Exact closed form solutions to nonlinear model of heat transfer in a straight fin

This article is concerned with the exact closed form solutions for heat transfer in a straight fin when the thermal conductivity and heat transfer coefficients are temperature dependent so that conduction and heat transfer terms have the form of strong nonlinearity given by power laws. It is assumed the shape for a straight fin with a rectangular profile is linear dependent with respect to fin thickness. A full discussion and exact analytical solution in the implicit form is 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.