Thermal analysis of a convective–conductive–radiative annular porous fin with variable thermal parameters and internal heat generation

Abstract

The thermal characteristics of annular porous fins with rectangular and hyperbolic cross-sections and internal heat generation were comprehensively studied by the homotopy perturbation method (HPM). The convective–conductive–radiative mode of heat transfer was considered in the current analysis. All thermal parameters were considered as a function of temperature. An approximate closed-form solution was obtained by solving the nonlinear heat transfer equation using HPM. Darcy’s model was employed to formulate the governing equation of heat transfer through porous media. Unknown constants were the initial approximations of the solution and were evaluated based on the boundary and initial conditions of the problem. The effects of pores and different thermal parameters on the dimensionless temperature distribution and the fin efficiency were graphically presented. In order to evaluate the accuracy of the closed-form solution, the obtained results (for both dimensional and non-dimensional forms) were validated by numerical solutions.