A theoretical analysis of a viscous flow in a corrugated curved channel enclosing a porous medium is carried out. The alignment of the corrugations of the outer and the inner curved walls is taken arbitrarily, and the corrugations are considered to be sinusoidal in nature with periodicity. The flow problem is described by Darcy–Brinkman model, derived in the curvilinear coordinates. The effects of the channel curvature, the wall corrugations and the medium permeability are studied through the boundary perturbation technique, for small corrugation amplitude. A substantial effect of the porous medium on the flow is observed when compared to that of the flow in a corrugated curved channel with clear conduit, especially for low permeability medium. Flow enhancement is found to take place for small corrugation wavenumbers, and maximum augmentation is realized for the completely out-of-phase alignment of the two corrugated curved walls. However, the flow reduces for large enough wavenumbers, and the alignment of corrugated curved walls eventually becomes irrelevant, with no influence on the flow. For low permeability medium, the results also show no effect of the wall alignment on the flow. In general, the effect of the channel curvature on the corrugated curved channel flow is discussed relative to a corrugated straight channel flow to demonstrate the implications of the wall geometry enclosing the porous medium.

中文翻译：

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波纹弯曲通道中的达西-布林克曼流

对包围多孔介质的波纹弯曲通道中的粘性流动进行了理论分析。外弯壁和内弯壁的波纹对齐是任意取的，波纹被认为是具有周期性的正弦波性质。流动问题由在曲线坐标中导出的 Darcy-Brinkman 模型描述。通过边界微扰技术研究了通道曲率、壁波纹和介质渗透率对小波纹幅度的影响。当与具有透明管道的波纹弯曲通道中的流动相比时，观察到多孔介质对流动的显着影响，特别是对于低渗透性介质。发现小波纹波数会发生流动增强，两个波纹弯曲壁的完全异相对齐实现了最大的增强。然而，对于足够大的波数，流动会减少，并且波纹弯曲壁的排列最终变得无关紧要，对流动没有影响。对于低渗透介质，结果也显示壁对齐对流动没有影响。通常，通道曲率对波纹弯曲通道流动的影响是相对于波纹直通道流动进行讨论的，以证明封闭多孔介质的壁几何形状的影响。对于低渗透介质，结果也显示壁对齐对流动没有影响。通常，通道曲率对波纹弯曲通道流动的影响是相对于波纹直通道流动进行讨论的，以证明封闭多孔介质的壁几何形状的影响。对于低渗透介质，结果也显示壁对齐对流动没有影响。通常，通道曲率对波纹弯曲通道流动的影响是相对于波纹直通道流动进行讨论的，以证明封闭多孔介质的壁几何形状的影响。