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Exact solution of fin problem with linear temperature-dependent thermal conductivity

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

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

51--61

In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.