Some nonlinear heat transfer equations solved by three approximate methods

Heat transfer equations are such phenomena which mostly occur nonlinearly, hence solving them has been one of the most time-consuming and difficult affairs among researchers of heat transfer. Therefore, many researchers and scientist of both heat transfer and mathematics have recently paid much attention to find and develop approximate solutions. Perturbation method is a traditional method which has got some limitations (clearly mentioned throughout this work). To overcome the difficulties and limitations of the above method many new ones have recently been introduced, two of which are Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). In this paper, three equations of a lumped system, temperature distribution of a fin and freezing of a saturated fluid are solved through these methods and the results are compared, and ultimately it is shown that HPM and VIM are two mathematical tools that have recovered the limitations of the traditional perturbation method and that they are widely applicable in engineering and physics.