Discrete ordinates solution of radiative heat transfer in a refractive two-layer slab with collimated irradiation

Abstract

In this study, radiative heat transfer in a layered absorbing-scattering slab with collimated irradiation is analyzed by a modified discrete ordinates method. A large number of discrete ordinates are employed in the present computation to simulate the angular redistribution and internal reflection of radiation caused by the continuous variation of refractive index in each layer and the Fresnel reflection at the interface. The present results show that the radiative properties of the layer exposed to the external irradiation have stronger influence, and a smaller variation of refractive index in the layer causes less internal reflection and more contribution of backward scattering to the normal-hemispherical reflectance. Thus, a smaller gradient of refractive index in the layer exposed to the external irradiation corresponds to a larger reflectance and a smaller transmittance for a conservative case. When the absorption by the slab is strong, the effects of the internal reflection are minor. Also, the reflectance increases with the increase of the albedo of the layer exposed to the external irradiation. The influences of optical thicknesses and interface reflections are also investigated.