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The Maximum Power Cycle Operating Between a Heat Source and Heat Sink with Finite Heat Capacities

  • Osama M. Ibrahim ORCID logo EMAIL logo and Raed I. Bourisli ORCID logo
Published/Copyright: July 8, 2021
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Journal of Non-Equilibrium Thermodynamics
From the journal Journal of Non-Equilibrium Thermodynamics Volume 46 Issue 4

Abstract

This study aims to identify the thermodynamic cycle that produces the maximum possible power output from a heat source and sink with finite heat capacities. Earlier efforts used sequential Carnot cycles governed by heat transfer rate equations to determine the maximum power cycle. In this paper, a hypothesis is proposed where the heat capacities of the heat addition and rejection processes of the proposed maximum power cycle are assumed to match the heat source and sink, respectively. The result is a simple thermodynamic model that approximately defines the performance and shape of the proposed maximum power cycle, which are compared and verified with the shape and performance of optimized sequential Carnot cycles with closely matching results.

Keywords: heat power cycles; maximum work, maximum power; sequential Carnot cycles; finite heat source and sink

Acknowledgment

We gratefully acknowledge the support of Kuwait University.

  1. Conflict of interest: The authors declare no conflict of interest.

  2. Data availability statement: The datasets generated or analyzed during the current study are available from the author upon reasonable request.

Appendix A
Table 1

Counterflow heat exchanger effectiveness equations for the Carnot, Brayton, and MP cycles [28], [29].

Heat power cycle Heat exchanger Equation
Carnot cycle Hot-side heat exchanger ε H = 1 − exp ( − N T U H )
Cold-side heat exchanger ε L = 1 − exp ( − N T U L )
Brayton cycle*

MP cycle		 Hot-side heat exchanger ε H = 1 − exp − N T U H ( 1 − C r H ) 1 − C r H exp − N T U H ( 1 − C r H ) ( C r H < 1 )
ε H = N T U H 1 + N T U H ( C r H = 1 )
Cold-side heat exchanger ε L = 1 − exp − N T U L ( 1 − C r L ) 1 − C r L exp − N T U L ( 1 − C r L ) ( C r L < 1 )
ε H = N T U L 1 + N T U L ( C r L = 1 )

  1. N T U H and N T U L are the number of heat transfer units of the hot- and cold-side heat exchangers.

  2. C r H = C ˙ H , min C ˙ H , max ; C r L = C ˙ L , min C ˙ L , max

  3. C ˙ H , max is the larger value of C ˙ H and C ˙ w f , while C ˙ L , max is the larger value of C ˙ L and C ˙ w f .

  4. The numbers of transfer units, N T U H and N T U L , in the Bryton cycle case are based on the minimum heat capacity rates.

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Received: 2020-08-15
Revised: 2021-05-03
Accepted: 2021-06-14
Published Online: 2021-07-08
Published in Print: 2021-10-31

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/jnet-2020-0086
Keywords for this article
heat power cycles; maximum work, maximum power; sequential Carnot cycles; finite heat source and sink

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Non-Equilibrium Molecular Dynamics Study of the Influence of Branching on the Soret Coefficient of Binary Mixtures of Heptane Isomers
  4. On the Physical Background of Nerve Pulse Propagation: Heat and Energy
  5. Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows
  6. Continuum Modeling Perspectives of Non-Fourier Heat Conduction in Biological Systems
  7. The Maximum Power Cycle Operating Between a Heat Source and Heat Sink with Finite Heat Capacities
  8. Size Effects and Beyond-Fourier Heat Conduction in Room-Temperature Experiments
  9. The Role of Internal Irreversibilities in the Performance and Stability of Power Plant Models Working at Maximum ϵ-Ecological Function
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