Optimal configuration of an irreversible heat engine with fixed compression ratio

The cycle that maximizes the average power output of a class of irreversible heat engines has been obtained using optimal control theory. This class of heat engines is distinguished by being endoreversible, having a fixed compression ratio and being irreversible because of linear heat conduction. The optimal cycle is found to have eight branches including two fixed-volume branches, two isothermal branches, and two maximum-power branches. Maximum-power branches are defined and discussed in detail. It is shown that the maximum-power cycle contains no adiabatic branches. Two special limits are analyzed in detail, the Curzon-Ahlborn limit and the large-compression-ratio limit. The fixed-compression-ratio constraint and the periodicity of the engine require special attention which lends this problem some purely mathematical interest.