Experimental and numerical studies (using the finite element method) were conducted in a rectangular vessel for a high Prandtl number fluid (Pr = 880 at 25°C). The pattern of convective rolls is perturbed by lateral heating of one of the smaller sides of the box. The wave number of the roll pattern is within a narrow range (±10 percent at R = 4.6RC where R and Rc are the Rayleigh number and its critical value of Be´nard convection). The formation of a large roll induced by the lateral heating causes a slight variation in the wave number of the rolls, accompanied by the disappearance of pairs of rolls, or single rolls, depending on the boundary conditions at the other small side of the enclosure. In all instances, this disappearance respects the mechanical coupling between the rolls. Temperature and velocity fields are assessed, as well as the heat transfer. The transient states observed during the experimentation are well reproduced by the two-dimensional numerical model developed for this study.
Issue Section:
Natural and Mixed Convection
1.
Ahlers
G.
1980
, “Effect of Departures From the Oberbeck-Boussinesq Approximation on the Heat Transport of Horizontal Convecting Fluid Layers
,” J. Fluid Mech.
, Vol. 98
, pp. 137
–148
.2.
Bathe
K. J.
Dong
J.
1987
, “Solution of Incompressible Viscous Fluid Flow with Heat Transfer Using ADINA-F
,” Computer & Structures
, Vol. 26
, pp. 17
–31
.3.
Bercovier
M.
Pironneau
O.
1979
, “Error Estimates for Finite Element Solution of the Stokes Problem in the Primitive Variables
,” Numer. Math.
, Vol. 33
, pp. 211
–224
.4.
Berge, P., Pomeau, Y., and Vidal, Ch., 1988, L’ordre dans le chaos, Hermann, Paris.
5.
Breton, J. L., 1989, “Similitude et stabilite´ des e´coulements de convection naturelle dans une cavite´ ferme´e a` haut nombre de Rayleigh (Pie`ce d’Habitation),” Thesis, Universite´ Paul Sabatier, Toulouse, France.
6.
Bu¨hler
K.
Kirchartz
K. R.
Oertel
H.
1979
, “Steady Convection in a Horizontal Fluid Layer
,” Acta Mech.
, Vol. 31
, pp. 155
–171
.7.
Busse
F. H.
1967
, “The Stability of Finite Amplitude Cellular Convection and Its Relation to an Extremum Principle
,” J. Fluid Mech.
, Vol. 30
, Part 4, pp. 625
–649
.8.
Busse
F. H.
Whitehead
J. A.
1971
, “Instabilities of Convection Rolls in a High Prandtl Number Fluid
,” J. Fluid Mech.
, Vol. 47
, pp. 305
–320
.9.
Busse
F. H.
1978
, “Non Linear Properties of Convection
,” Rep. Prog. Phys.
, Vol. 41
, pp. 1929
–1967
.10.
Carey, G. F., and Oden, J. T., 1986, Finite Elements: Fluid Mechanics, Vol. 6, Prentice-Hall, Englewood Cliffs, NJ.
11.
Catton
I.
1972
, “The Effect of Insulating Vertical Walls on the Onset of Motion in a Fluid Heated From Below
,” Int. J. Heat and Mass Transfer
, Vol. 15
, pp. 665
–672
.12.
Cerisier
P.
Rahal
S.
Cordonnier
J.
Lebon
G.
1998
, “Thermal Influence of Boundaries on the Onset of Rayleigh-Be´nard Convection
,” Int. J. Heat and Mass Transfer
, Vol. 41
, pp. 3309
–3320
.13.
Chikhaoui, A., 1989, “Stabilite´ des e´coulements thermoconvectifs dans unecouche fluide soumise a` un gradient thermique horizontal,” Thesis, Universite´ d’Aix-Marseille II, France.
14.
Croquette
V.
1989
, “Convective Pattern Dynamics of Low Prandtl Number: Part I
,” Contemp. Phys.
, Vol. 30
, pp. 113
–133
.15.
Daniels
P. G.
Wang
P.
1994
, “Numerical Study of Thermal Convection in Tall Laterally Heated Cavities
,” Int. J. Heat and Mass Transfer
, Vol. 37
, pp. 375
–386
.16.
De Vahl Davis
G.
Jones
I. P.
1983
, “Natural Convection in a Square Cavity: A Comparison Exercise
,” Int. J. Numerical Methods in Fluids
, Vol. 3
, pp. 227
–248
.17.
De Vahl Davis
G.
1983
, “Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution
,” Int. J. Numerical Methods in Fluids
, Vol. 3
, pp. 249
–264
.18.
Elder
J. W.
1965
, “Turbulence Free Convection in a Vertical Slot
,” J. Fluid Mech.
, Vol. 23
, pp. 99
–111
.19.
Farhadieh
R.
Tankin
R. S.
1974
, “Interferometric Study of Two-Dimensional Be´nard Convection Cells
,” J. Fluid Mech.
, Vol. 66
, pp. 739
–752
.20.
Gollub
J. P.
Mc Carriar
A. R.
Steinman
J. F.
1982
, “Convection Pattern Evolution and Secondary Instabilities
,” J. Fluid Mech.
, Vol. 125
, pp. 259
–281
.21.
Gray
D. D.
Giorgini
A.
1976
, “The Validity of the Boussinesq Approximation for Liquids and Gases
,” Int. J. Heat and Mass Transfer
, Vol. 19
, pp. 545
–551
.22.
Imberger
J.
1974
, “Natural Convection in a Shallow Cavity with Differentially Heated End Walls. Part 3. Experimental Results
,” J. Fluid Mech.
, Vol. 65
, pp. 247
–260
.23.
Jaeger
M.
Medale
M.
Randriamampianina
A.
1996
, “Numerical Modeling of Buoyancy-Driven Flows in a Rotating Cylindrical Cavity: Comparison of a Finite Element Model with a Spectral Model
,” Numerical Heat Transfer, Part A
, Vol. 30
, pp. 779
–798
.24.
Karyakin
Y. E.
Sokovishin
YU. A.
Martynenko
O. G.
1988
, “Transient Natural Convection in Triangular Enclosures
,” Int. J. Heat and Mass Transfer
, Vol. 31
, pp. 1759
–1766
.25.
Kirchartz
K. R.
Oertel
H.
1988
, “Three-Dimensional Thermal Cellular Convection in Rectangular Boxes
,” J. Fluid Mech.
, Vol. 192
, pp. 249
–186
.26.
Kolodner
P.
Walden
R. W.
Passner
A.
Surko
C. M.
1986
, “Rayleigh-Be´nard Convection in an Intermediate-Aspect-Ratio Rectangular Container
,” J. Fluid Mech.
, Vol. 163
, pp. 195
–226
.27.
Koschmieder
E. L.
1996
, “On Convection on a Uniformly Heated Plane
,” Beitr. Phys. Atmos.
, Vol. 39
, pp. 1
–11
.28.
Koschmieder
E. L.
Pallas
S. G.
1974
, “Heat Transfer Through a Shallow, Horizontal Convecting Fluid Layer
,” Int. J. Heat Mass Transfer
, Vol. 17
, pp. 991
–1002
.29.
Koschmieder
E. L.
1974
, “Be´nard Convection
,” Adv. Chem. Phys.
, Vol. 26
, pp. 177
–212
.30.
Koschmieder, E. L., 1993, Be´nard Cells and Taylor Vortices, Batchelor, ed. Cambridge University Press, Cambridge, UK.
31.
Krishnamurti
R.
1970
, “On the Transition to Turbulent Convection. Part 1. The Transition From Two-to Three Dimensional Flow
,” J. Fluid Mech.
, Vol. 42
, pp. 295
–307
.32.
Krishnan
R.
1985
, “A Finite Element Approximation of the Be´nard Problem
,” Communications in Applied Numerical Methods
, Vol. 1
, pp. 317
–324
.33.
Le Quere
P.
1991
, “Accurate Solutions to the Square Thermally Driven Cavity at High Rayleigh Number
,” Computer Fluids
, Vol. 20
, No. 1
, pp. 29
–41
.34.
Leontiev
A. J.
Kirdyashkin
A. G.
1968
, “Experimental Study of Flow Patterns and Temperature Fields in Horizontal Free Convection Liquid Layers
,” Int. J. Heat and Mass Transfer
, Vol. 11
, pp. 1461
–1466
.35.
Manneville, P., 1990, Dissipative Structures and Weak Turbulence, Academic Press, London.
36.
Nield
D. A.
1994
, “Convection Induced by an Inclined Temperature Gradient in a Shallow Horizontal Layer
,” Int. J. Heat and Fluid Flow
, Vol. 15
, No. 2
, pp. 157
–162
.37.
Paolucci
S.
Chenoweth
D. R.
1987
, “Departures from the Boussinesq Approximation in Laminar Be´nard Convection
,” Phys. Fluids
, Vol. 30
, pp. 1561
–1564
.38.
Patankar
S. V.
Spalding
D. B.
1972
, “A Calculation Procedure for Heat, Mass and Momentum Transfert in Three Dimensional Parabolic Flows
,” Int. J. Heat and Mass Transfer
, Vol. 15
, pp. 1787
–1806
.39.
Patterson
C.
Imberger
J.
1980
, “Unsteady Natural Convection in Rectangular Cavity
,” J. Fluid Mech.
, Vol. 100
, pp. 65
–86
.40.
Schlu¨ter
A.
Lortz
D.
Busse
F. M.
1965
, “On the Stability of Steady Finite Amplitude Convection
,” J. Fluid Mech.
, Vol. 23
, pp. 129
–144
.41.
Schoepf
W. J.
Patterson
C.
1995
, “Natural Convection in Side Heated Cavity: Visualization of the Initial Flow Features
,” Fluid Mech.
, Vol. 295
, pp. 357
–379
.42.
Simpkins
P. G.
Chen
K. S.
1986
, “Convection in Horizontal Cavities
,” J. Fluid Mech.
, Vol. 166
, pp. 21
–39
.43.
Stork
K.
Mu¨ller
U.
1972
, “Convection in Boxes: Experiments
,” J. Fluid Mech.
, Vol. 54
, pp. 599
–611
.44.
Taylor
C.
Ijam
A. Z.
1979
, “A Finite Element Numerical Solution of Natural Convection in Enclosed Cavities
,” Computer Methods in Applied Mechanics and Engineering
, Vol. 19
, pp. 429
–446
.45.
Wang
P.
Daniels
P. G.
1994
, “Numerical Study of Thermal Convection in Shallow Cavities with Conducting Boundaries
,” Int. J. Heat and Mass Transfer
, Vol. 37
, No. 3
, pp. 387
–399
.46.
Willis
G. E.
Deardorff
J. W.
Somerville
R. C.
1972
, “Roll Diameter Dependence in Rayleigh Convection and Its Effect Upon the Heat Flux
,” J. Fluid Mech.
, Vol. 54
, pp. 351
–368
.
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