**ABSTRACT**

The simultaneous influences of surface inclination, magnetic field and internal heat generation in porous fins with radiative-convective heat transfer is explored using homotopy perturbation method. The efficacy of the method is displayed through the verification of the results with numerical method using Runge-Kutta. Also, significance of surface inclination, magnetic field, internal heat generation and other parameters on the heat management enhancement of thermal systems using the analytical solutions presented by the method are discussed. The graphical representation of the thermal behaviour of the extended surfaces is presented for pictorial discussion. The results illustrate that the augmentations of the surface inclination, magnetic field, conductive-radiative, conductive-convective and porosity cause the extended surface temperature to reduce as a result of increased rate of heat flow via the passive device. Also, an increase in the internal heat generation causes the fin temperature to fall and the rate of heat transfer from the fin to decrease. It is hoped that the study will assist in proper thermal analysis of fins for effective thermal managements of engineering systems.

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