INFLUENCE OF OPERATING TEMPERATURES ON THE SOLAR ADSORPTION REFRIGERATION MACHINE USING THE ACTIVATED CARBON-METHANOL PAIR

Biram Dieng, Mamadou Lamine Solly and Mouhamadou Lamine Cisse Research Team In Renewable Energies, Materials And Laser of Department of Physics, Alioune Diop University of Bambey, Bambey, Senegal. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 05 May 2020 Final Accepted: 10 June 2020 Published: July 2020

Or; m: is the concentration (adsorbed mass per unit of adsorbent mass); w 0 : is the maximum adsorption capacity (volume of adsorbate / mass of adsorbent); : is the specific mass of the liquid adsorbate; D: is the affinity coefficient; n: is a characteristic parameter of the adsorbent-adsorbate pair. Ps: saturation pressure of the adsorbate. Knowledge of the properties of the couple is necessary for the calculation of the amount of heat received or transferred by the AC-35 activated carbon couple. They are presented in the following table:

Simplifying assumptions:
We make the following assumptions: 1. We consider that the adsorbed phase is liquid, 2. The adsorbent bed is made up of identical AC-35 activated carbon grains which are distributed uniformly. 3. The physical properties of the liquid, the metal and the adsorbent are constant and homogeneous. 4. The thermal resistance between the metal tube and the adsorbent bed is neglected. 5. The adsorbent bed is homogeneous and isotropic. 6. The porous particles of activated carbon are incompressible

Calculation of COP
The COPth coefficient of performance of the machine for such a cycle takes account of the thermal balances on the adsorber, the condenser and the evaporator is given by: : is the refrigeration production or the quantity of cold produced on the evaporator (kJ).

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: is the quantity of heat supplied to the absorber (kJ).

Qf expression
The amount of cold produced at the evaporator is given by: 13 The first term of this equation represents the heat absorbed for the evaporation of the refrigerant at the evaporation temperature . The second term represents the sensible heat necessary to bring the condensate from its condensation temperature to that of evaporation Or: L(T) et represent respectively the latent heat of evaporation and the specific heat of the adsorbate in the liquid state.
: is the mass of the solid adsorbent contained in the adsorber is the cyclic mass of the adsorbate, calculated as follows: -=m ( )-m ( ) 14 is the adsorbed mass corresponding to the adsorption temperature and the evaporation pressure (figure 1), calculated using the Dubinin-Astakhov model : is the adsorbed mass corresponding to the regeneration temperature Tg and the condensation pressureP c (Figure 2), calculated using the Dubinin-Astakhov model.

Expression Qc
The adsorber receives energy from the hot source, part of which will be used to heat the metal parts of the adsorber, another part used to heat the adsorbent and adsorbate and the rest used for desorption [13]. 15 , et are sensitive heats, respectively used for the heating of the adsorbent, the metal parts of the adsorber and the adsorbate.
: is the heat required for desorption corresponding to the mass of the adsorbed desorbed. For the rest, we accept the hypothesis of incompressibility of liquids and solids, which leads to: Cp=Cv. Cp: is the specific heat at constant pressure. Cv: is the specific heat at constant volume. Sensitive heat of the adsorbent ( ) : is the heat required to bring the temperature of the solid adsorbent from temperature to temperature. , it is given by [ Où: is the isosteric heat of adsorption dm :differentiation of the adsorbed mass from equation 7 dm = n 20 During the desorption-condensation phase, the pressure is constant and equal to the saturation pressure at the condensation temperature. So the heat of desorption becomes: The total heat supplied to the adsorber becomes: n D dT 22 Oùq st is the isosteric heat of adsorption, defined by the following equation: q th = L (Tc) +RT + 23 Results and Discussion:-Model validation: Figure (2) represents a comparison of the COPth obtained from the proposed model and that given by Wassila. We note that the representative curves of these two models have almost the same appearance with a slight difference between them but acceptable. So from this comparison, we admit that our program works perfectly well.

Effect of regeneration temperature:
The regeneration temperature is the highest possible temperature reached by the system at the end of the desorptioncondensation phase. Thus its effect on the performance of the machine is greater than that of other operating temperatures. Figure (3 . This reduction in COPth shows that the optimal performance of the system is obtained only for a certain value of Tg and the continuation of the heating of the system only serves to increase the temperature of the activated carbon, the temperature of the metal parts of the adsorber and the temperature of the residual methanol.
The regeneration temperature Tg is a design variable which must be optimized. Generally, it is optimized to be able to obtain a large quantity of cycled mass and to avoid the decomposition of the refrigerant [1]. As methanol is the refrigerant, the regeneration temperature is limited to 150 ° C [2], since methanol decomposes beyond this value, which will block the adsorption process where the system stops. Effect of adsorption temperature on the coefficient of performance: Figures 5 and 6 respectively illustrate the variation of COPth and the variation of the cycled mass as a function of Tg and Ta with Tc = 303.15 K and Te = 272.15 K. In these two figures, we clearly see the increase in Ta is accompanied by a decrease in COPth and a decrease in the cycled mass. These results were predictable because, according to the Dubinin-Astakhov model, an increase in Ta leads to a decrease in the maximum adsorbable mass at the start of the refrigeration cycle. Thus, there is a decrease in the mass cycled with Ta hence the decrease COPth. So from these remarks, we suggest to have a better performance of the machine to always try to start the thermodynamic cycle by the lowest possible adsorption temperature so that the mass adsorbed at this temperature is the greatest possible.

Effect of evaporation temperature:
The evaporation temperature is an important parameter which greatly affects the performance of solar adsorption refrigerators. Its effect on the thermal coefficient of performance COPth and on the quantity of methanol cycled is evaluated respectively in figure (9) and in figure (10). On figure (9), we note that the coefficient of performance increases with the evaporation temperature Te. This increase in COPth with the evaporation temperature is explained by the fact that the saturation pressure Ps (Te) of methanol increases with Te which causes an increase in the cyclic mass of methanol illustrated in figure (10).

Conclusion:-
In this work, the numerical simulation allowed us to clearly see that the operating temperatures of the machine have a very important influence on the performance of the system. So it emerges from this study that the optimization of an adsorption refrigeration machine for better performance inevitably requires mastery and control of the machine's operating temperatures; which is not easy because the evolution of operating temperatures depends on several random factors related to the type of climate in which the experiment is carried out. Bibliography:-