Spectral collocation method for radiative–conductive porous fin with temperature dependent properties

Abstract

In this work, spectral collocation method is presented to predict the thermal performance of convective–radiative porous fin with temperature dependent convective heat transfer coefficient, fin surface emissivity and internal heat generation. In this approach, the dimensionless fin temperature distribution is approximated by Lagrange interpolation polynomials at spectral collocation points. The differential form of the governing equation is formulated by the Darcy model, and is transformed to a matrix form of algebraic equation. The accuracy of the SCM is verified by compared with numerical results by the homotopy perturbation method and the finite volume method. The node convergence rate of the SCM approximately follows an exponential law, and the computational time of the SCM do not significantly increase with the increasing of collocation points. The effects of various geometric and thermo-physical parameters on the dimensionless fin temperature, fin efficiency and heat transfer rate are comprehensively analyzed. In addition, optimum design analysis is also carried out.