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.