A Comparison between 3-D Analytical and Finite Difference Method for a Trapezoidal Profile Fin

A comparison is made of the temperature distribution and heat loss from a trapezoidal profile fin using two different 3-dimensional methods. These two methods are analytical and finite difference methods. In the finite difference method 78 nodes are used for a fourth of the fin. A trapezoidal profile fin being the height of the fin tip is half of that of the fin base is chosen arbitrarily as the model. One of the results shows that the relative error in the total convection heat loss obtained by using 78 nodes in the finite difference method as compared to the heat conduction through the fin root obtained by analytic method seems to be good (i.e., -3.5% <relative error< 1.0%) for the following range ; Bi<0.3, L<2 and 0.4<w<10.