Minimum power consumption of multistage irreversible Carnot heat pumps with heat transfer law of <i>q</i> ∝ (Δ<i>T</i>)<sup> <i>m</i> </sup>
Lingen Chen, Shaojun Xia
Abstract
Abstract For the given initial finite high-temperature heat reservoir temperature, continuous Hamilton–Jacobi–Bellman equations are established to obtain optimal finite high-temperature heat reservoir temperature for minimum power consumption of multistage Carnot heat pumping system with generalized convective heat transfer law [ q ∝ (Δ T ) m ]. Analytical expression of optimal heat reservoir temperature with Newtonian heat transfer law ( m = 1) is obtained based on generalized optimization results for minimum power consumption. For other heat transfer laws ( m ≠ 1), numerical solutions for minimum power consumption are provided. Optimization results for multistage Carnot heat pumps are compared with maximum power output solutions of multistage irreversible Carnot heat engines.