The Instability of Flow Through a Slowly Diverging Pipe With Viscous Heating

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Kirti Chandra Sahu
Keyword(s):  
Stability Analysis ◽  
Prandtl Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Energy Equation ◽  
Pipe Wall ◽  
Negligible Effect ◽  
Viscous Heating ◽  
Fluid Viscosity ◽  
Flow Through

The nonparallel linear stability analysis of flow through a slowly diverging pipe undergoing viscous heating is considered. The pipe wall is maintained at constant temperatures and Nahme’s law is applied to model the temperature dependence of the fluid viscosity. A one-parameter family of velocity profiles for the basic state is obtained for small angles of divergence. The nonparallel stability equations for the disturbance velocity coupled to a linearized energy equation are derived and solved using a spectral collocation method. Our results indicate that increasing viscous heating, characterized by increasing Nahme number, is destabilizing. The Prandtl number has a negligible effect on the linear stability characteristics. The Grashof number stablizes the flow for Gr>106, below which it has a negligible effect.

Weak Turbulence in Small Prandtl Number Convection in Porous Media

2010 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Prandtl Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Weak Turbulence ◽  
Numerical Computations ◽  
Prandtl Numbers ◽  
Convection In Porous Media

The dynamics of weak turbulence in small Prandtl number convection in porous media is substantially distinct than the corresponding dynamics for moderate and large Prandtl numbers. Linear stability analysis is performed and its results compared with numerical computations to reveal the underlying phenomena.

Linear stability analysis of cylindrical Rayleigh–Bénard convection

2012 ◽  
Vol 711 ◽  
pp. 27-39 ◽  
Author(s):  
Bo-Fu Wang ◽  
Dong-Jun Ma ◽  
Cheng Chen ◽  
De-Jun Sun
Keyword(s):  
Stability Analysis ◽  
Prandtl Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Axisymmetric Flow ◽  
Base Flow ◽  
Prandtl Numbers ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated sidewall are investigated by linear stability analysis. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1, for aspect ratio $A$ ($A= H/ R= \mathrm{height} / \mathrm{radius} $) equal to 1, 0.9, 0.8, 0.7, respectively. We found that there still exists stable non-trivial axisymmetric flow beyond the second bifurcation in certain ranges of Prandtl number for $A= 1$, $0. 9$ and 0.8, excluding the $A= 0. 7$ case. The finding for $A= 0. 7$ is that very frequent changes of critical mode (azimuthal Fourier mode) of the second bifurcation occur when the Prandtl number is changed, where five kinds of steady modes $m= 1, 2, 8, 9, 10$ and three kinds of oscillatory modes $m= 3, 4, 6$ are presented. These multiple modes indicate different flow structures triggered at the transitions. The instability mechanism of the flow is explained by kinetic energy transfer analysis, which shows that the radial or axial shear of base flow combined with buoyancy mechanism leads to the instability results.

scholarly journals A linear stability analysis of large-Prandtl-number thermocapillary liquid bridges

2008 ◽  
Vol 41 (12) ◽  
pp. 2094-2100 ◽  
Author(s):  
B. Xun ◽  
P.G. Chen ◽  
K. Li ◽  
Z. Yin ◽  
W.R. Hu
Keyword(s):  
Stability Analysis ◽  
Prandtl Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Liquid Bridges
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