Page 217 - Mechanical Engineers' Handbook (Volume 4)

206 Heat-Transfer Fundamentals

C 1.00
Re 2300, Ma 0.2
v v
(ƒ Re ) 16
v
v
C 1 1/2
1
v
2
2 Ma v
Re 2300, Ma 0.2
v
v
(ƒ Re ) 0.038 2(r )q 3/4
h,v
v
v
A h
v
v ƒg
C 1.00
Re 2300, Ma 0.2
v
v
(ƒ Re ) 0.038 2(rq 3/4
h,v
v
v
A h
v
v ƒg
C 1 1/2
1
v
2
2 Ma v
Since the equations used to evaluate both the Reynolds number and the Mach number
are functions of the heat transport capacity, it is necessary to first assume the conditions of
the vapor flow. Using these assumptions, the maximum heat capacity, q , can be determined
c,m
by substituting the values of the individual pressure drops into Eq. (1) and solving for q .
c,m
Once the value of q is known, it can then be substituted into the expressions for the vapor
c,m
Reynolds number and Mach number to determine the accuracy of the original assumption.
Using this iterative approach, accurate values for the capillary limitation as a function of the
operating temperature can be determined in units of W-m or watts for (qL) and q ,
c,m c,m
respectively.
The viscous limitation in heat pipes occurs when the viscous forces within the vapor
region are dominant and limit the heat pipe operation:
P v 0.1
P v
for determining when this limit might be of a concern. Due to the operating temperature
range, this limitation will normally be of little consequence in the design of heat pipes for
use in the thermal control of electronic components and devices.
The sonic limitation in heat pipes is analogous to the sonic limitation in a converging–
diverging nozzle and can be determined from
A h RT 1/2
q s,m vv ƒg v v v
2( 1)
v
where T is the mean vapor temperature within the heat pipe.
v
Since the liquid and vapor flow in opposite directions in a heat pipe, at high enough
vapor velocities, liquid droplets may be picked up or entrained in the vapor flow. This
entrainment results in excess liquid accumulation in the condenser and, hence, dryout of the
evaporator wick. Using the Weber number, We, defined as the ratio of the viscous shear
force to the force resulting from the liquid surface tension, an expression for the entrainment
limit can be found as