Forward and inverse nonlinear heat transfer analysis for optimization of a constructal T-shape fin under dry and wet conditions

•New direct analysis for T-shape dry and wet fins is proposed.•Inverse analysis for optimized dimensions of a T-shape fin is also suggested.•Five optimum geometrics are estimated by modified differential evolution.•Temperature distribution in optimum T-shape fins is determined. 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-vari