Flow of a liquid layer over heated topography
Flow of a liquid layer over heated topography
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DOI：
10.1098/rspa.2012.0409
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发表时间：
2012-12
期刊：
影响因子：
--
通讯作者：
M. Blyth;A. Bassom
中科院分区：
文献类型：
--
作者：
M. Blyth;A. Bassom
考虑了从下加热的粘性液体层在倾斜不均匀壁面上的流动。假定流动发生在零雷诺数下，热p<s:1>数足够小，层内温度场受拉普拉斯方程控制。在给定壁面温度分布和牛顿冷却定律的情况下，重点是描述液体层的表面轮廓，特别是研究壁面加热对其的影响。推导出了当壁面形貌幅值较小时有效的线性化理论，并用边界元法计算的一些非线性结果加以补充。结果表明，在正弦壁面上流动时，液体层可以通过壁面差热完全变平。对于具有向下台阶的平壁上的流动，演示了如何通过在台阶附近适当的局部壁面冷却来消除先前工人已经确定的毛细脊。
The flow of a viscous liquid layer over an inclined uneven wall heated from below is considered. The flow is assumed to occur at zero Reynolds number and the thermal Péclet number is taken to be sufficiently small that the temperature field inside the layer is governed by Laplace’s equation. With a prescribed wall temperature distribution and Newton’s Law of cooling imposed at the layer surface, the emphasis is placed on describing the surface profile of the liquid layer and, in particular, on studying how this is affected by wall heating. A linearized theory, valid when the amplitude of the wall topography is small, is derived and this is complemented by some nonlinear results computed using the boundary element method. It is shown that for flow over a sinusoidally shaped wall the liquid layer can be completely flattened by differential wall heating. For flow over a flat wall with a downwards step, it is demonstrated how the capillary ridge that has been identified by previous workers may be eliminated by suitable localized wall cooling in the vicinity of the step.