Convection cellular patterns

Heat transfer in horizontal enclosed spaces involves two distinct situations. If the upper plate is maintained at a higher temperature than the lower plate, the lower-density fluid is above the higher-density fluid and no convection currents will be experienced. In this case the heat transfer across the space will be by conduction alone and Nus = 1.0, where 8 is still the separation distance between the plates. The second, and more interesting, case is experienced when the lower plate has a higher temperature than the upper plate. For values of Grs below about 1700, pure conduction is still observed and Nu = 1.0. As convection begins, a pattern of hexagonal cells is formed as shown in Fig. 7-12. These patterns are called Benard cells [33]. Turbulence begins at about Gr6 = 50,000 and destroys the cellular pattern. 

In the preceding section, we have examined a variety of steady thermocapillary and diffusocapillary flows. Not all such flows are stable and in fact surface tension variations at an interface can be sufficient to cause an instability. We consider here the cellular patterns that arise with liquid layers where one boundary is a free surface along which there is a variation in surface tension. It is well known that an unstable buoyancy driven cellular convective motion can result when a density gradient is parallel to but opposite in direction to a body force, such as gravity. An example of this type of instability was discussed in Section 5.5 in connection with density gradient centrifugation. 

It was known that jets about to disintegrate first become wavy or varicose, then break up into a string of equal-sized detached masses that form droplets. Similarly, the experimentally observed regular cellular pattern in free convection suggested that the displacements (or velocities, etc.) resulting from the introduction and growth of disturbances would be spacially periodic, and that the different modes by which a system would fall away from an unstable equilibrium could be characterized in terms of one, two, or three time-independent wavelengths. 

At low Rayleigh numbers, Wragg (W6) found a smaller Ra dependence, resembling more the dependence in laminar free convection. In this range of Ra numbers, a cellular flow pattern is believed to exist, analogous to that of thermal and surface tension-driven cellular convection (Benard cells F3). In the range where the convection is turbulent, the Ra1/3 dependence has been confirmed over seven powers of Ra by Ravoo (R9), who used a centrifuge to vary the body force at constant bulk composition. 

For Gr, < 920, mass transfer could be represented by the forced-convection correlation and for Gr, > 920, by the free-convection correlation ofFenech and Tobias (F3). Tobias and Hickman (T2) also inferred the existence of cellular vortex flow near the electrode from deposition patterns, the induction length for this behavior agreeing with Eq. (44). 

Four principal patterns of convection were distinguished when pure liquids were employed cells, streamers, ribs, and vermiculated rolls. These names were chosen in an attempt to describe the actual appearance of the convection patterns and in accordance with historical designations. Examples are shown in Fig. 21. The patterns depicted there were exhibited in all of the liquids under various conditions. In particular, cells appeared to be the dominant patterns in all liquids for depths of 2 mm or less, and the cell size for the various liquids at the 1-mm and 2-mm depths is shown in Table VI. For a thin (< 2 mm) layer of given liquid evaporating into still air, the cell size increased with the depth of the liquid layer, and the flow which the cellular schlieren pattern represented was the same as that observed by Benard (see Fig. 3). These cells were quite immobile and generally neither grew nor decayed in size with time. A direct stream of dry nitrogen onto the surface of the liquid sharpened the cell peripheries and tended to reduce the cell size. 

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