Approximate solution to the radiative equilibrium between concentric spheres

doi:10.1016/0022-4073(72)90162-8

Journal of Quantitative Spectroscopy and Radiative Transfer

Volume 12, Issue 4, April 1972, Pages 511-518

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Abstract

An approximate method was developed for the study of the radiative energy transfer through a gray gas layer enclosed between black concentric spheres which are maintained at uniform but different temperatures. The basic concept consists of assuming a temperature distribution through the gas layer, and assigning appropriate jump boundary conditions to evaluate the flux distribution using the exact integral equation governing the flux for this geometry. The approximate solutions have been found to agree very well (6 per cent maximum deviation) with the existing exact numerical solution throughout the entire range of optical thickness.

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Radiation transfer in an isotropically scattering homogeneous solid sphere
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Radiative heat transfer in an absorbing, emitting, isotropically scattering sphere with a diffusively reflecting and emitting boundary is solved by the Galerkin method. By using the expressions given in this work, the radiation heat flux, the angular distribution of radiation intensity and the divergence of the radiation heat flux anywhere in the sphere can be determined with a high degree of accuracy for all values of the single scattering albedo, from small to moderately large optical radii. Results are presented for representative cases to illustrate the accuracy and the convergence of the method.
Radiative transfer in a gray isothermal spherical layer
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The local radiative flux in an isothermal spherical layer is systematically investigated. The functions $h_{1} (τ; τ_{1}) τ^{2}$ and $h_{2} (τ; τ_{1}, τ_{2}) τ^{2}$ , analogous to the planar functions E₃(τ−τ₁) and E₃(τ₂−τ), are studied and tabulated. Limiting solutions are presented and evaluated. The radiative flux from an isothermal spherical layer is presented in graphical and tabular form. A comprehensive review of radiative transfer in a spherical geometry is performed.

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Approximate solution to the radiative equilibrium between concentric spheres

Abstract

JQSRT

JQSRT

JQSRT

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer