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Diffuse approximation method for solving natural convection in porous media

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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.

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Abbreviations

H :

height of the cavities

I :

functional

K :

permeability

〈p(M i ,M)〉 :

line vector of monomials

p T :

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

α t :

thermal diffusivity

β :

coefficient of thermal expansion

σ:

practical aperture of the weighting function

ϕ:

scalar field

ω(M, M i ):

weighting function

Ψ:

streamfunction

ν:

kinematic viscosity

References

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    Nayroles, B., Touzot, G. and Villon, P.: l'approximation diffuse,C.R. Acad. Sci. Paris, Série II,313 (1991), 293–296.

  3. 3.

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    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.

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    Barbosa Mota, J. P. and Saatdjian, E.: Hysteresis en convection naturelle entre deux cylindres concentriques poreux, Société Française des Thermiciens, Colloque annuel, 1993.

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Prax, C., Sadat, H. & Salagnac, P. Diffuse approximation method for solving natural convection in porous media. Transp Porous Med 22, 215–223 (1996). https://doi.org/10.1007/BF01143516

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Key words

  • natural convection
  • diffuse approximation
  • control volume finite-element method