In this paper, we propose a general methodology by which a universal temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, that is valid for high Rayleigh number flows, can be recast into a correlation for the Nusselt number. We then evaluate its adequacy for three types of flows: (a) fully developed flows (e.g., the infinite channel), (b) developing flows (e.g., the vertical flat plate boundary layer), and (c) complex flows (e.g., Rayleigh-Bénard convection and the differentially heated square cavity). The correlation for the Nusselt number, in general, contains a logarithmic term, usually missing in earlier studies, with which we are able to match existing direct numerical simulations or experimental data very well for both fully developed and complex flows.
Issue Section:
Technical Briefs
1.
Boudjemadi
, R.
, Mapu
, V.
, Laurence
, D.
, and Le Quere
, P.
, 1997, “Budgets of Turbulent Stresses and Fluxes in a Vertical Slot Natural Convection at Rayleigh Ra=105 and 5.4×105
,” Int. J. Heat Fluid Flow
0142-727X, 18
, pp. 70
–79
.2.
Verseteegh
, T. A. M.
, and Nieuwstadt
, F. T. M.
, 1999, “A Direct Numerical Simulation of Natural Convection Between Two Infinite Vertical Differentially Heated Walls: Scaling Laws and Wall Functions
,” Int. J. Heat Mass Transfer
0017-9310, 42
, pp. 3673
–3693
.3.
Wang
, M.
, Fu
, S.
, and Zhang
, G.
, 2002, “Large Scale Spiral Structures in Turbulent Natural Convection Along Vertical Plates
,” Phys. Rev. E
1063-651X, 66
, pp. 066306
.4.
Betts
, P. L.
, and Bokhari
, I. H.
, 2000, “Experiments on Turbulent Natural Convection in an Enclosed Tall Cavity
,” Int. J. Heat Fluid Flow
0142-727X, 21
, pp. 675
–683
.5.
Tsuji
, T.
, and Nagano
, Y.
, 1988, “Characteristics of a Turbulent Natural Convection Boundary Layer Along a Vertical Flat Plate
,” Int. J. Heat Mass Transfer
0017-9310, 31
, pp. 2101
–2111
.6.
Cheesewright
, R.
, 1968, “Turbulent Natural Convection From a Vertical Plane Surface
,” ASME J. Heat Transfer
0022-1481, 90
, pp. 1
–8
.7.
George
, W. K.
, and Capp
, S. P.
, 1979, “A Theory for Natural Convection Turbulent Boundary Layer Next to Heated Vertical Surfaces
,” Int. J. Heat Mass Transfer
0017-9310, 22
, pp. 813
–826
.8.
Henkes
, R. A. W. M.
, 1990, “Natural Convection Boundary Layers
,” Ph.D. thesis, Delft University of Technology, The Netherlands.9.
de Vahl Davis
, G.
, and Jones
, I. P.
, 1983, “Natural Convection in a Square Cavity: A Comparison Exercise
,” Int. J. Numer. Methods Fluids
0271-2091, 3
, pp. 249
–264
.10.
Ampofo
, F.
, and Karayiannis
, T. G.
, 2003, “Experimental Benchmark Data for Turbulent Natural Convection in an Air Filled Square Cavity
,” Int. J. Heat Mass Transfer
0017-9310, 46
, pp. 3551
–3572
.11.
Cheesewright
, R.
, King
, K. J.
, and Ziai
, S.
, 1989, “Experimental Data for the Validation of Computer Codes for the Prediction of Two Dimensional Buoyant Cavity Flows
,” Significant Questions in Buoyancy Affected by Cavity Flows
, J. A. C.
Humphry
et al., eds., ASME
, New York
, pp. 75
–81
.12.
Dixit
, H. N.
, and Babu.
, V.
, 2006, “Simulation of High Rayleigh Number Natural Convection in a Square Cavity Using the Lattice Boltzmann Method
,” Int. J. Heat Mass Transfer
0017-9310, 49
, pp. 727
–739
.13.
Castaing
, B.
, Gunaratne
, G.
, Heslot
, F.
, Kadanoff
, L.
, Libchaber
, S.
, Thomae
, S.
, Wu
, X.
, Zaleski
, G.
, and Zanetti
, G.
, 1989, “Scaling of Hard Thermal Turbulence in Rayleigh-Bénard Convection
,” J. Fluid Mech.
0022-1120, 204
, pp. 1
–30
.14.
Shraiman
, B. I.
, and Siggia
, E. D.
, 1990, “Heat Transport in High-Rayleigh Number Convection
,” Phys. Rev. A
1050-2947, 42
, pp. 3650
–3653
.15.
Wu
, X. Z.
, and Libchaber
, A.
, 1992, “Scaling Relations in Thermal Turbulence: The Aspect Ratio Dependence
,” Phys. Rev. A
1050-2947, 45
, pp. 842
–845
.16.
Chavanne
, X.
, Chilla
, F.
, Chabuad
, B.
, and Castaing
, B.
, 2001, “Turbulent Rayleigh Bénard Convection in Gaseous and Liquid He
,” Phys. Fluids
1070-6631, 13
, pp. 1300
–1320
.17.
Nikolaenko
, A.
, and Ahlers
, G.
, 2003, “Nusselt Number Measurements for Turbulent Rayleigh-Bénard Convection
,” Phys. Rev. Lett.
0031-9007, 91
, pp. 084501
.18.
Niemala
, J. J.
, and Sreenivasan
, K. R.
, 2003, “Confined Turbulent Convection
,” J. Fluid Mech.
0022-1120, 481
, pp. 355
–384
.19.
Roche
, P. E.
, Castaing
, B.
, Chabaud
, B.
, and Hebral
, B.
, 2004, “Heat Transfer in Turbulent Rayleigh-Bénard Convection Below the Ultimate Regime
,” J. Low Temp. Phys.
0022-2291, 134
, pp. 1011
–1042
.20.
Kerr
, R.
, 1996, “Rayleigh Number Scaling in Numerical Convection
,” J. Fluid Mech.
0022-1120, 310
, pp. 139
–179
.21.
Grötzbach
, G.
, 1990, “Simulation of Turbulent Flow and Heat Transfer for Selected Problems of Nuclear Thermal-Hydraulics
,” Proc. First International Conference on Supercomputing in Nuclear Applications (SNA ’90)
, Mito
, Japan
.22.
Wörner
, M.
, 1994, “Direkte Simulation of Turbulenter Rayleigh-Bénard Konvektion in flüssigem Natrium
,” Ph.D. thesis, University of Karlsruhe.23.
Hartlep
, T.
, 2004, “Strukturbildung and Turbulenz. Eine Numerische Studie zur Turbulenten Rayleigh-Bénard Konvektion
,” Ph.D. thesis, University of Göttingen.24.
Hölling
, M.
, and Herwig
, H.
, 2006, “Asymptotic Analysis of Heat Transfer in Turbulent Rayleigh Bénard Convection
,” International Journal of Heat and Mass Transfer
, to be published.25.
Schlichting
, H.
, and Gersten
, K.
, 2003, Boundary Layer Theory
, Springer Verlag
, Heidelberg, Germany
.26.
Hölling
, M.
, and Herwig
, H.
, 2005, “Asymptotic Analysis of the Near Wall Region of Turbulent Natural Convection Flows
,” J. Fluid Mech.
0022-1120, 541
, pp. 383
–397
.27.
Bejan
, A.
, 1984, Convection Heat Transfer
, John Wiley
, New York
.28.
Wolfstein
, M.
, 1969, “The Velocity and Temperature Distribution of One-Dimensional Flow With Turbulence Augmentation and Pressure Gradient
,” Int. J. Heat Mass Transfer
0017-9310, 12
, pp. 301
–318
.29.
FLUENT 6.2 Documentation, 2005, FLUENT INC, USA.
30.
Tieszen
, S.
, Ooi
, A.
, Durbin
, P.
, and Behnia
, M.
, 1998, “Modelling of Natural Convection Heat Transfer
,” Proceedings of the Centre for Turbulence Research
, Stanford University
, CA
, pp. 287
–301
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