Study on optimal performance and working temperatures of endoreversible forward and reverse carnot cycles

The connection between the expressions of optimization performances of Carnot heat engines, refrigerators and heat pumps, which operate subject to irreversible heat flow, is studied. We consider the endoreversible forward and reverse Carnot cycles and analyse the expressions which relate efficiency, refrigeration and heating coefficients to power, refrigeration and heating rates, respectively. It is found and proved that when one of the optimal relations is derived the others are also determined, and give the unified formulation of the related optimal working temperatures of the forward and reverse Carnot cycles by isentropic temperature ratio exponent. Finally, several new optimal performance relations are derived for forward and reverse Carnot cycles under nonlinear heat transfer, and some major results in the references are easily deduced and unified in this paper.