Spectral Method For Radiative Heat Transfer In Variable Physical Properties Media

In recent decades, great achievements have been made by researchers for numerical computation radiative heat transfer in variable physical properties participating media. Many numerical methods have been proposed by scholars, such as zone method, Monte Carlo method, discrete ordinates method, spherical harmonics method, and so on. Because solving the governing equation of radiative heat transfer in variable physical properties media is more difficult than it in constant physical properties, the problems of radiative heat transfer in the variable physical properties participating media were just solved using the low-order numerical methods. So, it is necessary to develop a high accurate, efficient and simple numerical method to solve the two-dimensional radiative transfer problems in variable physical properties media.The spectral methods are accurate with spectral accuracy. They have been widely used in the fields of high accurate numerical calculations. The spectral methods can almost completely overcome the drawbacks of low order methods, and can efficiently provide very high accurate results, while their solution procedures are very simple. Chebyshev collocation spectral method is used for solving the problem of two-dimensional radiative heat transfer in variable physical properties media. The spatial domain is discretized by the spectral collocation method, and the angular domain is discretized by the conventional discrete ordinates method. We use Matlab to write codes and run them to finish our calculations. The present work mainly contains two parts:1. Chebyshev collocation spectral method is used to solve the two-dimensional radiative heat transfer problem with variable absorption coefficient and scattering coefficient. Four cases are considered, they include non-scattering or scattering and radiation heat equilibrium media. Based on the physical meaning, the symmetry is used to verify our results. The results show that the spectral method can be efficiently used to solve the problem of two-dimensional radiative heat transfer with variable absorption coefficient and scattering coefficient, and our results are accurate and reliable.2. Chebyshev collocation spectral method is used to solve the two dimensional combined conduction and radiation heat transfer problem with variable thermal conductivity. The grid and ray independency tests are carried out first, and our results are compared with those available in the references with or without variable thermal conductivity. It shows that our results are still very accurate just only using a few grids. The effects of physical parameters such as variable thermal conductivity parameter, conduction-radiation parameter, scattering albedo, surface emissivity, optical thickness and geometry parameters (such as aspect ratio) on heat transfer have been studied.