Page 183 - Mechanical Engineers' Handbook (Volume 4)

172 Heat-Transfer Fundamentals

In turbulent flow, the heat-transfer coefficient for tubes in the first row is smaller than that
of the subsequent rows. However, beyond the fourth or fifth row, the heat-transfer coefficient
becomes approximately constant. For tube banks with more than twenty rows, 0.7 Pr
6
500, and 1000 Re D,max 2 10 , the average Nusselt number for the entire tube bundle
can be expressed as 10
m
) Pr 0.36 (Pr /Pr ) 0.25
Nu C(Re D,max s
D
where all fluid properties are evaluated at T except Pr , which is evaluated at the surface

s
temperature. The constants C and m used in this expression are listed in Table 14, and the
Reynolds number is based on the maximum fluid velocity occurring at the minimum free
flow area available for the fluid. Using the nomenclature shown in Fig. 12, the maximum
fluid velocity can be determined by
S
V T V
max
S D
T
for the aligned or staggered configuration provided
2
2

S (S /2) (S D)/2
T
L
T
or as
S T
V max 2 2 2 V
S (S /2)

L T
for staggered if
2
2

S (S /2) (S D)/2
T
L
T
Liquid Metals in Cross-Flow over Banks of Tubes
The average Nusselt number for tubes in the inner rows can be expressed as
Nu 4.03 0.228(Re D,max Pr) 0.67
D
which is valid for 2 10 Re D,max 8 10 and Pr 0.03 and the fluid properties are
4
4
evaluated at the mean film temperature. 11
High-Speed Flow over a Flat Plate
When the free stream velocity is very high, the effects of viscous dissipation and fluid
compressibility must be considered in the determination of the convection heat transfer. For
Table 14 Constants C and m of Heat-Transfer Coefficient for the Banks in Cross-Flow
Configuration Re D,max C m
3
Aligned 10 –2 10 5 0.27 0.63
3
Staggered 10 –2 10 5 0.35(S T /S L ) 1/5 0.60
(S T /S L 2)
Staggered 10 –2 10 5 0.40 0.60
3
(S G /S L 2)
5
Aligned 2 10 –2 10 6 0.21 0.84
5
Staggered 2 10 –2 10 6 0.022 0.84