Optimal configuration of a finite mass reservoir isothermal chemical engine for maximum work output with linear mass transfer law

Abstract

An isothermal endoreversible chemical engine operating between a finite high-chemical- potential reservoir and an infinite low-chemical-potential reservoir in which the mass transfer between the working fluid and the mass reservoirs obeys the linear mass-transfer law [$g \propto \Delta \mu $], is put forward in this paper. Optimal control theory is applied to determine the optimal cycle configuration corresponding to the maximum work output for the fixed total cycle time. The optimal cycle configuration is an isothermal endoreversible chemical engine cycle in which the chemical potential (concentration) of the key component in the finite high-chemical- potential mass reservoir and that in the working fluid change nonlinearly with time. The difference in chemical potentials (ratio of the concentrations) between the key component in the finite mass reservoir and the working fluid is a constant, and the chemical potential (concentration) of the key component in the working fluid at the low chemical potential side is also a constant. A numerical example is provided, and the effects of the concentration changes in the key component in the finite high-chemical-potential reservoir on the optimal configuration of the chemical engine are analyzed. The obtained results are compared with those obtained for an endoreversible heat engine operating between a finite heat source and an infinite heat sink with Newton's heat transfer law [$q \propto \Delta T$] in the heat transfer processes. The object studied in this paper is general, and the results could provide some guidelines for the optimal design and operation of real chemical engines.