文章基本信息

标题：Hamilton–Jacobi–Bellman equations and dynamic programming for power-optimization of radiative law multistage heat engine system
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作者：Shaojun Xia ; Lingen Chen ; Fengrui Sun 等
期刊名称：International Journal of Energy and Environment
印刷版ISSN：2076-2895
电子版ISSN：2076-2909
出版年度：2012
卷号：3
期号：3
页码：359-382
出版社：International Energy and Environment Foundation (IEEF)
摘要：A multistage endoreversible Carnot heat engine system operating with a finite thermal capacity high-temperature black photon fluid reservoir and the heat transfer law is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the general optimization results, the analytical solution for the case with pseudo-Newtonian heat transfer law is further obtained. Since there are no analytical solutions for the radiative heat transfer law, the continuous HJB equations are discretized and the dynamic programming (DP) algorithm is adopted to obtain the complete numerical solutions, and the relationships among the maximum power output of the system, the process period and the fluid temperatures are discussed in detail. The optimization results obtained for the radiative heat transfer law are also compared with those obtained for pseudo-Newtonian heat transfer law and stage-by-stage optimization strategy. The obtained results can provide some theoretical guidelines for the optimal designs and operations of solar energy conversion and transfer systems.