A differential evolution algorithm for maximizing heat dissipation in stepped fins

In this work, a differential evolution (DE)-based inverse analysis has been reported for maximizing the heat transfer rate from a rectangular stepped finned surface satisfying a given volume. The temperature dependency in all modes of heat transfer has been taken into the consideration, thereby making the problem highly nonlinear. In addition to conventional insulated tip assumption that signifies a linear case, nonlinear analysis with fin tip comprising simultaneous convection and radiation is also carried out. Furthermore, a numerical analysis of the transient behavior is done with the aid of the finite difference method. Due to unavailability of inverse analysis of stepped fins (literature supports this claim), for solving the problem using the DE, the concept of multiplicity of solutions satisfying a given criterion is used to search appropriate step configurations satisfying a fixed fin volume. Thereafter, step dimensions meeting the highest possible rate of heat transfer have been realized. During the DE-based optimization process, approximate analytical solutions formulated on the Adomian decomposition method (ADM) have been used for updating the pertinent fin temperature distribution. The proposed ADM-DE combination is observed to converge into a unique solution that yields the optimized design conditions under the imposed constraints.