On the Thermal Instability of Superposed Porous and Fluid Layers

1982 ◽  
Vol 104 (1) ◽  
pp. 160-165 ◽  
Author(s):  
C. W. Somerton ◽  
I. Catton
Keyword(s):  
Rayleigh Number ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Stability Parameter ◽  
Graphical Form ◽  
Onset Of Convection ◽  
Porous Bed ◽  
Wide Range ◽  
Fluid Layers ◽  
Independent Parameters

A solution is presented for the problem of predicting the onset of convection for a system consisting of a volumetrically heated porous bed saturated with and overlaid with a fluid, heated or cooled from below. Results are presented in graphical form in terms of the external Rayleigh number based on the fluid layer, which is shown to be the sole stability parameter of the problem. A wide range of independent parameters are investigated and physical justification for the behavior of the instability with respect to them is given. Finally, the results are compared with the two bounding cases of the problem and are found to be in agreement with them.

Convection in heated fluid layers subjected to time-periodic horizontal accelerations

2008 ◽  
Vol 596 ◽  
pp. 313-332 ◽  
Author(s):  
W. PESCH ◽  
D. PALANIAPPAN ◽  
J. TAO ◽  
F. H. BUSSE
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Shear Instability ◽  
Heteroclinic Cycle ◽  
Onset Of Convection ◽  
Acceleration Amplitude ◽  
Fluid Layers ◽  
Roll Axis ◽  
Small Acceleration

A theoretical study is presented of convection in a horizontal fluid layer heated from below or above which is periodically accelerated in its plane. The analysis is based on Galerkin methods as well as on direct numerical simulations of the underlying Boussinesq equations.Shaking in a fixed direction breaks the original isotropy of the layer. At onset of convection and at small acceleration, we find longitudinal rolls, where the roll axis aligns parallel to the acceleration direction. With increasing acceleration amplitude, a shear instability takes over and transverse rolls with the axis perpendicular to the shaking direction nucleate at onset. In the nonlinear regime, the longitudinal rolls become unstable against transverse modulations very close to onset which leads to a kind of domain chaos between patches of symmetry degenerated oblique rolls.In the case of circular shaking, the system is isotropic in the time average sense, however, with a broken chiral symmetry. The onset of convection corresponds to the transverse roll case studied before with the roll axis selected spontaneously. With increasing Rayleigh number, a heteroclinic cycle is observed with the roll changing its orientation periodically in time. At even higher Rayleigh number, this heteroclinic cycle becomes chaotic similarly to the case of the Küppers–Lortz instability.

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.

scholarly journals Conduction and convection heat transfer characteristics of water-based au nanofluids in a square cavity with differentially heated side walls subjected to constant temperatures

2014 ◽  
Vol 18 (suppl.1) ◽  
pp. 189-200 ◽  
Author(s):  
Primoz Ternik ◽  
Rebeka Rudolf
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Base Fluid ◽  
Volume Fraction ◽  
Heat Transfer Characteristics ◽  
Square Cavity ◽  
Onset Of Convection ◽  
Transfer Characteristics ◽  
Wide Range ◽  
Water Based

The present work deals with the natural convection in a square cavity filled with the water-based Au nanofluid. The cavity is heated on the vertical and cooled from the adjacent wall, while the other two horizontal walls are adiabatic. The governing differential equations have been solved by the standard finite volume method and the hydrodynamic and thermal fields were coupled together using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticles? volume fraction on the heat transfer characteristics of Au nanofluids at the given base fluid?s (i.e. water) Rayleigh number. Accurate results are presented over a wide range of the base fluid Rayleigh number and the volume fraction of Au nanoparticles. It is shown that adding nanoparticles in a base fluid delays the onset of convection. Contrary to what is argued by many authors, we show by numerical simulations that the use of nanofluids can reduce the heat transfer rate instead of increasing it.

Thermal Instability of Compressible Micropolar Fluid in the Presence of Suspended Particles

2012 ◽  
Vol 28 (2) ◽  
pp. 239-246 ◽  
Author(s):  
N. Rani ◽  
S. K. Tomar
Keyword(s):  
Dispersion Relation ◽  
Rayleigh Number ◽  
Micropolar Fluid ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Stationary Convection ◽  
Presence And Absence ◽  
Number Curve

AbstractA problem of thermal instability of a compressible micropolar fluid layer heated from below in the presence of suspended particles has been investigated. Dispersion relation is derived and Rayleigh number curve is then plotted against the wavenumber at different values of compressibility parameter for a model example. Compressibility is found to be responsible to destabilize the system in the presence and absence of suspended particles for both stationary and over stationary convection.

scholarly journals Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source

2019 ◽  
Vol 8 (1) ◽  
pp. 546-558 ◽  
Author(s):  
Amit Mahajan ◽  
Reena Nandal
Keyword(s):  
Porous Media ◽  
Heat Generation ◽  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Heat Extraction ◽  
Graphical Form ◽  
Nonlinear Stability Analysis ◽  
Penetrative Convection ◽  
Onset Of Convection

Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.

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.

Thermosolutal convection in a solution with large negative Soret coefficient

1976 ◽  
Vol 74 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Douglas R. Caldwell
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Power Law ◽  
Fluid Layer ◽  
Pure Water ◽  
Low Frequency ◽  
Thermosolutal Convection ◽  
Soret Coefficient ◽  
Onset Of Convection ◽  
Rayleigh Benard

The large negative Soret coefficient of 1N-LiI gives rise in a Rayleigh-Bénard experiment to a density distribution which is observed to stabilize the fluid layer for values of the Rayleigh number as large as 196 times the value of 1708 for the onset of convection in a pure fluid. The Soret transport also affects the convective heat flux. A power law relating heat flux and temperature difference is found with the same exponent as is found in pure fluids but with a lower value of the multiplicative constant. The Rayleigh number at the onset of power-law behaviour depends on the Soret coefficient. Three types of oscillation are seen: transient oscillations at onset, low frequency fluctuations at low Rayleigh number, and higher frequency oscillations similar to those observed in pure water. The intermediate state found after onset in NaCl solutions is not found in LiI.

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.

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