Pattern selection in the thermal convection of non-Newtonian fluids

2011 ◽  
Vol 668 ◽  
pp. 500-550 ◽  
Author(s):  
BASHAR ALBAALBAKI ◽  
ROGER E. KHAYAT
Keyword(s):  
Fluid Layer ◽  
Shear Thickening ◽  
Newtonian Fluids ◽  
Critical Threshold ◽  
Physical Parameters ◽  
Pattern Selection ◽  
Nonlinear Analyses ◽  
Weakly Nonlinear ◽  
Shear Thickening Fluids ◽  
The Stability

The thermogravitational instability in a fluid layer of a non-Newtonian medium heated from below is investigated. Linear and weakly nonlinear analyses are successively presented. The fluid is assumed to obey the Carreau–Bird model. Although the critical threshold is the same as for a Newtonian fluid, it is found that non-Newtonian fluids can convect in the form of rolls, squares or hexagons, depending on the shear-thinning level. Similar to Newtonian fluids, shear-thickening fluids convect only in the form of rolls. The stability of the convective steady branches is carried out to determine under which specific conditions a pattern is preferred. The influence of the rheological and physical parameters is examined and discussed in detail.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

2010 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

scholarly journals Air-Aided Shear on a Thin Film Subjected to a Transverse Magnetic Field of Constant Strength: Stability and Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-24 ◽  
Author(s):  
Mohammed Rizwan Sadiq Iqbal
Keyword(s):  
Magnetic Field ◽  
Inertial Force ◽  
Transverse Magnetic ◽  
Nonlinear Analyses ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Constant Strength ◽  
Long Time ◽  
The Stability ◽  
The One

The effect of air shear on the hydromagnetic instability is studied through (i) linear stability, (ii) weakly nonlinear theory, (iii) sideband stability of the filtered wave, and (iv) numerical integration of the nonlinear equation. Additionally, a discussion on the equilibria of a truncated bimodal dynamical system is performed. While the linear and weakly nonlinear analyses demonstrate the stabilizing (destabilizing) tendency of the uphill (downhill) shear, the numerics confirm the stability predictions. They show that (a) the downhill shear destabilizes the flow, (b) the time taken for the amplitudes corresponding to the uphill shear to be dominated by the one corresponding to the zero shear increases with magnetic fields strength, and (c) among the uphill shear-induced flows, it takes a long time for the wave amplitude corresponding to small shear values to become smaller than the one corresponding to large shear values when the magnetic field intensity increases. Simulations show that the streamwise and transverse velocities increase when the downhill shear acts in favor of inertial force to destabilize the flow mechanism. However, the uphill shear acts oppositely. It supports the hydrostatic pressure and magnetic field in enhancing films stability. Consequently, reduced constant flow rates and uniform velocities are observed.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

Shear-Thickening Flow Between Coaxial Cylinders

2011 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow; however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

Stability of Two-Immiscible-Fluid Systems: A Review of Canonical Plane Parallel Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Alireza Mohammadi ◽  
Alexander J. Smits
Keyword(s):  
Fluid Layer ◽  
Future Research ◽  
Immiscible Fluid ◽  
Weakly Nonlinear ◽  
Plane Parallel ◽  
Fluid Systems ◽  
Parallel Flows ◽  
Lower Fluid ◽  
And Performance ◽  
The Stability

A brief review is given on the stability of two-fluid systems. Our interest is primarily driven by drag reduction using superhydrophobic surfaces (SHS) or liquid-infused surfaces (LIS) where the longevity and performance strongly depends on the flow stability. Although the review is limited to immiscible, incompressible, Newtonian fluids with constant properties, the subject is rich in complexity. We focus on three canonical plane parallel flows as part of the general problem: pressure-driven flow, shear-driven flow, and flow down an inclined plane. Based on the linear stability, the flow may become unstable to three modes of instabilities: a Tollmein–Schlichting wave in either the upper fluid layer or the lower fluid layer, and an interfacial mode. These instabilities may be further categorized according to the physical mechanisms that drive them. Particular aspects of weakly nonlinear analyses are also discussed, and some directions for future research are suggested.

Rolls versus squares in thermal convection of fluids with temperature-dependent viscosity

1987 ◽  
Vol 178 ◽  
pp. 491-506 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Temperature Dependent Viscosity ◽  
Weakly Nonlinear ◽  
Expansion Procedure ◽  
The Stability ◽  
Dependent Viscosity

We consider finite-amplitude thermal convection, in a horizontal fluid layer. The viscosity of the fluid is dependent upon its temperature. Using a weakly nonlinear expansion procedure, we examine the stability of two-dimensional roll and three-dimensional square planforms, in order to determine which should be preferred in convection experiments. The analysis shows that the roll planform is preferred for low values of the ratio of the viscosities at the top and bottom boundaries, but the square planform is preferred for larger values of the ratio. At still larger values, subcritical convection is predicted. We also include the effects of boundaries having finite thermal conductivity, which enables favourable comparison to be made with experimental studies. A discrepancy between the present work and a previous study of this problem (Busse & Frick 1985) is discussed.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Tandem Arrangement ◽  
Square Cylinders ◽  
Shear Thickening Fluids ◽  
Power Law Index

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

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