A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

1.
Cole, J., and Roshko, A., 1954, “Heat Transfer From Wires at Reynolds Numbers in the Oseen Range,” Proceeding of Heat Transfer and Fluid Mechanics Institute, University of California, Berkeley, CA, pp. 13–23.
2.
Collis
D. S.
, and
Willams
M. J.
,
1959
, “
Two-Dimensional Convection From Heated Wires at Low Reynolds Numbers
,”
J. Fluid Mech.
, Vol.
6
, pp.
357
384
.
3.
Dennis
S. C. R.
,
Hudson
J. D.
, and
Smith
N.
,
1968
, “
Steady Laminar Forced Convection From a Circular Cylinder at Low Reynolds Numbers
,”
Physics of Fluids
, Vol.
11
, pp.
933
940
.
4.
Hieber
C. N.
, and
Gebhart
B.
,
1968
, “
Low Reynolds Number Heat Transfer From a Circular Cylinder
,”
J. Fluid, Mech.
, Vol.
32
, pp.
21
28
.
5.
Illingworth, C. R., 1963, “Flow at Small Reynolds Number,” in Laminar Boundary Layers L. Rosenhead, ed., Claredon Press, Oxford.
6.
Morgan
V. T.
,
1975
, “
The Overall Convection Heat Transfer from Smooth Circular Cylinder
,”
Advances in Heat Transfer
, Vol.
11
, Academic Press, NY, pp.
199
264
.
7.
Nakai
S.
, and
Okazaki
T.
,
1975
, “
Heat Transfer From a Horizontal Circular Wire at Small Reynolds and Grashof Numbers
,”
Int. J. Heat and Mass Transfer
, Vol.
18
, pp.
387
396
.
8.
Van Dyke, M., 1975, Perturbation Methods in Fluid Mechanics, The Parabolic Press, Stanford, CA, p. 152.
9.
Wood
W. W.
,
1968
, “
Calculation for Anemometry With Fine Hot Wires
,”
J. Fluid Mech.
, Vol.
32
, pp.
9
22
.
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