Page 353 - Mechanical Engineers' Handbook (Volume 4)

342 Heat Pipes

Re 2300 and Ma 0.2
v
v
ƒ Re 0.038 2rq 3/4 (17)
h,v
v
v
A h ƒg , C 1.0
v
v
It should be noted that Eq. (17) was determined based on a round channel. Because the
equations used to evaluate both the Reynolds number and the Mach number are functions
of the heat-transport capacity, it is first necessary to assume the conditions of the vapor flow,
and an iterative procedure must be used to determine the vapor pressure.
If the heat pipe is overcharged and/or the heat pipe is operating at a high cooling rate,
the location of the wet point, where the pressures in the vapor and the liquid are equal,
should be close to the beginning of the condensing section. In this case, only the total
pressure drop in the evaporating and condensing sections is needed in the calculation of the
9
capillary limitation. Equation (13) becomes
p C(ƒ Re ) v
v
v
r
v
a
e
2
2rA h ƒg q[0.5L (1 F Re ) L ] (18)
v v
h,v
where the correction factor, F, in Eq. (18) can be determined by
7 1.7Re r exp 7.51L a
F (19)
9 36 10 Re r Re L e
r
The radial Reynolds number, Re , in Eqs. (18) and (19) is defined by
r
v r
Re v lvv (20)
r
v
where v is the interfacial velocity. For evaporation, v 0; for condensation, v 0.
lv
lv
lv
3.2 Boiling Limit
When boiling occurs near the evaporating wall in the wick, two consequences result. First,
the amount of thin film evaporation at the solid–liquid–vapor interface dramatically decreases
as the boiling condition dominates the phase change behavior of the system. Second, the
vapor forming at the base of the wick structure forms a blanket of vapor, preventing reentry
of the working fluid. Since the vapor conductivity of working fluid is much lower than the
fluid conductivity, the overall conductivity of the wick structure will experience a significant
decrease. Obviously, boiling heat transfer in the wick should be avoided as this condition
could lead to early dryout of the heat pipe.
If the wick is constructed such that the temperature difference between the wall tem-
perature of the evaporator and the saturation temperature, T T , remains less than the
w
s
boiling superheat for a given pressure, bubble formation will not occur near the wall in the
wick. When the local working fluid temperature inside the wick exceeds the saturation tem-
perature corresponding to the local pressure and nucleation occurs, the bubbles that are
formed will collapse and boiling will be avoided if the superheat is not sufficiently large.
The equilibrium state for the bubbles, or the state at which the bubbles no longer collapse,
is that thermodynamic state for which the Gibbs free energy between the liquid and vapor
phases is minimized. Using the Clausius-Clapyeron relation, the superheat can be found as
2 T (p ) 1 1
T T (p ) s l (21)
s
l
l
hr v l
ƒg e
If the vapor density is much smaller than the liquid density, Eq. (21) may be reduced to