Application of metaheuristic algorithms for solving inverse radiative boundary design problems with discrete power levels

Abstract

In this study, an analysis for solving inverse radiative boundary design problem with discrete design variables is developed and presented when radiation is the dominant mode of heat transfer. An absorbing, emitting, and participating medium is considered in radiative equilibrium. The discrete ordinate method (DOM) is implemented to solve the radiative transfer equation (RTE). The goal of the design problem is to find the optimum power of heaters from a discrete set of powers in such a way that they produce the desired temperature and heat flux profile over the design surface. Therefore, several metaheuristic optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), and its modified forms such as PSO with Constriction Factor (PSO-CF), PSO with repulsion factor (PSO-RF) and PSO with adaptive inertia weight (PSO-W) are explored to solve the inverse problem. The accuracy of the direct solution of radiative heat transfer is examined by comparison of the present results with findings from the literature. Then the efficiency and accuracy of the optimization methods are assessed by their ability of finding and reconstructing of the results from the direct solution. Finally, the effects of some thermos-physical properties including the absorption coefficient, emissivity of the heater surface and design surface, on the optimum solutions are examined. The comparison of the results revealed that the genetic optimization algorithm converged faster and with fewer calculations of the objective function compared to other optimization techniques.