Computational Methods in Radiative Heat Transfer

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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.