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Layered Marangoni convection with the Navier slip condition
Sādhanā ( IF 1.6 ) Pub Date : 2021-03-18 , DOI: 10.1007/s12046-021-01585-5
Natalya V Burmasheva , Valentina V Privalova , Evgeniy Yu Prosviryakov

A new exact solution to the problem of Marangoni layered convection is obtained. This solution describes a layered steady-state flow of a viscous incompressible fluid at varying gradients of temperature and pressure. The velocity components depend only on the transverse coordinate; the temperature and pressure fields are three-dimensional. The Marangoni effect is observed on the upper free surface of the fluid layer. On the lower solid surface of the fluid layer, three different cases of defining boundary conditions are considered: the no-slip condition, the perfect slip condition and the Navier slip condition. The obtained exact solution is determined by the interaction of three flows: a flow caused by pressure drop (the Poiseuille flow), a flow caused by heating/cooling and the effect of the gravity force (the thermogravitational flow), and a flow caused by heating/cooling and the fluid surface tension effect (the thermocapillary flow). The obtained exact solutions in the case of each of the three types of boundary conditions specified on the lower surface are analyzed in detail. It has been proved that, when certain ratios of the boundary value problem parameters are fulfilled, the velocity components may acquire stagnation points, this being indicative of the presence of counterflow areas in the fluid layer under consideration. In particular, the presence of up to two stagnation points in each of the two longitudinal velocity components may cause a stratification of the velocity field in more than two regions. The obtained exact solution of the Marangoni layered convection problem can describe flows in thin films through the variation of the geometric anisotropy factor.



中文翻译:

Navier滑动条件下的分层Marangoni对流

获得了一种新的精确解决Marangoni分层对流问题的方法。该解决方案描述了在温度和压力变化的梯度下,粘性不可压缩流体的分层稳态流动。速度分量仅取决于横向坐标;而速度分量仅取决于横向坐标。温度和压力场是三维的。在流体层的上部自由表面上观察到了马兰戈尼效应。在流体层的下部固体表面上,考虑了三种定义边界条件的情况:无滑移条件,理想滑移条件和Navier滑移条件。所获得的精确解是由三个流的相互作用确定的:由压降引起的流(泊泊流),由加热/冷却引起的流以及重力作用(热引力流),以及由加热/冷却和流体表面张力效应引起的流动(热毛细流动)。对在下表面上指定的三种边界条件中的每一种情况下获得的精确解进行详细分析。已经证明,当满足一定比例的边界值问题参数时,速度分量会获得停滞点,这表明所考虑的流体层中存在逆流区域。特别地,在两个纵向速度分量的每一个中存在多达两个停滞点可能导致速度场在两个以上区域中分层。所获得的Marangoni分层对流问题的精确解可以通过几何各向异性因子的变化来描述薄膜中的流动。

更新日期:2021-03-19
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