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General exact solution of the fin problem with variable thermal conductivity and variable heat transfer coefficient

A. H. Abdel Kader, M. S. Abdel Latif, H. M. Nour


In this paper, Lie point symmetry method is used to obtain the general exact solution of nonlinear fin equation which governing heat transfer in rectangular fin with variable thermal conductivity and heat transfer coefficient. Some forms for heat transfer coefficient and thermal conductivity are introduced. The associated exact solution is obtained in each case. The general relation among the thermal conductivity, the fin efficiency, the heat transfer coefficient and the thermo-geometric parameter is obtained.


Lie point symmetry, thermal conductivity, heat transfer coefficient, fin equation.

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