Conduction-radiation heat transfer in a gray semi-transparent medium: combining integral transforms and discrete ordinate method

This work presents a novel approach to solve the unsteady one-dimensional coupled heat conduction -radiation problem for a gray semi -transparent, absorbing, emitting, and diffusing medium, non -linearly anisotropic, bounded by two gray parallel -plane surfaces that are diffuse in emission, and diffuse and specular in reflection. A combination of the Discrete Ordinate Method (DOM), to discretize the angular coordinate of the Radiative Transfer Equation (RTE), and the Generalized Integral Transform Technique (GITT), to solve the energy equation, is proposed as solution methodology. Results are presented in terms of the temperature field, incident radiation, hemispherical reflectance, and conductive, radiative and total heat fluxes. The versatility and the accuracy of the methodology are verified/validated with solutions of the literature for different phase functions, conduction -radiation coupling parameters, and albedo, emphasizing the effects of these parameters, as well as, the characteristics of the present methodology for different kinds of quadrature rules. The results show that the combination DOM/GITT proved to be adequate as a tool for solving the governing equations of the coupled conduction -radiation problem.