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Steady one-dimensional heat flow in a longitudinal triangular and parabolic fin. (English) Zbl 1229.34043
Summary: We consider a heat transfer problem of a longitudinal fin with triangular and parabolic profiles. Both thermal conductivity and heat transfer coefficient are assumed to be temperature-dependent and given by power laws. We construct exact solution when the problem is linearizable. In the other case, classical Lie symmetry techniques are employed to analyze the problem. The obtained exact solutions satisfy the realistic boundary conditions. The effects of the applicable physical parameters such as the thermo-geometric fin parameter and the fin efficiency are analyzed.

##### MSC:
 34B60 Applications of boundary value problems involving ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 35Q79 PDEs in connection with classical thermodynamics and heat transfer
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