Comparison of the diffusion approximation and the discrete ordinates method for the investigation of heat transfer in glass

Heat transfer by combined conduction and radiation has been investigated in a one-dimensional glass layer. The layer is semitransparent to radiation and the dependence of the absorption coefficient on wavelength is accounted for. The discrete ordinates method and the diffusion approximation are used to analyze radiative transfer. The differencing scheme for the discrete ordinates method has been investigated to obtain the constant total heat flux distribution across the glass layer as required by the energy conservation equation, and the best uniformity is obtained with the diamond scheme. The results predicted by the discrete ordinates method are in good agreement with those based on the exact (integral) equation formulation of radiative transfer. The diffusion approximation greatly underpredicts the temperature and heat flux distributions in the glass layer when the thickness or the opacity of the layer is small. The predictions of the diffusion approximation are only reasonable for thick glass layers. This approximation should be used with extreme caution to obtain quantitatively accurate results.