Skip to main content
SpringerLink
Log in

Unsteady Free Convection along an Infinite Vertical Flat Plate Embedded in a Stably Stratified Fluid-Saturated Porous Medium

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The problem of unsteady free convection heat transfer from a one-dimensional (parallel) flow along an infinite vertical flat plate embedded in a thermally stratified fluid-saturated porous medium is considered. Flows are induced by a sudden change in the arbitrary temporal plate temperature. By a formal reduction of the corresponding boundary value problems to well-known Fourier heat conduction problems, analytical solutions of the Darcy and energy equations are obtained. Several special cases are discussed in detail.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M. Abramowitz I. A. Stegun (1964) Handbook of Mathematical Function Dover New York

    Google Scholar 

  • D. Angirasa G. P. Peterson (1997) ArticleTitleNatural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium Int. J. Heat Mass Transfer 40 4329–4335

    Google Scholar 

  • D. Angirasa G. P. Peterson I. Pop (1997) ArticleTitleCombined heat and mass transfer by natural convection in a saturated thermally stratified porous medium Numerical Heat Transfer 31 255–272

    Google Scholar 

  • A. Bejan (1984) Convection Heat Transfer Wiley New York

    Google Scholar 

  • A. Bejan A. D. Kraus (Eds) (2003) Heat Transfer Handbook Wiley New York

    Google Scholar 

  • A. Bejan I. Dincer S. Lorente A. F. Miguel A. H. Reis (2004) Porous and Complex Flow Structures in Modern Technologies Springer New York

    Google Scholar 

  • R. Bradean P. J. Heggs D. B. Ingham I. Pop (1998) Convective heat flow from suddenly heated surfaces embedded in porous media D. B. Ingham I. Pop (Eds) Transport Phenomena in Porous Media Pergamon Oxford 411–438

    Google Scholar 

  • H. S. Carslaw J. C. Jaeger (1993) Conduction of Heat in Solids Clarendon Press Oxford

    Google Scholar 

  • C.-K. Chen C.-R. Lin (1995) ArticleTitleNatural convection from an isothermal vertical surface embedded in a thermally stratified high-porosity medium Int. J. Engng. Sci. 33 131–138 Occurrence Handle10.1016/0020-7225(94)E0038-K

    Article  Google Scholar 

  • P. Cheng W. J. Minkowycz (1977) ArticleTitleFree convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike J. Geophys. Res. 82 2040–2044

    Google Scholar 

  • J. Dey (1989) ArticleTitleA simple technique for approximate solutions of the Falkner-Skan equation Acta Mechanica 77 299–305 Occurrence Handle10.1007/BF01178328

    Article  Google Scholar 

  • T. Govindarajulu M. B. K. Moorty (1992) ArticleTitleAn approximate solution for free convection flows in a thermally stratified porous medium Appl. Sci. Res. 49 83–89 Occurrence Handle10.1007/BF00382744

    Article  Google Scholar 

  • D. B. Ingham I. Pop (Eds) (1998) Transport Phenomena in Porous Media NumberInSeriesvol. II Pergamon Oxford

    Google Scholar 

  • D. B. Ingham A. Bejan E. Mamut I. Pop (Eds) (2004) Emerging Technologies and Techniques in Porous Media Kluwer Dordrecht

    Google Scholar 

  • C. H. Johnson P. Cheng (1978) ArticleTitlePossible similarity solutions for free convection boundary layers adjacent to flat plates in porous media Int. J. Heat Mass Transfer 21 709–718 Occurrence Handle10.1016/0017-9310(78)90032-7

    Article  Google Scholar 

  • F. C. Lai I. Pop F. A. Kulacki (1990) ArticleTitleNatural convection from isothermal plates embedded in thermally stratified porous media AIAA J. Thermophys. 4 533–535

    Google Scholar 

  • E. Magyari I. Pop B. Keller (2003) ArticleTitleEffect of viscous dissipation on the Darcy forced convection flow past a plane surface J. Porous Media 6 111–122

    Google Scholar 

  • E. Magyari I. Pop B. Keller (2004a) ArticleTitleAnalytic solutions for unsteady free convection in porous media J. Engng. Math. 48 93–104 Occurrence Handle10.1023/B:ENGI.0000011914.16863.06

    Article  Google Scholar 

  • Magyari E., Pop I. and Keller B. (2004b). Unsteady free convection past an infinite vertical flat plate subject to a step change in the surface temperature or heat flux in a stratified porous medium (submitted).

  • A. Nakayama H. Koyama (1987a) ArticleTitleAn integral method for free convection from a vertical heated surface in a thermally stratified porous medium Wärme- und Stoffübertr 21 297–300

    Google Scholar 

  • A. Nakayama H. Koyama (1987b) ArticleTitleEffect of thermal stratification on free convection within a porous medium AIAA J. Thermophys. 1 282–285

    Google Scholar 

  • A. Nakayama H. Koyama (1989) ArticleTitleSimilarity solutions for buoyancy-induced flows over a nonisothermal curved surface in a thermally stratified porous medium Appl. Sci. Res. 46 309–322 Occurrence Handle10.1007/BF01998548

    Article  Google Scholar 

  • D. A. Nield A. Bejan (1999) Convection in Porous Media EditionNumber2 Springer New York

    Google Scholar 

  • I. Pop D. B. Ingham (2001) Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media Pergamon Oxford

    Google Scholar 

  • I. Pop D. B. Ingham J. H. Merkin (1998) Transient convection heat transfer in a porous medium: external flows D. B. Ingham I. Pop (Eds) Transport Phenomena in Porous Media Pergamon Oxford 205–231

    Google Scholar 

  • A. Shapiro E. Fedorovich (2004a) ArticleTitleUnsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid J. Fluid Mech. 498 333–352 Occurrence Handle10.1017/S0022112003006803

    Article  Google Scholar 

  • A. Shapiro E. Fedorovich (2004b) ArticleTitlePrandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid Int. J. Heat Mass Transfer 47 4911–4927 Occurrence Handle10.1016/j.ijheatmasstransfer.2004.04.035

    Article  Google Scholar 

  • P. Singh K. Sharma (1990) ArticleTitleIntegral method to free convection in thermally stratified porous medium Acta Mechanica 83 157–163 Occurrence Handle10.1007/BF01172977

    Article  Google Scholar 

  • P. Singh K. Tewari (1993) ArticleTitleNon-Darcy free convection from vertical surfaces in thermally stratified porous media Int. J. Engng. Sci. 31 1233–1242 Occurrence Handle10.1016/0020-7225(93)90128-H

    Article  Google Scholar 

  • H. S. Takhar I. Pop (1987) ArticleTitleFree convection from a vertical flat plate to a thermally stratified Darcian fluid Mech. Res. Comm. 14 81–86

    Google Scholar 

  • K. Tewari P. Singh (1992) ArticleTitleNatural convection in a thermally stratified fluid saturated porous medium Int. J. Engng. Sci. 30 1003–1007 Occurrence Handle10.1016/0020-7225(92)90025-C

    Article  Google Scholar 

  • K. Vafai (Eds) (2000) Handbook of Porous Media Marcel Dekker New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair of Physics of Buildings, Institute of Building Technology, Swiss Federal Institute of Technology (ETH), Zürich, CH-8093, Zürich, Switzerland

    E. Magyari & B. Keller

  2. Faculty of Mathematics, University of Cluj, R-3400, Cluj, CP 253, Romania

    I. Pop

Authors
  1. E. Magyari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Pop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Pop.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Magyari, E., Pop, I. & Keller, B. Unsteady Free Convection along an Infinite Vertical Flat Plate Embedded in a Stably Stratified Fluid-Saturated Porous Medium. Transp Porous Med 62, 233–249 (2006). https://doi.org/10.1007/s11242-005-1292-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-005-1292-6

Keywords

Search

Navigation