Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques

Abstract

The purpose of this paper is a thermal optimal control problem using four types of minimization technique. The four types of minimization techniques are the weighted gradient method, the Newton based method, the modified steepest descent method and the steepest descent method using weighting adaptation. The formulation is based on the optimal control theory in which the performance function is expressed by the computed and targeted temperatures. The optimal values can be obtained by minimizing the performance function. The thermal fluid flow is described by the Boussinesq approximated incompressible Navier-Stokes equation and the energy equation is analyzed. BFGS is applied to calculate the Hessian matrix which is used in the Newton-based method. The traction given by the perturbation for the Lagrange multiplier is used in the BFGS method.