Solution Of One-Dimensional Radiative Heat Transfer In Graded Index Media By Spectral Method

Many numerical methods have been developed for solving radiative heat transfer problems in graded index media, such as, a curved ray—tracing method, a combined curved ray-tracing and pseudo-source adding method, a discrete ray-tracing method, a discrete ordinates method, a finite volume method, a finite element method, etc. By comprehensive comparison, the methods based on discretization of the differential form of radiative transfer equation possess very good flexibility. However, there are still some disadvantages existing in the former methods. It is necessary to develop a high accurate, efficient and simple numerical method to solve radiative transfer equation in graded index media.Spectral methods can somewhat overcome the drawbacks of low order methods, and can provide accurate results, while their solution procedures of spectral methods are efficient and simple. The author develops and studies the characteristics of spectral methods to solve radiative heat transfer problems in graded index media. The present research contains two parts:1. The spectral method is used to solve one—dimensional radiative transfer equation in graded index media. The numerical stability of spectral methods is investigated for solving radiative heat transfer under the both cases of scattering media and non—scattering media. Numerical results by the spectral methods are compared with those available data in references. The results show that the spectral methods have a good accuracy and efficiency for solving one—dimensional radiative heat transfer problems in graded index media even using few nodes.2. Spectral methods are presented to solve coupled radiative and conductive heat transfer problems in one—dimensional graded index media. The feasibility study of spectral methods is studied for solving coupled radiative and conductive heat transfer problems under the both cases of a linear refractive index and a sinusoidal refractive index. An error comparison is made between presents results and those from references. The final conclusions can be obtained that:the spectral methods can be used to solve the coupled radiative and conductive heat transfer problems in one—dimensional graded index media accurately, efficiently and simply. Increase with the number of nodes, the calculation error is exponential decrease for different values of conduction—radiation parameter.