Optimization of the specific rate of refrigeration in combined refrigeration cycles

The optimization problem of a combined refrigeration cycle formed by two endoreversible Carnot refrigeration cycles in series without intermediate reservoirs has been studied using finite-time thermodynamics. The fundamental relation between cooling quantity and coefficient of performance (COP) of the combined cycle is derived for a general physical model of a combined cycle. Relations are derived between the SROR (=optimal specific rate of refrigeration, i.e. the average rate of refrigeration per unit of total heat-transfer surface area) and the COP for a piston-type, stable flow model of combined cycles. Our results may be extended to an endoreversible, combined refrigeration cycle formed by more than two endoreversible Carnot refrigeration cycles.