Optimal performance of an irreversible refrigerator with variable-temperature heat reservoirs

An irreversible cycle model of a refrigerator operating between two variable-temperature heat reservoirs is established and used to analyse the performance of the refrigerator affected by the irreversibility of finite-rate heat transfer between the working substance of the refrigerator and the heat reservoirs, heat leak between the heat reservoirs, and internal irreversibilities of the working substance. The coefficient of performance of the refrigerator is optimized for a given cooling load. The influence of intake temperatures of heat reservoirs, thermal capacity of heat reservoirs, efficiency of heat exchangers, heat leak and internal irreversibilities on the performance of the system is discussed. The optimal ratio of the times spent on two processes of heat transfer to and from the working substance is determined. Some new results which are conducive to the optimal design and operation of real refrigerator systems are obtained and several special cases are discussed in detail.