Natural convection and pattern interaction in a two-dimensional vertical slot

Laminar natural convection is investigated in an infinite vertical slot which has one wall with a corrugated profile, and which is subject to either a uniform or periodic heating profile. This configuration has the attractive feature that it enables a study of the effects that may be produced via the interaction of heating and topography patterns. It is found that the addition of the grooves to an isothermal plate leads to a reduction in the vertical fluid flow and an increase of the transverse heat flow. In contrast, imposing sinusoidal heating on a flat surface generates convection that appears as counter-rotating rolls but there is no net vertical flow. The combination of the two effects of corrugation together with periodic heating leads to a plethora of flow patterns involving a combination of rolls and stream tubes that carry the fluid along the slot. The details of this vertical flow are governed by a pattern interaction effect dictated by the relative positions of the heating and corrugation patterns; when hot spots of the imposed heating overlap the peaks in the grooves the net flow is upward; in contrast, when they lie over the troughs the resultant flow is downward. The interplay between the thermal and geometrical effects weakens as the wavelength of the structure is reduced. The inclusion of a sufficiently strong uniform heating also seems to wash away the pattern interaction effect.