A forced analytical scheme applied to a two dimensional fin  An unsuccessful venture
Abstract
A comparison is made of the temperature profile in and the heat transfer from a 2D triangular fin, computed using a nontraditional (forced) separation of variables scheme and a finite difference method. The finite difference method is presumed to be the standard. In particular, comparisons of the heat loss from the triangular fin using these two methods as a function of fin size ratio and the values of the Biot number from 0.01 to 1.0 are made where the root temperature and fin's convection coefficients are assumed constant. The results show that (1) the variation of temperature along the fin wall and the heat loss from the fin obtained using the forced method becomes close to those values given by the finite difference method as the value of the Biot number decreases and (2) when Bi is less than 0.1, the forced analytic scheme appears to be an adequate but approximate analytical method applicable to the triangular fin. Unfortunately, when the 1D approximation for this fin is included in this comparison, the forced scheme has larger error than the 1D approximation.
 Publication:

AIAA, 28th Thermophysics Conference
 Pub Date:
 July 1993
 Bibcode:
 1993thph.confV....K
 Keywords:

 Cooling Fins;
 Temperature Profiles;
 Thermal Analysis;
 Two Dimensional Bodies;
 Biot Number;
 Convective Heat Transfer;
 Eigenvalues;
 Finite Difference Theory;
 Fluid Mechanics and Heat Transfer