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Oscillations of a heated solid surface in an oncoming fluid flow can increase heat transfer from the solid to the fluid. Previous studies have investigated the resulting heat transfer enhancement for the case of a circular cylinder undergoing translational or rotational motions. Another common geometry, the flat plate, has not been studied as thoroughly. The flat plate sheds larger and stronger vortices that are sensitive to the plate’s direction of oscillation. To study the effect of these vortices on heat transfer enhancement, we conduct two-dimensional numerical simulations to compute the heat transfer from a flat plate with different orientations and oscillation directions in an oncoming flow with Reynolds number 100. We consider plates with fixed temperature and fixed heat flux, and find large heat transfer enhancement in both cases. We investigate the effects of the plate orientation angle and the plate oscillation direction, velocity, amplitude and frequency, and find that the plate oscillation velocity and direction have the strongest effects on global heat transfer. The other parameters mainly affect the local heat transfer distributions through shed vorticity distributions. We also discuss the input power needed for the oscillating-plate system and the resulting Pareto optimal cases. 

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ($$Nu$$) between hot and cold walls, for a given rate of viscous dissipation by the flow ($$Pe^2$$), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a$$Pe^{-1/3}$$scaling of horizontal lengths. The corresponding rate of heat transfer$$Nu \sim Pe^{2/3}$$. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large$$Pe$$.