Abstract
The study deals with the three-dimensional natural convection in closed cubic cavities. The boundary conditions were set as two walls (forward and backward) at constant but different temperatures and adiabatic and conducting walls in top and bottom. In the remaining walls the adiabatic condition was used. The Navier–Stokes and energy equations were discretized with the finite volume method using staggered Cartesian meshes. The characteristic flow patterns for a few values of the Rayleigh number up to 107 and of the Prandtl number Pr = 0.71 are shown. Analysis of the different boundary conditions influence on the thermal field and the effects in the determination of local and averaged heat transfer coefficient are also performed. We noticed a good agreement with experimental data.
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Abbreviations
- g :
-
Gravitational acceleration
- L :
-
Cavity height
- Nu:
-
Local Nusselt number
- Num :
-
Mean Nusselt number
- \( \overline{\rm Nu} \) :
-
Overall Nusselt number
- \( p = {{pL^{2} } \mathord{\left/ {\vphantom {{pL^{2} } {\left( {\rho \nu^{2} } \right)}}} \right. \kern-0pt} {\left( {\rho \nu^{2} } \right)}} \) :
-
Dimensionless pressure field
- Ra:
-
Rayleigh number
- Pr:
-
Prandtl number
- \( t = {{t\nu } \mathord{\left/ {\vphantom {{t\nu } {L^{2} }}} \right. \kern-0pt} {L^{2} }} \) :
-
Time
- \( T_{c} , \, T_{h} \) :
-
Cooled and heated wall temperatures
- \( T = {{\left( {T - T_{\text{c}} } \right)} \mathord{\left/ {\vphantom {{\left( {T - T_{\text{c}} } \right)} {\left( {T_{\text{h}} - T_{\text{c}} } \right)}}} \right. \kern-0pt} {\left( {T_{\text{h}} - T_{\text{c}} } \right)}} \) :
-
Dimensionless temperature
- \( \vec{u} = {{\vec{u}L} \mathord{\left/ {\vphantom {{\vec{u}L} \nu }} \right. \kern-0pt} \nu } \) :
-
Dimensionless velocity field
- \( x,y,z \) :
-
Dimensionless Cartesian coordinates
- \( n + 1 \) :
-
Current time
- \( \alpha \) :
-
Thermal diffusivity coefficient
- \( \beta \) :
-
Thermal expansion coefficient
- \( \nu \) :
-
Kinematic viscosity
- \( \rho \) :
-
Specific mass
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Acknowledgments
The authors wish to thank to the FAPEMIG, CNPq and the CENPES/Petrobras for the financial support.
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Technical Editor: Horácio Vielmo.
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Padilla, E.L.M., Lourenço, M.A.S. & Silveira-Neto, A. Natural convection inside cubical cavities: numerical solutions with two boundary conditions. J Braz. Soc. Mech. Sci. Eng. 35, 275–283 (2013). https://doi.org/10.1007/s40430-013-0033-y
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DOI: https://doi.org/10.1007/s40430-013-0033-y