Geometric Optimization of T-shaped Fin and Inverted Fin Based on Minimum Entropy Generation Objective

Since energy management is one of the most critical concerns, it is essential to determine the engineering construct irreversibility. Determination of entropy generation as a basis for evaluation of the irreversibility of heat transfer processes has become a significant method to reflect the heat transfer quality. The current study is dedicated to geometric optimization of T-shaped fins and inverted fins (cavities) using the constructal method to reach the minimum entropy generation as the optimization objective. The temperature distribution is determined according to a 1D analytical model and a 2D numerical model for a T-shaped fin and a T-shaped cavity, respectively. Furthermore, a comparison is made between the present optimal designs relying on entropy generation minimization (EGM) and the optimal designs presented in the literature and based on thermal conductance maximization (TCM) for the fin and hotspot temperature minimization (HTM) for the cavity. While the two optimization approaches have the same constraints, the results reveal that the optimal designs mainly have significant dependence on the type of optimization objective. However, it is shown that the T-shaped fin optimized via EGM produces 24% less entropy than the design optimized by TCM, with the thermal conductance lower only by 4%. On the other hand, the EGM-based optimal cavity generates entropy by about 8% less than that of the HTM-based optimal cavity, with an approximately 19% rise in the hotspot temperature. Considering both objectives for a more comprehensive comparison, the current article introduces a multi-objective optimization for fin and cavity.