prabakaran rajamanickam, wilfried coenen & antonio l....
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Prabakaran Rajamanickam, Wilfried Coenen & Antonio L. Sánchez
University of California San Diego, La Jolla CA
APS DFD 2016
F. Kimura, K. Kitamura, M. Yamaguchi, T. Asami, Fluid flow and heat transfer of natural convection adjacent to upward-facing, inclined,
heated plates, Heat Transfer - Asian Research. 32 (3) (2003) 278–291
Vortex instability
Crossover point Wave instability
Low Mach number equations
Boussinesq approximation is justified when
Parameters
• Inclination angle
• Wall-to-ambient temperature ratio
• Local Grashof number
• Prandtl number
Similarity variables
Governing equations
Streamwise
velocity
TemperatureTransverse
velocity
Vortex instability
Base flow in local coordinates
Wave instability
Eigenvalue problem
P. Jeschke, H. Beer, J. Fluid Mech. 432 (2001) 313–339.
Local coordinates
• Principle of exchange of instabilities
holds
Haaland & Sparrow(1970)
• Two dimensional disturbance,
• Travelling waves
Streamwise vortices Travelling waves
Boussinesq Grashof number For Ideal gas,
For wave mode prevails for all angles
Plot base
velocity
here,
Put a dot for
Boussinesq
▪ The dependence of wall temperature in characterizing the stability mechanisms is studied explicitly since Boussinesqapproximations cease to be valid when
▪ Wave modes are found to be more sensitive to non-Boussinesqeffects compared to vortex mode.
▪ At higher temperatures, wave modes are most likely to prevail in reality for a wide of inclination angles, predicted by this work.
▪ The current work is an initial step towards non-Boussinesqnature of the concerned flow, which requires additional work for the development of heat transfer and other real life applications.