OPTIMIZATION FOR MINIMIZING POWER-CONSUMPTION OF A REAL MULTISTAGE HEAT PUMP SYSTEM UNDER A GENERALIZED HEAT TRANSFER LAW VIA HAMILTON-JACOBI-BELLMAN THEORYShaojun Xia ResumoThis paper investigated a multistage irreversible Carnot heat pump system (MICHPS) with a finite thermal capacity fluid source, and the heat transfer between the fluid source and the working fluid followed the generalized heat transfer law [ q ∝ (Δ(T^{n} ))^{m} ]. For the fixed initial fluid source temperature, the continuous Hamilton-Jacobi-Bellman (HJB) equations related to the optimal fluid temperature configurations for the minimum power consumption are obtained by applying optimal control theory. Based on the general optimization results, the analytical solution for the case with Newtonian law [ q ∝ Δ(T ) ] is further obtained. Since there exist no analytical solutions for the cases with the other laws, the continuous HJB equations are discretized and the dynamic programming (DP) algorithm is adopted to obtain the complete numerical solutions of the optimization problem, and the obtained optimization results are also compared to those for the multistage irreversible heat engine system. The obtained results provide a new, more strictly and realistic thermodynamic performance limit for work production and consumption of fluid flow processes, which is different from that given by the classical thermodynamics, and can provide some theoretical guidelines for the optimal designs and operations of practical energy conversion and transfer processes and systems. |
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