Using Moving Least Square With Particle Swarm Optimization to Solve Nonlinear Transient Convective–Radiative Heat Transfer Problems in the Existence of a Magnetic Field

Abstract

In the current research, a novel hybrid scheme is proposed to solve nonlinear equations arising in heat transfer through the combination of meta-heuristic algorithms and interpolation methods. In order to define a proper objective function for minimization by particle swarm optimization (PSO), the constrained problem is converted into an unconstrained one through the penalty method. Furthermore, the moving least square (MLS) technique is implemented to interpolate and approximate the derivatives appeared in the equation. The main problem for challenging this combined scheme is nonlinear transient convective–radiative heat transfer in existence of a magnetic field. To study the efficiency of the MLS, the results would be contrasted with those extracted by a finite difference method (FDM) based PSO approach. Through five distinctive examples, the evolutionary diagrams as well as temperature distributions found by different methods are displayed, and the effects of the constant parameters are investigated. Besides, the simulations of this research work clearly depict good agreements of the numerical results obtained by the suggested idea with those reported in literature.