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Rayleigh-Bénard convection for viscoplastic fluids
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10.1063/1.4790521
/content/aip/journal/pof2/25/2/10.1063/1.4790521
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4790521

Figures

Image of FIG. 1.
FIG. 1.

Rayleigh-Bénard setup.

Image of FIG. 2.
FIG. 2.

Rheological properties of Carbopol gels at = 293 K. (a) Steady-state rheometry: Shear stress as a function of shear rate. (Black diamonds: τ = 0.0047 Pa, diamonds: τ = 0.006 Pa, plus: τ = 0.01 Pa, crosses: τ = 0.009 Pa, black circles: τ = 0.031 Pa, triangles: τ = 0.045 Pa, black squares: τ = 0.104 Pa, dashed lines: Herschel-Bulkley model). (b) Oscillatory rheometry: Variation of (black diamonds) and (white diamonds) as function of the strain for a Carbopol gel τ = 0.006 Pa, and a frequency = 0.1 Hz.

Image of FIG. 3.
FIG. 3.

Steady-state response of a Carbopol gel (τ = 0.031 Pa) when different lower surfaces are used at = 293 K. In the case of rough or treated surfaces (black circles: sandpaper, white circles: treated PMMA) the abscissa represents the shear rate and the ordinate axis the shear stress. In the case of smooth surfaces or non-treated surface (black diamonds: glass, black triangles: copper alloy, white diamonds: raw PMMA), the results represent an average of the shear stress vs an apparent shear rate.

Image of FIG. 4.
FIG. 4.

Temperature difference Δ as a function of the total heat input , for different yield stress values of Carbopol gels. (Black diamonds: τ = 0.0047 Pa, diamonds: τ = 0.006 Pa, plus: τ = 0.01 Pa, crosses: τ = 0.009 Pa, black circles: τ = 0.031 Pa, triangles: τ = 0.045 Pa, black squares: τ = 0.104 Pa ; PMMA surfaces in the cavity-circles with crosses: treated PMMA and τ = 0.031 Pa, white circles: raw PMMA and τ = 0.031 Pa). (a) = 0.017 m; (b) = 0.03 m.

Image of FIG. 5.
FIG. 5.

Temperature difference Δ as a function of the total heat input , for different values of , τ, and slip condition (untreated copper alloy, glass, and PMMA surfaces). The black (resp. white) symbols represent the results obtained by increasing (resp. decreasing) . (a) = 0.01 m, τ = 0.006 Pa; (b): = 0.017 m, τ = 0.01 Pa.

Image of FIG. 6.
FIG. 6.

Temperature difference Δ as a function of the total heat input , for the value of = 0.01 m, τ = 0.031 Pa, and no-slip conditions (treated PMMA surfaces at walls). The black (resp. white) symbols represent the results obtained by increasing (resp. decreasing) .

Image of FIG. 7.
FIG. 7.

(a) Variation of βΔ as a function of for different Carbopol gels and surface conditions (white diamonds: τ = 0.006 Pa, slip surfaces (glass and copper alloy); crosses: τ = 0.009 Pa, slip surfaces (glass and copper alloy), black circles: τ = 0.031 Pa, slip surfaces (glass and copper alloy); white circles, white circles with crosses: τ = 0.031 Pa and, respectively, slip surfaces (raw PMMA), no-slip surfaces (treated PMMA)). (b) Variation of βΔ as a function of for one Carbopol gel (τ = 0.031 Pa) for the reference case: no-slip surfaces (treated PMMA).

Image of FIG. 8.
FIG. 8.

Evolution of the Nusselt number as a function of the inverse of the yield number 1/ for one Carbopol gel τ = 0.031 Pa, = 0.017 m (white circles with crosses: treated PMMA, white circles: raw PMMA).

Image of FIG. 9.
FIG. 9.

Shadowgraph visualizations for one Carbopol (τ = 0.031 Pa) at different values, = 0.017 m. (a) = 0.98, 1/ = 12; (b) = 1.12, 1/ = 59; (c) = 1.39, 1/ = 60; (d) = 1.84, 1/ = 63.

Tables

Generic image for table
Table I.

Identification of the gels coefficients and the values of yield stress obtained by both methods: Flow and oscillatory measurements at = 293 K.

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/content/aip/journal/pof2/25/2/10.1063/1.4790521
2013-02-08
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rayleigh-Bénard convection for viscoplastic fluids
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4790521
10.1063/1.4790521
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