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Thermal convection for large Prandtl numbers
1Department of Physics, University of Marburg, Renthof 6, D-35032 Marburg, Germany.
Physical Review Letters
|May 1, 2001
Summary
This study extends Rayleigh-Bénard convection theory for high Prandtl numbers (Pr). The Nusselt number (Nu) becomes independent of Pr, but a Nu(Pr) maximum is predicted for fixed Rayleigh numbers (Ra).
Area of Science:
- Fluid Dynamics
- Thermodynamics
- Convective Heat Transfer
Background:
- The Grossmann and Lohse (2000) model describes Rayleigh-Bénard convection.
- Previous models were limited in their applicability to very large Prandtl numbers.
Purpose of the Study:
- Extend the Grossmann and Lohse theory to very large Prandtl numbers.
- Provide full functional dependencies for Nusselt (Nu) and Reynolds (Re) numbers.
- Improve the description of scaling regime transitions.
Main Methods:
- Theoretical extension of existing Rayleigh-Bénard convection models.
- Analysis of the functional dependencies Nu(Ra,Pr) and Re(Ra,Pr).
Main Results:
- Nusselt number (Nu) found to be independent of Prandtl number (Pr) at very high Pr.
- Prediction of a maximum in Nu(Pr) for fixed Rayleigh numbers (Ra).
- Derivation of full functional dependencies, surpassing previous limiting power laws.
Conclusions:
- The extended theory offers a more realistic description of Rayleigh-Bénard convection across various scaling regimes.
- The findings are crucial for understanding heat and momentum transport in fluids with high viscosity.
- This work provides a more comprehensive theoretical framework for turbulent convection studies.