The complex interaction of forced and natural convections depends on flow regime and flow direction. Aiding flow occurs when both driving forces act in the same direction (heating upflow fluid and cooling downflow fluid), opposing flow occurs when they act in different directions (cooling upflow fluid and heating downflow fluid). To evaluate mixed convection methods, Heat Transfer Research, Inc. (HTRI) recently collected water and propylene glycol data in two vertical tubes of different tube diameters. The data cover wide ranges of Reynolds, Grashof, and Prandtl numbers and differing ratios of heated tube length to diameter in laminar, transition, and turbulent forced flow regimes. In this paper, we focus the buoyancy effect on forced convection of single-phase flows in vertical tubes with Reynolds numbers higher than 2000. Using HTRI data and experimental data in literature, we demonstrate that natural convection can greatly increase or decrease the convective heat transfer coefficient. In addition, we establish that natural convection should not be neglected if the Richardson number is higher than 0.01 or the mixed turbulent parameter $Ra1/3/(Re0.8 Pr0.4)$ is higher than 0.05 even in forced turbulent flow with Reynolds numbers greater than 10,000. High resolution Reynolds-averaged Navier–Stokes simulations of several experimental conditions confirm the importance of the buoyancy effect on the production of turbulence kinetic energy. We also determine that flow regime maps are required to predict the mixed convection heat transfer coefficient accurately.

1.
Incropera
,
F. P.
,
DeWitt
,
D. P.
,
Bergman
,
T. L.
, and
Lavine
,
A. S.
, 2007,
Fundamentals of Heat Transfer
, 6th ed.,
Wiley
,
New York
, pp.
593
594
.
2.
Jackson
,
J. D.
,
Cotton
,
M. A.
, and
Axcell
,
B. P.
, 1989, “
Studies of Mixed Convection in Vertical Tubes
,”
Int. J. Heat Fluid Flow
0142-727X,
10
(
1
), pp.
2
15
.
3.
Aicher
,
T.
, and
Martin
,
H.
, 1997, “
New Correlations for Mixed Turbulent Natural and Forced Convection Heat Transfer in Vertical Tubes
,”
Int. J. Heat Mass Transfer
0017-9310,
40
(
15
), pp.
3617
3626
.
4.
Joye
,
D. D.
,
Bushinsky
,
J. P.
, and
Saylor
,
P. E.
, 1989, “
Mixed Convection Heat Transfer at High Grashof Number in a Vertical Tube
,”
Ind. Eng. Chem. Res.
0888-5885,
28
(
12
), pp.
1899
1903
.
5.
Joye
,
D. D.
, and
Wojnovich
,
M. J.
, 1996, “
Aiding and Opposing Mixed-Convection Heat Transfer in a Vertical Tube: Loss of Boundary Condition at Different Grashof Numbers
,”
Int. J. Heat Fluid Flow
0142-727X,
17
(
5
), pp.
468
473
.
6.
Saylor
,
P. E.
, and
Joye
,
D. D.
, 1991, “
Hydrostatic Correction and Pressure Drop Measurement in Mixed Convection Heat Transfer in a Vertical Tube
,”
Ind. Eng. Chem. Res.
0888-5885,
30
(
4
), pp.
784
788
.
7.
Celata
,
G. P.
,
Dannibale
,
F.
,
,
A.
, and
Cumo
,
M.
, 1998, “
Upflow Turbulent Mixed Convection Heat Transfer in Vertical Pipes
,”
Int. J. Heat Mass Transfer
0017-9310,
41
(
24
), pp.
4037
4054
.
8.
Gnielinski
,
V.
, 1993, “
Heat Transfer in Forced Single-Phase Flow
,”
VDI Heat Atlas
,
V. D.
Ingenieure
, ed.,
VDI-Verlag
,
Düsseldorf
.
9.
Fluent, Inc., 2007, “Modeling Turbulence,” FLUENT 6.3 Documentation, Fluent, Inc., NH, Lebanon.