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Steady heat transfer through a radial fin with rectangular and hyperbolic profiles. (English) Zbl 1205.80035
Summary: We construct some exact solutions for the thermal diffusion in a fin with a rectangular profile and another with a hyperbolic profile. Both the thermal conductivity and the heat transfer coefficient are assumed to be temperature dependent. Moreover, the thermal conductivity and the heat transfer terms are given by the same power law in one case and distinct power laws in the other. A point transformation is introduced to linearize the problem when the power laws are equal. In the other case, classical Lie symmetry techniques are employed to analyze the problem. The exact solutions obtained satisfy the realistic boundary conditions. The effects of applicable physical parameters such as the thermo-geometric fin parameter and the fin efficiency are analyzed.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
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