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A Lie symmetry classification of a nonlinear fin equation in cylindrical coordinates. (English) Zbl 1474.35043

Summary: The nonlinear fin equation in cylindrical coordinates is considered. Assuming a radial variable heat transfer coefficient and temperature dependent thermal conductivity, a complete classification of these two functions is obtained via Lie symmetry analysis. Using these Lie symmetries, we carry out reduction of the fin equation and whenever possible exact solutions are obtained.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
35K59 Quasilinear parabolic equations
80A19 Diffusive and convective heat and mass transfer, heat flow
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