Natural convection and pattern interaction within an inclined two-dimensional slot

Natural convection within a heated, inclined slot with wavy walls is investigated. The coupling between the heating and topography patterns determines the properties of the flow and the effectiveness of this interaction can vary significantly as the slot inclination is adjusted. The analysis is two-dimensional and is likely to be a useful model for the flow in a slot of large cross-stream aspect ratio. Typically, the flow topology consists of a combination of rolls and stream tubes that carry the fluid along the conduit. It is shown that a judicious choice of inclination angle and careful positioning of the grooves relative to the temperature pattern can yield a flow rate greater than that achievable within a smooth slot. There is an optimal inclination and phase difference between the groove and heating patterns for which the flow rate is the greatest. The most effective inclination angle is a function of the wavelength and amplitude of the grooves, the heating intensity and the fluid Prandtl number.