Transient Stability and Convection in Impulsively Heated Porous Layers

2005 ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristofferson ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Transient Stability ◽  
Critical Rayleigh Number ◽  
Lower Surface ◽  
Darcy Number ◽  
Temperature Profiles ◽  
Temperature Dependent Viscosity ◽  
Onset Of Convection ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

Experiments are reported on initial instability and convection in a porous medium impulsively heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height-to-diameter ratio of 1.9. Heating is accomplished with a constant flux lower surface and a constant temperature upper surface. Results include measurement of the initial transition to convection, overall heat transfer coefficient over a range of Rayleigh-Darcy numbers, and temperature profiles. Time-averaged temperature profiles suggest the existence of a unicellular flow over the range of Rayleigh numbers of the present experiments. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac = 83/(1.08η−0.08η2) for 0.02 < η < 0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is represented by a new correlation form, Nu=0.047Ra0.91Pr0.11μμ00.72, where Ra is the Rayleigh-Darcy number, 400 < Ra < 5000, and the viscosity ratio is found sufficient to account for strongly temperature-dependent viscosity.

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

scholarly journals Effect of Soret and Temperature Dependent Viscosity on Thermohaline Convection in a Ferrofluid Saturating a Porous Medium

2014 ◽  
Vol 19 (2) ◽  
pp. 321-336
Author(s):  
R. Sekar ◽  
K. Raju
Keyword(s):  
Porous Medium ◽  
Fluid Layer ◽  
Effect Of Temperature ◽  
Stationary Mode ◽  
Free Boundaries ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Onset Of Convection ◽  
Wide Range ◽  
Dependent Viscosity

Abstract Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

Onset of convection in a variable-viscosity fluid

1982 ◽  
Vol 120 ◽  
pp. 411-431 ◽  
Author(s):  
Karl C. Stengel ◽  
Dean S. Oliver ◽  
John R. Booker
Keyword(s):  
Rayleigh Number ◽  
Viscosity Ratio ◽  
Variable Viscosity ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Onset Of Convection ◽  
Numerical Predictions ◽  
Dependent Viscosity

The Rayleigh number R, in a horizontal layer with temperature-dependent viscosity can be based on the viscosity at T0, the mean of the boundary temperatures. The critical Rayleigh number Roc for fluids with exponential and super-exponential viscosity variation is nearly constant at low values of the ratio of the viscosities at the top and bottom boundaries; increases at moderate values of the viscosity ratio, reaching a maximum at a ratio of about 3000, and then decreases. This behaviour is explained by a simple physical argument based on the idea that convection begins first in the sublayer with maximum Rayleigh number. The prediction of Palm (1960) that certain types of temperature-dependent viscosity always decrease Roc is confirmed by numerical results but is not relevant to the viscosity variations typical of real liquids. The infinitesimal-amplitude state assumed by linear theory in calculating Roc does not exist because the convection jumps immediately to a finite amplitude at R0c. We observe a heat-flux jump at R0c exceeding 10% when the viscosity ratio exceeds 150. However, experimental measurements of R0c for glycerol up to a viscosity ratio of 3400 are in good agreement with the numerical predictions when the effects of a temperature-dependent expansion coefficient and thermal diffusivity are included.

Heat transport by parallel-roll convection in a rectangular container

1987 ◽  
Vol 185 ◽  
pp. 205-234 ◽  
Author(s):  
R. W. Walden ◽  
Paul Kolodner ◽  
A. Passner ◽  
C. M. Surko
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Critical Rayleigh Number ◽  
Equation Model ◽  
Onset Of Convection ◽  
Infinite Layer ◽  
Lateral Extent ◽  
Prandtl Numbers ◽  
Rayleigh Numbers ◽  
Good Agreement

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

Natural Convection Inside a Bidisperse Porous Medium Enclosure

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Arunn Narasimhan ◽  
B. V. K. Reddy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Phase ◽  
Darcy Number ◽  
The Core ◽  
Side Walls ◽  
Porous Blocks ◽  
Rayleigh Numbers

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks (N2), macropore volume fraction (ϕE), and internal Darcy number (DaI) for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both DaI and DaE. At low Ra values, Nu is strongly affected by both DaI and ϕE. When N2 is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of Raϕ, DaE, DaI, and N2. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, RaϕDaE.

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