The present work deals with studying magneto-viscous fluid flow around a weakly permeable cylinder bounded by a cylindrical container under the effect of an applied magnetic field. Based on Happel and Kuwabara cell model technique, an analytical solution of the problem is evaluated. Considered flow is separated into the outer viscous fluid region and inner permeable region governed by modified Stoke’s equations and modified Darcy’s law, respectively. Applicable boundary conditions at the fluid porous interface are continuity of normal component of velocity, Saffman’s slip condition together with the continuity of pressure. The expressions for the drag, hydrodynamic permeability, and Kozeny constant for the permeable cylinder are achieved in this analysis. Numerical values of Kozeny constant against porosity are presented, and new results are also acquired. Analytical and numerical results that correspond to the earlier published works are obtained as reduction cases.

中文翻译：

---

使用Happel和Kuwabara细胞模型的MHD粘性流通过弱渗透圆柱体

目前的工作是研究在磁场作用下，由圆柱形容器界定的弱磁圆柱周围的磁粘性流体流动。基于Happel和Kuwabara细胞模型技术，评估了该问题的解析解。所考虑的流动分为外部粘性流体区域和内部渗透性区域，分别由修正的斯托克方程和修正的达西定律控制。在流体多孔界面处适用的边界条件是速度的法向分量的连续性，Saffman滑移条件以及压力的连续性。在该分析中获得了渗透筒的阻力，流体动力渗透率和Kozeny常数的表达式。给出了针对孔隙率的Kozeny常数的数值，并获得新的结果。还原案例获得了与较早发表的工作相对应的分析和数值结果。