Maximum efficiency of an irreversible heat engine with a distributed working fluid and linear phenomenological heat transfer law

Abstract

Maximum efficiency of an irreversible heat engine with a distributed working fluid, in which the heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [$q \propto \Delta (T^{ - 1})$], is studied in this paper by using finite-time thermodynamics based on Orlov and Berry's work$^{i}$. Two kinds of efficiencies are defined, and the problems are divided into three cases. Optimal control theory is used to determine the upper bounds of efficiencies of the heat engines for various cases. Numerical examples of the two efficiencies for the irreversible heat engine with lumped-parameter model working between variable temperature reservoirs are provided, and the effects of changes of the reservoir's temperature on the maximum efficiency of the heat engine are analyzed. The obtained results are also compared with those obtained by Orlov and Berry$^{ii}$ with Newtonian heat transfer law [$q \propto \Delta (T)$].