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Transient Couette flow in a rotating non-Darcian porous medium parallel plate configuration: network simulation method solutions

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The transient, viscous, incompressible, hydrodynamic Couette flow in a rotating porous medium channel is studied in this paper. The channel comprises a pair of infinitely long parallel plates which rotate with uniform angular velocity about an axis normal to the plates. The porous medium is simulated using a Darcy–Forchheimer drag force model which includes both bulk matrix porous drag (dominant at low Reynolds numbers) and second order inertial impedance (dominant at higher Reynolds numbers). The two-dimensional Navier–Stokes equations are reduced to a (z*, t*) coordinate system incorporating Coriolis terms, and appropriate initial and boundary conditions are prescribed. Separate porous drag body force terms are incorporated in both the primary and secondary flow momentum equations. Using a set of transformations, the model is rendered dimensionless and shown to be dictated by the Ekman number, Forchheimer number, Darcy number and Reynolds number in a (z, t) coordinate system. Numerical solutions are obtained for the transformed model using the Network Simulation Method. The influence of the hydrodynamic parameters are computed graphically and also the interaction of parameters on the velocity fields is discussed at length. Excellent agreement is found with earlier non-porous flow studies. The analysis has important applications in geophysics and also chemical engineering systems.

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coordinate along lower stationary plate


transverse coordinate for lower stationary plate (normal to X*)


coordinate normal to the x*–y* plane



K :

permeability of porous medium

u*, v*:

velocities in x*, yY*-directions (primary, secondary velocities)


uniform angular velocity of rotating parallel plate system

b :

Forchheimer quadratic drag parameter


kinematic viscosity of fluid

U :

velocity of translating upper plate

H :

separation of plates

z :

dimensionless coordinate normal to the x*–y* plane

t :

dimensionless time

u,v :

dimensionless velocities in x*, y*-directions (primary, secondary)

Re :

Reynolds number

Da :

Darcy number

Fs :

Forchheimer number

Ek :

Ekman number


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Bég, O.A., Takhar, H.S., Zueco, J. et al. Transient Couette flow in a rotating non-Darcian porous medium parallel plate configuration: network simulation method solutions. Acta Mech 200, 129–144 (2008).

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