Prediction of coupled radiative and conductive heat transfer in concentric cylinders with nonlinear anisotropic scattering medium by spectral collocation method

Abstract

Accurate prediction of the angular and spatial distributions of radiative intensity is a very important and challenging issue for the coupled radiation and conduction problem with nonlinear anisotropic scattering medium. Different with the traditional hybrid spectral methods, spectral collocation method associated with discrete ordinate method (SCM-DOM), the spectral collocation method is extended to discretized both angular and spatial domains of governing equations in concentric cylinders. The angular and spatial derivative terms of governing equations in the cylindrical coordinate system are approximated by high order Chebyshev polynomials instead of the low order finite difference schemes. The performance of SCM is evaluated by comparing with available data in literature. Numerical results show that convergence rates of angular and spatial nodes approximately follow the exponential decaying law. In addition, for nonlinear anisotropic scattering medium, the SCM provides smoother results and mitigates the ray effect. The SCM is a successful and efficient method to deal with coupled radiative and conductive heat transfer in concentric cylinders. Furthermore, the effects of various geometric and thermal physical parameters on dimensionless temperature and heat flux are comprehensively investigated.