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Natural convection in vertical permeable space

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Abstract

This article describes the natural convective heat transfer in a vertical space insulated with a permeable material. A numerical solution to the problem is given for Ra0 ⩽ 200, which is the range of interest to building technological applications. The variables and boundary conditions and their influence upon the convective heat transfer are discussed. Comparisons are made with previously published results.

Zusammenfassung

Diese Arbeit behandelt die WÄrmeübertragung durch natürliche Konvektion im senkrechten, mit porösem Material gefüllten Spalt. Es wird eine numerische Lösung für Ra0 ⩽ 200 angegeben; in diesem Bereich liegen die technischen Anwendungen im Bauwesen. Ferner werden die Variablen und die Randbedingungen sowie ihr Einflu\ auf die Konvektion diskutiert. Ein Vergleich mit früheren Versuchsergebnissen wird mitgeteilt.

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Abbreviations

d:

thickness of space m

h:

height of space m

hb :

height of crossbar m

x, z:

coordinate m

X, Z:

dimensionless coordinate

u, w:

velocity m/s

ψ :

streamfunction

T:

temperature K (‡C)

TC :

temperature of the cold side K (‡C)

TH :

temperature of the hot side K (‡C)

Tm :

mean temperature K (‡C)

δT:

temperature difference K (‡C)

θ :

dimensionless temperature

λ:

thermal conductivity W/mK

λ0 :

thermal conductivity in permeable material without convective flow W/mK

λb :

thermal conductivity in crossbar W/mK

a:

thermal diffusivity m2/s

a0 :

thermal diffusivity in permeable space m2/s

Cp :

specific heat J/kgK

Β :

coefficient of cubical expansion 1/K

B0 :

specific permeability m2

p:

pressure N/m2

η :

dynamic viscosity Ns/m2

Ν :

kinematic viscosity m2/s

ρ :

density kg/m3

g:

gravitational acceleration 9.81 m/s2

Pr:

Prandtl number

Ra:

Rayleigh number

Gr:

Grashof number

Nu:

Nusselt number

Ra0, Gr0 :

modified Rayleigh and Grashof numbers -

References

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Authors and Affiliations

  1. Institute of Technology, Building Technology, PO Box 725, S-22007, Lund, Schweden

    Claes G. Bankvall (Tekn. dr., docent)

Authors
  1. Claes G. Bankvall
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Bankvall, C.G. Natural convection in vertical permeable space. Wärme- und Stoffübertragung 7, 22–30 (1974). https://doi.org/10.1007/BF01438317

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  • DOI: https://doi.org/10.1007/BF01438317

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