Page 352 - Mechanical Engineers' Handbook (Volume 4)

3 Heat Transport Limitations 341

For uniform heat addition and rejection, Eq. (5) can be expressed as
p l
l
wƒg
KA h l Lq eff (8)
where q ˙m l h ƒg and the effective heat pipe length can be found as
L eff 0.5L L 0.5L c (9)
e
a
In many cases, an analytical expression for the permeability, K, shown in Eq. (8), is not
available. In such a case, semiempirical correlations based on experimental data are usually
5
employed. For example, Marcus has described a method for calculating the permeability of
wrapped, screened wicks. This expression, which is a modified form of Blake-Kozeny equa-
tion, can be expressed as
23
d
K (10)
122(1 ) 2
In this expression, d is the wire diameter and is the wick porosity, which can be determined
as
1 –
SNd (11)
1
4
where N is the mesh number per unit length and S is the crimping factor (approximately
6
1.05). For the sintered particles, this equation takes the form
23
d
K s (12)
37.5(1 ) 2
is the average diameter of the sintered particles.
where d s
Vapor Pressure Drop
If the heat pipe is charged with an appropriate amount of working fluid and the wetting
point occurs at the cap end of condenser, the vapor pressure drop can be calculated by the
6
7
8
approach recommended by Peterson, Chi, and Dunn and Reay. Based on the one-
dimensional vapor flow approximation, the vapor pressure drop can be determined by
p C(ƒ Re ) v
v
v
v
2
2rA h ƒg Lq eff (13)
h,v
v v
where C is the constant that depends on the Mach number defined by
q
Ma (14)
v
A h (RT ) 1/2
ƒg
vv v
vv
The ratio of specific heats, , in Eq. (14) depends on the molecule types, which is equal to
v
1.67, 1.4, and 1.33 for monatomic, diatomic, and polyatomic molecules, respectively. Pre-
6
vious investigation summarized by Peterson have demonstrated that the friction factor Reyn-
olds number product, ƒ Re , and the constant, C, shown in Eq. (13) can be determined by
v
v
Re 2300 and Ma 0.2
v
v
(15)
ƒ Re constant, C 1.0
v
v
Re 2300 and Ma 0.2
v
v
ƒ Re constant, C 1 1/2 (16)
1
v
2
v
v
2 Ma v