Optimal configuration of a finite mass reservoir isothermal chemical engine for maximum work output with linear mass transfer law - Shaojun Xia.; Lingen Chen.; Fengrui Sun. (Revista Mexicana de Física, 2009)
An isothermal endoreversible chemical engine operating between a finitehigh-chemical- potential reservoir and an infinite low-chemical-potentialreservoir in which the mass transfer between the working fluid and the massreservoirs obeys the linear mass-transfer law [$g \propto \Delta \mu $], isput forward in this paper. Optimal control theory is applied to determinethe optimal cycle configuration corresponding to the maximum work output forthe fixed total cycle time. The optimal cycle configuration is an isothermalendoreversible chemical engine cycle in which the chemical potential (concentration) of the key component in the finite high-chemical- potentialmass reservoir and that in the working fluid change nonlinearly with time.The difference in chemical potentials (ratio of the concentrations)between the key component in the finite mass reservoir and the working fluidis a constant, and the chemical potential (concentration) of the keycomponent in the working fluid at the low chemical potential side is also aconstant. A numerical example is provided, and the effects of theconcentration changes in the key component in the finitehigh-chemical-potential reservoir on the optimal configuration of thechemical engine are analyzed. The obtained results are compared with thoseobtained for an endoreversible heat engine operating between a finite heatsource and an infinite heat sink with Newton's heat transfer law [$q \propto\Delta T$] in the heat transfer processes. The object studied in this paperis general, and the results could provide some guidelines for the optimal designand operation of real chemical engines.