Modern Engineering Thermodynamics

234 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
CASE STUDY: ENTROPY PRODUCTION IN HEAT PIPES
The application of basic thermodynamic principles recently produced
a new heat transfer technology. In 1939. the German engineer
E. Schmidt demonstrated that a hollow, sealed tube filled with
a liquid-vapor mixture could transfer several thousand times more
thermal energy than pure conduction in a solid copper rod with
the same dimensions as the tube.
Heat applied to the liquid region at the lower end of the tube
causes the quality of the mixture in the remainder of the tube to
increase. The additional vapor thus produced rises inside the tube
and condenses at the cooler end. This condensate then runs down
the inside wall of the tube to replenish the liquid at the lower
end. Figure 7.19a illustrates this process. A continuous circulation
of vapor and condensate occurs when a steady state condition has
been reached.
Since vaporization and condensation occur at the same temperature
under constant pressure conditions,theentireinsidevolume
of the tube reaches a constant temperature. Pure thermal conduction
in a solid rod requires both a radial and an axial temperature
gradient (see Figure 7.19c) to transport thermal energy.
Schmidt’s device, however, transports a great deal more thermal
energy very efficiently with essentially no temperature gradient
(see Figure 7.19d).
The name heat pipe was suggested for this device in 1963 by George
M. Grover of the Los Alamos Scientific Laboratory. The first significant
application of heat pipe technology occurred in the U.S. space
program, then it spread into a wide variety of commercial areas
including home furnaces and solar water heaters.
The steady state entropy production rate of a closed system heat
pipe with isothermal input and output surfaces is obtained from
the entropy rate balance as
Q
ð _S P Þ heat pipe
= ∑ _
T
net
Q
= _ T
−
out
Q _
T
in
= _Q T
in − T out
(7.67)
T in T out
If the heat pipe were truly isothermal throughout, then T in = T out and
the entropy production rate would be zero. But T in is always slightly
greater than T out due to a small radial temperature gradient in the
tube wall. However, these two temperatures are really very close to
each other so that the entropy production rate of the heat pipe is
actually quite small, making it a much more efficient heat transfer
device than pure thermal conduction alone.
Q out
Q in
(b) Gaugler type of heat pipe
Q out
Wick
Vapor
Vapor
Condensate
return by
Condensate
capillary
return
forces
by gravity
Q in
Q out
(a) Schmidt type of heat pipe
Q in Q in
T 0
Solid rod
T 0
Heat pipe
Q out
T 0
FIGURE 7.19
Heat pipe construction.
0 x L
(c) Temperature profile
in an uninsulated
solid rod fin
T 0
0 x L
(d) Temperature profile
in an uninsulated
heat pipe fin