Page 358 - Mechanical Engineers' Handbook (Volume 4)

3 Heat Transport Limitations 347

d
0 K 0 0 at s 0 (35)
ds
with Eq. (33), the evaporating thin-film profile is obtained and the temperature drop across
the evaporating thin film can be determined. As shown in Fig. 6, the heat-flux level through
the thin-film region can reach up to 1400 W/cm with a superheat of 1.0 C. The optimization
2
of thin-film evaporation in a high-heat-flux heat-pipe design plays a key role.

Temperature Drop in Vapor Flow
To find the vapor velocity distribution and vapor pressure drop in a heat pipe, a three-
dimensional model should be developed, in particularly, when the vapor space shape is
irregular and evaporation occurs near the interline region. To obtain an effective tool, a
simplified model can be used, wherein the pressure drop at a given z location is found using
a two-dimensional model, i.e.,

2

u v
u v 1 dp v (36)
2

x 2
y 2 dz
v
4
The friction factor can be obtained based on the vapor channel cross section and the vapor
flow along the z direction can be expressed as a one-dimensional momentum equation shown
as
dp v g sin u du v ƒ 2 u 2 (37)
v v
dz v v v dz v d h,v
The vapor pressure varies from the evaporator section to the condenser section, due to fric-
tional vapor flow, resulting in a temperature variation, which can be predicted by the Cla-
peyron equation, i.e.,

1.6E7 9.0E-7

1.4E7 8.0E-7
1.2E7 7.0E-7
Heat Flux (W/m 2 ) 1.0E7 5.0E-7 Flim Thickness, δ (m)
6.0E-7

8.0E6
4.0E-7
6.0E6
3.0E-7
4.0E6
2.0E-7
2.0E6
1.0E-7

0.0E0 0.0E0
0.0E-7
0.0E0 2.0E-7 4.0E-7 6.0E-7 8.0E-7 1.0E-6
s (m)
Figure 6 Heat-flux distribution in the thin-film region.