A numerical investigation of laminar natural convection heat transfer from small horizontal cylinders at near-critical pressures has been carried out. Carbon dioxide is the test fluid. The parameters varied are: pressure (P), (ii) bulk fluid temperature (Tb), (iii) wall temperature (Tw), and (iv) wire diameter (D). The results of the numerical simulations agree reasonably well with available experimental data. The results obtained are as follows: (i) At both subcritical and supercritical pressures, h is strongly dependent on Tb and Tw. (ii) For Tw < Tsat (for P < Pc) and Tw < Tpc (for P > Pc), the behavior of h as a function of Tw is similar; h increases with increase in Tw. (iii) For P > Pc and large Tw (Tw > Tpc), natural convection heat transfer occurring on the cylinder is similar that observed during film boiling on a cylinder. The heat transfer coefficient decreases as Tw increases. (iv) For subcritical pressures, the dependence of h on D is h ∝ D0.5 in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D0.24. (v) For supercritical pressures, the dependence of h on D is h ∝ D0.47 in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D−0.27. (vi) For a given P, the maximum heat transfer coefficient is obtained for conditions where Tb < Tpc and Tw ≥ Tpc. Analysis of the temperature and flow field shows that this peak in h occurs when k, Cp, and Pr in the fluid peak close to the heated surface.

References

References
1.
Hahne
,
E.
,
1985
, “
Natural Convection in the Near Critical Region and Its Application in Heat Pipes,
” Natural Convection: Fundamentals and Applications, S. Kakac, W. Aung, and R. Viskanta, eds.,
Springer-Verlag
,
Berlin
, pp.
774
826
.
2.
Simon
,
H. A.
, and
Eckert
,
E. R. G.
,
1963
, “
Laminar Free Convection in Carbon Dioxide Near Its Critical Point
,”
Int. J. Heat Mass Transfer
,
6
, pp.
681
690
.10.1016/0017-9310(63)90039-5
3.
Knapp
,
K. K.
, and
Sabersky
,
R. H.
,
1966
, “
Free Convection Heat Transfer to Carbon Dioxide Near the Critical Point
,”
Int. J. Heat Mass Transfer
,
9
, pp.
41
45
.10.1016/0017-9310(66)90055-X
4.
Abadzic
,
E.
, and
Goldstein
,
R. J.
,
1970
, “
Film Boiling and Free Convection Heat Transfer to Carbon Dioxide Near the Critical State
,”
Int. J. Heat Mass Transfer
,
13
, pp.
1163
1175
.10.1016/0017-9310(70)90006-2
5.
Neumann
,
R. J.
, and
Hahne
,
E. W. P.
,
1980
, “
Free Convective Heat Transfer to Supercritical Carbon Dioxide
,”
Int. J. Heat Mass Transfer
,
23
, pp.
1643
1652
.10.1016/0017-9310(80)90223-9
6.
Nishikawa
,
K.
, and
Ito
,
T.
,
1969
, “
An Analysis of Free Convective Heat Transfer From an Isothermal Vertical Plate to Supercritical Fluids
,”
Int. J. Heat Mass Transfer
,
12
, pp.
1449
1463
.10.1016/0017-9310(69)90027-1
7.
Hilal
,
M. A.
,
1978
, “
Analytical Study of Laminar Free Convection Heat Transfer to Supercritical Helium
,”
Cryogenics
,
18
, pp.
545
551
.10.1016/0011-2275(78)90158-3
8.
Seetharam
,
T. R.
, and
Sharma
,
G. K.
,
1979
, “
Free Convective Heat Transfer to Fluids in the Near-Critical Region From Vertical Surfaces With Uniform Heat Flux
,”
Int. J. Heat Mass Transfer
,
22
, pp.
13
20
.10.1016/0017-9310(79)90093-0
9.
Rousselet
,
Y.
,
Warrier
,
G. R.
, and
Dhir
,
V. K.
,
2013
, “
Natural Convection From Horizontal Cylinders at Near-Critical Pressures—Part I: Experimental Study
,”
ASME J. Heat Transfer
,
135
(2), p.
022501
.10.1115/1.4007672
10.
Paolucci
,
S.
,
1982
, “
On the Filtering of Sound From the Navier-Stokes Equations
,” Scandia National Laboratories, Technical Report No. SAND82-8257.
11.
Zappoli
,
B.
,
Amiroudine
,
S.
,
Carlès
,
P.
, and
Ouazzani
,
J.
,
1996
, “
Thermoacoustic and Buoyancy-Driven Transport in a Square Side-Heated Cavity Filled With a Near-Critical Fluid
,”
J. Fluid Mech.
,
316
, pp.
53
72
.10.1017/S0022112096000444
12.
Muller
,
B.
,
1998
, “
Low Mach Number Asymptotics of the Navier-Stokes Equations
,”
J. Eng. Math.
,
34
, pp.
97
109
.10.1023/A:1004349817404
13.
Le Quéré
,
P.
,
Weisman
,
C.
,
Paillère
,
H.
,
Vierendeels
,
J.
,
Dick
,
E.
,
Becker
,
R.
,
Braack
,
M.
, and
Locke
,
J.
,
2005
, “
Modelling of Natural Convection Flows With Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions
,”
Math. Model. Numer. Anal.
,
39
, pp.
609
616
.10.1051/m2an:2005027
14.
Accary
,
G.
, and
Raspo
,
I.
,
2006
, “
A 3D Finite Volume Method for the Prediction of a Supercritical Fluid Buoyant Flow in a Differentially Heated Cavity
,”
Comput. Fluids
,
35
, pp.
1316
1331
.10.1016/j.compfluid.2005.05.004
15.
Mazumder
,
S.
,
2007
, “
On the Use of the Fully Compressible Navier-Stokes Equations for the Steady-State Solution of Natural Convection Problems in Closed Cavities
,”
ASME J. Heat Transfer
,
129
, pp.
387
390
.10.1115/1.2430726
16.
Hauke
,
G.
, and
Hughes
,
T. J. R.
,
1998
, “
A Comparative Study of Different Sets of Variables for Solving Compressible and Incompressible Flows
,”
Comput. Methods Appl. Mech. Eng.
,
153
, pp.
1
44
.10.1016/S0045-7825(97)00043-1
17.
NIST Standard Reference Database 23, REFPROP, Reference Fluid Thermodynamic and Transport Properties, Version 8.0.
18.
Ferziger
,
J. H.
, and
Peric
,
M.
,
1999
,
Computational Methods for Fluid Dynamics
,
Springer-Verlag
,
Berlin, Germany
.
19.
Khosla
,
P. K.
, and
Rubin
,
S. G.
,
1974
, “
A Diagonally Dominant Second-Order Accurate Implicit Scheme
,”
Comput. Fluids
,
2
, pp.
207
209
.10.1016/0045-7930(74)90014-0
20.
Waterson
,
N. P.
, and
Deconinck
,
H.
,
2007
, “
Design Principles for Bounded Higher-Order Convection Schemes – A Unified Approach
,”
J. Comput. Phys.
,
224
, pp.
182
207
.10.1016/j.jcp.2007.01.021
21.
Van Doormaal
,
J. P.
, and
Raithby
,
G. D.
,
1984
, “
Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows
,”
Numer. Heat Transfer
,
7
, pp.
147
163
.10.1080/01495728408961817
22.
Stone
,
H. L.
,
1968
, “
Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations
,”
SIAM Journal of Numerical Analysis
,
5
, pp.
530
558
.10.1137/0705044
23.
Saad
,
Y.
, and
Schultz
,
M. H.
,
1986
, “
GMRES: A Generalized Residual Algorithm for Solving Non-Symmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
7
, pp.
856
869
.10.1137/0907058
24.
Kuehn
,
T. H.
, and
Goldstein
,
R. J.
,
1980
, “
Numerical Solution to the Navier-Stokes Equations for Laminar Natural Convection About a Horizontal Isothermal Circular Cylinder
,”
Int. J. Heat Mass Transfer
,
23
, pp.
971
979
.10.1016/0017-9310(80)90071-X
25.
Saitoh
,
T.
,
Sajiki
,
T.
, and
Maruhara
,
K.
,
1993
, “
Bench Mark Solutions to Natural Convection Heat Transfer Problem Around a Horizontal Circular Cylinder
,”
Int. J. Heat Mass Transfer
,
36
, pp.
1251
1259
.10.1016/S0017-9310(05)80094-8
26.
Churchill
,
S. W.
, and
Chu
,
H. H. S.
,
1975
, “
Correlating Equations for Laminar and Turbulent Free Convection From a Horizontal Cylinder
,”
Int. J. Heat Mass Transfer
,
18
, pp.
1049
1053
.10.1016/0017-9310(75)90222-7
27.
Mills
,
A. F.
,
1999
,
Heat Transfer
,
2nd
ed.,
Prentice-Hall
,
Englewood Cliffs, NJ
.
28.
Kato
,
H.
,
Nishiwaki
,
N.
, and
Hirata
,
M.
,
1968
, “
Studies on the Heat Transfer of Fluids at a Supercritical Pressure
,”
Bull. Jpn. Soc. Mech. Eng.
,
11
, pp.
654
663
.10.1299/jsme1958.11.654
You do not currently have access to this content.