Finite thermal reservoirs effects on power-optimized continuous endoreversible carnot heat engine cycles

Studies of continuous Carnot cycles with finite thermal reservoirs in the past have considered neither the Second Law constraints of the cycle, nor the interdependence between the power cycle operating temperatures and the initial and final reservoir temperatures themselves. In this work it is shown that, when these are considered, the upper and lower power-optimized operating cycle temperatures can be semi-decoupled from each other. They remain coupled only through an expression for β opt (the hot end and cold end reservoir thermal capacitance ratio optimized for power) stemming from the Second Law constraint formulation. The novel semi-decoupling procedure which enables these new developments is itself a result of this Second Law formulation. This procedure also enables the expressions developed for the power-optimized operating temperatures for each of the thermal ends of the cycle to be semi-independent. Thus, one could easily extend the formulation approach given to consider various combinations of mixed heat transfer mode cycles. Two finite reservoir configuration cases are considered in this paper. For the more realistic case of finite reservoirs where only the in-flow source and sink temperatures and the source and the sink mass flow rates are prespecified (i.e., leaving the outflow source and sink temperatures as variables) the analyais yields a more fully power-optimized Carnot cycle than for the less realistic case of prespecified upper and lower reservoir inlet and outlet temperatures.