An accurate approach for thermal analysis of porous longitudinal, spine and radial fins with all nonlinearity effects - analytical and unified assessment

Abstract

The present study deals with a thermal analysis of porous fins subjected to internal heat generation, convection, and radiation energy transfer considering an actual system of analysis under the moving condition of the fin. The main aspiration to carryout this analysis is to establish a correct approach to derive the governing equation for energy transfer in porous fins. The physical explanation was given to require the modification of all existing analyses of porous fins to exchange heat with the surroundings. Three types of fins, namely longitudinal, annular, and spine, have been analyzed with the common mathematical expressions. The temperature distribution in fins has been obtained by employing the differential transform method for solving a high class nonlinear governing equation for all temperature dependent design variables adopted to develop an actual case study. The present approximate analytical method has been authenticated by the numerical technique based on the finite difference method. An excellent agreement of results between these two analyses has been investigated. Unlike all the published works allied with the porous fin, the present work establishes a correct thermal analysis with the key parameter porosity. A clear demonstration has been discussed to distinguish between the solid and porous fins which can be only conjunction with the porosity. The present method of analysis is equally suited for the solid fin also considering only the zero value of porosity to convert the porous fin into a solid fin directly. An optimization study has also been carried out for the maximization of heat transfer rate for a given volume of the solid fraction of a porous fin. The optimum results indicate that under a given design condition, there is an optimum value of porosity for which the heat transfer rate attains a maximum and it is always higher than the solid fin. Therefore, the enhancement of heat transfer can be significantly done by using porous fins for a constant volume of solid or weight of a fin. Finally, the results have been presented in a direction adopted to clearly visualize the superiority of the present study over that of the existing analyses, and to exhibit a difference between solid and porous fins.