Abstract:
This work deals with direct and inverse analysis of T-shaped dry and wet fins. Direct analysis is done to
study heat transfer performance, whereas inverse analysis is performed to simultaneously estimate five
optimum geometric parameters satisfying a prescribed fin volume. The modified differential evolution
(MDE) search algorithm is used to explore the required geometrical parameters pertaining to the stem
and the flange parts of the fin. In the present MDE, the mutant is generated using five distinct vectors
instead of three as conventionally practiced. Due to the existence of multiple solutions, the selection criterion
is based upon the fulfilment of different performance parameters. These involve individual maximization
of heat transfer rate, fin efficiency and fin effectiveness. Since the application of the
differential transformation method (DTM) is not yet demonstrated for nonlinear heat transfer analysis
of T-shaped wet fins, thus, for generating the heat transfer parameters using the inversely estimated geometric
parameters, a forward approach based on the DTM is used here. Parametric variations along with
necessary validations of the direct method are presented. Furthermore, a comparison of the present MDE
search-based inverse algorithm is done with a classical gradient-based optimization technique. It can be
highlighted from the present study that only when at-least three geometrical parameters are known,
then the classical method successfully yields heat transfer performance parameters comparable with
the MDE algorithm. From the optimization study, it is found that a particular value of fin performance
(heat transfer rate, efficiency, effectiveness) can be acquired with various values of surface area and even
at a given surface area, different fin performances can be obtained. However, a single and distinct operating
point is revealed where the performance index of the fin is maximized. For ensuring maximum possible
performance from constructal T-shape wet fins, it is recommended that for the present type of
problem, the present stochastic optimization method such as MDE must be used where the classical
deterministic methods suffer from inherent limitations on multi-variables optimization.
