Conduction-radiation heat transfer in non-gray semi-transparent planar media: Combining integral transforms and discrete ordinate method

•A hybrid approach to solve transient heat conduction-radiation problems.•Gray and non-gray semitransparent scattering planar media.•A combination of generalized integral transform and discrete ordinate methods.•An alternative tool for benchmarking conduction-radiation problems. This work presents a hybrid approach to solve the unsteady one-dimensional coupled heat conduction-radiation problem in a non-gray semitransparent planar medium. The diffusely absorbing/emitting medium scatters radiation anisotropically and is bounded by two gray or non-gray parallel planar surfaces that are diffuse in emission and diffuse or 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 a solution approach. To account for the spectrally varying nature of the radiative properties, the entire wavelength spectrum is discretized into bands in which the radiative properties are assumed to be constant. The versatility and accuracy of the proposed methodology are verified against data from the literature for different spectrally varying radiative parameters (extinction coefficient, absorption coefficient, albedo), scattering phase functions, and emissivity/reflectivity boundaries. The results obtained for the temperature field, incident radiation, and heat fluxes showed that the GITT/DOM combination is suitable for solving coupled conduction-radiation problems for gray or non-gray media and, due to its hybrid numerical-analytical nature, can be used as a benchmarking tool.