Minimum power consumption of multistage irreversible Carnot heat pumps with heat transfer law of q ∝ (ΔT) ^m

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 ∝ (ΔT) 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.