Integral transform solution of integro-differential equations in conduction-radiation problems |
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Authors: | I F Pinheiro L S de B Alves |
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Affiliation: | Department of Mechanical Engineering – TEM/PGMEC, Universidade Federal Fluminense – UFF, Niterói, RJ, Brazil |
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Abstract: | A new approach for solving nonlinear integro-differential equations in conductive-radiative heat transfer has been developed. The method relies on eigenfunctions expansions for the unknown potentials, following the hybrid analytical-numerical framework provided by the generalized integral transform technique. The problem of conjugated conduction–radiation in a finned-tube radiator is selected for illustrating the method, and a traditional numerical solution of the problem is performed for comparing the proposed approach. A thorough error analysis demonstrates that the proposed scheme is very effective for handling integro-differential problems. Finally, a parametric analysis is provided, demonstrating the effects of the dimensionless groups in the temperature distribution. |
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