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.

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 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.

scholarly journals Stability of a Buoyant Oldroyd-B Flow Saturating a Vertical Porous Layer with Open Boundaries

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 375
Author(s):  
Stefano Lazzari ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Critical Rayleigh Number ◽  
Stationary Flow ◽  
Vertical Axis ◽  
Seepage Flow ◽  
Neutral Stability ◽  
Linear Viscoelastic ◽  
Infinite Height ◽  
Limiting Case

The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with permeable and isothermal boundaries is investigated. Seepage flow is modelled through an extended version of Darcy’s law which accounts for the Oldroyd-B rheology. The basic stationary flow is parallel to the vertical axis and describes a single-cell pattern where the cell has an infinite height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. This analysis is performed numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are evaluated for different retardation time and relaxation time characteristics of the fluid. The study highlights the extent to which the viscoelasticity has a destabilising effect on the buoyant flow. For the limiting case of a Newtonian fluid, the known results available in the literature are recovered, namely a critical value of the Darcy–Rayleigh number equal to 197.081 and a corresponding critical wavenumber of 1.05950.

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.

scholarly journals Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

2021 ◽  
Author(s):  
Florinda Capone ◽  
Jacopo A. Gianfrani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Linear Instability ◽  
Brinkman Model ◽  
Linear Instability Analysis ◽  
Non Equilibrium

AbstractThe onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

scholarly journals Vadasz Number Effects on Convection in a Vertical Rotating Porous Layer, Placed Far from Axis of Rotation, and Subjected to Internal Heat Generation and Centrifugal Jitter

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 728-738
Author(s):  
Saneshan Govender
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Time Derivative ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Stability Criteria ◽  
Axis Of Rotation ◽  
Vadasz Number ◽  
The Impact

The flow and heat transfer in a rotating vertical porous layer, placed far from the axis of rotation, and subjected to internal heat generation and centrifugal jitter, is considered. The linear stability theory is used to determine the convection threshold, in terms of the critical Rayleigh number. Typical liquids used in engineering applications and heavy liquid metals are used to demonstrate conditions at which the Vadasz number is sufficiently small to warrant the retention of the time derivative in the momentum equation. When considering low amplitude and high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions. In summary, when the Vadasz number is large, centrifugal jitter has no impact on the convection stability criteria. In contrast, when the Vadasz number is small, centrifugal jitter impacts the convection stability criteria.

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.

Sign in / Sign up

Export Citation Format

Share Document