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首页> 外文期刊>Acta Ciencia Indica. Mathematics >FLOW OF A VISCOUS INCOMPRESSIBLE FLUID OF VARIABLE VISCOSITY THROUGH A POROUS MEDIUM BETWEEN TWO PARALLEL PLANES IN THE PRESENCE OF SUCTION/INJECTION
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FLOW OF A VISCOUS INCOMPRESSIBLE FLUID OF VARIABLE VISCOSITY THROUGH A POROUS MEDIUM BETWEEN TWO PARALLEL PLANES IN THE PRESENCE OF SUCTION/INJECTION

机译：在抽吸/注入作用下，通过两个平行平面上的多孔介质，可变粘度的可变粘度流体在两个平行平面上的流动

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摘要

In this paper, the steady flow of a viscous incompressible fluid between parallel infinitely long horizontal planes is considered. A layer of porous medium occupies the region adjacent to the upper plane. The two planes are kept at different constant temperatures and the viscosity of the fluid is assumed to vary exponentially with the temperature. The fluid motion is also subjected to a uniform suction and injection at the upper and lower planes respectively. The horizontal upper porous layer moves along with a constant velocity U. The lower plane is at rest. The Brinkman's law is modified for the flow through a moving porous medium. The vertical velocity is a constant. The horizontal velocity and temperature are functions of the vertical coordinate. The matching conditions are obtained using the law of conservation of momentum across the interface. The steady non-linear problem is solved subject to the boundary conditions at the two horizontal planes and the matching conditions at the interface. A shooting method known as the method of Adjoints is used to obtain the numerical solution. The effect of the presence of the porous layer is investigated in comparison with the case of a free fluid.
机译：在本文中，考虑了粘性不可压缩流体在无限长平行平行平面之间的稳定流动。一层多孔介质占据了邻近上平面的区域。这两个平面保持在不同的恒定温度下，并且假定流体的粘度随温度呈指数变化。流体运动还分别在上平面和下平面受到均匀的抽吸和注入。水平的上部多孔层以恒定的速度U移动。下部的平面处于静止状态。对于通过移动的多孔介质的流动，修改了布林克曼定律。垂直速度是一个常数。水平速度和温度是垂直坐标的函数。使用跨界面动量守恒定律获得匹配条件。根据两个水平面的边界条件和界面的匹配条件，解决了稳态非线性问题。使用称为“伴随法”的射击方法来获得数值解。与自由流体的情况相比，研究了多孔层的存在的影响。

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