The performance of finite-time refrigerators at the maximum cooling load with a specified power input

Abstract

The optimum coefficient of performance (COP) of the finite-time refrigerators based on the maximization of the cooling load at a specified power input is investigated. The Lagrange function for variational calculus is then established to mathematically handle the optimization process. The optimized COP is found to be dependent on the temperature and conductance of the thermal reservoirs as well as the irreversibility involved in the heat transfer processes. Thermodynamic explanations are put forward to recommend higher thermal conductance for the cold reservoir compared to that of the hot reservoir so that a higher COP value can be obtained. A dimensionless irreversibility factor, which reflects the irreversible extent of the finite-time heat transfer between the working substance and the thermal reservoirs, is defined and shown to have significant impact on the COP. The optimized COP value tends to that of the Carnot cycle in the limit of reversible processes. Finally, an algebraic expression describing the optimal COP in terms of the key parameters is offered to simplify the numerical representation of the results and also to facilitate the future follow-up studies.