Optimal piston speed ratio analyses for irreversible Carnot refrigerator and heat pump using finite time thermodynamics, finite speed thermodynamics and direct method

An irreversible Carnot refrigeration and heat pump cycle model with external irreversibilities caused by finite rate of heat transfer, heat leakage from heat sink to heat source and internal irreversibilities caused by finite piston speed, friction and gas throttling is established by using the combination of finite time thermodynamics, finite speed thermodynamics and direct method. Different from the model of constant speed of the piston on the four branches, the piston speeds on the four branches in this model are assumed to be unequal. Expressions of cooling load and coefficient of performance (COP) of the Carnot refrigeration cycle as well as heating load and COP of the heat pump cycle are derived for a fixed cycle period. Numerical examples show that the curves of COP versus cooling load and COP versus heating load are parabolic like ones, and there exist optimal finite piston speed ratios on the four branches, which lead to the maximum COPs. Moreover, the effects of the heat leakage coefficient on the optimal finite piston speed ratios and optimal working fluid temperatures are discussed.