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

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 moderate Re. The limiting Re value for the observability of such a fully developed solution is derived as a function of A(Re [les ] 20A). For Re [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 to Re. In the downwind region, where the flow is deflected by the endwall, a multi-roll structure is exhibited for Re [ges ] 1330. The number of rolls increases with Re. When Re > 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, for Pr = 0.015 only.

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“…While, for adiabatic surfaces, Parmentier et al [9] found that unsteady disturbances in the form of oblique waves are the most unstable. Furthermore, Ben Hadid and Roux [10][11][12] numerically studied the two-dimensional thermocapillary and thermocapillary-buoyant convection of fluid in an open cavity with various aspect ratios, and showed the existence of a multicellular steady flow and a transition from steady to oscillatory flow. Mundrane and Zebib [13] analyzed the onset of oscillatory flow for thermocapillary-buoyant convection, and found that a transition of steady state flow to unsteady flow occurs as soon as the Grashof number exceeds a lower bound value.…”