Endoreversible modeling and optimization of multistage isothermal chemical engines under linear mass transfer law via Hamilton–Jacobi–Bellman theory

A multistage continuous isothermal endoreversible chemical engine system with a finite driving fluid is investigated in this paper, and the mass transfer law obeys the linear mass transfer law[g propto Delta mu]. Under the condition that both the initial time and the initial key component concentration in the driving fluid are fixed, the maximum power output of the multistage chemical engine system and the corresponding optimal concentration configuration of the key component in the driving fluid are derived by applying Hamilton–Jacobi–Bellman (HJB) theory, and numerical examples for three different boundary conditions are given. The results show that the difference between the chemical potential of the key component and the Carnot chemical potential for the maximum power output is a constant, and the key component concentration in the driving fluid decreases with the increase of time nonlinearly; when both the process period and the final concentration of the key component are fixed, there is an optimal control strategy for the maximum power output of the multistage chemical engine system, and the maximum power outputs of the system and the corresponding optimal control strategies are different for different final concentrations. The obtained results can provide some theoretical guidelines for the optimal designs and operations of practical energy conversion systems.