Two-dimensional combined conduction and radiation heat transfer: Comparison of the discrete ordinates method and the diffusion approximation methods

Heat transfer by combined conduction and radiation in a two-dimensional semitransparent medium has been investigated. The discrete ordinates method (DOM) and the Rossland diffusion approximation are used to analyze radiative transfer. Glass is considered as an example of a radiation absorbing and emitting medium, and the spectral dependence of the absorption coefficient on wavelength is accounted for. The results predicted by the DOM are in good agreement with those based on the one-dimensional integral formulation. However, when the opacity of the medium is large, the DOM suffers from the numerical smearing, which distorts the radiative flux distribution. The diffusion approximation greatly underpredicts the temperature and flux distributions in the medium particularly when the thickness or the opacity of the medium is small. The predictions of the diffusion approximation are only reasonable for the thick layer. Hence, the approximatiom should be used with extreme caution to obtain quantitatively accurate results.