Maximum Power Output of Multistage Continuous and Discrete Isothermal Endoreversible Chemical Engine System with Linear Mass Transfer Law

Abstract

The maximum power output of a multistage isothermal endoreversible chemical engine system operating between a finite potential capacity high-chemical-potential reservoir and an infinite potential capacity low-chemical-potential environment with the linear mass transfer law is investigated in this paper. For the fixed initial time and fixed initial concentration of the key component in the high-chemical-potential reservoir, the continuous model is optimized by applying Hamilton-Jacobi-Bellman (HJB) theory and Euler-Lagrange equation, respectively, and the discrete model is optimized by applying dynamic programming method and discrete maximum principle, respectively. Numerical examples for the discrete model with three different boundary conditions are provided, and the results are also compared with those for the continuous model. The results show that both of the maximum power outputs of the limiting continuous and multistage discrete isothermal endoreversible chemical engine systems are equal to the difference between their classical reversible thermodynamic performance limits and a dissipation term. The relative concentration of the key component in the high-chemical-potential reservoir for the maximum power outputs of the continuous and discrete models decreases with the increase of time linearly. The relationships among the maximum power output of the system, the process period and the final concentration of the key component in the high-chemical-potential fluid reservoir are discussed in detail.