Thermal convection below a conducting lid of variable extent: Heat flow scalings and two-dimensional, infinite Prandtl number numerical simulations

2003 ◽  
Vol 15 (2) ◽  
pp. 455-466 ◽  
Author(s):  
A. Lenardic ◽  
L. Moresi
Keyword(s):  
Heat Flow ◽  
Prandtl Number ◽  
Numerical Simulations ◽  
Thermal Convection ◽  
Two Dimensional ◽  
Variable Extent

SYMMETRIC LARGE-SCALE VELOCITY FIELDS IN TWO-DIMENSIONAL THERMAL CONVECTION

1994 ◽  
Vol 04 (05) ◽  
pp. 1369-1374 ◽  
Author(s):  
J. PRAT ◽  
I. MERCADER ◽  
J.M. MASSAGUER
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Velocity Profile ◽  
Numerical Simulations ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Profile ◽  
Large Scale ◽  
Velocity Fields ◽  
Two Dimensional

Recent experiments on thermal convection in finite containers [Krishnamurti & Howard, 1981; Howard & Krishnamurti, 1986] show the presence of flows spanning the largest dimension of the container. Numerical simulations of 2D thermal convection showing large-scale flows of this kind have been presented elsewhere [Prat et al., 1993a, 1993b]. In every known example the large scale velocity field has been found to display a vertical profile either antisymmetric or showing rather small departures from antisymmetry. In contrast, theoretical group arguments support the existence of symmetric velocity profiles. In the present paper it will be shown that large-scale velocity fields with vertically symmetric velocity profile do exist. In spite of these flows not being dominant in the range of parameters explored, their geometry and dynamics will be discussed on the basis of a linear stability analysis.

Nonlinear thermal convection with finite conducting boundaries

1985 ◽  
Vol 152 ◽  
pp. 113-123 ◽  
Author(s):  
N. Riahi
Keyword(s):  
Stability Analysis ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Convection Pattern ◽  
Square Cells

Finite-amplitude thermal convection in a horizontal layer with finite conducting boundaries is investigated. The nonlinear steady problem is solved by a perturbation technique, and the preferred mode of convection is determined by a stability analysis. Square cells are found to be the preferred form of convection in a semi-infinite three-dimensional region Ω in the (γb,γt, P)-space (γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and P is the Prandtl number). Two-dimensional rolls are found to be the preferred convection pattern outside Ω. The dependence on γb, γt and P of the heat transported by convection is computed for the various solutions analysed in the paper.

Steady Rayleigh–Be´nard Convection in a Two-Layer System of Immiscible Liquids

1996 ◽  
Vol 118 (2) ◽  
pp. 366-373 ◽  
Author(s):  
A. Prakash ◽  
J. N. Koster
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection ◽  
Reasonable Agreement ◽  
Two Dimensional ◽  
Thermal Coupling ◽  
Layer System ◽  
Immiscible Liquids ◽  
Mechanical Coupling ◽  
Buoyancy Forces ◽  
Coupling Mode

Two-dimensional thermal convection in a system of two immiscible liquids heated from below is studied experimentally and numerically. Convection in the two-layer system is characterized by two distinct coupling modes between the layers. They are mechanical coupling and thermal coupling. These two coupling modes are visualized experimentally and found to be in reasonable agreement with numerical simulations. When buoyancy forces in both layers are of similar strength, thermal coupling is preferred. The mechanical coupling mode dominates when the buoyancy forces are very different in both layers.

scholarly journals Thermal convection in a magnetized conducting fluid with the Cattaneo–Christov heat-flow model

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160649 ◽  
Author(s):  
J. J. Bissell
Keyword(s):  
Rayleigh Number ◽  
Heat Flow ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Flow Model ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Conducting Fluid ◽  
Heat Flow Model ◽  
The Impact

By substituting the Cattaneo–Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar ( Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number R c ( c ) ( Q ) which exhibits inhibition of convection by the field according to R c ( c ) → π 2 Q as Q → ∞ , where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number R c ( o ) ( Q , P 1 , P 2 , C ) is given by a more complicated function of the thermal Prandtl number P 1 , magnetic Prandtl number P 2 and Cattaneo number C . To elucidate features of this dependence, we neglect P 2 (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour R c ( o ) → π Q / C , as Q → ∞ . One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value C T ( Q ); indeed, crucially we show that when Q is large, C T ∝ 1 / Q , meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.

Effect of Prandtl Number in Turbulent Buoyant Jet Simulation

2013 ◽  
Vol 631-632 ◽  
pp. 1001-1005
Author(s):  
Shao Bo Wang ◽  
Shen Guang Fang ◽  
Li Qin Cui
Keyword(s):  
Numerical Simulation ◽  
Prandtl Number ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Numerical Results ◽  
Two Dimensional ◽  
Turbulent Prandtl Number ◽  
Buoyant Jet ◽  
Reasonable Range ◽  
Axial Concentration

Turbulent Prandtl number used in numerical simulation has effect on exact prediction of velocity and heat transferring with two dimensional buoyant mathematical models. Various Prandtl number values advised by experiments are used to study its effect on numerical results approaching to real ones with model under axisymmetric coordinate. It shows that axial velocities can’t be affected by using various values of of Prandtl number in numerical simulations and can be predicted well. However, it affects the exact prediction of axial concentration to extent, and a smaller value of Prandtl number tends to forecast a smaller axial concentration than real one, and vice versa. A reasonable range of turbulent Prandtl number for various Reynold numbers was suggested.

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

1990 ◽  
Vol 55 (3-4) ◽  
pp. 137-160 ◽  
Author(s):  
B. J. Travis ◽  
C. Anderson ◽  
J. Baumgardner ◽  
C. W. Gable ◽  
B. H. Hager ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Two Dimensional ◽  
Cartesian Geometry

The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection

1990 ◽  
Vol 216 ◽  
pp. 71-91 ◽  
Author(s):  
Bryan Travis ◽  
Peter Olson ◽  
Gerald Schubert
Keyword(s):  
Aspect Ratio ◽  
Prandtl Number ◽  
Time Dependence ◽  
Thermal Convection ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
The Stability

The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra < 20000) calculations of the stability of two-dimensional rolls to cross-roll disturbances are in agreement with the predictions of Bolton & Busse for a fluid with a large but finite Prandtl number. Within the range 2 × 104 < Ra [les ] 5 × 105, steady rolls with basic wavenumber α > 2.22 (aspect ratio < 1.41) are stable solutions. Two-dimensional rolls with basic wavenumber α < 1.96 (aspect ratio > 1.6) are time dependent for Ra > 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra [les ] 105, but one case at Ra = 5 × 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box. started from random initial conditions. Calculations in a 3 × 3 × 1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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