Thermal Analysis of Coupled Radiation and Transient Conduction in Two-Dimensional Heterogeneous Media

Taking the advantages of the flexibility to deal with irregular geometry, numerical stability, and high-order local convergence, the discontinuous spectral element method (DSEM) was used for thermal analysis of coupled radiation and transient conduction in two-dimensional heterogeneous media. In the solving process, the spatial computational domain was discretized into several elements separated from each other, and high-order spectral nodes were used to discretize these elements. For the discrete coordinate form of the radiative transfer equation in a heterogeneous medium, the direction of radiant energy in a discrete angle was based to determine the upstream and downstream elements. Then, the upwind scheme was imposed to transmit radiation information in elements. For the transient energy conservation equation, the fully implicit difference scheme was adopted to discretize the transient term. Several examples of coupled radiation and transient conduction in the heterogeneous medium were chosen to test the linear convergence characteristic with increasing number of elements, and the exponential convergence characteristics with increasing nodes in the element. By comparing the results with those in the literature, it was found that the maximum relative error was less than 1 % in all cases, which confirmed the accuracy and efficiency of the discontinuous spectral element method. With an increase in radiation and thermal coupling parameters, the proportion of heat conduction in coupled heat transfer increased while the non-uniformity of the temperature field caused by heterogeneous media decreased. Consequently, a longer time was required for it to reach steady-state. © 2023 Xi'an Jiaotong University. All rights reserved.