**ABSTRACT**

In this study, finite difference method is used for the numerical analysis of the transient heat transfer analysis of a convective-radiative fin with functionally graded materials under the influence of Lorentz force is presented. Three cases of developed nonlinear thermal models of linear, quadratic, exponential and power-law variations of thermal conductivity are considered. The accuracy of the developed numerical code is verified as the results of the numerical solutions established good agreements with the results of the exact analytical solutions. Through the numerical solutions, parametric studies are carried out. From the results, it is shown that increase in radiative and magnetic field parameters as well as in-homogeneity index improve the thermal performance of the fin. Also, the transient responses reveal that the FGM fin with linear-law and power-law function shows the slowest and fastest thermal responses, respectively. This study will provide a very good platform for further studies on the design of extended surfaces where the surrounding fluid is influenced by a magnetic field.

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