The Application of Homotopy Analysis Method to Determine the Thermal Response of Convective-Radiative Porous Fins with Temperature-Dependent Properties

Abstract

In this paper, the Homotopy Analysis Method (HAM) is utilized to investigate the thermal response of a circular convective-radiative porous fin having a rectangular cross-section. It is assumed that internal heat generation depends linearly on the temperature for the solid part of the porous fin, while temperature-dependent functions are used for thermal conductivity and convective terms. The thermal conductivity and convective coefficient of heat transfer are supposed to change respectively as a nonlinear hyperbolic and as a power-law function of the temperature all through the fin length. The function employed for the thermal conductivity can be applied for the thermal analysis if for example fins are made of semiconductor materials. Additionally, the general form of convective function enables us to account for the convection heat transfer in different processes. The heat transfer analysis in the porous media is conducted through passage velocity in Darcy’s model. HAM is utilized to study the effects of different pertinent parameters and nondimensional numbers on the described problem. The accuracy and convergence of HAM are validated with numerical methods (i.e., Runge–Kutta method) as well as other published works that reveal an excellent agreement.