Optimization of forced convection heat transfer by using variational principle

Abstract

Using a variational method, the incompressible steady velocity fields are numerically determined so that they can optimize heat transfer in plane Couette flow. The velocity field is supposed to be periodic in the wall-parallel directions. The Prandtl number is set to unity, and the consistent boundary conditions are imposed on the velocity and temperature fields. The excess of the wall heat flux over the total energy dissipation is taken as an objective functional. At high Reynolds number, the optimal states exhibit three-dimensional velocity fields with large heat flux and small energy dissipation in comparison to a turbulent state. In this report, we discuss the roles of the three-dimensional vortex structures in the heat flux enhancement, and show the characteristic hierarchical vortex structure at high Reynolds number.