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Method of Weighted Residual Approach for Thermal Performance Evaluation of a Circular Pin fin: Galerkin Finite element Approach

Olanipekun AT, Oladosu TL, Faola AE

Method of weighted residual has been one of the foremost approximation solution to partial differential equation problem. Thermal performance efficiency of a tapered cast Aluminium (4.5% copper) fin with varying crossectional area in an electronic equipment cooling, has been determined using Galerkin finite element method. The fin is made of Aluminium and has a thermal conductivity k of 168 W/m2-°C. The base is held at Tb = 90°C at x = 0 and the ambient fluid temperature Ta = 25°C. The fin has a Varying cross-section Area length Lf of 0.03 m, and diameter of (D = 0.005 m, d = 0.002 m) with convective heat transfer coefficient h is 75 W/m2-°C and the tip at X = Lf is insulated. The material is discritized into four elements with five equally spaced nodes, designed to take to take a one dimensional setting and solved by the Galerkin finite element method, the fin efficiency is calculated and implemented in a matlab computer to be 80% fin efficient.