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On the minimum entropy production in steady state heat conduction processes

Author

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  • Kolenda, Z.
  • Donizak, J.
  • Hubert, J.

Abstract

On the basis of minimum entropy generation principle, a new formulation of the boundary value problems is proposed. Applying Euler–Lagrange variational formalism, a new mathematical form of heat conduction equation with additional heat source terms has been derived. To obtain a unique solution a special mathematical form of boundary conditions for 2D and 3D problems is required. As a result, entropy generation rate of the process can significantly be reduced, which leads to the decrease of the irreversibility ratio according to the Gouy–Stodola theorem. Minimization of entropy generation in heat conduction process is always possible by introducing additional heat sources.

Suggested Citation

  • Kolenda, Z. & Donizak, J. & Hubert, J., 2004. "On the minimum entropy production in steady state heat conduction processes," Energy, Elsevier, vol. 29(12), pages 2441-2460.
    • Handle: RePEc:eee:energy:v:29:y:2004:i:12:p:2441-2460
    DOI: 10.1016/j.energy.2004.03.049
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    Cited by:

    1. Xia, Shaojun & Chen, Lingen & Sun, Fengrui, 2011. "Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory," Energy, Elsevier, vol. 36(1), pages 633-646.
    2. Torabi, Mohsen & Zhang, Kaili, 2014. "Temperature distribution and classical entropy generation analyses in an asymmetric cooling composite hollow cylinder with temperature-dependent thermal conductivity and internal heat generation," Energy, Elsevier, vol. 73(C), pages 484-496.
    3. Xu, Mingtian, 2012. "Variational principles in terms of entransy for heat transfer," Energy, Elsevier, vol. 44(1), pages 973-977.
    4. Jilani, G. & Thomas, Ciby, 2014. "Effect of thermo-geometric parameters on entropy generation in absorber plate fin of a solar flat plate collector," Energy, Elsevier, vol. 70(C), pages 35-42.
    5. Torabi, Mohsen & Zhang, Kaili & Yang, Guangcheng & Wang, Jun & Wu, Peng, 2014. "Temperature distribution, local and total entropy generation analyses in asymmetric cooling composite geometries with multiple nonlinearities: Effect of imperfect thermal contact," Energy, Elsevier, vol. 78(C), pages 218-234.
    6. Torabi, Mohsen & Zhang, Kaili, 2014. "Classical entropy generation analysis in cooled homogenous and functionally graded material slabs with variation of internal heat generation with temperature, and convective–radiative boundary conditi," Energy, Elsevier, vol. 65(C), pages 387-397.
    7. Aziz, A. & Khan, W.A., 2011. "Classical and minimum entropy generation analyses for steady state conduction with temperature dependent thermal conductivity and asymmetric thermal boundary conditions: Regular and functionally grade," Energy, Elsevier, vol. 36(10), pages 6195-6207.
    8. Meng, Fankai & Chen, Lingen & Sun, Fengrui, 2011. "A numerical model and comparative investigation of a thermoelectric generator with multi-irreversibilities," Energy, Elsevier, vol. 36(5), pages 3513-3522.
    9. Igor Donskoy, 2022. "On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review," Energies, MDPI, vol. 15(19), pages 1-23, September.

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