Predicting radiative heat transfer in axisymmetric cylindrical enclosures using the collocation spectral method

In this paper, the collocation spectral method (CSM) is extended to solve the radiative transfer equation (RTE) in two-dimensional axisymmetric cylindrical medium, and an iterative solver based on Schur decomposition is developed for the spectral discretized equations. Then the performance of CSM is assessed by comparing with the semi-analytic solutions and the discrete ordinates method (DOM). The results show that the layout of angular grid points has great influence on the accuracy of CSM, and rearranging the angular grid can even reduce the ray effect. But a more reliable method to alleviate the ray effect is to decompose the radiative intensity into two components with separate treatments as the modified DOM proposed by Ramankutty and Crosbie (JQSRT, 57(1997) 107-140). Besides, the CSM can offer more accurate results than the DOM with acceptable computational cost and memory consumption, thus can be an alternative for the solution of RTE in cylindrical coordinates. However, the CSM loses its high order convergence accuracy for the two-dimensional problems due to the unavoidable non-smooth distribution of radiative intensity in both spatial and angular domains. Further treatments should be applied to improve the performance of CSM.