Results for the heat transfer of a fin with exponential-law temperature-dependent thermal conductivity and power-law temperature-dependent heat transfer coefficients

In this article, thermal behavior analysis of nonlinear fin problem with power-law heat transfer coefficient is studied to determine temperature distribution. This new supposition for the thermal conductivity, exponential-law temperature dependent, makes it to be nonlinear that is a general case in some sense. It is shown that the governing fin equation, that is, a nonlinear second-order differential equation, is exactly solvable with proper boundary conditions. To this purpose, the order of differential equation is reduced and then is converted into a total differential equation by multiplying a proper integration operant. An exact analytical solution is given to advance physical meaning, and the existence of unique solution for some specific values of the parameters of the model is demonstrated. The results are shown graphically. It is observed that fin efficiency is decreasing with respect to the power-law mode for heat transfer.