Iterative compact finite difference method for the numerical study of fully wet porous fins with different profile shapes

Abstract

This paper investigates the temperature distribution of porous fins with different profiles (rectangular, triangular, convex parabolic and concave parabolic profiles) under fully wet conditions. The porous fin material is Al and the tips are insulated. An iterative discrete method is employed to solve the nonlinear governing equations. For this purpose, the governing equations are converted into a sequence of linear differential equations by the quasi-linearization method. Then, the numerical solutions of these linear equations are estimated using the compact finite difference scheme. The main advantage of the method is that it does not require to solve the system of non-linear algebraic equations. Moreover, unlike the Padé standard finite difference method, there is no need to calculate the derivatives of the solution from the governing differential equation in order to obtain the finite difference formulas with higher accuracy. The convergence analysis of the method is studied in detail. The effect of geometric and thermophysical parameters on temperature distribution and fins' efficiency is discussed using the plotted graphs. Comparing our numerical solutions with those obtained by the least squares method and the Chebfun package in Matlab shows the accuracy and efficiency of the proposed method.