Thermal analysis of porous fins enclosure with the comparison of analytical and numerical methods

In this study, heat transfer though a porous fin with rectangular cross section is investigated. The Darcy model is utilized to simulate heat transfer in this porous media. It is assumed that the fin is one-dimensional, homogenous, the flow is laminar, and the generated heat is a linear function of temperature. In this research, three different analytical methods are used to obtain the temperature distribution after deriving the heat transfer equation. In order to validate the obtained solution the collocation method (CM) is compared with the results by a numerical method, in order to validate the solutions, homotopy perturbation method (HPM) and homotopy analysis method (HAM) are employed. This problem is solved for the general case, and the output is obtained as a relationship for one iteration. The effects of various parameters including convection (Nc), porosity (Sh), Rayleigh number (Ra) are examined in this research.