A Study on the Effects of Internal Heat Generation on the Thermal Performance of Solid and Porous Fins using Differential Transformation Method

In this study, the effects of internal heat generation on thermal performance of porous fin is theoretical investigated using differential transform method. The results of the developed analytical solutions are verified numerically and analytically using Runge-Kutta method coupled with shooting method and Galerkin weighted residual method, respectively. The parametric studies reveal that as the porosity parameter increase, the rate of heat transfer from the base of the fin and consequently improve the efficiency of the fin increase. Increase in the internal heat generation leads to increase in the value or the range of the thermal stability of the fin. However, a high value or an excessive internal heat generation results in an undesirable situation where some of the heat energy cannot escape to the sink and instead ends up flowing into the prime surface and the fin tends to store heat rather than dissipating it.  This scenario defeats the prime purpose of the cooling fin. Therefore, the operational parameters must be carefully chosen to ensure that the cooling fin retains its primary purpose of removing heat from the primary surface.