Skip to main content
SpringerLink
Log in

Non-Darcian Effects on the Flow of Viscous Fluid in Partly Porous Configuration and Bounded by Heated Oscillating Plates

  • Conference paper
  • First Online:
Modelling and Simulation in Fluid Dynamics in Porous Media

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 28))

Abstract

This chapter deals with the fluid flow and heat transfer in a channel partially filled with porous material bounded by parallel heated oscillating plates. The Darcy–Forchheimer and the Navier–Stokes equations are employed in the porous and clear fluid domains, respectively. At the interface, the flow boundary condition imposed is a stress jump together with a continuity of velocity. The thermal boundary condition is continuity of temperature and heat flux. Solutions for the flow velocity and the solutions which take into account the convection term for the temperature field are obtained numerically. The effects of permeability parameter, Prandtl number, Reynolds number, Forchheimer coefficient, viscosity ratio and thermal conductivity ratio on the flow fields, skin friction, and heat transfer have been discussed. The results of the numerical calculations show good agreement with the analytical results for the simplified Darcy flow velocity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anderson, J.D. Jr.: Computational Fluid Dynamics: The Basic with Applications. McGraw-Hill, New York (1995)

    Google Scholar 

  2. Aydin, O., Kaya, A.: Non-Darcian forced convection flow of a viscous dissipating fluid over a flat plate embedded in a porous medium. Transport Porous Med. 73, 173–186 (2008)

    Article  Google Scholar 

  3. Aydin, O., Kaya, A.: Reply to comments on “Non-Darcian forced convection flow of viscous dissipating fluid over a flat plate embedded in a porous medium”. Transport Porous Med. 73, 191–193 (2008)

    Article  Google Scholar 

  4. Beavers, G.S., Sparrow, E.M.: Non-Darcy flow through fibrous porous media. J. Appl. Mech. 36, 711–714 (1969)

    Article  Google Scholar 

  5. Beavers, G.S., Sparrow, E.M., Rodenz, D.E.: Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres. J. Appl. Mech. 40, 655–660 (1973)

    Article  Google Scholar 

  6. Bujurke, N.M., Hiremath, P.S., Biradar, S.N.: Impulsive motion of a non-Newtonian fluid between two oscillating parallel plates. Appl. Sc. Res. 45, 211–231 (1988)

    Article  MATH  Google Scholar 

  7. Cvetkovic, V.D.: A continuum approach to high velocity flow in a porous medium. Transport Porous Med. 1, 63–97 (1986)

    Article  Google Scholar 

  8. Debnath, L., Ghosh, A.K.: On unsteady hydromagnetic flows of a dusty fluid between two oscillating plates. Appl. Sc. Res. 45, 353–365 (1988)

    Article  MathSciNet  Google Scholar 

  9. Deng, C., Martinez, D.M.: Viscous flow in a channel partially filled with a porous medium and with wall suction. Chem. Eng. Sci. 60, 329–336 (2005)

    Article  Google Scholar 

  10. Dybbs, A., Edwards, R.V.: A new look at porous media fluid mechanics—Darcy to turbulent. In Bear, J., Corapcioglu, M.Y. (eds.) Fundamentals of Transport Phenomena in Porous Media, pp. 199–256. Martinus Nijhoff, Dordrecht (1984)

    Google Scholar 

  11. Givler, R.C., Altobelli, S.A.: A determination of the effective viscosity for the Brinkman-Forchheimer flow model. J. Fluid Mech. 258, 355–370 (1994)

    Article  Google Scholar 

  12. Gobin, D., Goyeau, B.: Natural convection in partially porous media: a brief overview. Int. J. Num. Methods Heat Fluid Flow 18, 465–490 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hassanizadeh, S.M., Gray, W.G.: High velocity flow in porous media. Transport Porous Med. 2, 521–531 (1987)

    Article  Google Scholar 

  14. Hayat, T.: Exact solutions of a dipolar fluid flow. Acta Mec. Sin. 19, 308–314 (2003)

    Article  MathSciNet  Google Scholar 

  15. Ingham, D.B., Pop, I., Cheng, P.: Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation. Transport Porous Med. 5, 381–398 (1990)

    Article  Google Scholar 

  16. Joseph, D.D., Nield, D.A., Papanicolaou, G.: Nonlinear equation governing flow in a saturated porous medium. Water Resour. Res. 18, 1049–1052 (1982)

    Article  Google Scholar 

  17. Kaviany, M.: Principles of Heat Transfer in Porous Media, 2nd edn. Springer, New York (1995)

    Book  MATH  Google Scholar 

  18. Kuznetsov, A.V.: Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid. Int. J. Heat Mass Transf. 41, 2556–2560 (1998)

    Article  MATH  Google Scholar 

  19. Kuznetsov, A.V.: Analytical studies of forced convection in partly porous configurations. In: Vafai, K. (ed.) Handbook of Porous Media, pp. 269–310. Mercel Dekker, New York (2000)

    Chapter  Google Scholar 

  20. Martys, N., Bentz, D.P., Garboczi, E.J.: Computer simulation study of the effective viscosity in Brinkman’s equation. Phys. Fluids 6, 1434–1439 (1994)

    Article  MATH  Google Scholar 

  21. Murty, P.V.S.N., Singh, P.: Effect of viscous dissipation on a non-Darcy natural convective regime. Int. J. Heat Mass Transf. 40, 1251–1260 (1997)

    Article  Google Scholar 

  22. Nield, D.A.: Resolution of a paradox involving viscous dissipation and non-linear drag in a porous medium. Transport Porous Med. 41, 349–357 (2000)

    Article  MathSciNet  Google Scholar 

  23. Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (2006)

    Google Scholar 

  24. Ochoa-Tapia, J.A., Whitaker, S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid-I. Theoretical development. Int. J. Heat Mass Transf. 38, 2635–2646 (1995)

    Article  MATH  Google Scholar 

  25. Ochoa-Tapia, J.A., Whitaker, S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid-II. Comparison with experiment. Int. J. Heat Mass Transf. 38, 2647–2655 (1995)

    Article  Google Scholar 

  26. Payne, L.E., Rodrigues, J.F., Straughan, B.: Effect of anisotropic permeability on Darcy’s law. Math. Method Appl. Sci. 24, 427–438 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. Rajagopal, K.R.: On a hierarchy of approximate models for flows of incompressible fluids through porous solids. Math. Method Appl. Sci. 17, 215–252 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  28. Rees, D.A.S., Magyari, E.: Comments on the paper “Non-Darcian forced-convection flow of viscous dissipating fluid over a flat plate embedded in a porous medium” by Aydin, O. and Kaya, A., Transport in Porous Media. Transport Porous Med. 73, 187–189 (2008). doi:10.1007/s11242-007-9200-x

    Google Scholar 

  29. Sekharan, E.C., Ramanaiah, G.: Unsteady flow between two oscillating plates. Def. Sc. J. 32, 99–104 (1982)

    MATH  Google Scholar 

  30. Sharma, P.K., Chaudhary, R.C., Sharma, B.K.: Flow of viscous incompressible fluid in a region partially filled with porous medium and bounded by two periodically heated oscillating plates. Bull. Cal. Math. Soc. 97, 263–274 (2005)

    MATH  Google Scholar 

  31. Vafai, K.: Convective flow and heat transfer in variable porosity media. J. Fluid Mech. 147, 233–259 (1984)

    Article  MATH  Google Scholar 

  32. Vafai, K., Tien, C.L.: Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transf. 24, 195–203 (1981)

    Article  MATH  Google Scholar 

  33. Whitaker, S.: Flow in porous media: part-I, a theoretical derivation of Darcy’s law. Transport Porous Med. 1, 3–25 (1986)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NIT Calicut, NIT(P.O), 673601, Calicut, India

    S. Panda

  2. OUAT, Bhubaneswar, 751003, India

    M. R. Acharya

  3. Silicon Institute of Technology, Bhubaneswar, 751024, India

    A. Nayak

Authors
  1. S. Panda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. R. Acharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Panda .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    José A. Ferreira

  2. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    Sílvia Barbeiro

  3. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    Gonçalo Pena

  4. Inst. Computational Engineering &, Sciences (ICES), University of Texas, Austin, Austin, 78712, Texas, USA

    Mary F. Wheeler

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this paper

Cite this paper

Panda, S., Acharya, M.R., Nayak, A. (2013). Non-Darcian Effects on the Flow of Viscous Fluid in Partly Porous Configuration and Bounded by Heated Oscillating Plates. In: Ferreira, J., Barbeiro, S., Pena, G., Wheeler, M. (eds) Modelling and Simulation in Fluid Dynamics in Porous Media. Springer Proceedings in Mathematics & Statistics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5055-9_11

Download citation

Publish with us

Policies and ethics

Search

Navigation