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Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity. (English) Zbl 1261.35140
Summary: This study investigates the exact solutions of a nonlinear fin problem with temperature-dependent thermal conductivity and the heat transfer coefficient. Both the conduction and heat transfer terms are given by the same power law in one case and the distinct power law in the other. Classical Lie symmetry techniques are employed to construct the exact solutions which satisfy the realistic boundary conditions. The effects of the physical applicable parameters such as the thermo-geometric fin parameter and the fin efficiency are analyzed.

##### MSC:
 35Q79 PDEs in connection with classical thermodynamics and heat transfer 35A30 Geometric theory, characteristics, transformations in context of PDEs 80A20 Heat and mass transfer, heat flow (MSC2010)
##### Keywords:
nonlinear fin equation; heat transfer; invariant solutions
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##### References:
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