Spectral Collocation Method for Transient Conduction-Radiation Heat Transfer

Abstract

A spectral collocation method is developed to solve transient coupled conduction and radiation heat transfer problems. For both the radiative transfer equation and the energy equation, the spatial domain is discretized by the spectral collocation method. The angular domain is discretized by the discrete-ordinates method for radiative transfer equation. The formulations and implementation of the spectral collocation with discrete-ordinates method reveal its high efficiency. Because of the exponential convergence of spectral methods in space, a very high accuracy can be obtained, even though a small number of nodes are used for the present problems. Numerical results in onedimensional planar and two-dimensional rectangular geometries by the spectral collocation with discrete-ordinates methodarecomparedwithavailableresultsintheliterature.Thesecomparisonsindicatethatthespectralcollocation with discrete-ordinates method for transient conduction–radiation heat transfer is accurate and efficient. Effects of variousparameters,suchasthescatteringalbedo,theconduction–radiationparameter,andtheopticalthicknessare studied for absorbing, emitting, and isotropically scattering media.