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Classical Lie point symmetry analysis of a steady nonlinear one-dimensional fin problem. (English) Zbl 1234.35277
Summary: We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.

MSC:
34C14 Symmetries, invariants of ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
80A20 Heat and mass transfer, heat flow (MSC2010)
Software:
REDUCE
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