Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots

Chen, Yen-Ming; Pearlstein, Arne J.

doi:10.1017/s0022112089000236

Cited by 77 publications

(41 citation statements)

References 47 publications

(75 reference statements)

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“…The effect of horizontal AC electric field on the stability of a plane convective flow of a vertical dielectric fluid layer has been investigated for over a wide range of Prandtl numbers by Takashima and Hamabata [16] . They found that a transition from stationary to travelling-wave instability occurs at a certain value of Pr between 12.4 and 12.5, which was later supported by Chen and Pearlstein [17] . Fujimura [18] showed that the transition value of Pr is given by 12.45425644.…”

Section: Introductionmentioning

confidence: 75%

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Shankar

Kumar

Shivakumara

2016

Applied Mathematical Modelling

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a b s t r a c tThe combined effect of couple stresses and a uniform horizontal AC electric field on the stability of buoyancy-driven parallel shear flow of a vertical dielectric fluid between vertical surfaces maintained at constant but different temperatures is investigated. Applying linear stability theory, stability equations are derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c , the critical wave number a c and the critical wave speed c c are computed for wide ranges of couple stress parameter c , AC electric Rayleigh number R ea and the Prandtl number Pr . Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number even in the presence of couple stresses but increases significantly with increasing c . Moreover, the effect of increasing R ea is to instill instability, while the couple stress parameter shows destabilizing effect in the stationary mode but it exhibits a dual behavior if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

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Section: Introductionmentioning

confidence: 75%

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Shankar

Kumar

Shivakumara

2016

Applied Mathematical Modelling

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“…This triple-valued stability boundary is a direct consequence of the existence of closed disconnected neutral curves ͑CDNCs͒ previously found in stability analyses of isothermal flows, 7,31 quiescent fluid layers in which the density depends on two or more stratifying agencies with different diffusivities, [34][35][36][37] in a buoyancy-driven flow in an inclined layer, 38 in differentially rotating flows between differentially heated concentric vertical cylinders, 39 and in a two-phase parallel shear flow with a deformable interface. 40 For Re= 140 ͑a value near the middle of the triple-valued range͒, the critical neutral curves in Fig.…”

Section: ␤ = 001mentioning

confidence: 59%

Linear stability of spiral Poiseuille flow with a radial temperature gradient: Centrifugal buoyancy effects

Cotrell

McFadden

2005

Physics of Fluids

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For spiral Poiseuille flow with a radial temperature gradient and radius ratio = R i / R o = 0.5, we have computed complete linear stability boundaries for several values of the rotation rate ratio = ⍀ o / ⍀ i , where R i and R o are the inner and outer cylinder radii, respectively, and ⍀ i and ⍀ o are the corresponding ͑signed͒ angular speeds. The effects of gravity are neglected, but the variation of density with temperature induces radial buoyancy effects through the centripetal acceleration term in the radial momentum equation. The analysis extends previous results with no axial flow ͑Reynolds number Re=0͒ to the range of Re for which the annular Poiseuille flow is stable and accounts for arbitrary disturbances of infinitesimal amplitude. For Ͻ 2 and a temperature gradient consistent with the Boussinesq approximation, we show that over the entire range of Re considered the stability boundaries do not differ significantly from those found for the isothermal case by Cotrell and Pearlstein ͓"The connection between centrifugal instability and TollmienSchlichting-like instability for spiral Poiseuille flow," J. Fluid. Mech. 509, 331 ͑2004͔͒. For Ͼ 2 and Re= 0, we show for the first time that the flow is destabilized for any positive value of the radial buoyancy parameter ͑i.e., ␤ = ␣ o ⌬T͒, where ⌬T = T o − T i is the temperature difference between the outer and inner cylinder walls, respectively, and ␣ o is the coefficient of thermal expansion. This differs significantly from the isothermal results which show that there is no linear instability for 0 ഛ Reഛ Re min in the absence of centrifugal buoyancy effects, where Re min is the turning point value in the isothermal results.

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“…Thangam and Chen [5] found that variable viscosity fluid becomes less stable when P r exceeds 100. But a more accurate study made by Chen and Pearlstein [8] exhibited the effect of viscosity variation even for low values of P r. In addition they reported that Gr c is weakly dependent on P r when the onset of stability is steady in nature and verified the asymptotic relation Gr c ∝ P r −1/2 . The stability of nonisothermal flow induced by a constant pressure gradient between two parallel plates was discussed by Pinarbasi and Liakopoulos [10] with exponential temperature-viscosity relationship.…”

Section: Introductionmentioning

confidence: 93%

“…Unfortunately the expansion functions used by some of the Russian works cited by Gershuni and Zhukhovitskii [4] did not form a complete set (Gallagher [7]). Hence to remove the disparity and clarify the issue of P r tr , Chen and Pearlstein [8] reexamined the study using more number of terms in their Galerkin method. Their study revealed the value 12.5 for P r tr .…”

Section: Introductionmentioning

confidence: 99%

Hydromagnetic stability of convective flow of variable viscosity fluids generated by internal heat sources

Saravanan¹,

Kandaswamy

2004

Z. angew. Math. Phys.

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The stability of convective motion of a variable viscosity fluid contained in a vertical layer generated by uniformly distributed internal heat sources in the presence of a transverse magnetic field is studied. The viscosity of the fluid is assumed to depend on the temperature. The undisturbed steady state motion is assumed to consist of purely vertical motion with a nonlinear temperature distribution across the layer. The equations were solved by the spectral collocation method. The results show that thermal running waves are the most unstable modes and dominate the shear modes when the viscosity decreases.

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Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots

Cited by 77 publications

References 47 publications

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Linear stability of spiral Poiseuille flow with a radial temperature gradient: Centrifugal buoyancy effects

Hydromagnetic stability of convective flow of variable viscosity fluids generated by internal heat sources

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