Skip to main content
SpringerLink
Log in

An exact solution for non-darcy free convection from a horizontal line source of heat

Eine exakte Lösung der nicht-darcy'schen freien Konvektion von einer horizontalen, linienförmigen Wärmequelle

  • Published:
Wärme - und Stoffübertragung Aims and scope Submit manuscript

Abstract

In this paper we consider the free convection from a horizontal line source of heat which is embedded in an unbounded porous medium saturated with a fluid at rest under gravity. The convective fluid and the porous medium are in local thermal equilibrium.

Zusammenfassung

In dem Aufsatz wird die freie Konvektion von einer horizontalen, linienförmigen Wärmequelle untersucht, die in ein unbegrenztes poröses Medium eingebettet ist. Die Poren des porösen Mediums sind mit einem Fluid gefüllt, das unter Schwerkrafteinfluß ruht. Das strömende Fluid und das poröse Medium sind örtlich im thermischen Gleichgewicht.

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

Access this article

Log in via an institution

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

Abbreviations

c p :

specific heat of convective fluid

F o :

parameter,=χα/(vl>g

g :

acceleration due to gravity

k :

thermal conductivity of the saturated porous medium

l :

typical length scale of body

Q :

heat flux per unit length of a line source

Ra :

Rayleigh number, =gβQl/α2μcp

Ra x :

local Rayleigh number, =xg βQx/ a2μcp

T :

temperature

T ∞ :

temperature of ambient fluid

u, ν :

x andy components of velocity

x, y :

coordinates vertically upwards and normal to axis of plume

X, Y :

non-dimensional coordinates vertically upwards and normal to axis of plume

α :

equivalent themal diffusivity

β :

coefficient of thermal expansion

η :

similarity variable

θ :

non-dimensional temperature

x :

permeability of porous medium

μ :

viscosity of convective fluid

v :

kinematic viscosity of convective fluid

ϱ:

density of convective fluid

ψ :

stream function

Ψ :

non-dimensional stream function

χ :

the Forchheimer's coefficient

References

  1. Cheng, P.: Natural convection in a porous medium: External Flows. Proceedings of the Advanced Study Institute on Natural Convection: Fundamentals and Applications, ed. by S. Kakac, W. Aung and R. Viskanta. Washington DC: Hemisphere 1985

    Google Scholar 

  2. Wooding, R. A.: Convection in a saturated medium at large Rayleigh or Péclet number. J. Fluid Mech. 15 (1963) 527–544

    Google Scholar 

  3. Merkin, J. H.: Free convection boundary layers on axisymmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium. Int. J. Heat Mass Transfer 22 (1979) 1461–1462

    Google Scholar 

  4. Ackroyd, J. A. D.: On the laminar compressible boundarylayer with stationary origin on a moving flat wall. Proc. Camb. Phil. Soc. 63 (1967) 871–893

    Google Scholar 

  5. Fand, R. M.; Steinberger, T. E.; Cheng, P.: Natural convection heat transfer from a horizontal cylinder in a porous medium. Int. J. Heat Mass Transfer (to appear)

  6. Bejan, A.; Poulikakos, D.: The non-Darcy regime for vertical boundary layer natural convection in a porous medium. Int. J. Heat Mass Transfer 27 (1984) 717–722

    Google Scholar 

  7. Ingham, D. B.: The non-Darcy free convection boundary-layer on axi-symmetric and two-dimensional bodies of arbitrary shape. Int. J. Heat Mass Transfer (to appear)

  8. Cheng, P.: Private communication

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, England

    D. B. Ingham

Authors
  1. D. B. Ingham
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ingham, D.B. An exact solution for non-darcy free convection from a horizontal line source of heat. Wärme- und Stoffübertragung 22, 125–127 (1988). https://doi.org/10.1007/BF01052976

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01052976

Keywords

Search

Navigation