Skip to main content
SpringerLink
Log in

General Heterogeneity Effects on the Onset of Convection in a Porous Medium

  • Chapter
Emerging Topics in Heat and Mass Transfer in Porous Media

Part of the book series: Theory and Applications of Transport in Porous Media ((TATP,volume 22))

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  • Beck JL (1972) Convection in a box of porous material saturated with fluid. Physics of Fluids 15:1377–1383

    Article  Google Scholar 

  • Braester C, Vadasz P (1993) The effect of a weak heterogeneity of a porous medium on natural convection. Journal of Fluid Mechanics 254:345–362

    Article  MATH  MathSciNet  Google Scholar 

  • Gheorghitza SI (1961) The marginal stability in porous inhomogeneous media. Proceedings of the Cambridge Philosophical Society 57:871–877

    Article  MATH  MathSciNet  Google Scholar 

  • Finlayson BA (1972) The method of weighted residuals and variational principles. Academic Press, New York

    MATH  Google Scholar 

  • Gounot J, Caltagirone JP (1989) Stabilité et convection naturelle au sein d’une couche poreuse non homogène. International Journal of Heat and Mass Transfer 32:1131–1140

    Article  MATH  Google Scholar 

  • Kuznetsov AV, Nield DA (2007) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: Double diffusive case. Transport in Porous Media, to appear

    Google Scholar 

  • Leong JC, Lai FC (2001) Effective permeability of a layered porous cavity. ASME Journal of Heat Transfer 123:512–519

    Article  Google Scholar 

  • Leong JC, Lai FC (2004) Natural convection in rectangular layers porous cavities. Journal of Thermophysics and Heat Transfer 18:457–463

    Article  Google Scholar 

  • McKibbin R (1986) Heat transfer in a vertically-layered porous medium heated from below. Transport in Porous Media 1:361–370

    Google Scholar 

  • McKibbin R, O’Sullivan MJ (1980) Onset of convection in a layered porous medium heated from below. Journal of Fluid Mechanics 96:375–393

    Article  MATH  MathSciNet  Google Scholar 

  • McKibbin R, O’Sullivan MJ (1981) Heat transfer in a layered porous medium heated from below. Journal of Fluid Mechanics 111:141–173

    Article  MATH  Google Scholar 

  • McKibbin R, Tyvand PA (1982) Anisotropic modelling of thermal convection in multilayered porous media. Journal of Fluid Mechanics 118:315–319

    Article  MATH  Google Scholar 

  • McKibbin R, Tyvand PA (1983) Thermal convection in a porous medium composed of alternating thick and thin layers. International Journal of Heat and Mass Transfer 26:761–780

    Article  Google Scholar 

  • McKibbin R, Tyvand PA (1984) Thermal convection in a porous medium with horizontal cracks. International Journal of Heat and Mass Transfer 27:1007–1023

    Article  Google Scholar 

  • Nield DA (1987) Convective heat transfer in porous media with columnar structure. Transport in Porous Media 2:177–185

    Article  Google Scholar 

  • Nield DA (1994) Estimation of an effective Rayleigh number for convection in a vertically inhomogeneous porous medium or clear fluid. International Journal of Heat and Fluid Flow 15: 337–340

    Article  Google Scholar 

  • Nield DA, Bejan A (2006) Convection in porous media, 3rd edition. Springer, New York

    Google Scholar 

  • Nield DA, Simmons CT (2007) A discussion on the effect of heterogeneity on the onset of convection in a porous medium. Transport in Porous Media 68:413–421

    Article  MathSciNet  Google Scholar 

  • Nield DA, Kuznetsov AV (2007a) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium. International Journal of Heat and Mass Transfer 50:1909–1915; erratum 4512–4512

    Article  MATH  Google Scholar 

  • Nield DA, Kuznetsov AV (2007b) The onset of convection in a shallow box occupied by a heterogeneous porous medium with constant flux boundaries. Transport in Porous Media 67:441–451

    Article  MathSciNet  Google Scholar 

  • Nield DA, Kuznetsov AV (2007c) The effects of combined horizontal and vertical heterogeneity and anisotropy on the onset of convection in a porous medium. International Journal of Thermal Sciences 46:1211–1218

    Article  Google Scholar 

  • Nield DA, Kuznetsov AV (2007d) The effects of combined horizontal and vertical heterogeneity on the onset of transient convection in a porous medium. Journal of Porous Media to appear

    Google Scholar 

  • Nield DA, Kuznetsov AV (2007e) The onset of convection in a porous medium occupying an enclosure of variable width. ASME Journal of Heat Transfer to appear

    Google Scholar 

  • Nield DA, Kuznetsov AV (2007f) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a bidisperse porous medium. International Journal of Heat and Mass Transfer 50:3329–3339

    Article  MATH  Google Scholar 

  • Prasad A, Simmons CT (2003) Unstable density-driven flow in heterogeneous porous media: A stochastic study of the Elder [1967b] “short heater” problem, Water Resources Research 39 (1): {#}1007

    Google Scholar 

  • Rees DAS, Riley DS (1990) The three-dimensionality of finite-amplitude convection in a layered porous medium heated from below. Journal of Fluid Mechanics 211:437–461

    Article  MATH  MathSciNet  Google Scholar 

  • Simmons CT, Fenstemaker TR, Sharp JM (2001) Variable-density flow and solute transport in heterogeneous porous media: Approaches, resolutions and future challenges. Journal of Contaminant Hydrology 52:245–275

    Article  Google Scholar 

  • Vadasz P (1990) Bifurcation phenomena in natural convection in porous media. In: Heat Transfer, vol 5, Hemisphere, Washington, DC, pp 147–152

    Google Scholar 

  • Beck JL (1972) Convection in a box of porous material saturated with fluid. Physics of Fluids 15:1377–1383

    Article  Google Scholar 

  • Braester C, Vadasz P (1993) The effect of a weak heterogeneity of a porous medium on natural convection. Journal of Fluid Mechanics 254:345–362

    Article  MATH  MathSciNet  Google Scholar 

  • Gheorghitza SI (1961) The marginal stability in porous inhomogeneous media. Proceedings of the Cambridge Philosophical Society 57:871–877

    MATH  MathSciNet  Google Scholar 

  • Finlayson BA (1972) The method of weighted residuals and variational principles. Academic Press, New York

    MATH  Google Scholar 

  • Gounot J, Caltagirone JP (1989) Stabilité et convection naturelle au sein d’une couche poreuse non homogène. International Journal of Heat and Mass Transfer 32:1131–1140

    Article  MATH  Google Scholar 

  • Kuznetsov AV, Nield DA (2007) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: Double diffusive case. Transport in Porous Media, to appear

    Google Scholar 

  • Leong JC, Lai FC (2001) Effective permeability of a layered porous cavity. ASME Journal of Heat Transfer 123:512–519

    Article  Google Scholar 

  • Leong JC, Lai FC (2004) Natural convection in rectangular layers porous cavities. Journal of Thermophysics and Heat Transfer 18:457–463

    Article  Google Scholar 

  • McKibbin R (1986) Heat transfer in a vertically-layered porous medium heated from below. Transport in Porous Media 1:361–370

    Google Scholar 

  • McKibbin R, O’Sullivan MJ (1980) Onset of convection in a layered porous medium heated from below. Journal of Fluid Mechanics 96:375–393

    Article  MATH  MathSciNet  Google Scholar 

  • McKibbin R, O’Sullivan MJ (1981) Heat transfer in a layered porous medium heated from below. Journal of Fluid Mechanics 111:141–173

    Article  MATH  Google Scholar 

  • McKibbin R, Tyvand PA (1982) Anisotropic modelling of thermal convection in multilayered porous media. Journal of Fluid Mechanics 118:315–319

    Article  MATH  Google Scholar 

  • McKibbin R, Tyvand PA (1983) Thermal convection in a porous medium composed of alternating thick and thin layers. International Journal of Heat and Mass Transfer 26:761–780

    Article  Google Scholar 

  • McKibbin R, Tyvand PA (1984) Thermal convection in a porous medium with horizontal cracks. International Journal of Heat and Mass Transfer 27:1007–1023

    Article  Google Scholar 

  • Nield DA (1987) Convective heat transfer in porous media with columnar structure. Transport in Porous Media 2:177–185

    Article  Google Scholar 

  • Nield DA (1994) Estimation of an effective Rayleigh number for convection in a vertically inhomogeneous porous medium or clear fluid. International Journal of Heat and Fluid Flow 15: 337–340

    Article  Google Scholar 

  • Nield DA, Bejan A (2006) Convection in porous media, 3rd edition. Springer, New York

    Google Scholar 

  • Nield DA, Simmons CT (2007) A discussion on the effect of heterogeneity on the onset of convection in a porous medium. Transport in Porous Media 68:413–421

    Article  MathSciNet  Google Scholar 

  • Nield DA, Kuznetsov AV (2007a) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium. International Journal of Heat and Mass Transfer 50:1909–1915; erratum 4512–4512

    Article  MATH  Google Scholar 

  • Nield DA, Kuznetsov AV (2007b) The onset of convection in a shallow box occupied by a heterogeneous porous medium with constant flux boundaries. Transport in Porous Media 67:441–451

    Article  MathSciNet  Google Scholar 

  • Nield DA, Kuznetsov AV (2007c) The effects of combined horizontal and vertical heterogeneity and anisotropy on the onset of convection in a porous medium. International Journal of Thermal Sciences 46:1211–1218

    Article  Google Scholar 

  • Nield DA, Kuznetsov AV (2007d) The effects of combined horizontal and vertical heterogeneity on the onset of transient convection in a porous medium. Journal of Porous Media to appear

    Google Scholar 

  • Nield DA, Kuznetsov AV (2007e) The onset of convection in a porous medium occupying an enclosure of variable width. ASME Journal of Heat Transfer to appear

    Google Scholar 

  • Nield DA, Kuznetsov AV (2007f) The effects of combined horizontal and vertical heterogeneity on the onset of convection in a bidisperse porous medium. International Journal of Heat and Mass Transfer 50:3329–3339

    Article  MATH  Google Scholar 

  • Prasad A, Simmons CT (2003) Unstable density-driven flow in heterogeneous porous media: A stochastic study of the Elder [1967b] “short heater” problem, Water Resources Research 39 (1): {#}1007

    Google Scholar 

  • Rees DAS, Riley DS (1990) The three-dimensionality of finite-amplitude convection in a layered porous medium heated from below. Journal of Fluid Mechanics 211:437–461

    Article  MATH  MathSciNet  Google Scholar 

  • Simmons CT, Fenstemaker TR, Sharp JM (2001) Variable-density flow and solute transport in heterogeneous porous media: Approaches, resolutions and future challenges. Journal of Contaminant Hydrology 52:245–275

    Article  Google Scholar 

  • Vadasz P (1990) Bifurcation phenomena in natural convection in porous media. In: Heat Transfer, vol 5, Hemisphere, Washington, DC, pp 147–152

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    D.A. Nield

Authors
  1. D.A. Nield
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Northern Arizona University, Flagstaff, AZ, U.S.A

    Peter Vadász

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media B.V

About this chapter

Cite this chapter

Nield, D. (2008). General Heterogeneity Effects on the Onset of Convection in a Porous Medium. In: Vadász, P. (eds) Emerging Topics in Heat and Mass Transfer in Porous Media. Theory and Applications of Transport in Porous Media, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8178-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-8178-1_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8177-4

  • Online ISBN: 978-1-4020-8178-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation