modeling, three different scenarios are built, including causes and effects of accident risks that define a basis for further risk assessment by communicating objects.

The methodology used is the one usually practised in audit or studies of risks and dangers and also in the impact procedures.

#### **4.1. Methodology**

The methodology used for scenarios definition aims at characterizing, analyzing, and assessing the risks in warehouse. Those risks can have two different causes: due to logistic exploitation (e.g., shipping, handling, storage), or due to external causes such as flooding, lightning.

This first analysis, find all the regulatory constraints aims to identifying and at recording, through various tools, the potential hazards that may occur in the retailer warehouse and its operating system. The natural and human environment hazards are also analyzed. These steps are intended to identify external attackers at the retailer warehouse.

#### *4.1.1. Risk evaluation*

6 Will-be-set-by-IN-TECH

**Figure 2.** Identification of storage compatibilities between dangerous goods. The letter F means inflammable, F+ means very inflammable, T means toxic, Xi means very irritant, means O oxidizing, Xn

constitute a risk assessment strategy to mitigate the risk of chemical reactions.

incompatibilities for storage that is why the maintain of segregation between products

Once dangerous goods are stored in separate places of a warehouse, other sources of risks

Within the framework of scenarios modeling, three different scenarios are built, including causes and effects of accident risks that define a basis for further risk assessment by

The methodology used is the one usually practised in audit or studies of risks and dangers

The methodology used for scenarios definition aims at characterizing, analyzing, and assessing the risks in warehouse. Those risks can have two different causes: due to logistic exploitation (e.g., shipping, handling, storage), or due to external causes such as flooding,

means noxious, N means polluting and C means corrosive.

• Storage conditions (humidity, heat, cold, light);

**4. Risk study in warehouse by scenarios**

remain:

• Container falls; • Container damages;

communicating objects.

**4.1. Methodology**

lightning.

and also in the impact procedures.

An analysis of the warehouse neighborhood is conducted in order to identify targets and their vulnerabilities and to characterize the severity of the dangerous phenomena. Equipments that may be impacted (eg. racks, clarks, trucks) due to internal or external logistics processes are also identified.

#### *4.1.2. Preliminary risk analysis*

A rating of hazardous phenomena identified enable to identify major accidents and through a combination of different criteria:

Following this preliminary risk evaluation, we can discard non significant risk, which are evaluated as low gravity, and probability. Therefore, we perform a detail analysis over the major identified risks.

This rating corresponds to a hierarchy through a matrix (gravity/probability) allow identifying two categories of risk:

#### **4.2. Scenario 1: Aerosol explosion**

The warehouse is likely to receive products classified under the heading 1412 UN code, bottles generating aerosols. The propellant gases contained in these bottles is most of the time of butane or propane under pressure.

In this scenario, we describe the explosion of aerosol (air freshener). It is considered as an inflammable.

#### *4.2.1. Risk evaluation*

The principle of a generating bottle of aerosols is to allow the propulsion of the product (lacquer, deodorant, adhesive, maintenance product, ...) out of the bottle thanks to a gas under pressure contained in the bottle. Common bottles have a varying volume from 50 to 500 ml and contain between 30 and 150 G of product plus propellant gas.

The behavior in fire of aerosols generators of depends on one hand nature on propellant gas and on the other hand on the nature of the conditioned liquid. Therefore, if the propellant gas

#### 8 Will-be-set-by-IN-TECH 192 Risk Management – Current Issues and Challenges Dynamic Risk Management Strategies with Communicating Objects in the Supply Chain of Chemical Substances Within the European Union 9

is a flammable gas standard butane or propane, there is a risk of explosion. The bottles are then dispersed by missile effect and can be in their turn a propagator of fire.

The following scenario develops the consequences of a fire truck loaded with pallets at a unloading dock site. The fire or explosion of aerosols and fertilizer is due to inflammation of a palette (mechanical heating, inflammation, engine, non-compliance with the prohibition of smoking). We left the assumption that a cigarette would be has the origin of the starting point of fire. We leave the principles which another vehicle charged with manure would be been parked on the quay dimensioned. The starting point of fire and the propagation with the truck containing of manure cause effects missile, explosions, and dangerous heat fluxes for the man as well as the toxic dispersion of smoke, of projection has missile effect as well as

Dynamic Risk Management Strategies with Communicating Objects in the Supply Chain of Chemical Substances Within the European Union

193

Accidental discharge is related to the presence of liquid products on site. The spill may trigger the leakage of an important quantity of hazardous liquid. A leakage of hazardous substances can occur due to the fall of one or more pallets of a rack but also due to a weakness in on (or a series) of container (bottle, can). A spill of hazardous substances can have an impact on the

Because of the loss of integrity of a container, a liquid will flow and form a pool of dangerous liquid which mainly function of the topography, the viscosity of the product and quantity. The multitude of references and stored products do not enable to study exhaustively all dangerous chemical reactions. However, all possible precautions are taken to avoid storing

This scenario occurred and may occur throughout the life of the installations and no person will be impacted. We will find a fall of pallet that will provoke liquid spill which is the starting point of fire, projection missiles effect, various explosions and propagation of smoked and gas

According to the nature of fire, it must there have a respect of the means of extinction, in this case of figure it will be impossible to respect this standard, and the means of extinction set up,

In this section, we model the scenarios presented previously by UML diagrams to describe the sequential chain of events following an accident. In particular, we are interested in identifying

As we said, the accidents are evaluated by several measures, by the place and by the number of persons within this place. The type of accidents we consider and which can occur during the manipulation of dangerous goods is correlated to the chemical features of those goods.

the main damages and consequences of accidents involving dangerous goods.

Further, the main effects we consider in our scenarios are the followings:

• Release of substances which are toxic to health and to the environment;

discharge of water and product polluting for environment.

**4.4. Scenario 3: Hazardous liquid spill**

environment and on people.

incompatible products in a single cell.

dangerous for the man and the environment.

will cause a pollution of the natural environment.

*4.4.2. Preliminary risk analysis*

**4.5. Scenarios modelling**

*4.4.1. Risk evaluation*

In the same way, if the liquids contained are flammable liquids, they will support the fire. The generators of aerosols are thus the subject to specific storage, depending on the nature of the containing products (gas and/or liquid).

#### *4.2.2. Preliminary risk analysis*

Based on the calculating probability scale and the calculation of gravity scale, this scenario occurred and may occur throughout the life of the installations and no person will be impacted.

The method used to assess the effects of an explosion of aerosols in a warehouse is multi-energy model. Explosion cloud formed by the gas contained in a bottle would not reach the thresholds of overpressure. Regardless of the distance to the cloud, a target suffers less than 20 mbar pressure which causes no human and material damage. We consider the explosion of the cloud formed by the simultaneous outbreak of 100 bottles of aerosols, which is extremely unlikely even when taking into account that the bottles are for most made on aluminium.


*3.2. Sampling*

A random probability sampling method was followed to obtain a representative sample of the South African population in the large urban areas [56], i.e., metropolitan areas and cities with a population size of 250,000 or more and included Cape Town, Johannesburg, Durban, East Rand, Pretoria, Port Elizabeth, the Vaal area, East London, Pietermaritzburg, Bloemfontein, and Welkom (Figure 2). For the standard random selection procedure starting points were selected at random and a Kish-grid used to select individual respondents [58]. A large sample size of 2000 was chosen to reduce the effect of sampling errors [56,59,60].

**Figure 2.** Metropolitan areas and cities included in the study.

## *3.3. Questionnaire Design*

Being part of a larger survey, one of the questionnaire sections made up the constructs of the TPB. The TPB constructs contain statements which measured respondents' behavior, intentions to behave, attitudes, subjective norms, and perceived behavioral control. The sequence of questions can influence survey results [60]. Therefore, the behavior questions preceded the attitude questions to prevent alignment of the easier factual accounts of behavior to the aspirations acquired with answering the attitude and other questions [60]. The starting point of items within a set, e.g., the attitude items, was also rotated.

Where applicable, and similar to many other TPB studies [54], 7-point Likert-type rating scales [61] and 7-point semantic differential scales were used. The statements were anchored on either side with strongly agree/strongly disagree or, for example, with bad/good.

3.3.1. Theory of Planned Behavior Latent Variables

A summary of the items that made up each of the constructs of the TPB is provided below.

#### 3.3.2. Testing of the Questionnaire

The draft questionnaire was tested in a pilot study to be able to sharpen the measuring instruments, to identify ambiguities and questions which might cause uneasiness, and to ensure workability of the data [56,60]. During the course of one day, tenants and shoppers in a shopping center were approached and the purpose of the study explained. The volunteers were offered a paid-for hot drink at a pre-arranged coffee shop where they could sit and relax while completing the questionnaire.

Fifty-nine individuals completed the pilot questionnaire on an anonymous basis. Each construct (measuring tool) was tested statistically for consistency and reliability. After completion of the pilot study the questionnaire was shortened to only include those questions that would add the most value.

#### 3.3.3. Data Collection

Due to the nature, sample size, time frames, and geographical distribution of the proposed sample, a professional survey company that was able to meet the survey requirements, was contracted to include the questions in their annual survey. The interviews were conducted face-to-face at respondents' homes. If a respondent refused to participate, the respondent was substituted using the same procedure in another household. At no stage was or can the identity of the individual respondent be linked back to the data.

The CSIR provided the wording of an accompanying briefing pamphlet which stated the purpose of the study, how the information will be used, and on whose behalf the specific part of the survey is conducted. The relevant contact details of the principle researcher and the CSIR Research Ethics Committee member were provided. The first statement on the questionnaire was a tick box with an acknowledgement from the participant that he/she received the pamphlet and was sufficiently informed before answering the questions. Participation was on a voluntary basis without receiving any rewards or incentives for taking part in the survey.

#### **4. Statistical Method**


**Ming Liu**

Dr. Ming Liu is now an associate professor at MSE of XJTU. He received his PhD at USTB under the supervision of Prof. Xiaogang Li in January 2017. He was a postdoctoral fellow in TU Delft from October 2019 to October 2021 under the supervision of Prof. J.M.C. Mol.

Currently, he is mainly engaged in the research of "Corrosion and mechanical behavior of metal materials". He is responsible for many grants from NSFC, International Postdoctoral Exchange Program, Shaanxi Natural Science Foundation, Postdoctoral Project and enterprise projects. He has published many high level papers and has been cited more than 1000 times.


Contents

Preface

Currently, digital imaging is used widely in various real-life applications. There are a number of potential digital imaging applications such as television, photography, robotics, remote sensing, medical diagnosis, reconnaissance, architectural and engineering design, art, crime prevention, geographical information systems, communication, intellectual property, retail catalogs, nudity detection, face finding, industrial, and others. The increasing trends, needs, and applications of imaging make it more difficult to process images for desired objectives. This leads to the idea of capturing, storing, finding, retrieving, analyzing, and using images in everyday life in the computing environment. Being a computer-based technology, digital imaging carries out automatic processing, manipulation, and interpretation of visual information. It plays a significant and important role in various aspects of real life. It is also highly useful in many areas, disciplines, and fields of art, science,

This book is specifically dedicated to digital imaging education, research, applications, techniques, tools, and algorithms that originate from fields such as image processing, computer vision, pattern recognition, signal processing, artificial intelligence, intelligent systems, and soft computing. In general, this comprehensive book contains state-of-the-art chapters focusing on the latest developments using theories, methods, approaches, algorithms, analyses, display of images, visual

The six chapters from academicians, practitioners, and researchers from different disciplines of life explore the latest developments, methods, approaches, and applications of digital imaging in a variety of fields and endeavors. The book is compiled with a view to providing researchers, academicians, and readers with an in-depth

The target audience of this book are professionals and researchers working in the field of digital imaging in various disciplines, e.g. computer science, computer engineering, information technology, information and communication sciences, education, health, libraries, and others. The book is also targeted at scientists, engineers, researchers, practitioners, academicians, and related industry professionals

Sarfraz begins the book with an introductory chapter on digital image processing which describes digital imaging is used widely in various real-life applications. This chapter is specifically dedicated to digital imaging history, methodologies, tasks,

This is followed by a chapter titled "Fast Motion Estimation's Configuration Using Diamond Pattern and ECU, CFM, and ESD Modes for Reducing HEVC Computational Complexity" by Khemiri et al., who mention that the high performance of the high-efficiency video coding (HEVC) standard makes it more suitable for high-definition resolutions. This encoding performance is coupled with tremendous encoding complexity, compared to the earlier H.264 (also referred to as

and provides an in-depth discussion of the latest advances.

and technology.

information, and videos.

discussion of the latest advances.

software, and applications.