Influence of Thermal and Flow Boundary Perturbations on Convection Heat Transfer Characteristics : Numerical Analysis based on Adjoint Formulation

Abstract

A mumerical approach based on adjoint formulation of convection heat transfer is proposed to predict the change of heat transfer characteristics for arbitrary thermal and flow boundary perturbations. In order to obtain the adjoint system of the convection heat transfer problem, we formally linearize the governing equations by the perturbation method and then derive the adjoint system for the perturbation system. As a result, it is shown that the numerical solutions of the base and the adjoint problems enable us to predict the changes of heat transfer characteristics, such as a change of total heat transfer rate or a change of temperature at a specific location, when the thermal and flow boundary conditions are perturbed. An application example is presented to demonstrate the proposed method.