ISSN Online: 2377-424X
International Heat Transfer Conference 12
Integral Transform Solutions of Diffusion and Eigenvalue Problems Within Arbitrarily Shaped Domains
Résumé
Diffusion and Sturm-Liouville type problems dened within irregular multidimensional regions are analytically and automatically solved through integral transforms, by making use of the mixed symbolic-numerical Mathematica platform. The approach is illustrated for linear two-dimensional diusion and eigenvalue problems, and formal exact solutions are obtained. Two alternative approaches are considered, by either
handling the intermediate exact eigenvalue problem, or by direct integral transformation of the original diffusion
problem. A cylindrical region test case with known exact solution is rst considered, and treated as an irregular region in the cartesian coordinate system. Then, a more complex conguration, represented by the Brazilian map as provided by a set of points in the plane, is analyzed for both the associated eigenvalue and diusion problems.