Abstract
The unsteady thermocapillary flow and the free surface variation in a two-dimensional, thin liquid layer are investigated theoretically. The temperature is fixed at one end and sinusoidally varied at the other. By employing sine series expansions, the asymptotically oscillatory solutions of the u-velocity distribution and the free surface deformation are solved exactly. It is found that there exists an inversely proportional relation between τ u, the u-velocity time scale and τ s, the free-surface variation time scale, when the free surface has a maximum oscillation. Near the maximum oscillation conditions, the u-velocity may assume a uni-directional distribution across the layer depth. Furthermore, the deformation of the free surface becomes smaller when the gravity effect becomes more important.
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