تجزیه و تحلیل عملکرد از پمپ گرما، یخچال و فریزر با درجه حرارت مخزن متغیر

Performance analysis of totally irreversible heat pumps and refrigerators has been developed by means of the second law of thermodynamics. The machine operates steadily between two variable temperature heat reservoirs. The results show that the optimal balance between the sizes of the heat exchangers at the hot and cold ends of the machine is affected by the ratio E (or E′). Also, the heat delivered by the heat pump and the heat removed by the refrigerator varies significantly with E (or E′). Conversely, the coefficient of performance does not depend on E (or E′). Finally, the effect of the internal irreversibility diminishes at Eh/Ec<1, for heat pumps and at Eh/Ec>1, for refrigerators.

Nowadays, second law analysis of thermodynamic systems has become a prominent topic in thermal engineering. Since Curzon and Ahlborn [1] published their landmark paper on the efficiency of a Carnot engine at maximum power output in 1975, many studies on second law analysis of thermodynamic systems have been presented by many authors. Most of these studies concern the performance of heat engines [2], [3], [4], [5], [6], [7], [8], [9], [10] and [11]. Less work was devoted to study the performance of heat pumps and refrigerators [12], [13], [14], [15] and [16]. These studies generally discuss the second law analysis of endoreversible (internally reversible) or totally irreversible (internally and externally) systems with constant reservoir temperatures. Practically, the heat reservoirs have finite thermal capacitance rates. Consequently, the temperature in the reservoirs is not constant. Therefore, the system performance depends on the magnitude of the thermal capacitance rates and the temperature variations of the reservoirs. This work is devoted to making a second law analysis of totally irreversible heat pumps and refrigerators with variable reservoir temperatures.

The thermodynamic optimization principles of irreversible heat pumps and refrigerators have been developed using second law analysis. The machines operate steadily between two variable temperature heat reservoirs. The two design rules of the total thermal conductance constraint and the total heat transfer area constraint for heat exchange at the two ends of the machine have been considered. For both heat pumps and refrigerators, it can be concluded that: 1. The optimum ratio xopt (or αopt) depends on the ratio Eh/Ec (or E′h/E′c). A decrease in the ratio Eh/Ec leads to an increase in xopt for heat pumps and a decrease in xopt for refrigerators. 2. Decrease in the ratio Eh/Ec leads to a decrease in the heat delivered by the heat pump. Conversely, the heat removed by the refrigerator increases. 3. For both heat pumps and refrigerators, the coefficients of performance are not functions of the ratio Eh/Ec. The relation between them is still like that for constant temperature heat reservoirs ( Eq. (64)). 4. The effect of the internal irreversibility diminishes for heat pumps when the ratio Eh/Ec becomes smaller than 1. For refrigerators, the effect of the internal irreversibility diminishes when the ratio Eh/Ec becomes greater than 1. 5. As for the machines with constant reservoir temperatures, the total heat transfer area is divided by the same ratio between the two ends of both the heat pump and the refrigerator. Also, an optimal temperature ratio across the inner compartment is still absent.