Optimal configuration of heat engines for maximum efficiency with generalized radiative heat transfer law

Abstract

Optimal configuration of a class of endoreversible heat engines with generalized radiative heat transfer law $[q \propto \Delta (T^n)]$ has been determined by this paper. The optimal cycle that maximizes the efficiency of the engines with fixed input energy has been obtained using optimal-control theory, and the differential equations are solved by Taylor series expansion. It is shown that the optimal cycle for maximum efficiency has eight branches including two isothermal branches, four maximum-efficiency branches and two adiabatic branches. The interval of each branch has been obtained, as well as the solutions of the temperatures of heat reservoirs and working fluid. Numerical examples are given for the optimal configurations with $n {=} - 1$, $n {=} 1$, $n {=} 2$, $n {=} 3$ and $n {=} 4$, respectively. The results obtained are compared with each other and with those results obtained for maximum power output.