Thermal Instability of Convection in a Rotating Nanofluid Saturated Porous Layer Placed at a Finite Distance From the Axis of Rotation

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
S. Govender
Keyword(s):  
Porous Layer ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Analytical Investigation ◽  
Onset Of Convection ◽  
Axis Of Rotation ◽  
Offset Distance ◽  
Gravity Effects ◽  
Saturated Porous Layer ◽  
Finite Distance

An analytical investigation for the onset of convection in a vertical porous layer saturated by a nanofluid is presented when the porous layer is placed some finite distance from the axis of rotation. A linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid. This study reconfirms that the Taylor number and gravity effects are passive, and that the most critical mode is roll cells aligned with the vertical axis of rotation. The critical Rayleigh number is presented in terms of the nanofluid parameters and offset distance for stationary convection.

Thermal Instability in a Rotating Vertical Porous Layer Saturated by a Nanofluid

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
S. Govender
Keyword(s):  
Stability Analysis ◽  
Porous Layer ◽  
Thermal Instability ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Analytical Investigation ◽  
Oscillatory Convection ◽  
Critical Mode ◽  
Axis Of Rotation ◽  
Gravity Effects

An analytical investigation of the onset on convection in a vertical porous layer saturated by a nanofluid is presented. The Darcy model is used for the vertical porous layer and a linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid. This study reveals that the Taylor number and gravity effects are passive, and that the most critical mode is roll cells aligned with the vertical axis of rotation. The critical Rayleigh number is presented in terms of the nanofluid parameters for both stationary and oscillatory convection.

Onset of Convection in a Fluid Saturated Porous Layer Overlying a Solid Layer Which is Heated by Constant Flux

1999 ◽  
Vol 121 (4) ◽  
pp. 1094-1097 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Critical Rayleigh Number ◽  
Hydrothermal Systems ◽  
Solid Layer ◽  
Onset Of Convection ◽  
Constant Flux ◽  
Saturated Porous Layer ◽  
Bottom Heating ◽  
Temperature Heating

The thermoconvective stability of a porous layer overlying a solid layer is important in seafloor hydrothermal systems and thermal insulation problems. The case for constant flux bottom heating is considered. The critical Rayleigh number for the porous layer is found to increase with the thickness of the solid layer, a result opposite to constant temperature heating.

scholarly journals The Effect of Open Boundaries on the Buoyant Viscoelastic Flow in a Vertical Porous Layer

2021 ◽  
Author(s):  
Stefano Lazzari ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Critical Rayleigh Number ◽  
Stationary Flow ◽  
Vertical Axis ◽  
Seepage Flow ◽  
Neutral Stability ◽  
Saturated Porous Layer ◽  
Linear Viscoelastic ◽  
Vertical Height

The Oldroyd–B model for a linear viscoelastic fluid is employed to investigate the buoyant flow in a vertical porous layer with permeable boundaries kept at different uniform temperatures. Seepage flow in the viscoelastic fluid saturated porous layer is modelled through an extended version of Darcy’s law taking into account the Oldroyd–B rheology. The basic stationary flow is parallel to the vertical axis and describes a single–cell vertical pattern where the cell has an infinite vertical height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. The neutral stability curves and the values of the critical Rayleigh number are evaluated numerically for different retardation time and relaxation time characteristics of the fluid.

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

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.

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).

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