Page 456 - Bird R.B. Transport phenomena

436 Chapter 14 Interphase Transport in Nonisothermal Systems

0.010
0.009
0.008
-^ 0.007 f
J 0.006 -LID- 60 - ' 2 versus Re for long smooth pipe
/
~" 0.005 X V i^n 180
^ 0.004 И
X! о.ооз s\ 7\ *==

^ 0.002

О «N
0.001
10 3 10 4 10
DG D{v zP )
Re =
Fig» 14.3-2. Heat transfer coefficients for fully developed flow in smooth tubes. The lines for lami-
nar flow should not be used in the range RePrD/L < 10, which corresponds to (T - T ) /(T - Т )
o
ь }
0
b 2
< 0.2. The laminar curves are based on data for RePrD/L > 10 and nearly constant wall tem-
>
perature; under these conditions h and h are indistinguishable. We recommend using h , as op-
]n
[n
a
posed to the h suggested by Sieder and Tate, because this choice is conservative in the usual heat-
a
exchanger design calculations [E. N. Sieder and G. E. Tate, Ind. Eng. Chem., 28,1429-1435 (1936)].
4
which is based on Eq. (C) of Table 14.2-1 and Problem 12D.4. The numerical coefficient
in Eq. (C) has been multiplied by a factor of \ to convert from h loc to /z , and then further
ln
modified empirically to account for the deviations due to variable physical properties.
This illustrates how a satisfactory empirical correlation can be obtained by modifying
the result of an analytical derivation. Equation 14.3-17 is good within about 20% for RePr
D/L > 10, but at lower values of RePr D/L it underestimates ft considerably. The occur-
ln
1/ 3
rence of Pr in Eqs. 14.3-16 and 17 is consistent with the large Prandtl number asymp-
tote found in §§13.6 and 12.4.
The transition region, roughly 2100 < Re < 8000 in Fig. 14.3-2, is not well understood
and is usually avoided in design if possible. The curves in this region are supported by
2
experimental measurements but are less reliable than the rest of the plot.
The general characteristics of the curves in Fig. 14.3-2 deserve careful study. Note
that for a heated section of given L and D and a fluid of given physical properties, the or-
dinate is proportional to the dimensionless temperature rise of the fluid passing
through—that is, (T — T )/(T — T ) . Under these conditions, as the flow rate (or
b2 M 0 b ln
Reynolds number) is increased, the exit fluid temperature will first decrease until Re
reaches about 2100, then increase until Re reaches about 8000, and then finally decrease
again. The influence of L/D on /t is marked in laminar flow but becomes insignificant
ln
for Re > 8000 with L/D > 60.

Equation (C) is an asymptotic solution of the Graetz problem, one of the classic problems of heat
4
convection: L. Graetz, Ann. d. Physik, 13, 79-94 (1883), 25, 337-357 (1885); see J. Leveque, Ann. Mines
(Series 12), 13, 201-299, 305-362, 381-415 (1928) for the asymptote in Eq. (C). An extensive summary
can be found in M. A. Ebadian and Z. F. Dong, Chapter 5 of Handbook of Heat Transfer, 3rd edition,
(W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho, eds.), McGraw-Hill, New York (1998).