Theoretical Limit on COP of a Heat Pump from a Sequential System

The theoretical limit on Coefficient of performance (COP), which is maximum and ideal one, is investigated with a sequential Carnot heat pump where multiple Carnot heat pumps are interconnected in parallel. Using fundamental relations from thermodynamics and heat transfer, the performance of a sequential Carnot heat pump is obtained analytically. The erect of major parameters of the system, such as the number of individual heat pumps in a sequential system, the number of transfer unit of heat exchangers, and temperatures of heat sources, on the performance is researched. Also, expressions for ideal COP derived by limit calculation when the system has an infinite number of Carnot heat pumps or infinite number of transfer unit are suggested. For example, the most ideal COP is the ratio of the final heat source temperature to the difference between the initial and final heat source temperature. To support the result of theoretical analysis, a simple simulation of sequential Carnot heat pumps is carried out with thermodynamic properties of real refrigerants. The result of a simulation quite accords with that of theoretical analysis.