The use of patterned heating in controlling pressure losses within sloping channels

Abstract

The effectiveness of utilizing heating patterns as a drag-reduction tool in sloping channels is analysed. The usefulness of heating is judged by determining the pressure gradient required to maintain the same flow rate as in the isothermal case. The key to reducing pressure loss is the formation of separation bubbles, although these bubbles are washed away at relatively large Reynolds numbers. The bubbles reduce the direct contact between the stream and the side walls, thereby reducing the friction experienced by the flow. Moreover, the fluid inside the bubbles tends to rotate, a motion provoked by longitudinal temperature gradients. This rotation also seems to reduce the resistance. On the other hand, the existence of the bubbles tends to obstruct the stream, increasing the flow resistance. In general, channels oriented close to horizontal experience a relatively small pressure loss, but this loss grows markedly as the channel inclines towards the vertical. When modest heating is applied, the pressure loss is approximately proportional to the square of the associated Rayleigh number. It is also shown that if the heating wavelength is too short or too long, the heating loses its effectiveness. In certain circumstances, it turns out that the theoretical pressure-gradient reduction achieved by judicious heating is so large that it exceeds the pressure gradient required to drive the flow in the isothermal problem. The conclusion is that in these instances, a pressure gradient of the opposite sign must be applied to prevent flow acceleration.