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High Rayleigh number convection in a one-dimensional model
1Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
Summary
This study models one-dimensional convection, revealing stable, single-cell convection even at high Rayleigh numbers. Nonlinear analysis provides accurate heat transport scaling, avoiding turbulence.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Heat transfer
Background:
- Burgers' equation models fluid flow.
- Buoyancy drives convection.
- Rayleigh number quantifies convective instability.
Purpose of the Study:
- Develop a 1D convection model.
- Analyze stability and nonlinear behavior.
- Determine heat transport scaling.
Main Methods:
- Modified Burgers' equation with buoyancy.
- Linear stability analysis.
- Numerical simulations.
- Large Rayleigh number approximation.
Main Results:
- Instability onset at critical Rayleigh number.
- Steady, single-cell convection observed.
- No transition to turbulence up to 10^5 times critical Rayleigh number.
- Closed-form solutions for heat transport scaling.
Conclusions:
- The model exhibits stable convection.
- Nonlinear analysis accurately predicts heat transport.
- High Rayleigh numbers do not induce turbulence in this 1D model.
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