Maximum power output of multistage irreversible heat engines under a generalized heat transfer law by using dynamic programming

A multistage irreversible carnot heat engine system operating between a finite thermal capacityhigh-temperature fluid reservoir and an infinite thermal capacity low-temperature environment witha generalized heat transfer law [q / .
.t n//m] is investigated in this paper. optimal control theory isapplied to derive the continuous hamilton-jacobi-bellman (hjb) equations, which determine the optimalfluid temperature configurations for maximum power output under the conditions of fixed initial time andfixed initial temperature of the driving fluid. based on the universal optimization results, the analyticalsolution for the case with newtonian heat transfer law (m d 1; n d 1) is further obtained. since thereare no analytical solutions for other heat transfer laws, the continuous hjb equations are discretized andthe dynamic programming (dp) algorithm is performed to obtain the complete numerical solutions ofthe optimization problem. then the effects of the internal irreversibility and heat transfer laws on theoptimization results are analyzed in detail. the results obtained can provide some theoretical guidelinesfor the optimal design and operation of practical energy conversion and transfer processes and systems.