The optimization problem of a combined refrigeration cycle formed by t
wo endoreversible Carnot refrigeration cycles in series without interm
ediate reservoirs has been studied using finite-time thermodynamics. T
he fundamental relation between cooling quantity and coefficient of pe
rformance (COP) of the combined cycle is derived for a general physica
l model of a combined cycle. Relations are derived between the SROR (=
optimal specific rate of refrigeration, i.e. the average rate of refri
geration 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.