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HEAT PIPE HEAT EXCHANGER
CH308-PROCESS EQUIPMENT DESIGN
Problem Statement:
To design a heat pipe - heat exchanger system for recovering about 80%
of the thermal energy from exhaust air of the ventilator of a commercial
building. The air flow in the ventilator is 6800 m3/hr (standard
conditions) at an air velocity of 9100 m3/hr. The temperature of the
exhaust air is 297 K and the outside air winter temperature is normally
around 278 K (occasionally falling to 261 K).
Solution:
Introduction
While the general principle of heat pipes using gravity dates back
to the steam age, the benefits of employing capillary action were first
noted by George Grover at Los Alamos National Laboratory in 1963.
Heat pipes have since been used extensively in space craft as a means
for managing internal temperature conditions.
What is a heat pipe?
A tubular device that is very efficient in transferring heat. Using a metal
container (aluminum, copper, etc.) that holds a liquid (water, acetone,
etc.) under pressure, the inner surface of the tube is lined with a porous
material that acts as a wick. When heat is applied to the outer area of
the tube, the liquid inside the tube boils and vaporizes into a gas that
moves through the tube seeking a cooler location where it condenses.
Using capillary action, the wick transports the condensed liquid back to
the evaporation area.
What distinguishes heat pipe from other conventional heat
exchangers?
 No external pumping is required for the working fluid. (works on
capillary action)
 Ability to act as a thermal flux transformer. (Heat is transferred
from the source to the sink through the working fluid)
 Efficient in tapping energy from small temperature gradients.
Working:
Heat pipes employ evaporative cooling to transfer thermal energy from
one point to another by the evaporation and condensation of a working
fluid or coolant.
When one end of the heat pipe is heated the working fluid inside the
pipe at that end evaporates and increases the vapour pressure inside
the cavity of the heat pipe. The latent heat of evaporation absorbed by
the vaporization of the working fluid reduces the temperature at the hot
end of the pipe.
The vapour pressure over the hot liquid working fluid at the hot end of
the pipe is higher than the equilibrium vapour pressure over
condensing working fluid at the cooler end of the pipe, and this pressure
difference drives a rapid mass transfer to the condensing end where the
excess vapour releases its latent heat, warming the cool end of the pipe.
Non-condensing gases (caused by contamination for instance) in the
vapour impede the gas flow, and reduce the effectiveness of the heat
pipe, particularly at low temperatures, where vapour pressures are low.
The velocity of vibrating molecules in a gas is approximately the speed
of sound and in the absence of non condensing gases, this is the velocity
with which they travel in the heat pipe.
The condensed working fluid then flows back to the hot end of the pipe.
In the case of vertically-oriented heat pipes the fluid may be moved by
the force of gravity. In the case of heat pipes containing wicks, the fluid
is returned by capillary action.
In summary: inside a heat pipe, "hot" vapor flows in one direction,
condenses to the liquid phase, which flows back in the other direction to
evaporate again and close the cycle. One reason for the effectiveness of
heat pipes is the amount of heat that an evaporating fluid absorbs and
then returns when it condenses. For water for instance, to evaporate
one gram of water takes as much heat as would be needed to raise that
same gram of water by 80 degrees C.
Design Considerations:
The three basic components of a heat pipe are:
 container
 working fluid
 wick or capillary structure
Container
The function of the container is to isolate the working fluid from the
outside environment. It has to therefore be leak-proof, maintain the
pressure differential across its walls, and enable transfer of heat to take
place from and into the working fluid.
Selection of the container material depends on many factors. These are
as follows:
 Compatibility (both with working fluid and external environment)
 Strength to weight ratio
 Thermal conductivity
 Ease of fabrication, including welding, malleability and ductility
 Porosity
 Wettability
Aluminium proves to be a good selection for the container owing to its
high strength to weight ratio, non-porous nature and high thermal
conductivity.
Working fluid
A first consideration in the identification of a suitable working fluid is
the operating vapour temperature range. Within the approximate
temperature band, several possible working fluids may exist, and a
variety of characteristics must be examined in order to determine the
most acceptable of these fluids for the application considered. The
prime requirements are:
 compatibility with wick and wall materials
 good thermal stability
 wettability of wick and wall materials
 vapor pressure not too high or low over the operating
temperature range
 high latent heat
 high thermal conductivity
 low liquid and vapor viscosities
 high surface tension
 acceptable freezing or pour point
In the operating temperature range (260-300K), the most efficient
among the several possible working fluids is Ammonia.
Wick Structure
It is a porous structure made of materials like steel, alumunium, nickel
or copper in various ranges of pore sizes. They are fabricated using
metal foams, and more particularly felts, the latter being more
frequently used. By varying the pressure on the felt during assembly,
various pore sizes can be produced. By incorporating removable metal
mandrels, an arterial structure can also be molded in the felt. Carbon
fiber filaments have many fine longitudinal grooves on their surface,
have high capillary pressures and are chemically stable. A number of
heat pipes that have been successfully constructed using carbon fibre
wicks seem to show a greater heat transport capability. The prime
purpose of the wick is to generate capillary pressure to transport the
working fluid from the condenser to the evaporator. It must also be able
to distribute the liquid around the evaporator section to any area where
heat is likely to be received by the heat pipe.
The most common types of wicks that are used are Sintered Powder,
Grooved Tube and Screen Mesh. Groove tube is used in the design
because the small capillary driving force generated by the axial grooves
is suitable for low power heat pipes when operated horizontally.
Design Limitations:
There are five heat transport limitations of a heat pipe:
 Viscous limit
 Sonic limit
 Entrainment limit
 Capillary / Wicking limit
 Burnout limit
Design Specifications:
Staggered arrangement of the heat pipe bundles proved to be the most
efficient conformation.
Symbol
Value
V
flow rate of the air stream
6800 m3/hr
v
Velocity
9100 m/hr
ro
Outer radius
4 cm
ri
Inner radius
2 cm
D
Average outer diameter
6 cm
tp
Thickness of the pipe
0.2 cm
T
Fin thickness
1 cm
H
Length of the heat pipe
100 cm
D
Thickness of wick
0.5 cm
N
No. of fins per unit length
50/m
Kw
Effective wick thermal conductivity 6.7 Wm-1K-1
Ae
Evaporator wall area
0.283 m2
Ac
Condenser wall area
0.283 m2
ST
Transverse pitch
9 cm
SL
Longitudinal pitch
6 cm
SD
Diagonal pitch
7.5 cm
he
Heat
transfer
coefficient
at 88.2 Wm-2K-1
evaporator outer surface
Thermal conductivity of heat pipe 229 Wm-1K-1
wall (Aluminium)
K


ST

 2( S D  D) 
For the considered arrangement of tubes, we get umax  u 
Re 
Dumax 
And the Correlation for heat transfer coefficients is given

he D
 C0 Re n
by Nu 
k
Resistances to Heat Transfer across the evaporator section:
1
 R1 
Resistance on outer surface on the evaporator side
he Ae
log(r 2 / r1)
 R2 
Resistance of the container material
2 kAe
d
 R3 
Resistance due to the wick material
kw Ae
The thermal resistances corresponding to the vapour liquid surfaces
are neglected.
R=R1+R2+R3 = 0.04635
ΔT=297-279=18
Qh= ΔT/R = 388W
Q = 0.8*6800/3600*1.2*1006.3*(297-261)
= 65670W
No. of pipes = QT/Qh = 65670/388 ≈ 170
Area of flow = V/v = 6800/9100 = 0.75 m2
The staggered arrangement would have 10 pipes in a row and 17
such rows across which the exhaust air blows through.
This heat exchanger would recover 80% of the energy in the exhaust
gas. This would raise the temperature of the inlet cold air by 180C.
Limits:
Entrainment:
The inertial forces due to the vapor pressure will shear the liquid
flow in the capillaries and work against the surface tension. Weber
number which is defined as the ratio between inertial vapor forces
and liquid surface tension provides a convenient measure of likely
v v 2 z
hood of entrainment. We 
It is assumed that entrainment will
2 l
occur when We=1. This gives entrainment limit axial flux as
 2v L2 l 
q 
 . The value of z depends on wick structure and
z


material properties. It needs to be determined experimentally. Even
for a z value as high as 106, q = 500 is the limiting case.
Capillary / Wick limit:
In order for the heat pipe to operate the maximum capillary
pumping head (∆Pc,max) must be greater than the total pressure drop
inside the pipe.
∆Pc,max >= ∆Pl + ∆Pv + ∆Pg
Where,
∆Pl is the pressure drop required to return the liquid from tye
condenser to the evaporator.
∆Pv is the pressure drop necessary to cause the vapour to flow
from the evaporator to the condenser.
∆Pg is the gravitational head
If this condition is not met the wick will dry out in the evaporator region
and the pipe will not operate.
Formula:
   L   KA   2 l gl

Qmax   l l  

sin

  592W


l
r

 e
l
 l 

Sonic Limit:
The decrease in the thermal resistance between the condenser
and heat sink reduces the condenser region temperature, but does not
increase the heat flow which leads to choked flow condition.
At higher temperature choking at the evaporators exit may limit the
total power handling capability of the pipe.
Formula:
 AmCo L
Q v
 761625
2(  1)
Viscous Limit:
At low temperature, viscous forces will restrict the flow of the
vapour down the pipe.
Busse has given the following relation which determines the maximum
rate of heat transfer in the pipe.
Formula:
rv 2 L v Pv
q
16v leff
This can be applied only at low temperatures. So we neglect this effect
in this problem.
Reference:
 Heat Pipes by P Dunn & D A Reay
 Heat Transfer by M Necati Ozisik
 Encyclopedia of Chemical Technology Vol.12
 T P Cotter, Theory of Heat Pipes LA-3246-MS, University of California,
Los Alamos, N.M.1965