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.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 52171317 and 51779262
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This paper is supported by The National Natural Science Foundation of China (Project Nos. 52171317 and 51779262). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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