Page 356 - Mechanical Engineers' Handbook (Volume 4)

3 Heat Transport Limitations 345

in the wick, the heat will transfer through the wick and evaporation will only occur at the
liquid–vapor–solid interface. The heat transfer across the wick is dominated by the heat
conduction. The temperature drop across the wick in the evaporator can be determined by
q
T e,wick c wick (31)
k
eff
As shown in Eq. (31), the effective thermal conductivity of a wick plays a key role in the
temperature drop in the wick. Since the effective thermal conductivity depends on the work-
ing fluid, porosity, and geometric configuration, it is very hard to find the exact effective
thermal conductivity theoretically. Nevertheless, several approximations for the effective ther-
mal conductivity have been developed. A list of common expressions for determining the
effective thermal conductivity of the wick is presented in Table 3. It is clear from each of
the listed expressions that the effective thermal conductivity of the wick is a function of the
solid conductivity, k , the working fluid conductivity, k , and the porosity. In each of the
s
l
relations, lim →0 k eff k and lim →1 k eff k ; however, the manner by which the effective
s
l
conductivity varies between the limiting cases is drastically different depending on the type
of arrangement of the wick structure. Comparing the various effective conductivity relations,
as illustrated in Table 3 and Fig. 4, it becomes clear that sintering the metallic particles
dramatically enhances the overall thermal conductivity.
Similar to the temperature drop calculation for the evaporator, the temperature drop
across the wick in the condenser can be found as
q
T c,wick c wick (32)
k eff

Temperature Drop across the Liquid–Vapor Interface
If heat is added to the wick structure, the heat is transferred through the wick filled with the
working fluid, reaching the surface where the liquid–vapor–solid interface exists. There, by
utilizing the thin-film evaporation, the heat is removed. The temperature drop across the
evaporating thin film, as shown in Fig. 5, can be calculated from the thin-film thickness by
solving the equations governing the heat transfer and fluid flow in the thin-film region. 13
The film thickness profile for a flat surface can be described by

Table 3 Expressions for Wick Effective Thermal Conductivities for Various Geometries

Wick Condition Expression for Effective Thermal Conductivity
Sintered k [2k k 2 (k k )]
1
s
1
s
s
k Sintered
2k k (k k )
s 1 s 1
Packed spheres k [(2k k ) 2(1 )(k k )]
1 1 s 1 s
k PackedSpheres
(2k k ) (1 )(k k )
1
s
s
1
Wick and liquid in series kk s
1
k Series
k k (1 )
1
s
Wick and fluid in parallel k Parallel k k (1 )
s
1
Wrapped screens k [(k k ) (1 )(k k )]
1
s
1
1
s
k WrappedScreen
(k k ) (1 )(k k )
1
s
1
s