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Natural convection in inclined hemispherical cavities

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Abstract

The effect of inclination on the convective motion in hemispherical cavities is studied by a numerical method for steady state laminar conditions. The three-dimensional equations which describe the process are solved for a Rayleigh number of 10000 and a Prandtl number of unity. It is shown that the axially symmetric motion which exists when the base of the hemisphere is horizontal, becomes three-dimensional when the hemisphere is inclined. The modes of motion are described for values of inclination between 0° and 90° to the horizontal and are related to the components of the buoyancy force.

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Abbreviations

a :

radius of the sphere

C p :

specific heat at constant pressure

F :

body force per unit volume

g :

gravitational acceleration

Gr :

Grashof number =gβa 3(T′ h−T′0)/ν 2

k :

coefficient of thermal conductivity

l :

dimension of length

Pr :

Prandtl number =ρ oCpν/k

r :

radial coordinate

Ra :

Rayleigh number =Gr Pr= [ρ oCpgβa 3(T′ h−T′0)]/(νk)

T :

temperature

t :

time

V :

velocity vector

α :

angle of inclination

β :

coefficient of thermal expansion

Δr :

mesh increment in the radial direction

Δθ :

mesh increment in the polar direction

Δφ :

mesh increment in the azimuthal direction

ψ :

vector potential

φ :

azimuthal coordinate

θ :

polar coordinate

ν :

kinematic viscosity

ρ :

fluid density

ξ :

vorticity vector

0:

reference (initial) state

h :

refers to the temperature of heated zone

r :

radial component of vector

θ :

polar component of vector

φ :

azimuthal component of vector

References

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Authors and Affiliations

  1. Div. of Mech. Eng., Commonwealth Sci. & Ind. Res. Org., Victoria, Australia

    A. Cabelli

Authors
  1. A. Cabelli
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Cabelli, A. Natural convection in inclined hemispherical cavities. Appl. Sci. Res. 33, 45–73 (1977). https://doi.org/10.1007/BF00383192

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  • DOI: https://doi.org/10.1007/BF00383192

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