The numerical solution was obtained using an Alternating Direction Implicit method. Both a stream tube-real tube and a real tube-real tube model were investigated. The conditions for significant diffusion of momentum upstream of the plane of expansion are specified. Eddy characteristics and flow field development are predicted as functions of the flow behavior index n and of the Reynolds number. Some results showing the influence of the expansion ratio are presented. Experimental data are presented to verify the numerical model. Streak photography was used for recording flow patterns and a multiple flash technique was used for point velocity measurement. Fluid properties were determined with an R16 Weissenberg Rheogoniometer. The measured reattachment lengths, the recorded flow patterns, and the developing axial velocity field all show excellent agreement with the numerical predictions.
When a layer of liquid is heated from below at a rate which exceeds a certain critical value, a two- or three-dimensional motion is generated. This motion arises from the action of buoyancy and surface tension forces, the latter being due to variations in the temperature of the liquid surface.The two-dimensional form of the flow has been studied by a numerical method. It consists of a series of rolls, rotating alternately clockwise and anticlockwise, which are shown to be symmetrical about the dividing streamlines. As well as a detailed description of the motion and temperature of the liquid, and of the effects on these characteristics of variations in the Rayleigh, Marangoni, Prandtl and Biot numbers, a study has been made of the conditions under which the motion first starts, the wavelength of the rolls and the rate of heat transfer across the liquid layer.
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