Acta Mechanica

, 200:129

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

  • O. Anwar Bég
  • H. S. Takhar
  • Joaquín Zueco
  • A. Sajid
  • R. Bhargava
Article

Abstract

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.

List of symbols

Dimensional

X*

coordinate along lower stationary plate

Y*

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

Z*

coordinate normal to the x*–y* plane

T*

time

K

permeability of porous medium

u*, v*

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

Ω

uniform angular velocity of rotating parallel plate system

b

Forchheimer quadratic drag parameter

ν

kinematic viscosity of fluid

U

velocity of translating upper plate

H

separation of plates

Dimensionaless

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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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • O. Anwar Bég
    • 1
    • 6
  • H. S. Takhar
    • 2
    • 7
  • Joaquín Zueco
    • 3
  • A. Sajid
    • 4
  • R. Bhargava
    • 5
  1. 1.Aerodynamics Program, Aerosciences Academic Wing, British Aerospace SystemsKing Faisal Air AcademyRiyadhKingdom of Saudi Arabia
  2. 2.Department of Engineering, Design & TechnologyManchester Metropolitan UniversityManchesterUK
  3. 3.ETS Ingenieros Industriales Campus Muralla del Mar, Departamento de Ingenieria Térmica y FluidosUniversidad Politecnica de CartagenaCartagena (Murcia)Spain
  4. 4.Burnage, ManchesterUK
  5. 5.Mathematics DepartmentIndian Institute of TechnologyRoorkeeIndia
  6. 6.Magnetohydrodynamics Research, Civil Engineering ProgramCastle CollegeSheffieldEngland, UK
  7. 7.Sale, ManchesterEngland, UK

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