Advertisement

Transport in Porous Media

, Volume 22, Issue 2, pp 215–223 | Cite as

Diffuse approximation method for solving natural convection in porous media

  • C. Prax
  • H. Sadat
  • P. Salagnac
Article

Abstract

The diffuse approximation is presented and applied to natural convection problems in porous media. A comparison with the control volume-based finite-element method shows that, overall, the diffuse approximation appears to be fairly attractive.

Key words

natural convection diffuse approximation control volume finite-element method 

Nomenclature

H

height of the cavities

I

functional

K

permeability

〈p(Mi,M)〉

line vector of monomials

pT

p-transpose

M

current point

Nu

Nusselt number

Ri

inner radius

Ro

outer radius

Ra

Rayleigh number

x, y

cartesian coordinates

u, v

velocity components

T

temperature

〈αM〉

vector of estimated derivatives

αt

thermal diffusivity

β

coefficient of thermal expansion

σ

practical aperture of the weighting function

ϕ

scalar field

ω(M, Mi)

weighting function

Ψ

streamfunction

ν

kinematic viscosity

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nayroles, B., Touzot, G. and Villon, P.: Generalizing the finite element method. Diffuse approximation and diffuse elements,Comput. Mech. 10 (1992), 307–318.Google Scholar
  2. 2.
    Nayroles, B., Touzot, G. and Villon, P.: l'approximation diffuse,C.R. Acad. Sci. Paris, Série II,313 (1991), 293–296.Google Scholar
  3. 3.
    Baliga, B. R. and Patankar, S. V.: A new finite element formulation for convection diffusion problems,Numerical Heat Transfer 3 (1980), 393–409.Google Scholar
  4. 4.
    Baliga, B. R. and Patankar, S. V.: A control volume finite-element method for two-dimensional fluid flow and heat transfer,Numerical Heat Transfer 6 (1983), 245–261.Google Scholar
  5. 5.
    Prakash, C. and Patankar, S. V.: A control volume-based finite-element method for solving the Navier-Stokes equations using equal order velocity-pressure interpolation,Numerical Heat Transfer 8 (1985), 259–280.Google Scholar
  6. 6.
    Ni, J. and Beckermann, C.: Natural convection in a vertical enclosure filled with anisotropic porous media,J. Heat Transfer 113 (1991), 1033.Google Scholar
  7. 7.
    Shiralkar, G. S., Haajizadeh, M. and Tien, C. L.: Numerical study of high Rayleigh number convection in a porous enclosure,Numerical Heat Transfer 6 (1983), 223–234.Google Scholar
  8. 8.
    Kim, C. J. and Ro, S. T.: Numerical investigation on bifurcative natural convection in an air-filled horizontal annulus,Proc. Tenth Internat. Heat Transfer Conference, Brighton, U.K., Vol. 7, 1994, pp. 85–90.Google Scholar
  9. 9.
    Barbosa Mota, J. P. and Saatdjian, E.: Hysteresis en convection naturelle entre deux cylindres concentriques poreux, Société Française des Thermiciens, Colloque annuel, 1993.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • C. Prax
    • 1
  • H. Sadat
    • 1
  • P. Salagnac
    • 1
  1. 1.Laboratoire d'Etudes Thermiques, URA CNRS 1403PoitiersFrance

Personalised recommendations