Computational Methods in Radiative Heat Transfer

这项研究的一个重要组成部分是研究平面平行介质以及球体和圆柱体中的组合模式、辐射和传导以及热传递问题。对于所需的特解，将使用一种特别简洁的形式，以及求解辐射方程的经典球谐方法，在求解这两个方程时都不需要粗略的近似。这项研究的一部分将集中在寻求更好地了解可能导致标准迭代解失去收敛的热传递机制。这项研究项目的第二个组成部分，球谐方法将被用来开发一类多组或非灰色辐射输运问题的解。要考虑的多群模型允许一般的各向异性散射律，并从任何群转移到任何群。所开发的解的计算方面有待研究，许多测试用例的数值结果有待开发。一旦建立了非灰色问题的求解技术，并对平面平行情况进行了数值测试，则将对球对称和柱对称问题进行一些扩展。

A significant component of this investigation is the study combined-mode, radiation and conduction, heat-transfer problems in plane- parallel media and in spheres and cylinders. An especially concise form for the required particular solution will be used, along with the classical spherical-harmonics method of solving the radiation equation can be carried out without gross approximations in the solution of either equation. A portion of this study will be focused on seeking better understanding of the heat-transfer mechanisms that can give rise to a loss of convergence in standard iterative solutions. A second component of this research project, the spherical-harmonics method is to be used to develop solutions to a class of multi-group or non-grey radiation-transport problems. The multi-group model to be considered allows a general anisotropic scattering law and transfer from any group to any group. Computational aspects of the developed solutions are to be investigated, and numerical results for numerous test cases are to be developed. Once the solution technique for the non-grey has been established and tested numerically for the plane-parallel case, some extensions will then be made to problems with spherical and cylindrical symmetry.