scholarly journals Time-Periodic Heating in Boussinesq-Stokes Suspension with Three Diffusing Components

2021 ◽  
Vol 12 (5) ◽  
pp. 6516-6532
Keyword(s):  
Rayleigh Number ◽  
Perturbation Method ◽  
Convective Flow ◽  
Lower Boundary ◽  
Linear Case ◽  
Periodic Heating ◽  
Time Periodic

The effect of time-periodic heating in Boussinesq-Stokes suspension with three diffusing components has been carried out for the linear case. The correction Rayleigh number is obtained by applying the perturbation method to effectually control the convective flow by varying amplitude and frequency of modulation, and the eigenvalues are obtained by the Venezian approach. The time-periodic heating has been carried out for three cases: symmetric, asymmetric, and modulating only the lower boundary. It is found that the system is stable for smaller values whereas unstable for moderate values of frequency of modulation.

MHD Natural Convection Slip Flow through Vertical Porous Plates with Time-Periodic Boundary Conditions

2018 ◽  
Vol 388 ◽  
pp. 135-145
Author(s):  
Samuel Olumide Adesanya ◽  
L. Rundora ◽  
R.S. Lebelo ◽  
K.C. Moloi
Keyword(s):  
Convective Flow ◽  
Decomposition Method ◽  
Hartmann Number ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Periodic Boundary Conditions ◽  
Temperature Profiles ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Time Periodic

In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel is investigated. Due to channel porosity, the asymmetrical slip conditions are imposed on both walls. The coupled dimensionless partial differential equations are reduced to a system of second-order boundary-value problems based on some flow assumptions and solved by Adomian decomposition method (ADM). Variations in velocity and temperature profiles are presented and discussed in detail. The result of the analysis revealed that increasing Hartmann number decreases the flow velocity while the slip parameters enhance the flow.

Numerical Simulation of Magneto-Convection in an Enclosure

2009 ◽  
Author(s):  
M. Ghassemi ◽  
M. Pirmohammadi
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Convective Flow ◽  
Transfer Rate ◽  
Temperature Fields ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Molten Sodium ◽  
Linear Differential ◽  
The Magnetic Field

Natural-convection flow in the presence of a magnetic field in an enclosure heated from bottom and cooled from top is considered. The fluid (molten sodium) properties are function of temperature. To solve the governing non-linear differential equations (mass, momentum and energy) a finite volume code based on PATANKAR’s SIMPLER method is utilized. The results for different Rayleigh and Hartmann numbers show that the strength of the magnetic field has significant effects on the flow and temperature fields. The convection becomes stronger as the Rayleigh number increases while the magnetic field suppresses the convective flow and the heat transfer rate. When the magnetic field is weak and the Rayleigh number is high, the convection is dominant.

scholarly journals ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

2002 ◽  
Vol 12 (11) ◽  
pp. 2501-2522 ◽  
Author(s):  
ISABEL MERCADER ◽  
JOANA PRAT ◽  
EDGAR KNOBLOCH
Keyword(s):  
Rayleigh Number ◽  
Lower Boundary ◽  
Two Dimensions ◽  
External Parameter ◽  
Onset Of Convection ◽  
Current Dissipation ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Spatial Resonance ◽  
Rayleigh Benard

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature difference across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these effects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic.

scholarly journals Internal Variability of the Winter Stratosphere. Part II: Time-Dependent Forcing

2008 ◽  
Vol 65 (7) ◽  
pp. 2375-2388 ◽  
Author(s):  
R. K. Scott ◽  
L. M. Polvani ◽  
D. W. Waugh
Keyword(s):  
Lower Boundary ◽  
Polar Vortex ◽  
Internal Variability ◽  
Time Dependent ◽  
Random Wave ◽  
Frequency Locking ◽  
Wave Forcing ◽  
Wave Flux ◽  
Time Periodic ◽  
Zero Time

Abstract This paper considers the effect of time-dependent lower boundary wave forcing on the internal variability found to appear spontaneously in a stratosphere-only model when the forcing is perfectly steady. While the time-dependent forcing is found to modulate the internal variability, leading in some cases to frequency locking of the upper-stratospheric response to the forcing, the temporal and spatial structure of the variability remains similar to the case when the forcing is time independent. Experiments with a time-periodic modulation of the forcing amplitude indicate that the wave flux through the lower boundary is only partially related to the instantaneous forcing, but is more significantly influenced by the condition of the polar vortex itself. In cases of purely random wave forcing with zero time mean, the stratospheric response is similar to that obtained with steady forcing of magnitude equal to the root-mean-square of the time-varying forcing.

Natural convection in a mushy layer

1991 ◽  
Vol 224 ◽  
pp. 335-359 ◽  
Author(s):  
M. Grae Worster
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Solid Fraction ◽  
Convective Flow ◽  
Mushy Layer ◽  
Governing Equations ◽  
Downward Flow ◽  
Asymptotic Regime

Governing equations for a mushy layer are analysed in the asymptotic regime Rm [Gt ] 1, where Rm is an appropriately defined Rayleigh number. A model is proposed in which there is downward flow everywhere in the mushy layer except in and near localized chimneys, which are characterized by having zero solid fraction. Upward, convective flow within the chimneys is driven by compositional buoyancy. The radius of each chimney is determined locally by thermal balances within a boundary layer that surrounds it. Simple solutions are derived to determine the structure of the mushy layer away from the immediate vicinity of chimneys in order to demonstrate the gross effects of convection upon the solidification within the layer.

Time-Dependent Double-Diffusive Instability in a Density-Stratified Fluid along a Heated Inclined Wall

1978 ◽  
Vol 100 (4) ◽  
pp. 653-658 ◽  
Author(s):  
C. F. Chen
Keyword(s):  
Rayleigh Number ◽  
Convective Flow ◽  
Stratified Fluid ◽  
Horizontal Layer ◽  
Critical Values ◽  
Time Dependent ◽  
Free Layer ◽  
Heating Wall ◽  
Vertical Walls ◽  
Double Diffusive

We consider a stably stratified fluid contained between two parallel sloping plates. At t = 0, the lower plate is given a step increase in temperature; a time-dependent convective flow is generated. Stability of such a flow with respect to double-diffusive mechanism is analyzed. The method is the same one used by Chen [6] in treating a similar problem with vertical walls. The predicted critical values of Rayleigh number and wavelength compare favorably with those observed experimentally. No overstability is encountered up to 75 deg of inclination of the heating wall to the vertical. For a horizontal layer, however, instability starts in an overstable mode. The frequency of the overstable mode compares favorably with that predicted by Veronis [7] for a free-free layer.

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.

Natural Convective Flow in a Three Enclosure System Involving Two High Aspect Ratio Side Enclosures Joined to a Large Square Enclosure With Interfacial Heat Generation

2003 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Generation ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Square Enclosure ◽  
Number Variation ◽  
Resistance To Heat

A numerical study of free convective flow in a vertical joined three enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is joined to a second high aspect ratio rectangular side enclosure which has the same height as the first side enclosure, the two enclosures being separated by a vertical impermeable dividing wall which offers no resistance to heat transfer. The second side enclosure is joined to a larger square enclosure, the vertical dividing wall between these two enclosures also being impermeable and offering no resistance to heat transfer. The vertical wall of the square main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. There is a uniform rate of heat generation in the dividing wall between the inner side enclosure and the main enclosure. The situation considered is an approximate model of a double-paned window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. In some such cases there can be significant heat generation in the blind due to the absorbtion of solar energy, this being modeled by the heat generation in the one dividing wall. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number, dimensionless width of the side enclosures and dimensionless heat generation rate in the blind on the Nusselt number have been investigated. The results show that for a fixed Rayleigh number and for a given dimensionless first (i.e., outer) side enclosure width, there is a minimum in the Nusselt number variation with the dimensionless width of the second side enclosure. An approximate solution for the Nusselt number variation with the dimensionless width of the second side enclosure for small values of this dimensionless width has also been derived.

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