Enhanced heat transport in thermal convection with suspensions of rod-like expandable particles

Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh–Bénard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane. The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in cold regions. The heat transport is enhanced at relatively large Rayleigh number ( $\textit {Ra}$ ) but reduced at small $\textit {Ra}$ . We demonstrate that the increase of Nusselt number arises from the particle–boundary layer interactions: the particles act as ‘active’ mixers of the flow and temperature fields across the boundary layers.

Convection by a horizontal thermal gradient

This paper considers a paradigm large-Prandtl-number, large-Rayleigh-number forced convection problem suggested by the batch melting process in the glass industry. Although the fluid is heated from above, non-uniform heating in the horizontal direction induces thermal boundary layers in which colder liquid is driven over hotter liquid. This leads to an interesting selection problem in the boundary layer analysis, whose resolution is suggested by a combination of analytical and numerical evidence.

A local nonlinear solution as an approximation to low-frequency spanwise jitter in thermoconvective flows

A shallow fluid-filled cavity with a longitudinal applied temperature gradient is subjected to spanwise accelerations (g-jitter) representing the space-based microgravity environment. A simplified slot model is introduced to describe the buoyancy-driven flow and advected temperature fields produced in the cavity. Numerical solutions indicate that boundary layer behaviour can manifest itself in the limit of strong g-jitter (large Rayleigh number Ra). However, boundary layer thicknesses do not obey the conventional Ra−1/4 scaling that typically arises in free thermal convection problems. This anomalous scaling results from the three-dimensional complexity of the flow and advected temperature fields, which are not themselves produced by a single fixed applied temperature change. Three different regimes are identified at large Rayleigh number characterized by the shapes of the advected temperature profiles. These regimes are selected according to the values of the Biot number Bi and an aspect ratio parameter. Simple models are presented of the boundary layer behaviour which reproduce, in each regime, the numerically predicted scalings for boundary layer thickness and advected temperature. These models give a succinct overall picture of the slot behaviour in the buoyancy-dominated limit.

The effect of rotation on vertical Bridgman growth at large Rayleigh number

Convection effects in the melt of a vertical Bridgman furnace, used for solidifying a dilute binary alloy, are known to cause significant, and undesirable, non-uniformity in the alloy. We have found previously that non-axisymmetry significantly degrades the performance of the furnace at large Rayleigh number, Ra, and small Biot number, [Bscr ]. There have been a number of studies on improvement of the alloy quality by the introduction of additional forces into the melt flow – magnetic forces or d'Alembert forces due to various sorts of acceleration of the ampoule. In this paper, we explore the effects on the radial segregation generated by rotating the ampoule about its vertical axis. We determine that the magnitude of segregation is proportional to the product of [Bscr ] and the thickness of the thermal layer on the crystal–melt interface. As the rotation, as measured by a Taylor number, [Tscr ], increases beyond O(Ra1/3), the thermal layer thickens and so the segregation increases. Finally, at [Tscr ] = O(Ra1/2), the thermal adjustment occurs on outer scales, and hence the solutal concentration increases to O([Bscr ]). Hence rotation about the vertical axis actually degrades performance!