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Natural convection and conduction heat transfer in open shallow cavities with bounding walls

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Abstract

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 106 to 1012, conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.

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Abbreviations

A :

Enclosure aspect ratio, H/L

c p :

Heat capacity, J/kg K

g :

Acceleration due to gravity, m/s2

h :

Horizontal wall thickness, m

H :

Cavity height, m

k :

Thermal conductivity, W/m K

k r :

Solid to fluid thermal conductivity ratio, =k/kf

L :

Cavity width, m

ℓ:

End wall thickness, m

Nu :

Nusselt number, Eq. 5

p :

Pressure, Pa

P :

Dimensionless pressure, =(p−p∞)L2/ρ α2

Pr:

Prandtl number =ν/α

q′′:

Heat flux, W/m2

q :

Dimensionless heat flux, −θX

Ra:

Rayleigh number, =gβq′′L4/(ν α k)

t :

Time, s

U, V:

Dimensionless fluid velocities, =uL/α, vL/α

\({\dot V}\) :

Dimensionless volume flow rate through the opening

X,Y:

Dimensionless Cartesian coordinates, =x/L, y/L

x, y:

Cartesian coordinates

α:

Thermal diffusivity, m2/s

β:

Volumetric coefficient of thermal expansion, 1/K

ν:

Kinematic viscosity, m2/s

ρ:

Fluid density, kg/m3

ψ:

Stream function

θ:

Dimensionless temperature =(T − T∞)/(Lq′′/k)

φ:

Inclination angle of the heated wall from the horizontal, °

τ:

Dimensionless time, α t/L2

-:

Average

a:

Air

ext:

Extremum

f:

Fluid

in:

Into cavity

loc:

Local

max:

Maximum

min:

Minimum

out:

Out of cavity

∞:

Ambient value

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Acknowledgements

Financial support by Natural Sciences and Engineering Research Council of Canada is acknowledged.

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Authors and Affiliations

  1. Ecole Polytechnique, Box 6079, Centre Ville, Montreal, QC, H3C 3A7, Canada

    O. Polat & E. Bilgen

Authors
  1. O. Polat
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  2. E. Bilgen
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Corresponding author

Correspondence to E. Bilgen.

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Polat, O., Bilgen, E. Natural convection and conduction heat transfer in open shallow cavities with bounding walls. Heat Mass Transfer 41, 931–939 (2005). https://doi.org/10.1007/s00231-004-0597-2

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  • DOI: https://doi.org/10.1007/s00231-004-0597-2

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