Analytical description of the radiative-conductive heat transfer in a gray medium contained between two diffuse parallel plates

https://doi.org/10.1016/j.apm.2017.11.033Get rights and content
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Highlights

  • Analytical solutions for the temperature and heat flux for thermal radiation and conduction-radiation heat transfer.

  • Discrete ordinates method used algebraically to find analytical solutions.

  • Analytical solutions with an accuracy higher than 99.9 ones.

Abstract

Explicit analytical solutions for the temperature and heat flux in a gray medium contained between two diffuse parallel plates are derived for both pure thermal radiation and coupled conduction-radiation heat transfer. This is achieved by combining the integral equations for the heat flux and temperature predicted by the radiative transfer equation with the corresponding predictions of the discrete ordinates method. The algebraic formulation of this well-known method is used to derive analytical results that agree with their corresponding numerical ones with an accuracy greater than 99.9%, for a large interval of optical thicknesses and conduction-to-radiation factors. The explicit and original solutions, for both pure radiation and radiative-conductive heat transfer, therefore solve the problem of one dimensional steady-state heat transfer in gray cavities.

Keywords

Radiative-conductive heat transfer
Two diffuse parallel plates
Analytical temperature solution
Analytical heat flux solution

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