A CONTINUOUS SENSITIVITY EQUATION APPROACH TO OPTIMAL DESIGN IN MIXED CONVECTION

Abstract

In this paper, we consider the design of a mixed convection system to achieve optimum heat transfer properties. Our design methodology consists of using an adaptive finite element method to obtain approximations for both flow and sensitivity variables. These quantities allow us to calculate values of a design objective function and its gradient. A BFGS/trust-region optimization algorithm uses this information to find optimum parameter values. The adaptive remeshing strategy is constructed to ensure accurate resolution of both flow and sensitivity variables throughout the design iterations. We present this methodology along with numerical results that include a validation of the effectiveness of our remeshing strategy along with the solution to an optimal design problem.