Abstract. An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy's model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.

In this study, the Least Square Method (LSM) is a powerful and easy to use analytic tool for predicting the temperature distribution in a porous fin which is exposed to uniform magnetic field. The heat transfer through porous media is simulated using passage velocity from the Darcy's model. It has been attempted to show the capabilities and wide-range applications of the LSM in comparison with a type of numerical analysis as Boundary Value Problem (BVP) in solving this problem. The results reveal that the present method is very effective and convenient, and it is suggested that LSM can be found widely applications in engineering and physics.

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