Darcy–Brinkman Flow in a Corrugated Curved Channel

Abstract

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.