Group classification of fin equation with variable thermal properties. (English) Zbl 1211.35141

Summary: A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Lie Group theory is applied to the equation. Group classification with respect to the thermal conductivity and heat transfer coefficient is performed. Results are summarized in a table for convenience. Some similarity transformations are used to convert the partial differential equation into an ordinary differential equation.


35K55 Nonlinear parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
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