On the intensification of thermal drift

Consider the flow through a channel with grooved edges on one (or both) side(s). If heating is applied to the boundaries, thermal drift is the flow generated by the interaction of the groove and heating patterns. It is known that, if one side of a channel is smooth while the other is grooved, the application of heating forms a so-called ‘thermal drift engine’. Two thermal drift engines are activated if both surfaces are grooved, and these may reinforce or oppose each other. Carefully choosing these engines can lead to an intensification of the thermal drift. The interplay of two drift engines is explored using a horizontal slot with grooves that have a sinusoidal profile with a prescribed wavenumber $\alpha $ . It is shown that the strength of the flow decreases proportional to $\alpha $ as $\alpha \to 0$ and proportional to ${\alpha ^{ - 1}}$ as $\alpha \to \infty $ . We determine the value of $\alpha $ corresponding to the strongest flow and characterize how the conclusions should be modified if a uniform heating component is added to the heating pattern.