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0.35

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

B

Stot

tst =1.6

tst =1.5

tst =1.4

Fig. 6 Total entropy generated to reach a refrigerated space temperature set point temperature

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1.4

1.6

1.8

2

2.2

2.4

2.6 x 10-4

B

Sin

tst =1.6

tst =1.5

tst =1.3

Fig. 7 Internal Total entropy generated to reach a refrigerated space temperature set point

temperature

Modeling, Simulation, and Optimization of an Irrerversible Solar Absorption. . .

1187

4

Results and Discussion

The search for system thermodynamic optimization opportunities starts by moni-

toring the behavior of refrigeration space temperature τL in time, for three dimen-

sionless collector size parameter B, while holding the other constants, that is,

dimensionless collector temperature τH ¼ 1.5 and dimensionless collector stagna-

tion temperature τst ¼ 1.8.

Figure 2 shows that during the heat-up period, the temperature of the evaporator

starts to decrease linearly, and then it decreases very slowly. Here, the reaction of

the evaporator is seen strongly affected by the generator behavior. This temperature

starts rising linearly and then it becomes stable. As the temperature of the generator

is higher, more heat is absorbed in the evaporator. While, the temperature of the

evaporator is decreasing very slowly the temperature of the generator still

maintained quite constantly, indicating that the equilibrium state has reached

(Abdullah and Hien 2010). Also, there is an intermediate value of the collector

size parameter B, between 0.063 and 0.175, such that the temporal temperature

gradient is maximum, minimizing the time to achieve prescribed set point temper-

ature (τL , set ¼ 0.97).

The optimization with respect to the collector size B is pursued in Fig. 3 for time

set point temperature for three different values of the collector stagnation temper-

ature τst and heat source temperatures τH ¼ 1.3. The time θset decreases gradually

according to the collector size parameter M until reaching a minimum time θset,min

and then it increases. This confirms the results found previously (Fig. 2). The

existence of an optimum for the thermal energy input



QH is not due to the

irreversible model aspects. However, an optimal thermal energy input 

QH results

when the irreversible equations are constrained by the recognized total external

conductance inventory, UA in Eq. (14), which is finite, and the generator operating

temperature TH. These constraints are the physical reasons for the existence of the

optimum point. The minimum time to achieve prescribed temperature is the same

for different values of the stagnation temperature τst.

During the transient operation and to reach the desired set point temperature,

there are an internal generated by the working fluid and a total entropy generated by

the cycle, which is obtained by integrating Eqs. (23) and (25) in time. Figures 4 and

5 show the behavior of internal and total entropy generated during the simulation

time for three different collector size parameters (B ¼ 0.03, 0.04, 0.1), holding τH,

and τst constant (τH ¼ 1.3 and τst ¼ 1.6). From these figures, it is observed that the

entropy rises with the increase of time and it is clear on the basis of the second law

of thermodynamics that the entropy production is always positive for an irreversible

cycle.

Figures 6 and 7 display the effect of the collector size on the internal and total

entropy up to θset. It can be inferred that there is minimum entropy generated for a

certain collector size B.

The variation of evaporator heat transfer with size collector parameters is

predicted and shown in Fig. 8. It can be identified from the simulation results that

1188

B. Yasmina et al.

the cooling capacity increases from the beginning of the refrigeration system start-

up. This phenomenon is typical of the system start-up working regime when there is

a refrigerant hot flow inside the evaporator that would heat the interior of the

refrigerator while the refrigeration system cooling capacity increases. Afterward,

evaporator heat transfer reaches a maximum when the steady-state condition is

attained in the refrigerator interior. The maximum cooling capacity obtained for the

tested refrigerator was 0.0143, for the different values of the stagnation tempera-

ture. Maximum cooling capacity does not mean minimum entropy generation by

the cycle.

5

Conclusions

A thermodynamic transient regime simulation of a solar-driven absorption refrig-