scholarly journals GLOBAL STABILITY FOR THERMAL CONVECTION IN A COUPLE-STRESS FLUID WITH TEMPERATURE AND PRESSURE DEPENDENT VISCOSITY

2013 ◽  
Vol 35 (3) ◽  
pp. 85-102 ◽  
Author(s):  
◽  
Shalu Choudhary ◽  
P. K. Bharti

Abstract We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.

Author(s):  
Sunil ◽  
Shalu Choudhary ◽  
Amit Mahajan

Abstract.A nonlinear stability threshold for convection in a rotating couple-stress fluid saturating a porous medium with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple-stress fluid parameter


Author(s):  
B Straughan

We show that the global nonlinear stability threshold for convection with a thermal non-equilibrium model is exactly the same as the linear instability boundary. This result is shown to hold for the porous medium equations of Darcy, Forchheimer or Brinkman. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The equivalence of the linear instability and nonlinear stability boundaries is also demonstrated for thermal convection in a non-equilibrium model with the Darcy law, when the layer rotates with a constant angular velocity about an axis in the same direction as gravity.


2019 ◽  
Vol 41 (1) ◽  
pp. 13-20
Author(s):  
Shalu Choudhary ◽  

Abstract We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.


2015 ◽  
Vol 10 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Neminath Bujappa Naduvinamani ◽  
Siddangouda Apparao ◽  
Hiremath Ayyappa Gundayya ◽  
Shivraj Nagshetty Biradar

2011 ◽  
Vol 66 (8-9) ◽  
pp. 512-518 ◽  
Author(s):  
Jaw-Ren Lin ◽  
Li-Ming Chu ◽  
Chi-Ren Hung ◽  
Rong-Fang Lu

Abstract According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893) [1], the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation.


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