A Comparison of Four Solution Methods for the Analysis of a Trapezoidal Fin

A comparison is made of the temperature profile and the heat loss from a trapezoidal fin using four methods. These four methods are the one- and two-dimensional analytical, the two-dimensional finite difference and a two-dimensional modified finite difference method. The two-dimensional analytical method was arbitrarily chosen as the reference. The non-dimensional fin length is restricted to be less than 2 to prevent errors which might occur due to large values of Δx in the finite difference methods. The values of the Biot number range from 0.01 to 1.0 while the thermal conductivity of the fin and fin’s convection coefficients are assumed constant. The results show that (1) in the view of the heat loss from the trapezoidal fin, all four methods can be used to obtain the solutions within 3% with each other for the given range of Biot number and the non-dimensional fin length, (2) for the non-dimensional temperature, the one-dimensional analytical method does not produce good results as compared to the other three methods when the Biot number is 1.0, and (3) by using a two-dimensional modified finite difference method instead of the two-dimensional finite difference method, the relative difference in the heat loss as compared to a two-dimensional analytical method is reduced considerably.