The Effect of Nonlinear Density Stratification on the Stability of a Vertical Water Layer in the Conduction Regime

Shaaban, Aly H.; Özişik, M.N.

doi:10.1115/1.3245531

Cited by 7 publications

(3 citation statements)

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“…For some Pr, our neutral curves appear to be disconnected ( figure 3a, 6). We note that the steady and oscillatory neutral curves reported for various Pr by Birikh et al (1972), Bergholz (1978), and Shaaban & Ozisik (1983) are qualitatively similar to ours, although the trial functions used by Birikh et al do not form a complete set, the basic state considered by Bergholz includes a streamwise temperature gradient, and the equation of state used by Shaaban & Ozisik includes a density maximum.…”

Section: Constant-viscosity Jluid In a Vertical Slotsupporting

confidence: 80%

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

Chen

Pearlstein

1989

J. Fluid Mech.

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The stability of the buoyancy-driven parallel shear flow of a variable-viscosity Newtonian fluid between vertical or inclined plates maintained at different temperatures is studied theoretically. The analysis is capable of dealing with arbitrary viscosity-temperature relations. Depending on the Prandtl number, angle of inclination, and form of the viscosity-temperature variation, the flow may become unstable with respect to two-dimensional longitudinal or transverse disturbances. Outstanding questions arising in previous investigations of the stability of parallel free-convection flows of constant-viscosity fluids in inclined slots and of variable-viscosity fluids in vertical slots are discussed. We find that, in a variable-viscosity fluid, non-monotonic dependence of the critical Rayleigh number on the inclination angle can occur at significantly higher Prandtl numbers than is possible in the constant-viscosity case. Results are also presented for the stability of the free-convection flow of several glycerol-water solutions in an inclined slot.

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Section: Constant-viscosity Jluid In a Vertical Slotsupporting

confidence: 80%

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

Chen

Pearlstein

1989

J. Fluid Mech.

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“…The onset of multicellular convection patterns is a typical phenomenon also for vertical fluid layers [7][8][9], where a side-heating configuration is induced by boundaries kept at different uniform temperatures. Interestingly enough, the onset of multicellular convection patterns destabilizing the conduction regime was ruled out in the case of a vertical porous slab.…”

Section: Introductionmentioning

confidence: 99%

Anisotropy and the Onset of the Thermoconvective Instability in a Vertical Porous Layer

Barletta

Celli

2021

Journal of Heat Transfer

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The thermoconvective instability of the parallel vertical flow in a fluid saturated porous layer bounded by parallel open boundaries is studied. The open boundaries are assumed to be kept at constant uniform pressure while their temperatures are uniform and different, thus forcing a horizontal temperature gradient across the layer. The anisotropic permeability of the porous layer is accounted for by assuming the principal axes to be oriented along the directions perpendicular and parallel to the layer boundaries. A linear stability analysis based on the Fourier normal modes of perturbation is carried out by testing the effect of the inclination of the normal mode wave vector to the vertical. The neutral stability curves and the critical Rayleigh number for the onset of the instability are evaluated by solving numerically the stability eigenvalue problem.

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“…Thangam, Zebib and Chen (1981) and Yanase and Kohno (1985) treated the case of fluid with a vertical salinity gradient. Water near the maximum density point was considered by Hassab and Sorour (1982) and Shaaban and Ozisik (1983). Internal1y heated fluid in a vertical layer was treated by Takashima (1983Takashima ( , 1990 and Takashima and Hamabata (1985), and internal1y heated fluid in an inclined layer was treated by Takashima (1989Takashima ( ,1991.…”

Section: Introductionmentioning

confidence: 99%

The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of a transverse magnetic field

Tomita

1994

Fluid Dyn. Res.

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The stability of natural convection of an electrically conducting fluid which is confined between two parallel vertical plates maintained at constant and different temperatures and is permeated by a transverse magnetic field is analyzed using linear stability theory. In deriving the equations governing the stability, a simplification is made using the fact that the magnetic Prandtl number Pm for most electrically conducting fluids is extremely small. The Chebyshev collocation method is used to obtain the eigenvalue equation, which is then solved numerically. The critical Grashof number Go the critical wavenumber a., and the critical wave speed c.. are obtained for a wide range of the Prandtl number P and for several selected values of the Hartmann number M. It is found that the magnetic field has a stabilizing effect on the convection flow against both stationary and travelling-wave disturbances. The detailed values of P, Gp a., and cc at the point of transition from stationary to travelling-wave mode are also obtained for several selected values of M.

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The Effect of Nonlinear Density Stratification on the Stability of a Vertical Water Layer in the Conduction Regime

Cited by 7 publications

References 0 publications

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

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

Anisotropy and the Onset of the Thermoconvective Instability in a Vertical Porous Layer

The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of a transverse magnetic field

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