Page 407 - Mechanical Engineers' Handbook (Volume 4)

396 Cooling Electronic Equipment

Vd
hd B n
Nu (57)
k ƒ ƒ
where V is the free stream velocity and where the constants B and n depend on the Reynolds

number as indicated in Table 5.
12
It has been pointed out that Eq. (57) assumes a natural turbulence level in the oncoming
air stream and that the presence of augmentative devices can increase n by as much as 50%.
The modifications to B and n due to some of these devices are displayed in Table 6.
24
5
Equation (57) can be extended to other fluids spanning a range of 1 Re 10 and
0.67 Pr 300:

hd )Pr 0.25
Nu (0.4Re 0.5 0.06Re 0.67 0.4 (58)
k w
where all fluid properties are evaluated at the free stream temperature except , which is
w
the fluid viscosity at the wall temperature.
Noncircular Cylinders in Cross-flow
It has been found 12 that Eq. (57) may be used for noncircular geometries in cross-flow
provided that the characteristic dimension in the Nusselt and Reynolds numbers is the di-
ameter of a cylinder having the same wetted surface equal to that of the geometry of interest
and that the values of B and n are taken from Table 7.

Flow across Spheres
For airflow across a single sphere, it is recommended that the average Nusselt number when
4
17 Re 7 10 be determined from 22
Vd
hd 0.37 0.6

Nu (59)
k ƒ ƒ
25
and for 1 Re 25 ,
hd
Nu 2.2Pr 0.48Pr(Re) 0.5 (60)
k
For both gases and liquids in the range 3.5 Re 7.6 10 and 0.7 Pr 380 24
4
hd )Pr 0.25

Nu 2 (4.0Re 0.5 0.06Re 0.67 0.4 (61)
k
w
Table 5 Constants for Eq. (11)
Reynolds Number Range B n
1–4 0.891 0.330
4–40 0.821 0.385
40–4000 0.615 0.466
4000–40,000 0.174 0.618
40,000–400,000 0.0239 0.805