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Classical entropy generation analysis in cooled homogenous and functionally graded material slabs with variation of internal heat generation with temperature, and convective–radiative boundary conditions

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  • Torabi, Mohsen
  • Zhang, Kaili

Abstract

This article investigates the classical entropy generation in cooled slabs. Two types of materials are assumed for the slab: homogeneous material and FGM (functionally graded material). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM slab the thermal conductivity is modeled to vary in accordance with the rule of mixtures. The boundary conditions are assumed to be convective and radiative concurrently, and the internal heat generation of the slab is a linear function of temperature. Using the DTM (differential transformation method) and resultant temperature fields from the DTM, the local and total entropy generation rates within slabs are derived. The effects of physically applicable parameters such as the thermal conductivity parameter for the homogenous slab, β, the thermal conductivity parameter for the FGM slab, γ, gradient index, j, internal heat generation parameter, Q, Biot number at the right side, Nc2, conduction–radiation parameter, Nr2, dimensionless convection sink temperature, δ, and dimensionless radiation sink temperature, η, on the local and total entropy generation rates are illustrated and explained. The results demonstrate that considering temperature- or coordinate-dependent thermal conductivity and radiation heat transfer at both sides of the slab have great effects on the entropy generation.

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  • 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.
    • Handle: RePEc:eee:energy:v:65:y:2014:i:c:p:387-397
    DOI: 10.1016/j.energy.2013.11.020
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    References listed on IDEAS

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    1. Ibáñez, Guillermo & López, Aracely & Pantoja, Joel & Moreira, Joel & Reyes, Juan A., 2013. "Optimum slip flow based on the minimization of entropy generation in parallel plate microchannels," Energy, Elsevier, vol. 50(C), pages 143-149.
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    1. 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.
    2. Torabi, Mohsen & Zhang, Kaili, 2015. "Temperature distribution, local and total entropy generation analyses in MHD porous channels with thick walls," Energy, Elsevier, vol. 87(C), pages 540-554.
    3. 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.
    4. Torabi, Mohsen & Zhang, Kaili & Yang, Guangcheng & Wang, Jun & Wu, Peng, 2015. "Heat transfer and entropy generation analyses in a channel partially filled with porous media using local thermal non-equilibrium model," Energy, Elsevier, vol. 82(C), pages 922-938.

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