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On linear stability of Rayleigh–Bénard Poiseuille flow of viscoplastic fluids
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10.1063/1.2987435
/content/aip/journal/pof2/20/10/10.1063/1.2987435
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2987435

Figures

Image of FIG. 1.
FIG. 1.

Velocity and temperature profiles for . The unyielded region corresponds to the gray region which is delimited by dashed lines.

Image of FIG. 2.
FIG. 2.

Evolution of the effective viscosity in the lower yielded region for different values of . [(—–: , ); (- - -: , ); (: , ); (: , )].

Image of FIG. 3.
FIG. 3.

Critical modes of the perturbation: temperature (left) and stream function (right) (—: modulus of and ); (- - -: real part of and ); (: imaginary part of and ); and .

Image of FIG. 4.
FIG. 4.

Critical conditions as function of the width of the plug zone for , : (a) critical Rayleigh number; (b) critical wave number.

Image of FIG. 5.
FIG. 5.

Critical (a) Rayleigh number and (b) wave number as function of the width of the plug zone for , . [Squares: in the Orr–Sommerfeld equation; circles: , dashed lines: (a) , (b) .] “V” means viscous dissipation effect, “S” the viscosity stratification effect, and “M” the modification of the unyielded zone width.

Image of FIG. 6.
FIG. 6.

Critical (a) Rayleigh number and (b) wave number as function of the width of the plug zone for , . [Nabla symbols: , when Bingham terms are forced to zero; dashed lines: (a) and (b) ; triangles: .] S is used for the viscosity stratification effect and “T” for the effect of the thermal conduction in the unyielded region.

Image of FIG. 7.
FIG. 7.

Critical modes of the perturbation: temperature (left) and stream function (right) (—: , ); (- - -: , ); (: , ); and .

Image of FIG. 8.
FIG. 8.

Sufficient stability conditions of mixed convection flow involving Bingham fluid at . Stability diagram in the (a) plane and (b) plane [triangles: ], [squares: ], [circles: ].

Image of FIG. 9.
FIG. 9.

Critical (a) Rayleigh number and (b) wave number as function of the width of the plug zone for , . (Circles: ; squares: in the Orr–Sommerfeld equation; nabla symbols: when Bingham terms are forced to zero; dashed line: ; triangles: , .)

Image of FIG. 10.
FIG. 10.

Comparison between critical Rayleigh numbers obtained by the linear modal and energetic analyses, respectively, as function of the Reynolds number for and (△ symbols: ), ( symbols: ).

Image of FIG. 11.
FIG. 11.

Computed results of (circles) and its asymptotic behavior (straight line) given by Eq. (80) for . Comparison with (black squares).

Tables

Generic image for table
Table I.

Critical conditions in terms of and for different values of (plane Poiseuille case).

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/content/aip/journal/pof2/20/10/10.1063/1.2987435
2008-10-02
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On linear stability of Rayleigh–Bénard Poiseuille flow of viscoplastic fluids
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2987435
10.1063/1.2987435
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