Page 179 - Mechanical Engineers' Handbook (Volume 4)

168 Heat-Transfer Fundamentals

Table 12 Nusselt Numbers for Fully Developed Laminar Flow for Tubes of Various Cross Sections a
Geometry
(L/DH 100) Nu H1 Nu H2 Nu r
3.608 3.091 2.976

4.123 3.017 3.391

5.099 4.35 3.66

6.490 2.904 5.597

8.235 8.235 7.541
5.385 — 4.861

4.364 4.364 3.657

a
Nu H1 average Nusselt number for uniform heat flux in flow direction and uniform wall temperature at particular
flow cross section.
Nu H2 average Nusselt number for uniform heat flux both in flow direction and around periphery.
Nu Hrr average Nusselt number for uniform wall temperature.

equation gives good correlation for the combined entry length, i.e., that region where the
5
thermal and velocity profiles are both developing or for short tubes:
1/3

D
Nu hD 1.86(Re D Pr) 0.14
D
1/3
k L s
for T constant, 0.48 Pr 16,700, 0.0044 / 9.75, and (Re Pr D/L) 1/3
s
D
s
( / ) o.14 2.
s
In this expression, all of the fluid properties are evaluated at the mean bulk temperature
except for , which is evaluated at the wall surface temperature. The average convection
s
heat-transfer coefficient h is based on the arithmetic average of the inlet and outlet temper-
ature differences.
Turbulent Flow in Circular Tubes
In turbulent flow, the velocity and thermal entry lengths are much shorter than for a laminar
flow. As a result, with the exception of short tubes, the fully developed flow values of the
Nusselt number are frequently used directly in the calculation of the heat transfer. In general,
the Nusselt number obtained for the constant heat flux case is greater than the Nusselt number
obtained for the constant temperature case. The one exception to this is the case of liquid
metals, where the difference is smaller than for laminar flow and becomes negligible for Pr
6
1.0. The Dittus-Boelter equation is typically used if the difference between the pipe
surface temperature and the bulk fluid temperature is less than 6 C (10 F) for liquids or 56 C
(100 F) for gases: