Abstract:
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.
