Evaluation of a Differential Evolution/Constructal Design Algorithm for Geometrical Optimization of Double T-Shaped Cavity Intruded into a Heat Generating Wall

Abstract

In the present work it is investigated the performance of an algorithm that associates Differential Evolution and Constructal Design for geometrical optimization of a heat transfer problem. It is considered the intrusion of a cooled Double T-shaped cavity into a rectangular conducting solid wall with internal heat generation. The main purpose here is to evaluate the algorithm capability to reproduce the effect of geometric ratios over the dimensionless maximum excess of temperature (performance indicator of the heat transfer problem), as well as, the influence of Differential Evolution (DE) parameters over the optimization analysis. The definition of search space for each degree of freedom and problem constraints is performed with Constructal Design, while the Differential Evolution algorithm is used in the optimization process. Here parameters as mutation operator (M), crossover constant (CR), differential amplification factor (F), Population Size (PS) and Generations number (G) are evaluated. A theoretical recommendation about the suitable parameters set for the optimization algorithm for this kind of heat transfer problem is proposed. Results indicated that the crossover constant (CR) and amplification factor (F) are important parameters for suitable prediction of the effect of degrees of freedom over thermal performance. Moreover, when CR = 0.7 and F = 1.5 results obtained with the algorithm are more robust for the achievement of the best shapes and requires lower number of iterations (IT = PS × G) for reproduction of effect of geometric variables over performance.