Summary
Natural convection flow of the micropolar fluid in a partially divided rectangular enclosure has been investigated numerically. The enclosure is partially divided by a conductive vertical divider protruding from the floor of the enclosure. The present work simulates the thermal behaviors of the micropolar fluid in the enclosure. The streamlines and the isotherms of the fluid are plotted for both the transient and steady states. Besides, emphasis is placed on the influences of the location and the height of the divider on the flow and the temperature fields. In addition, the effects of the conductivity of the divider, the Rayleigh number of the fluid and the aspect ratio of the enclosure on the heat transfer, and the differences of the heat transfer performance between the Newtonian and the micropolar fluids are also surveyed. The developed governing equations are solved by the cubic spline collocation scheme. The results indicate that the effects of the location and the height of the divider on the flow field and the temperature field are significant. Furthermore, the heat transfer in the enclosure is strongly effected by vortex viscosity and Rayleigh number.
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Abbreviations
- B :
-
material parameter,L 2 /j
- g :
-
gravitational acceleration
- G :
-
dimensionless angular velocity
- h :
-
divider height
- H :
-
enclosure height
- j :
-
micro-inertia per unit mass
- Kv :
-
vortex viscosity
- KR :
-
ratio of thermal conductivities of the divider and the fluid
- L :
-
enclosure width
- Nu:
-
Nusselt number
- Pr:
-
Prandtl number
- r :
-
radius
- Ra:
-
Rayleigh number
- t :
-
time,sec.
- T :
-
temperature
- u :
-
horizontal velocity
- U :
-
dimensionless horizontal velocity
- v :
-
vertical velocity
- V :
-
dimensionless vertical velocity
- x,y :
-
Cartesian coordinates
- X,Y :
-
dimensionless Cartesian coordinates
- α:
-
thermal diffusivity
- β:
-
coefficient of thermal expansion
- Δ:
-
material parameter,KV/μ
- γ:
-
spin gradient viscosity
- λ:
-
material parameter, γ/jμ
- μ:
-
dynamic viscosity
- ⋎:
-
kinematic viscosity
- θ:
-
dimensionless temperature
- σ:
-
angular velocity component
- τ:
-
dimensionless time
- ω:
-
vorticity
- ω:
-
dimensionless vorticity
- ψ:
-
stream function
- Ψ:
-
dimensionless stream function
- c :
-
cold wall
- d :
-
divider region
- h :
-
hot wall
- w :
-
wall
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Wang, S.G., Li, T.Y. & Hsu, P.T. Natural convection of micropolar fluid in a partially divided enclosure. Acta Mechanica 136, 41–53 (1999). https://doi.org/10.1007/BF01292297
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DOI: https://doi.org/10.1007/BF01292297