In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.
Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 12, 2015; final manuscript received May 26, 2016; published online June 28, 2016. Assoc. Editor: Alan McGaughey.
Anbarloei, M., and Shivanian, E. (June 28, 2016). "Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient." ASME. J. Heat Transfer. November 2016; 138(11): 114501. https://doi.org/10.1115/1.4033809
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