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This work establishes an exact analytical solution for the nonlinear transient thermal model of porous fin subjected to magnetic field with temperature-dependent internal heat generation. With the aid of Laplace transform method, the developed exact analytical model is used to study the impacts of the model parameters on the thermal performance of the fin. Through the developed symbolic heat transfer models using the exact analytical method, parametric studies show that increase in porosity, convective, radiative and magnetic parameters increase the rate of heat transfer from the fin and consequently improve the efficiency of the fin. It is established that the exact analytic solution can serve as basis for comparison of any other method of analysis of the problem and it can also provide platform for improvement in the design of porous fin in heat transfer equipment.

Exact Solutions for Nonlinear Transient Heat Transfer of Porous Fin Subjected to Magnetic Field with Variable Internal Heat Generation