Optimal Configuration and Performance of Heat Engines with Heat Leak and Finite Heat Capacity

Abstract

The optimal configuration of a class of two-heat-reservoir heat engine cycles in which the maximum work output can be obtained under a given cycle time is determined with the considerations of heat leak, finite heat capacity high-temperature source and infinite heat capacity low-temperature heat sink. The heat engine cycles considered in this paper include: (1) infinite low- and high-temperature reservoirs without heat leak, (2) infinite low- and high-temperature reservoirs with heat leak, (3) finite high-temperature source and infinite low-temperature sink without heat leak, and (4) finite high-temperature source and infinite low-temperature sink with heat leak. It is assumed that the heat transfer between the working fluid and the reservoirs obeys Newton's law. It is shown that the existence of heat leak doesn't affect the configuration of a cycle with an infinite high-temperature source. The finite heat capacity of a high temperature source without heat leak makes the cycle a generalized Carnot heat engine cycle. There exists a great difference of the cycle configurations for the finite high-temperature source with heat leak and the former three cases. Moreover, the relations between the optimal power output and the efficiency of the former three configurations are derived, and they show that the heat leak affects the power versus efficiency characteristics of the heat engine cycles.