Unsteady Thermal Boundary Condition Effects on Forced Convection Heat Transfer

A numerical analysis based on adjoint formulation of unsteady forced convection heat transfer is proposed to generally evaluate the heat transfer characteristics under arbitrary thermal boundary conditions. A numerical solution of the adjoint problem enables us to predict the heat transfer characteristics, such as the total transfer rate or the temperature at a specific location, for arbitrary time changes of the thermal boundary conditions. Moreover, using the numerical solution of the adjoint problem, we can obtain the optimal thermal boundary conditions in both time and space to maximize the heat transfer at arbitrary time. Numerical solutions of the adjoint problem in a lid-driven cavity are presented to illustrate the capability of the present method.