Page 460 - Bird R.B. Transport phenomena

440 Chapter 14 Interphase Transport in Nonisothermal Systems

Flow Around a Cylinder
A cylinder in a stationary fluid of infinite extent does not admit a steady-state solution.
Therefore the Nusselt number for a cylinder does not have the same form as that for a
sphere. Whitaker recommends for the mean Nusselt number 4
IIL \ 1 / 4
1/2
Nu m = (0.4 Re + 0.06 Re2/3 04 (14.4-7)
)Pr ( ^ J
5
j
in the range 1.0 < Re < 1.0 X 10 , 0.67 < Pr < 300, and 0.25 < ^/>o < 5.2. Here, as in
Eq. 14.4-6, the values of viscosity and thermal conductivity in Re and Pr are those at the
approaching stream temperature. Similar results are available for banks of cylinders,
which are used in certain types of heat exchangers. 4
5
Another corelation, based on a curve-fit of McAdams' compilation of heat transfer
6
coefficient data, and on the low-Re asymptote in Problem 12B.6, is
2/3
= (0.376Re 1/2 + 0.057Re )Pr 1/3 0.92 l ,1/3
Nu m 4.18Re
(14.4-8)
This correlation has the proper behavior in the limit that Pr —» <», and also behaves prop-
erly for small values of the Reynolds number. This result can be used for analyzing the
steady-state performance of hot-wire anemometers, which typically operate at low
Reynolds numbers.

Flow Around Other Objects
We learn from the preceding three discussions that, for the flow around objects of shapes
other than those described above, a fairly good guess for the heat transfer coefficients
can be obtained by using the relation
J / 3 (14.4-9)

in which Nu, W/0 is the mean Nusselt number at zero Reynolds number. This generaliza-
tion, which is shown in Fig. 14.4-2, is often useful in estimating the heat transfer from ir-
regularly shaped objects.

2.0

1.5 - Cylinders (Eq. 14.4-8)

Flat plates (Eq. 14.4-2) _
1.0 -

0.5
\ Fig. 14.4-2. Graph comparing the
Spheres (Eq. 14.4-5) and Eq. 14.4-9 Nusselt numbers for flow around flat
_ j | | | i plates, spheres, and cylinders with
0.1 10 100 10 3 10 4 10 5 Eq. 14.4-9.

5
W. E. Stewart (to be published).
6
W. H. McAdams, Heat Transmission, 3rd edition, McGraw-Hill, New York (1954), p. 259.