Performance optimization of an irreversible Carnot refrigerator with finite mass flow rate

The present study develops a theoretical model for the optimization of an irreversible Carnot refrigerator subject to a constraint of finite mass flow rate, which includes internal as well as external irreversibilities. By introducing two dimensionless parameters as indicative of the mass flow rates for the refrigerator, the new model allows detailed analyses on the finite mass flow rate allocation problem of working fluids among the hot- and cold-side heat exchangers of Carnot refrigerators. The analytical solutions of the maximum coefficient of performance (COP) for irreversible Carnot refrigerators are obtained under the equivalent of the finite-flow rate constraint. Furthermore, the influences of major parameters on the maximum COP and the corresponding mass flow rate allocation are examined and shown by numerical examples. The obtained results may provide a theoretical guidance for the optimal design and operation of real refrigerators.