Effect of free surface shape on combined thermocapillary and naturalconvection

Abstract

Combined thermocapillary and natural convection in an open square cavity with differentially-heated side walls is studied numerically as well as experimentally. The test fluid is silicone oil with Prandtl number of 105. The shape of fluid-free surface is made either flat or curved to study its effect on the flow. A finite difference scheme to deal with a curved free surface is developed. The experimental results shown agree with the numerical results. With the curved-free surface, the flow and local heat transfer rate are reduced in the corner regions, and a sharp peak in heat transfer rate at the top edge of the cold wall disappears. NomenclatureBo = static Bond number, pgL 2 cr Bo = dynamic Bond number, GrIRcr Gr = Grashof number, gjSATL 3 /*' 2 g = gravitational acceleration h = free surface height L = container dimension Nu = local Nusselt number, Eq. (14) Pr = Prandtl number RO.-surface tension Reynolds number, cr r T = temperature nondimensionalized as (T -T C )/AT T c = cold wall temperature (u, v) = velocity in (;t, y) domain nondimensionalized by v/L (x, y) = coordinate system, (Fig. 1) j8 = volumetric expansion coefficient in Gr AT = temperature difference between hot and cold wall ju, = viscosity v = kinematic viscosity (£, 17) = coordinates, Eq. (1) p = density cr = surface tension o> = temperature coefficient of surface tension T -shear stress at free surface 4> = inclination angle of free surface i f f = stream function 0} = vorticity

Thermocapillary flow with evaporation and condensation at low gravity. Part 1. Non-deforming surface

“…Figure 15 compares the half-cavity Y-distributions for 75" and 15", and clearly indicates a suppression of circulation at larger contact angles. This result seems to contradict Kamotani & Platt (1992) who noted a decrease in circulation intensity with smaller w . The disparity is primarily due to the asymmetric heating conditions that they imposed versus the symmetric heating considered in this paper.…”

“…Assuming a prescribed contact angle, Cuvelier & Driessen (1986) found that the free boundary is highly sensitive to Ca. Furthermore, Kamotani & Platt (1992) recently showed that variation in surface geometry could greatly influence convection within the cavity for thermocapillary-buoyancy-driven flow. Through experiments and numerical analysis, they compared the convection and heat transfer characteristics of a flat and curved 10"contact angle surface, and noted a marked reduction in thermocapillarity, flow intensity and local heat transfer rate with the highly curved surface.…”

Microgravity experiments and analysis of oscillatory thermocapillary flows in cylindrical containers

“…The numerical scheme for curved free surface is described by Kamotani & Platt (1992). The grid system is similar to the one used for the flat surface.…”

“…The unicellular structure agrees well with the observed pattern. As discussed by Kamotani & Platt (1992), the flow with the concave free surface tends to be slower than that with the flat surface, for two reasons. One is that the average flow passage is narrower and the other is that the direction of the thermocapillary force varies along the free surface, which makes it less effective in driving the flow cell.…”

Marangoni convection of non‐Newtonian power law fluids in a shallow rectangular cavity

“…Despite the assumption that a planar liquid-gas interface (often termed as free surface) simplifies the analyses, the free surface can be quite curved in low g and 1g environments where thermocapillary flow is important as demonstrated by Yih (1968). Several works have been devoted to deformed liquid-gas interfaces; see for instance, Cuvelier and Driessen (1986), Strani et al (1983), Keller and Bergman (1990), Kamotani and Platt (1992) and Avare (1994). Nevertheless, the assumption of a flat free surface is still often used and seems appropriate for metallic melts and oils for which the capillary number is generally small (Favre, 1997).…”