Combined Radiation–Conduction Heat Transfer in Layered Media With Graded Refractive Index

Abstract

Abstract. The combined steady-state heat transfer by radiation and conduction in one-dimensional layered participating media with graded refractive index is studied. The radiation intensity is modeled by the radiative transfer equation (RTE). The radiative flux generated is coupled to the thermal conduction flux by the energy conservation equation (ECE). The discrete spherical harmonics method (DSHM) is used for the angular discretization of the RTE, and the Chebyshev spectral method (CSM) is adopted to solve the RTE and ECE in the spatial domain. The method developed allows the evaluation of temperature profiles, radiation intensities, and radiative fluxes in multilayer systems with continuously varying refractive index. The method developed is efficient and accurate, and provides results that are in line with the literature. The influences of certain characteristics of the semitransparent medium are evaluated, in particular the scattering albedo, the boundary emissivity, and the variation in the refractive index. The method developed is applicable to the study of combined radiation-conduction heat transfer in an atmosphere alone or coupled to a body of water. It should be noted that the evaluation of radiative transfer in an inhomogeneous atmosphere without coupling with conductive heat transfer can cause errors in excess of 5% in the temperature profile given in advance.