Thermocapillary convection in long horizontal layers of low-Prandtl-number melts subject to a horizontal temperature gradient

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Abstract
Thermocapillary convection arising in small-depth layers (long horizontal cavities) subject to a horizontal temperature gradient is studied numerically. A broad range of values of the Reynolds-Marangoni number,Re, is considered for three values of the aspect ratio (A= length/height). For the largest aspect ratio considered,A= 25, the fully developed Poiseuille-Couette solution is reached, but only for moderateRe. The limitingRevalue for the observability of such a fully developed solution is derived as a function of A(Re[les ] 20A). ForRe[les ] 20A, the flow exhibits three distinct regimes, in the upwind, central and downwind regions, respectively. The Poiseuille-Couette solution (when it exists) fills the central region, and the flow is accelerated, in the upwind region, to reach this Poiseuille-Couette solution at a distance that is proportional toRe.In the downwind region, where the flow is deflected by the endwall, a multi-roll structure is exhibited forRe[ges ] 1330. The number of rolls increases withRe.WhenRe> 20A, the upwind and downwind regions coalesce and some of the downwind rolls can be suppressed. Most of the computations concern interfacial conditions (with fixed temperature distribution) for which the dynamical solution is decoupled from the thermal one. A few thermal solutions are given herein, forPr= 0.015 only.

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