In terms of a dimensionless number, ΠN∼Ra/1+Pr−1, introduced by Arpacı (1986, 1990, 1995) for buoyancy driven flows, Ra and Pr respectively being the usual Rayleigh and Prandtl numbers, two well-known correlations (Churchill and Chu, 1975) for natural convection next to a vertical isothermal plate are reduced in terms of ΠL=Ra/1+0.492Pr−1 to Nu=0.67ΠL1/4,103⩽ΠL⩽109, for the laminar case, and in terms of ΠT=Ra/1+0.164Pr−1 to Nu=0.15ΠT1/3,109⩽ΠT⩽1012, for the turbulent case.

Issue Section:
Technical Notes
Keywords:
Heat Transfer, Microscale, Modeling, Natural Convection, Turbulent, natural convection, laminar flow, boundary layer turbulence, boundary layers
Topics:
Buoyancy, Flow (Dynamics), Heat transfer, Natural convection, Turbulence
1.
Arpacı
;,
V. S.
,
1986
, “
Microscales of Turbulence and Heat Transfer Correlations
,”
Int. J. Heat Mass Transf.
,
29
, pp.
1071
–
1078
.
2.
Arpacı
;,
V. S.
,
1990
, “
Microscales of Turbulence and Heat Transfer Correlations
,”
Annu. Rev. Heat Transfer
,
3
, pp.
195
–
231
.
3.
Arpacı
;,
V. S.
,
1995
, “
Buoyant Turbulent Flow Driven by Internal Energy Generation
,”
Int. J. Heat Mass Transf.
,
38
, pp.
2761
–
2770
.
4.
Squire, H. B., 1938, Modern Developments in Fluid Dynamics, S. Goldstein ed., Oxford University Press, Oxford.
5.
Catton, I., 1978, “Natural Convection in Enclosures,” 6th Int. Heat Transfer Conf., Toronto, 6, pp. 13–31.
6.
Bertin
,
H.
, and
Ozoe
,
H.
,
1986
, “
Numerical Study of Two-dimensional Natural Convection in a Horizontal Fluid Layer Heated from Below, by Finite-Element Method: Influence of Prandtl Number
,”
Int. J. Heat Mass Transf.
,
29
, pp.
439
–
449
.
7.
Bejan
,
A.
, and
Lage
,
J. L.
,
1990
, “
The Prandtl Number Effect on the Transition in Natural Convection along a Vertical Surface
,”
ASME J. Heat Transfer
,
112
, pp.
787
–
790
.
8.
Vitharana
,
V. L.
, and
Lykoudis
,
P. S.
,
1994
, “
Criteria for Predicting the Transition to Turbulence in Natural Convection along a Vertical Surface
,”
ASME J. Heat Transfer
,
116
, pp.
633
–
638
.
9.
Arpacı
;,
V. S.
, and
Li
,
C. Y.
,
1995
, “
Turbulent Forced Diffusion Flames
,”
Combust. Flame
,
102
, pp.
170
–
178
.
10.
Arpacı
;,
V. S.
, and
Selamet
,
A.
,
1991
, “
Microscales of Buoyancy Driven Turbulent Diffusion Flames
,”
Combust. Flame
,
86
, pp.
203
–
215
.
11.
Arpacı
;,
V. S.
, and
Kao
,
S.-H.
,
1997
, “
Microscales of Turbulent Rotating Flows
,”
Int. J. Heat Mass Transf.
,
40
, pp.
3819
–
3826
.
12.
Arpacı
;,
V. S.
, and
Kao
,
S.-H.
,
1998
, “
Thermocapillary Driven Turbulent Heat Transfer
”
ASME J. Heat Transfer
,
120
, pp.
214
–
219
.
13.
Tennekes, H., and Lumley, J. L., 1972, A First Course in Turbulence, MIT Press, Cambridge, MA.
14.
Churchill
,
S. W.
, and
Chu
,
H. H. S.
,
1975
, “
Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate
,”
Int. J. Heat Mass Transf.
,
18
, pp.
1323
–
1329
.
15.
Le Fevre, E. J., 1956, “Laminar Free Convection from a Vertical Plane Surface,” Proc. 9th Int. Congress on Applied Mechanics, Brussels, 4, p. 168.
16.
McDonald
,
J. S.
, and
Connolly
,
T. J.
,
1960
, “
Investigation of Natural Convection Heat Transfer in Liquid Sodium
,”
Nucl. Sci. Eng.
,
8
, pp.
369
–
377
.
Copyright © 2001
 by ASME
You do not currently have access to this content.