Thermocapillary cell in a horizontal moving liquid layer with heating from above

Abstract

The problem of thermocapillary convection that develops in a thin stationary liquid layer, heated locally from above,hasbeen considered in [i] in the constant layer thickness approximation. The exact solution of eouations of capillary convection that had been obtained in [I] for large blarangoni numbers (M >> i) made it possible to determine the convection rate and the dimensions of the convective cell. The solution given in [I], which holds for the Prandtl numbers Pr ~> i, has been generalized in [2] to encompass the case of liquid metals (Pr < I). The problem from [i] was considered in its rigorous statement in [3] with an allowance for the curvature of the free liGuid surface. This made it possible to determine the effect of gravity and surface deformation on the cell structure and define the applicability scope of the simple analytical solution [I, 2]. On the basis of the results obtained in [1-3], a dyanmic thermocapillary model of the vacuum-arc cathode spot has been proposed in [4]. This model relates the high speed of a cathode spot moving over the electrode surface to the high rate of convective heat transfer. It is interesting to examine the problem of steady-state thermocapillary convection in a thin, horizontal moving liquid layer with local heating from above.