Abstract
Using a variational method, two- and three-dimensional incompressible steady velocity fields are numerically determined so that they can maximize the dissimilarity between heat transfer and momentum transfer in plane Couette flow. The Prandtl number is set to be unity, and the same boundary conditions are imposed on the velocity and temperature fields. The Stanton number (heat transfer) and friction coefficient (momentum transfer) for the two-dimensional (streamwise-independent or spanwise-independent) optimal states and the three-dimensional optimal state are compared with those for a corresponding turbulent state. In spite of the similar configuration of the velocity and the temperature, not only the three-dimensional optimal but the two-dimensional ones are found to achieve the much larger Stanton number and the less friction coefficient than the turbulent state.
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