The fluid flow in a circular tube filled with a porous medium is important in packed-bed catalytic reactors. Due to gravity the fluid only partially fills the inclined tube. The Darcy–Brinkman equation is solved by two different highly efficient boundary collocation methods. The flow rate depends on the porous medium parameter which quantifies permeability and the level of fill of the fluid. It is found that there exists an optimum level of fill for which the flow rate is maximized. Asymptotic approximation for small permeability is also obtained.

中文翻译：

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充满多孔介质的倾斜圆形管中的通道流

在填充床催化反应器中，在填充有多孔介质的圆管中的流体流动很重要。由于重力，流体仅部分填充倾斜管。Darcy-Brinkman方程是通过两种不同的高效边界搭配方法求解的。流速取决于多孔介质参数，该参数可量化渗透率和流体填充水平。发现存在最佳填充水平，其流速最大。还获得了小渗透率的渐近逼近。