Thermal Stability of Horizontally Superposed Porous and Fluid Layers

1989 ◽  
Vol 111 (2) ◽  
pp. 357-362 ◽  
Author(s):  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Darcy Number ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Porous Layers ◽  
Fluid Layers ◽  
Comprehensive Picture

The results of stability analyses for the onset of convective motion are reported for the following three horizontally superposed systems of porous and fluid layers: (a) a porous layer sandwiched between two fluid layers with rigid top and bottom boundaries, (b) a fluid layer overlying a layer of porous medium, and (c) a fluid layer sandwiched between two porous layers. By changing the depth ratio dˆ from zero to infinity, a set of stability criteria (i.e., the critical Rayleigh number Rac and the critical wave number ac) is obtained, ranging from the case of a fluid layer between two rigid boundaries to the case of a porous layer between two impermeable boundaries. The effects of k/km (the thermal conductivity ratio), δ (the square root of the Darcy number), and α (the nondimensional proportionality constant in the slip condition) on Rac and ac are also examined in detail. The results in this paper, combined with those reported previously for Case (a) (Pillatsis et al., 1987), will provide a comprehensive picture of the interaction between a porous and a fluid layer.

Thermal Instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layers

1987 ◽  
Vol 109 (3) ◽  
pp. 677-682 ◽  
Author(s):  
G. Pillatsis ◽  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Layer ◽  
Thermal Instability ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Fluid Layers

A linear stability analysis is performed for a horizontal Darcy porous layer of depth 2dm sandwiched between two fluid layers of depth d (each) with the top and bottom boundaries being dynamically free and kept at fixed temperatures. The Beavers–Joseph condition is employed as one of the interfacial boundary conditions between the fluid and the porous layer. The critical Rayleigh number and the horizontal wave number for the onset of convective motion depend on the following four nondimensional parameters: dˆ ( = dm/d, the depth ratio), δ ( = K/dm with K being the permeability of the porous medium), α (the proportionality constant in the Beavers–Joseph condition), and k/km (the thermal conductivity ratio). In order to analyze the effect of these parameters on the stability condition, a set of numerical solutions is obtained in terms of a convergent series for the respective layers, for the case in which the thickness of the porous layer is much greater than that of the fluid layer. A comparison of this study with the previously obtained exact solution for the case of constant heat flux boundaries is made to illustrate quantitative effects of the interfacial and the top/bottom boundaries on the thermal instability of a combined system of porous and fluid layers.

Throughflow effects on convective instability in superposed fluid and porous layers

1991 ◽  
Vol 231 ◽  
pp. 113-133 ◽  
Author(s):  
Falin Chen
Keyword(s):  
Porous Layer ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Single Layer ◽  
Layer Depth ◽  
Onset Of Convection ◽  
Precise Control ◽  
Porous Layers

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

scholarly journals Mixed Convection in Superposed Nanofluid and Porous Layers Inside Lid-Driven Square Cavity

2015 ◽  
Vol 10 (2) ◽  
Keyword(s):  
Mixed Convection ◽  
Porous Layer ◽  
Volume Fraction ◽  
Darcy Number ◽  
Momentum Exchange ◽  
Square Cavity ◽  
Porous Layers ◽  
Adverse Action ◽  
Nanoparticles Volume Fraction ◽  
The Right

Mixed convection in a lid-driven composite square cavity is studied numerically. The cavity is composed of two layers; a Cu–water nanofluid layer superposed a porous layer. The porous layer is saturated with the same nanofluid. The left and right walls of the cavity are thermally insulated. The bottom wall which is in contact with the porous layer is isothermally heated and being lid to the left, while the top wall is isothermally cooled and being lid to the right. Cavity walls are impermeable except the interface between the porous layer and the nanofluid. Maxwell-Brinkman model is invoked for the momentum exchange within the porous layer. Equations govern the conservation of mass, momentum, and energy within the two layers were modeled and solved numerically using under successive relaxation (USR) up- wind finite difference scheme. Four pertinent parameters are studied; nanoparticles volume fraction φ (0.0 - 0.05), porous layer thickness Wp (0.1 - 0.9), Darcy number Da (10-7 – 10-1), and Richardson number Ri (0.01 - 10). The results have showed that the existence of the porous layer in a specified value can enhance the convective heat transfer when Ri ≥ 1, while an adverse action of nanoparticles is recorded when Da ≥ 10-4.

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

1989 ◽  
Vol 207 ◽  
pp. 311-321 ◽  
Author(s):  
Falin Chen ◽  
C. F. Chen
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Convective Stability ◽  
Onset Of Convection ◽  
Temperature Distributions ◽  
Critical Wavelength ◽  
Crystal Film ◽  
Flux Curve

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).

scholarly journals Effect of Vertical Vibrations on the Onset of Binary Convection

2013 ◽  
Vol 18 (3) ◽  
pp. 899-910 ◽  
Author(s):  
M.S. Swamy
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Lewis Number ◽  
Wave Number ◽  
Closed Form Expression ◽  
Effective Control ◽  
Regular Perturbation ◽  
Binary Fluid ◽  
Vertical Vibrations

Abstract In the present work the linear stability analysis of double diffusive convection in a binary fluid layer is performed. The major intention of this study is to investigate the influence of time-periodic vertical vibrations on the onset threshold. A regular perturbation method is used to compute the critical Rayleigh number and wave number. A closed form expression for the shift in the critical Rayleigh number is calculated as a function of frequency of modulation, the solute Rayleigh number, Lewis number, and Prandtl number. These parameters are found to have a significant influence on the onset criterion; therefore the effective control of convection is achieved by proper tuning of these parameters. Vertical vibrations are found to enhance the stability of a binary fluid layer heated and salted from below. The results of this study are useful in the areas of crystal growth in micro-gravity conditions and also in material processing industries where vertical vibrations are involved

scholarly journals Concordancing in ESP Class Rooms

2014 ◽  
Vol 4 (3) ◽  
pp. 434-439
Author(s):  
Sameh Benna ◽  
Olfa Bayoudh
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Analysis ◽  
Wave Number ◽  
Gravity Modulation ◽  
Non Linear ◽  
The Stability ◽  
Time Periodic

The effect of time periodic body force (or g-jitter or gravity modulation) on the onset of Rayleigh-Bnard electro-convention in a micropolar fluid layer is investigated by making linear and non-linear stability analysis. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. This normally occurs in satellites and in vehicles connected with micro gravity simulation studies. A linear and non-linear analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. The linear theory is based on normal mode analysis and perturbation method. Small amplitude of modulation is used to compute the critical Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transport.

Flows in Rotating Cylinders With a Porous Lining

2007 ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

Convection in a viscoelastic fluid-saturated sparsely packed porous layer

1990 ◽  
Vol 68 (12) ◽  
pp. 1446-1453 ◽  
Author(s):  
N. Rudraiah ◽  
P. V. Radhadevi ◽  
P. N. Kaloni
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Critical Rayleigh Number ◽  
Maxwell Fluid ◽  
Wave Number ◽  
Jeffrey Fluid ◽  
Oscillatory Convection ◽  
Viscoelastic Parameters ◽  
Jeffreys Model

The linear stability of a viscoelastic fluid-saturated sparsely packed porous layer heated from below is studied analytically using the Darcy–Brinkman–Jeffreys model with different boundary combinations. The Galerkin technique is employed to determine the criterion for the onset of oscillatory convection. The effects of the viscoelastic parameters, the Prandtl number, and the porous parameter on the critical Rayleigh number, the wave number, and the frequency are analyzed. The results are compared with those obtained for both a Darcy–Jeffrey fluid and a Maxwell fluid. It is shown that under certain conditions for the viscoelastic parameters, the flow is overstable. The possibility of the occurrence of bifurcation is also discussed.

Subcritical convective instability Part 1. Fluid layers

1966 ◽  
Vol 26 (4) ◽  
pp. 753-768 ◽  
Author(s):  
Daniel D. Joseph ◽  
C. C. Shir
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Source ◽  
Linear Theory ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Heat Sources ◽  
Fluid Layers ◽  
Rayleigh Numbers

This paper elaborates on the assertion that energy methods provide an always mathematically rigorous and a sometimes physically precise theory of sub-critical convective instability. The general theory, without explicit solutions, is used to deduce that the critical Rayleigh number is a monotonically increasing function of the Nusselt number, that this increase is very slow if the Nusselt number is large, and that a fluid layer heated from below and internally is definitely stable when $RA < \widetilde{RA}(N_s) > 1708/(N_s + 1)$ where Ns is a heat source parameter and $\widetilde{RA}$ is a critical Rayleigh number. This last problem is also solved numerically and the result compared with linear theory. The critical Rayleigh numbers given by energy theory are slightly less than those given by linear theory, this difference increasing from zero with the magnitude of the heat-source intensity. To previous results proving the non-existence of subcritical instabilities in the absence of heat sources is appended this result giving a narrow band of Rayleigh numbers as possibilities for subcritical instabilities.

The Effect of Suction on the Stability of Fluid between Horizontal Plates at Differing Temperatures

1985 ◽  
Vol 199 (2) ◽  
pp. 145-151 ◽  
Author(s):  
M M Sorour ◽  
M A Hassab ◽  
F A Elewa
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Stability Criteria ◽  
Thermal Boundary Conditions ◽  
Wide Range ◽  
Fluid Layers ◽  
The Stability ◽  
Horizontal Fluid Layer

The linear stability theory is applied to study the effect of suction on the stability criteria of a horizontal fluid layer confined between two thin porous surfaces heated from below. This investigation covers a wide range of Reynolds number 0 ≥ Re ≥ 30, and Prandtl number 0.72 ≥ Pr ≥ 100. The results show that the critical Rayleigh number increases with Peclet number, and is independent of Pr as far as Re < 3. However, for Re > 3 the critical Rayleigh number is function of both Pr and Pe. In addition, the analysis is extended to study the effect of suction on the stability of two special superimposed fluid layers. The results in the latter case indicate a more stabilizing effect. Furthermore, the effect of thermal boundary conditions is also investigated.

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