Abstract
The effect of sidewall conductance on Nusselt number for the Rayleigh-Bénard convection is examined by performing nearly identical sets of experiments with sidewalls made of three different materials. These experimental results are utilized to extrapolate and estimate the Nusselt number for an ideal zero-thermal-conductivity sidewall case, which is the case when the sidewalls are perfectly insulating. A semi-analytical model is proposed, based on the concept of extended surfaces, to compute the discrepancy in Nusselt number caused by the presence of finite thermal conductance of the sidewalls. The predictions obtained using this model are found to be in good agreement with the corresponding experimentally determined values.
Issue Section:
Micro/Nanoscale Heat Transfer
References
1.
Goldstein
,
R. J.
, and
Tokuda
,
S.
, 1980
, “
Heat Transfer by Thermal Convection at High Rayleigh Numbers
,” Int. J. Heat Mass Transfer
,
23
(5
), pp. 738
–740
.10.1016/0017-9310(80)90022-82.
Castaing
,
B.
,
Gunaratne
,
G.
,
Heslot
,
F.
,
Kadanoff
,
L.
,
Libchaber
,
A.
,
Thomae
,
S.
,
Wu
,
X. Z.
,
Zaleski
,
S.
, and
Zanetti
,
G.
, 1989
, “
Scaling of Hard Thermal Turbulence in Rayleigh-Bénard Convection
,” J. Fluid Mech.
,
204
(1
), pp. 1
–30
.10.1017/S00221120890016433.
Goldstein
,
R. J.
,
Chiang
,
H. D.
, and
See
,
D. L.
, 1990
, “
High Rayleigh-Number Convection in a Horizontal Enclosure
,” J. Fluid Mech.
,
213
(1
), pp. 111
–126
.10.1017/S00221120900022454.
Wu
,
X. Z.
, and
Libchaber
,
A.
, 1992
, “
Scaling Relations in Thermal Turbulence: The Aspect-Ratio Dependence
,” Phys. Rev. A
,
45
(2
), p. 842
.10.1103/PhysRevA.45.8425.
Belmonte
,
A.
,
Tilgner
,
A.
, and
Libchaber
,
A.
, 1994
, “
Temperature and Velocity Boundary Layers in Turbulent Convection
,” Phys. Rev. E
,
50
(1
), pp. 269
–281
.10.1103/PhysRevE.50.2696.
Ciliberto
,
S.
,
Cioni
,
S.
, and
Laroche
,
C.
, 1996
, “
Large-Scale Flow Properties of Turbulent Thermal Convection
,” Phys. Rev. E
,
54
(6
), pp. R5901
–R5904
.10.1103/PhysRevE.54.R59017.
Xu
,
X.
,
Bajaj
,
K. M.
, and
Ahlers
,
G.
, 2000
, “
Heat Transport in Turbulent Rayleigh-Bénard Convection
,” Phys. Rev. Lett.
,
84
(19
), p. 4357
.10.1103/PhysRevLett.84.43578.
Niemela
,
J. J.
,
Skrbek
,
L.
,
Sreenivasan
,
K. R.
, and
Donnelly
,
R. J.
, 2000
, “
Turbulent Convection at Very High Rayleigh Numbers
,” Nature
,
404
(6780
), pp. 837
–840
.10.1038/350090369.
Chavanne
,
X.
,
Chilla
,
F.
,
Chabaud
,
B.
,
Castaing
,
B.
, and
Hebral
,
B.
, 2001
, “
Turbulent Rayleigh-Bénard Convection in Gaseous and Liquid He
,” Phys. Fluids
,
13
(5
), pp. 1300
–1320
.10.1063/1.135568310.
Fleischer
,
A. S.
, and
Goldstein
,
R. J.
, 2002
, “
High-Rayleigh-Number Convection of Pressurized Gases in a Horizontal Enclosure
,” J. Fluid Mech.
,
469
, pp. 1
–12
.10.1017/S002211200200174X11.
Xia
,
K. Q.
,
Lam
,
S.
, and
Zhou
,
S. Q.
, 2002
, “
Heat-Flux Measurement in High-Prandtl-Number Turbulent Rayleigh-Bénard Convection
,” Phys. Rev. Lett.
,
88
(6
), p. 064501
.10.1103/PhysRevLett.88.06450112.
Niemela
,
J. J.
, and
Sreenivasan
,
K. R.
, 2003
, “
Confined Turbulent Convection
,” J. Fluid Mech.
,
481
, pp. 355
–384
.10.1017/S002211200300408713.
Nikolaenko
,
A.
,
Brown
,
E.
,
Funfschilling
,
D.
, and
Ahlers
,
G.
, 2005
, “
Heat Transport by Turbulent Rayleigh-Bénard Convection in Cylindrical Cells With Aspect Ratio One and Less
,” J. Fluid Mech.
,
523
, pp. 251
–260
.10.1017/S002211200400228914.
Niemela
,
J. J.
, and
Sreenivasan
,
K. R.
, 2006
, “
Turbulent Convection at High Rayleigh Numbers and Aspect Ratio 4
,” J. Fluid Mech.
,
557
, pp. 411
–422
.10.1017/S002211200600966915.
Urban
,
P.
,
Hanzelka
,
P.
,
Musilová
,
V.
,
Králík
,
T.
,
La Mantia
,
M.
,
Srnka
,
A.
, and
Skrbek
,
L.
, 2014
, “
Heat Transfer in Cryogenic Helium Gas by Turbulent Rayleigh-Bénard Convection in a Cylindrical Cell of Aspect Ratio 1
,” New J. Phys.
,
16
(5
), p. 053042
.10.1088/1367-2630/16/5/05304216.
Chong
,
K. L.
, and
Xia
,
K. Q.
, 2016
, “
Exploring the Severely Confined Regime in Rayleigh-Bénard Convection
,” J. Fluid Mech.
,
805
, p. R4–1
.10.1017/jfm.2016.57817.
Ahlers
,
G.
, 2000
, “
Effect of Sidewall Conductance on Heat-Transport Measurements for Turbulent Rayleigh-Bénard Convection
,” Phys. Rev. E
,
63
(1
), p. 0153031
.10.1103/PhysRevE.63.01530318.
Roche
,
P. E.
,
Castaing
,
B.
,
Chabaud
,
B.
,
Hébral
,
B.
, and
Sommeria
,
J.
, 2001
, “
Side Wall Effects in Rayleigh-Bénard Experiments
,” Eur. Phys. J. B
,
24
(3
), pp. 405
–408
.10.1007/s10051-001-8690-519.
Verzicco
,
R.
, 2002
, “
Sidewall Finite-Conductivity Effects in Confined Turbulent Thermal Convection
,” J. Fluid Mech.
,
473
, pp. 201
–210
.10.1017/S002211200200250120.
Madanan
,
U.
, and
Goldstein
,
R. J.
, 2018
, “
Prediction and Correction of Sidewall Conductance for Natural Convection in Horizontal Enclosures
,” 16th International Heat Transfer Conference (IHTC
), Beijing, China, Aug. 10–15, pp. 2731–2740.10.1615/IHTC16.cov.02135921.
Madanan
,
U.
, and
Goldstein
,
R. J.
, 2019
, “
Thermal Convection in Horizontal Rectangular Enclosures at Moderate Rayleigh Numbers: Effect of Sidewall Conductance and Aspect Ratio
,” Int. J. Heat Mass Transfer
,
136
, pp. 178
–185
.10.1016/j.ijheatmasstransfer.2019.02.07622.
Madanan
,
U.
, and
Goldstein
,
R. J.
, 2019
, “
Experimental Investigation on Very-high-Rayleigh-Number Thermal Convection in Tilted Rectangular Enclosures
,” Int. J. Heat Mass Transfer
,
139
, pp. 121
–129
.10.1016/j.ijheatmasstransfer.2019.05.01123.
Kline
,
S. J.
, and
Mcclintock
,
F. A.
, 1953
, “
Describing Uncertainties in Single-Sample Experiments
,” Mech. Eng.
,
75
, pp. 3
–8
.Copyright © 2019 by ASME
You do not currently have access to this content.