Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

Abstract

The collocation spectral method (CSM) is further developed to solve the transient conduction–radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev–Gauss–Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.