Page 355 - Mechanical Engineers' Handbook (Volume 4)

344 Heat Pipes

3.5 Sonic Limit
When the vapor velocity at the exit of the evaporating section reaches the local sound speed,
the vapor flow is choked. As the chocked flow occurs, the vapor flow rate will not respond
with the amount of heat added in the evaporator. The heat pipe has reached the maximum
heat transport, which is called the sonic limit. If the vapor flow in the heat pipe can be
approximated as one-dimensional flow with the assumptions of negligible frictional force
and ideal gas, the sonic limit can be readily derived from the conservation of energy and
momentum equations as follows:
q A h RT 1/2
v
v 0
s
ƒg
vv
2( 1) (26)
v
where T is the stagnation temperature, A and are the cross-sectional area and vapor
v
v
0
density, respectively, at the location where the local sound speed is reached. It should be
noted that this might occur at the exit to the evaporator or any location in the condenser
section if the cross-sectional area of vapor flow path changes.
3.6 Effective Thermal Conductivity
While those operating limitations described above dominate the design of a heat pipe, the
effective thermal conductivity provided by a heat pipe is a key factor for designing a highly
efficient heat-pipe cooling device. The effective thermal conductivity, k , is related to the
eff
total temperature drop, T total ,as
qL
k eff eff (27)
A T total
h
where A is the total cross-sectional area of heat pipe. The total temperature drop, T total ,
h
across the heat pipe is the sum of the temperature drop across the evaporator shell, T e,shell ;
the temperature drop across the wick structure in the evaporator, T e,wick ; the temperature
drop through the evaporating thin film, T e,film ; the temperature drop in the vapor flow, T ;
v
the temperature drop across the condensate film, T c,film ; the temperature drop across the
wick structure at the condenser, T c,wick ; and the temperature drop across the condenser shell,
T c,shell , i.e.,
t total T e,shell T e,wick T e,film T T c,film T c,wick T c,shell (28)
v
Temperature Drops across Shell and Wick
The temperature drop through the case shell material at both the evaporator and the condenser
can be calculated by
q
T e,shell ee,shell (29)
k shell
and
q
T c,shell cc,shell (30)
k shell
respectively. After heat is traveled through the wall, the heat reaches the working fluid in
the wick. Provided that the wick is saturated with the working fluid and no boiling occurs