Effects of heat leak on the performance characteristics of Carnot like heat engines and heat pumps

Effects of heat leakage on the performance characteristics of Carnot like heat engine and heat pump models are studied. The heat leakage term is assumed to be temperature dependent with non-Newtonian heat transfer law. Thus the heat leakage term is proportional to the temperature difference with exponent m. Values of m are considered in the range 0-2. It is shown that the power output of the heat engine is not affected due to the assumptions of the model, but the main effect is reducing the efficiency of the system. Correspondingly, considering heat pumps, the cooling rate and coefficient of performance (cop) are reduced due to heat leakage. The cooling is not a monotonic function of cop. This was not observed in previous studies with the assumption of a constant heat leakage term. Finally, characteristic curves are shown for both heat engines (power vs. efficiency curves) and for heat pumps (cooling rate vs. coefficient of performance curves).