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Heat Transfer Engineering, 28(11):954–965, 2007
Copyright
C
Taylor and Francis Group, LLC
ISSN: 01457632 print / 15210537 online
DOI: 10.1080/01457630701421810
Heat Transfer Studies of a Heat Pipe
VIKAS KUMAR
Centre for Development of Advanced Computing, Pune University Campus, Maharashtra, India
D. GANGACHARYULU and RAM GOPAL TATHGIR
Thapar Institute of Engineering and Technology, Punjab, India
The present investigation reports a theoretical and experimental study of a wire screen heat pipe, the evaporator section of
which is subjected to forced convective heating and the condenser section to natural convective cooling in air. The theoretical
study deals with the development of an analytical model based on thermal resistance network approach. The model computes
thermal resistances at the external surface of the evaporator and condenser as well as inside the heat pipe. A test rig has
been developed to evaluate the thermal performance of the heat pipe. The effects of operating parameters (i.e., tilt angle of
the heat pipe and heating ﬂuid inlet temperature at the evaporator) have been experimentally studied. Experimental results
have been used to compare the analytical model. The heat transfer coefﬁcients predicted by the model at the external surface
of the evaporator and condenser are reasonably in agreement with experimental results.
INTRODUCTION
The heat pipe has been recognized as a very efﬁcient heat
transport device. In conventional form, as shown in Figure 1,
it consists of an evacuated cylindrical container with a wick
structure on its inside surface. The wick is saturated with a com
patible working ﬂuid. Heat pipes are used in various thermal
engineering applications for heat removal and waste heat re
covery under forced convection as well as under natural con
vection [1–4]. Although forced convection cooling of engineer
ing equipment is more prevalent, there are still various types
of industrial/electronic equipment, such as oilcooled electrical
transformers and insulated gate bipolar transistors, of which the
radiators/heat sinks are subjected to cooling under natural con
vection due to its inherent advantages (e.g., a reduction in the
operating cost associated with forced convection, being noise
free, reliability [5–7]). To employ heat pipes for an industrial
application, it is desirable to know its thermal performance a
priori under various operating conditions. The thermal perfor
mance depends on various radial and axial thermal resistances
at the evaporator, condenser, and inside the heat pipe [1–4, 8].
The condenser thermal resistance decreases as the operating
temperature increases [9, 10]. A number of empirical correla
tions have been reported to determine individual heat transfer
Address correspondence to Dr. Vikas Kumar, Centre for Development of
Advanced Computing (CDAC), Pune University Campus, Ganeshkhind Road,
Pune, 411 007, Maharashtra, India. Email: vikaskumar
gupta@yahoo.com
coefﬁcient on the external surface of the evaporator and con
denser and inside the heat pipe [1, 11–13].
The work described in this paper includes the development of
an analytical model and experimental investigation at low tem
perature (40–70
◦
C). The evaporator portion of the heat pipe is
subjected to forced convection heating and the condenser portion
to natural convection cooling. Experimental studies have been
conducted at different heating ﬂuid temperatures and tilt angles.
Some typical experimental results have been used to compare
the individual and overall heat transfer coefﬁcient predicted by
the model with those obtained from experiments to validate the
model. This model could be useful for analyzing cooling design
of industrial equipment, which may use annular ﬁnned heat pipe
under natural convection.
HEAT PIPE DESIGN AND FABRICATION
The various considerations for the design of a heat pipe in
clude selection of working ﬂuid, container, wick materials, wick
design, and computation of heat transport limits. The working
ﬂuid is selected based on the cost, availability, compatibility
with wick and container materials, and operating vapor tem
perature range. The other prime considerations for selection of
working ﬂuid are wettability, good thermal stability, high latent
heat, high surface tension, low liquid and vapor viscosities, and a
vapor pressure not too high or low at the operating temperature
range. In the low temperature range of 30–200
◦
C, water has
954
V. KUMAR ET AL. 955
Figure 1 A schematic diagram of heat pipe.
better heat transport and conductance properties, as compared to
other working ﬂuids like ammonia, pentane, acetone, methanol,
heptane, and ethanol, and it is cheaply available. Based upon
these considerations, distilled water is chosen as the working
ﬂuid. The amount of working ﬂuid required should be sufﬁcient
to saturate the wick and ﬁll the core volume in the vapor phase.
The heat pipe should be neither underﬁlled nor overﬁlled. An
underﬁlled pipe may result in the degradation of performance
and an overﬁll may result in condenser blockage. The ﬂuid in
ventory required for the heat pipe has been calculated by using
the following equation [1]:
M = A
v
L
t
ρ
v
+ A
w
L
t
ε
o
ρ
l
(1)
Copper has been selected as the material for the heat pipe
container, considering its superior thermal conductance prop
erty, cost advantage, and ease of fabrication, and it is also com
patible with water [1]. Keeping these considerations in mind, a
copper pipe with 25.40 mm outer diameter and 22.00 mm inner
Table 1 Heat transport limitations of the heat pipe at different evaporator temperatures
Heat transport limit, W
Number Operating limit 30
◦
C40
◦
C50
◦
C60
◦
C70
◦
C80
◦
C90
◦
C 100
◦
C
1. Capillary
0
◦
tilt
∗
26.3 30.9 35.7 40.4 44.6 48.3 51.2 53.6
25
◦
tilt
∗
99.4 118.8 139.5 160.6 180.9 199.6 216.4 231.9
2. Sonic 6.0 × 10
3
9.4 × 10
3
1.4 × 10
4
2.2 × 10
4
3.4 × 10
4
5.1 × 10
4
7.5 × 10
4
1.1 × 10
5
3. Entrainment 4.0 × 10
3
4.8 × 10
3
5.9 × 10
3
7.1 × 10
3
8.6 × 10
3
1.0 × 10
4
1.2 × 10
4
1.4 × 10
4
4. Boiling 1.7 × 10
6
1.1 × 10
5
7.5 × 10
4
5.0 × 10
4
3.4 × 10
4
2.3 × 10
4
1.6 × 10
4
1.1 × 10
4
5. Viscous 6.5 × 10
6
9.6 × 10
6
1.4 × 10
7
2.0 × 10
7
3.0 × 10
7
4.3 × 10
7
6.0 × 10
7
8.3 × 10
7
∗
From horizontal axis.
diameter and having a length of 800 mm has been considered
for fabrication of the heat pipe. The gravityassisted heat pipes
permit the maximum liquid ﬂow rate for mesh with pore size
such as 100 or 150. Based on these considerations, two lay
ers of phosphorus bronze wire screen (125 mesh number and
0.085 mm diameter) have been considered for the fabrication
of the wick to maintain the optimum ratio of r
v
/r
o
approxi
mately equal to
√
2/3 [2, 14]. The evaporator length of the
heat pipe is 330 mm so that the aspect ratio (L
e
/d
o
) is greater
than 10.0 in order to get better thermal performance [15]. The
condenser length of the heat pipe is 400 mm, and it has been
provided with 41 annular aluminum ﬁns (50.8 mm diameter ×
0.3 mm thick) at a pitch of 9.0 mm to enhance the rate of heat
transfer [7].
Table 1 shows heat transport limitations of the heat pipe at dif
ferent operating conditions. The capillary limit has been found
to be the smallest of the operating limits. It increases with an
increase in the tilt angle of the heat pipe and evaporator surface
temperature.
In manufacturing the heat pipe, the copper pipe along with
wick has been cleaned. Subsequently, the pipe has been evacu
ated using a vacuum pumping system, followed by a leak test.
Distilled water has been used as working ﬂuid, and after charg
ing, the end of the ﬁll tube is ﬂattened and pinched using crimp
ing tool and welded using TIG (tungsten/inertgas) welding tech
niques. The fabricated heat pipe is suitable for cooling of indus
trial equipment operating at low temperature in the range of
40–90
◦
C.
ANALYTICAL MODEL
The heat pipe has been modeled by adopting a thermal resis
tance network approach. A schematic diagram of the associated
thermal resistances is shown in Figure 2. In the radial direction,
these resistances occur at the interface of the heat source and
external heat pipe wall, in the heat pipe wall, at the liquidwick
interface of the evaporator and condenser, and at the external
condenser section of the heat pipe and heat sink or surrounding.
In axial direction, the thermal resistances occur in the vapor core
between the evaporator and condenser. The thermal resistance
of vapor ﬂow from the evaporator to the condenser is very small
heat transfer engineering vol. 28 no. 11 2007
956 V. KUMAR ET AL.
Figure 2 Thermal resistance network of a heat pipe heated by a ﬂuid at an
average temperature of Th and cooled by a ﬂuid at an average temperature of
T
∞
.
compared to the thermal resistances, which exist at the external
surface of evaporator and condenser [3].
The analytical model has been formulated based on the com
putation of various individual thermal resistances at the external
surface of evaporator and condenser and inside the heat pipe [1,
13]. The overall heat transfer coefﬁcient of the heat pipe has
been computed as follows:
1
U
= R
h
+ R
HP
+ R
c
=
1
h
h
+
1
U
HP,p
+
1
h
c
(2)
The following parameters have been computed for developing
the model.
The heat transfer coefﬁcient on the external surface of evap
orator has been computed by using the following correlation
[11]:
h
h
= 4.55Re
0.733
Pr
0.362
(3)
where
Re =
vD
h
ν
,
v =
4V
f
π
D
2
− d
2
o
, and
D
h
=
D
2
− d
2
o
D + d
o
Heat transport rate of the heat pipe is calculated from the energy
balance:
Q = Heat input to the heat pipe
−heat losses from wooden box surface
= ˙mc
p
(T
i
− T
o
) − h
w
× A
sw
× (T
sw
− T
∞
) (4)
The external surface temperature of the evaporator has been
computed as follows:
T
p,e
=
T
i
+ T
o
2
−
Q
h
h
A
e
(5)
where
A
e
= πd
o
L
e
The internal heat transfer coefﬁcient of the heat pipe and the
condenser surface temperature are calculated based on the fol
lowing correlations [1].
Inside heat transfer coefﬁcient:
U
HP,p
=
1
R
p,e
+ R
w,e
+ R
v
+ R
w,c
+ R
p,c
(6)
Thermal resistance of heat pipe wall at evaporator:
R
p,e
=
r
o
t
p
2L
e
k
p
(7)
Thermal resistance of wick at evaporator:
R
w,e
=
r
2
o
t
w
2L
e
r
i
k
e,e
(8)
Effective thermal conductivity of liquid saturated wick at evap
orator:
k
e,e
=
k
l
[k
l
+ k
w
− (1 −ε
o
)(k
l
− k
w
)]
[k
l
+ k
w
+ (1 −ε
o
)(k
l
− k
w
)]
, k
e,e
= k
e,c
(9)
Thermal resistance of vapor ﬂow from evaporator to condenser:
R
v
=
πr
2
o
F
v
L
e
6
+ L
a
+
L
c
6
T
v,e
ρ
v
λJ
(10)
where
F
v
=
(f
v
Re
v
)ν
v
2A
v
r
2
h,v
λ
Thermal resistance of wick at condenser:
R
w,c
=
r
2
o
t
w
2L
c
r
i
k
e,c
(11)
Thermal resistance of heat pipe wall at condenser:
R
p,c
=
r
o
t
p
2L
c
k
p
(12)
External surface temperature of condenser:
T
p,c
= T
p,e
−
Q
U
HP,p
A
p
(13)
where A
p
is thecross sectional area of the heat pipe.
For determining the heat transfer coefﬁcient at the external
surface of condenser, thermophysical properties of air are cal
culated at ﬁlm temperature (T
f
):
T
f
=
(Wall temparature +Ambient temperature)
2
(14)
heat transfer engineering vol. 28 no. 11 2007
V. KUMAR ET AL. 957
Grashof number and Nusselt number are computed as follows
[6, 16]:
Gr =
gβ(T
p,c
− T
∞
)l
3
ν
2
(15)
where the characteristic length of ﬁnned surface, l, is calculated
from its basic deﬁnition given below:
l = S + 2 ∗ A
f
/P
f
(16)
For inclined position l is taken as l sin ψ, where ψ is the incli
nation angle from horizontal.
The following empirical relations [12] have been used for
calculating the Nusselt number. For laminar ﬂow,
Nu
plate
=0.68 +
0.670Ra
1/4
[1 +(0.492/ Pr)
9/16
]
4/9
for 0 < Ra < 10
9
(17)
For the entire range of Ra,
Nu
plate
=
0.825 +
0.387Ra
1/6
[1 + (0.492/ Pr)
9/16
]
8/27
2
(18)
The Nusselt number is modiﬁed by using a correction factor for
a cylinder:
Nu = Nu
plate
(1 + 1.43ζ
0.9
) (19)
where
ζ = (l/d
o
)Gr
−1/4
Heat transfer coefﬁcient on the outside surface of the condenser,
h
c
:
h
c
=
Nuk
l
(20)
Heat Transfer
The heat transported by the heat pipe includes heat transferred
by convection and radiation from the condenser surface:
Q
T
= Q
C
+ Q
R
(21)
The heat transferred by convection from condenser surface has
been computed as follows:
Q
C
= h
c
(A
o
+ A
f
η
f
)(T
p,c
− T
∞
) (22)
where, as given by [13], the overall ﬁn surface efﬁciency is
expressed as
η
f
= 1 −
A
f
A
c
(1 − η)
and the ﬁn effectiveness is given by
η =
tanh φ
φ
with the following parameters:
φ = mL(R
∗
)
exp(0.13mL−1.3863)
,
R
∗
=
d
f,o
d
o
, and
m =
2h
k
f
t
f
The heat transferred by radiation from condenser surface has
been computed as follows:
Q
R
= σ (A
o
+ A
f
η
f
)εF
T
4
p,c
− T
4
∞
(23)
Computer Code
The various equations used for the computation of overall
heat transfer coefﬁcient have been solved using an iterative pro
cedure by a computer code. The ﬂowchart of the program is
shown in Figure 3. The input parameters required for the code
are heating ﬂuid ﬂow rate and its temperature at the inlet of
evaporator jacket, geometry of heating ﬂuid path, dimensions
of heat pipe, wick and ﬁn, and ambient temperature. This pro
gram has three subroutines, called WATPROP, AIRPROP, and
METPROP, in which the properties of water, air, and metal are
calculated at different operating temperatures. The code com
putes individual heat transfer coefﬁcient on the external surface
of evaporator and condenser, inside the heat pipe, ﬁn efﬁciency,
and the overall heat transfer coefﬁcient.
TEST RIG
A schematic diagram of the test setup to evaluate the thermal
performance of the heat pipe is shown in Figure 4. The test rig
has been provided with hinged type iron stand such that the ther
mal performance of the heat pipe in the bottom heating mode
and the effect of air convection on the ﬁnned condenser can be
evaluated at different tilt angles to the horizontal. The evaporator
section of the heat pipe is enclosed in a cylindrical jacket made
of galvanized iron pipe (75 mm diameter and 450 mm length).
The evaporator heating jacket is insulated with glass wool and
housed in a wooden box, the angle of which can be changed.
The ﬁns at the heat pipe condenser end are exposed to ambi
ent environment with no forced convection. Hot water has been
used as the heating medium to supply the thermal energy to the
evaporator of the heat pipe. Water is heated using an electrical
heater in a heating tank, which is insulated with glass wool and
housed in a wooden box. The power input to the heater has been
controlled by a variac and measured by load manager (Elcontrol
Energy). The hot water from the heating tank has been circu
lated in ﬂexible PVC pipe using a pump through the cylindrical
jacket, which has provision for inlet and outlet. The calibrated
heat transfer engineering vol. 28 no. 11 2007
958 V. KUMAR ET AL.
Figure 3 Flowchart for thermal performance evaluation of a heat pipe.
rotameter has been used for measuring the ﬂow rate of hot water.
The dataacquisition system (Hewlett Packard34970) has been
used to monitor the axial temperature proﬁle at the external
surface of the heat pipe and the inlet and outlet of the evapo
rator jacket using Ttype copper/constantan thermocouple (R S
components, 2194680). Microfoil heat ﬂux sensors (RdF Cor
poration, 2045553) have been ﬁxed on the surface of wooden
box at different locations to measure the heat ﬂux through the
heat transfer engineering vol. 28 no. 11 2007
V. KUMAR ET AL. 959
Figure 4 A schematic diagram of test rig for heat pipe.
wooden box and its surface temperature to estimate its heat
loss.
EXPERIMENTAL PROCEDURE
The performance of the heat pipe has been studied by con
ducting several test runs at a constant ﬂow rate of heating
ﬂuid (0.0000161 m
3
/s) in the evaporator section under labora
tory conditions. The tilt angle of the heat pipe from the hor
izontal axis has been varied as 15
◦
,20
◦
,25
◦
,30
◦
, and 35
◦
,
as literature reports better thermal performance of the heat
pipe/thermosyphon at tilt angles varying from 15
◦
to 30
◦
[17–
19]. One more experiment was conducted under vertical con
dition to compare its thermal performance with inclined con
dition. The temperature of heating ﬂuid at the evaporator inlet
has been varied as 40
◦
C, 50
◦
C, 60
◦
C, and 70
◦
C. The ambi
ent temperature has been measured using a mercury thermome
ter. The variation in ambient temperature is in the range of 13
± 1
◦
C. The temperature data acquisition system and thermo
couples have been calibrated against a precision mercury ther
mometer at ice point and boiling point, and the variations have
been observed within the range of ±0.1
◦
C. The temperature
readings have been recorded after achieving the steadystate
operation of the heat pipe. The error in maintaining heating
ﬂuid temperature at the inlet of evaporator section is in the
range of ±0.5
◦
C and in ﬂow measurement it is of the order
of ±1.8%. The errors have been estimated using standard tech
niques [20, 21]. The standard deviation has been calculated as
follows:
σ =
N
1
(x
i
−
¯
X)
2
(N − 1)
(24)
The temperature difference between the inlet and outlet sections
of the evaporator jacket has been used to compute the heat
input to evaporator section. Individual heat transfer coefﬁcient
at the surface of wooden box has been determined at different
locations by using heat ﬂux sensors. The heat transport rate of
the heat pipe has been calculated as the difference between the
rate of heat input to the evaporator section and heat loss from
the wooden box. Individual heat transfer coefﬁcients at the
external surface of evaporator, inside the heat pipe, and at the
external surface of condenser have been determined based on
the rate of heat transport, temperature of heating ﬂuid, external
surface temperature of the heat pipe at the evaporator and
condenser, and ambient temperature.
EXPERIMENTAL RESULTS AND DISCUSSIONS
Heat Transport Rate
The effect of tilt angle on the rate of heat transport is shown in
Figure 5. The ﬁgure shows that the heat transport rate of the heat
pipe increases as the tilt angle of heat pipe increases from 15
◦
to
25
◦
, and it decreases beyond 25
◦
. The heat transport rate of heat
pipe at 25
◦
tilt angle is 1–16% more than that of the same under
vertical condition. The highest heat transport rate of the heat pipe
has been obtained as 79.9 W at 70
◦
C and 25
◦
tilt angle. The best
thermal performance of the heat pipe under this operating con
dition may be attributed to better exposure of condenser annular
ﬁnned surface to ambient environment and the optimum rate of
evaporation and condensate return to the evaporator, which re
sults in its lower internal and external thermal resistance. The
best thermal performance of heat pipe/thermosyphon has been
reported in the range of 15–30
◦
by various authors [17–19].
As the heating ﬂuid temperature increases at the inlet of evap
orator jacket, the heat transport rate of the heat pipe improves
Figure 5 Effect of tilt angle on the thermal performance of heat pipe.
heat transfer engineering vol. 28 no. 11 2007
960 V. KUMAR ET AL.
Figure 6 Effect of heating ﬂuid temperature on the evaporator heat transfer
coefﬁcient of the heat pipe.
signiﬁcantly due to an increase in the condenser surface temper
ature, which reduces external thermal resistance.
Heat Transfer Coefﬁcient
The outside heat transfer coefﬁcient of the evaporator at dif
ferent heating ﬂuid temperatures and tilt angles is presented in
Figure 6. It is greater at lower tilt angles in the range of 15–25
◦
at
70
◦
C heating ﬂuid temperature, as the temperature drop between
heating ﬂuid and outside evaporator surface temperature is less
as compared to other tilt angles (30–90
◦
). It increases at a higher
heating ﬂuid temperature due to reduction in its thermal resis
tance; however, a few exceptions have been observed in some
cases, which may be attributed to the slight variation in ambient
environment and experimental error. The maximum evaporator
heat transfer coefﬁcient has been found to be 696 W/(m
2
K) at
a15
◦
tilt angle and 70
◦
C heating ﬂuid temperature.
The internal heat transfer coefﬁcient of the heat pipe at a
different heating ﬂuid temperature and tilt angle is shown in
Figure 7. It increases with an increase in the tilt angle from 15
◦
to 90
◦
. It also increases as the heating ﬂuid temperature increases
from 40
◦
Cto70
◦
C, except in a few cases. The maximum inter
nal heat transfer coefﬁcient of the heat pipe has been found to
be 41,327 W/(m
2
K) at 90
◦
tilt angle and 70
◦
C heating ﬂuid
temperature.
Figure 7 Effect of heating ﬂuid temperature on the internal heat transfer co
efﬁcient of the heat pipe.
Figure 8 Effect of heating ﬂuid temperature on the condenser temperature of
the heat pipe.
The outside condenser surface temperature at different tilt
angles and heating ﬂuid temperatures is shown in Figure 8. The
maximum condenser temperature has been found to be 61.66
◦
C
at a 90
◦
tilt angle and 70
◦
C heating ﬂuid temperature, which is
1.77 times more than that at 40
◦
C.
The outside condenser side heat transfer coefﬁcient at various
heating ﬂuid temperatures and different tilt angles is shown in
Figure 9. In most of the cases, these coefﬁcients are found to be
maximum at 60
◦
C heating ﬂuid temperature except at 30
◦
and
35
◦
. It is higher at 25
◦
as compared to other tilt angle because
the rate of heat transport is higher at this angle, which may be
due to better buoyancy driven ﬂow in annular ﬁnned surface of
condenser. The condenser temperature is higher at 90
◦
but the
condenser heat transfer coefﬁcient is low, which is due to the fact
that the amount of heat transported resulting from the horizontal
position of annular ﬁns is less, as the boundary layer may not be
fully developed at the bottom surface of ﬁns.
The temperature drop across the evaporator and condenser is
due to various thermal resistances. A comparison of heat transfer
coefﬁcient at the external surface of evaporator and condenser
has been presented in Table 2 at a 25
◦
tilt angle. It shows that the
outside condenser heat transfer coefﬁcient under natural convec
tion is very low (9.7–12.1 W/m
2
K) as compared to the outside
evaporator heat transfer coefﬁcient of the heat pipe under forced
Figure 9 Effect of heating ﬂuid temperature on the condenser heat transfer
coefﬁcient of the heat pipe.
heat transfer engineering vol. 28 no. 11 2007
V. KUMAR ET AL. 961
Table 2 A comparison of heat transfer coefﬁcients of the heat pipe at
different heating ﬂuid temperatures at 25
◦
tilt angle in bottom heating mode
(based on the external surface area)
Evaporator heat Condenser side
Heating ﬂuid transfer coefﬁcient, heat transfer
Number temperature,
◦
C W/m
2
K coefﬁcient, W/m
2
K
1. 40.9 593 9.7
2. 49.5 574 10.2
3. 60.0 624 12.1
4. 70.3 672 11.8
convection, which varies in the range of 574 to 672 W/m
2
K.
The similar trend has been observed at other tilt angles as well.
The effect of tilt angle on overall heat transfer coefﬁcient is
shown in Figure 10. For tilt angles varying from 15
◦
to 25
◦
,
the overall heat transfer coefﬁcient increases as the heating ﬂuid
temperature increases (from 40
◦
Cto60
◦
C); however, this trend
has not been observed at 70
◦
C, which is due to the fact that the
heat transport rate increases marginally after 60
◦
C. The maxi
mum overall heat transfer coefﬁcient is found to be 11.85 W/(m
2

K) at 60
◦
C heating ﬂuid temperature and 25
◦
tilt angle. Although
the internal heat transfer coefﬁcient of the heat pipe at a 90
◦
tilt
angle is the highest, the outside evaporator and condenser heat
transfer coefﬁcients are lower as compared to the same at 25
◦
tilt angle.
Temperature Distribution of Heat Pipe
Figure 11 shows the external temperature distribution of the
heat pipe along its axial length at 70
◦
C heating ﬂuid tempera
ture. The temperature proﬁle in the evaporator section decreases
smoothly and linearly. The temperature drop has been found to
be small in the evaporator section along its axial length. The tem
perature drop between the heating ﬂuid and evaporator external
surface is small, which is due to a higher outside heat transfer
coefﬁcient at the evaporator and high heat carrying capacity of
heating ﬂuid (i.e., water), whereas in the condenser section, the
temperature drop is high along the external surface of the heat
pipe due to low outside heat transfer coefﬁcient as well as low
heat carrying capacity of cooling ﬂuid (i.e., ambient air). The
Figure 10 Effect of heating ﬂuid temperature on the overall heat transfer
coefﬁcient of the heat pipe.
Figure 11 External surface temperature of the heat pipe at 70
◦
C heating ﬂuid
temperature.
similar heat transfer characteristics have been shown by the heat
pipe at other heating ﬂuid temperatures, varying from 40
◦
Cto
60
◦
C.
The temperature drop across the external end of evaporator
and condenser at different heating ﬂuid temperatures and tilt
angles is shown in Figure 12. The temperature drop between
evaporator and condenser end at constant heating ﬂuid temper
ature decreases as the tilt angle increases from 15
◦
to 90
◦
.At
constant tilt angle, it increases as the heating ﬂuid temperature
increases from 40
◦
Cto70
◦
C, which indicates that more heat is
transported at the higher heating ﬂuid temperature. The maxi
mum temperature drop across the evaporator and condenser is
found to be 15.1 K at the 15
◦
tilt angle and 70
◦
C heating ﬂuid
temperature, but heat transport is not the maximum at this tilt an
gle. This indicates that the heat transport of a heat pipe depends
on tilt angle as well as heating ﬂuid temperature.
VALIDATION OF THE ANALYTICAL MODEL
To test the validity of the model, some typical experimental
heat transfer coefﬁcients obtained at a 25
◦
tilt angle have been
compared with the results predicted by the analytical model.
Figure 12 Effect of heating ﬂuid temperature on the temperature drop across
evaporator and condenser end of the heat pipe.
heat transfer engineering vol. 28 no. 11 2007
962 V. KUMAR ET AL.
Figure 13 Evaporator heat transfer coefﬁcient computed by the analytical
model and obtained from experiments.
Outside Evaporator Heat Transfer Coefﬁcient
A comparison of the outside evaporator heat transfer coefﬁ
cient and surface temperature, as determined by the developed
analytical model and the experimental values, are shown in Fig
ures 13 and 14, respectively. The evaporator heat transfer co
efﬁcient and surface temperature predicted by the model have
close agreement with experimental values. The variation is in the
range of 4–12% in the case of evaporator heat transfer coefﬁcient
and 1.7–2.9 % in the case of evaporator surface temperature.
Internal Heat Transfer Coefﬁcient
The internal heat transfer coefﬁcient and outside condenser
surface temperature predicted by the analytical model [1] and
the experimentally determined values are shown in Figures 15
and 16, respectively. It has been observed that the predicted
heat transfer coefﬁcients at different heating ﬂuid temperatures
are 2.5 to 3.6 times more as compared to the experimental val
ues; therefore, the predicted condenser temperature is on the
higher side (6.6–9.6%) as compared to the experimental value.
Figure 14 Evaporator surface temperature predicted by the analytical model
and measured experimentally.
Figure 15 Internal heat transfer coefﬁcient computed by the analytical model
and obtained from experiments.
The analytical prediction reveals that the thermal resistances of
the wick structure at the evaporator and condenser end are very
high, which governs the internal heat transfer coefﬁcient of the
heat pipe to a greater extent. The lower experimental value of
internal heat transfer coefﬁcient may be due to higher thermal
resistances of wick structure of the heat pipe and imperfect con
tact of wick to the heat pipe container wall. From the present
investigation, it has been found that the model overpredicts the
internal heat transfer coefﬁcient and condenser surface temper
ature. Terdtoon et al. [22] found that the condenser temperature
of a plastic heat pipe, predicted by the mathematical model of
Shiraishi et al. [23], is 13% higher than their experimental value.
The condenser temperature predicted by the analytical model of
Krishnamoorthy and Pillai [5] has been found to be 5% more
than their experimental value.
Outside Condenser Heat Transfer Coefﬁcient
Even though the Rayleigh number of cooling ﬂuid is in lam
inar ﬂow regime, the condenser heat transfer coefﬁcient, pre
dicted by Churchill and Chu (for all ranges of Rayleigh number)
[12] is closer (1–12%) to the experimental value as compared to
Figure 16 A comparison of the condenser temperature computed by the an
alytical model and measured experimentally.
heat transfer engineering vol. 28 no. 11 2007
V. KUMAR ET AL. 963
Figure 17 Outside condenser heat transfer coefﬁcient computed by the ana
lytical model and obtained from experiments.
Churchill and Chu’s correlation for laminar range, which varied
in the range of 5–18%. A comparison of condenser heat transfer
coefﬁcient predicted by the developed analytical model and the
experimental values is shown in Figure 17. The predicted heat
transfer coefﬁcient is higher as compared to the experimental
value, which is due to the fact that the model predicts a higher
value of internal heat transfer coefﬁcient and condenser temper
ature.
Overall Heat Transfer Coefﬁcient
The overall heat transfer coefﬁcient has been computed by
using the correlation proposed by Dobson and Kr¨oger [11], Chi
[1], and Churchill and Chu (for all ranges of Rayleigh number)
[12] in the analytical model. A comparison of the overall heat
transfer coefﬁcient predicted by the analytical model and exper
imentally determined values is shown in Figure 18. The overall
heat transfer coefﬁcient predicted by the analytical model is in
good agreement with experimental values, although there is a
deviation in the analytically computed value of an internal heat
transfer coefﬁcient. The value of the internal heat transfer coef
ﬁcient is very high, and it contributes practically nothing to the
Figure 18 Overall heat transfer coefﬁcient computed by the analytical model
and obtained from experiments.
overall heat transfer coefﬁcient, which is mostly governed by
condenser and to a much less degree by evaporator heat transfer
coefﬁcient. Therefore, the model developed could reasonably
predict the overall heat transfer coefﬁcient, as the variation is
within 9%.
The analysis has helped to validate the model, which would
be useful for the designer to evaluate the thermal performance
of a heat pipe under various operating conditions. The model
can reduce the design cycle of equipment by predicting differ
ent thermal resistances associated with heat pipe under various
operating conditions.
The analytical model prediction can be improved by incorpo
rating evaporation and condensation thermal resistances, which
is a suggested work for future study.
CONCLUSIONS
An analytical model, based on thermal resistance network
method, has been developed to compute the overall heat trans
fer coefﬁcient of a heat pipe in which the evaporator is exposed
to forced convection and the condenser to natural convection. A
test rig has been fabricated to evaluate its thermal performance.
Experimental studies have been conducted to characterize the
thermal behavior of the heat pipe, and some typical experimen
tal results have been used to validate the analytical model de
veloped. The conclusions drawn from present investigations are
summarized as follows.
The annular ﬁnned heat pipe gives better heat transport rate
under inclined condition as compared to vertical condition. The
heat transport rate of the heat pipe increases as the tilt angle in
creases from 15
◦
to 25
◦
at a constant heating ﬂuid temperature,
and it decreases beyond 25
◦
tilt angle. At a constant tilt angle,
the temperature drop across the evaporator and condenser sec
tions of the heat pipe increases, as the heating ﬂuid temperature
increases from 40
◦
Cto70
◦
C at the evaporator inlet. The maxi
mum heat transport rate of the heat pipe has been obtained at a
tilt angle of 25
◦
and 70
◦
C heating ﬂuid temperature.
The heat transfer coefﬁcient on the external surface of the
evaporator predicted by the analytical model is close to the ex
perimental value. The internal heat transfer coefﬁcient of the
heat pipe determined by the model is much higher than the
experimental value due to which a higher value of condenser
temperature is predicted. The outside condenser heat transfer
coefﬁcient predicted by the model is reasonably matching with
experimental value.
The overall heat transfer coefﬁcient computed by the ana
lytical model is in close agreement with the experimental val
ues because of closer prediction of the evaporator and con
denser heat transfer coefﬁcient at its external surface, whereas
the value of the internal heat transfer coefﬁcient is very high
and does not contribute signiﬁcantly to the overall heat transfer
coefﬁcient.
The model can be used as a design tool to evaluate the thermal
performance of heat pipe under various operating conditions.
heat transfer engineering vol. 28 no. 11 2007
964 V. KUMAR ET AL.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support provided by
management of Thapar Institute of Engineering and Technol
ogy, Patiala and Thapar Centre for Industrial Research and De
velopment, Patiala, India, for providing the necessary facilities
to carry out this research work. The authors wish to thank the
management of CDAC, Pune, India for providing the comput
ing facility as well as the encouragement for writing this paper.
NOMENCLATURE
A crosssection area, m
2
A
c
external surface area of condenser, m
2
A
e
external surface area of evaporator, m
2
A
f
ﬁn surface area, m
2
A
o
external condenser surface area without ﬁn, m
2
A
sw
surface area of wooden box, m
2
A
v
vapor core area, m
2
c
p
speciﬁc heat, J/(kgK)
D inner diameter of cylindrical jacket, m
d
f,o
ﬁn outside diameter, m
D
h
hydraulic diameter, m
d
o
outside heat pipe diameter, m
F shape factor, 0.28
F
v
frictional coefﬁcient for vapor, Pa/(Wm)
f
v
R
ev
drag coefﬁcient, 16
g acceleration due to gravity, m
2
/s
Gr Grashof number
h heat transfer coefﬁcient, W/(m
2
K)
h
h
external heat transfer coefﬁcient on evaporator,
W/(m
2
K)
h
w
heat transfer coefﬁcient of wooden box, W/(m
2
K)
i point number of the series
J mechanical heat equivalent, J/cal
k thermal conductivity, W/(mK)
k
e,c
effective thermal conductivity of liquid saturated wick
at condenser, W/(mK)
k
e,e
effective thermal conductivity of liquid saturated wick
at evaporator, W/(mK)
l characteristic length, m
L ﬁn length, m
L
a
adiabatic length of heat pipe, m
L
c
condenser length of heat pipe, m
L
e
evaporator length, m
L
t
total length of heat pipe, m
M mass of working ﬂuid, kg
˙m mass ﬂow rate, kg/s
N total number of measurements
Nu Nusselt number
P
f
ﬁn perimeter, m
Pr Prandtl number
Q heat transfer rate, W
R
c
condenser side convective resistance, m
2
K/W
R
h
evaporator side convective resistance, m
2
K/W
R
HP
total thermal resistance of heat pipe, m
2
K/W
r
h,v
vapor hydraulic radius, m
r
i
inside radius of heat pipe, m
r
o
outside radius of pipe, m
r
v
vapor core radius, m
R
p,c
thermal resistance of heat pipe wall at condenser,
m
2
K/W
R
p,e
thermal resistance of heat pipe wall at evaporator,
m
2
K/W
R
v
thermal resistance of vapor ﬂow from evaporator to
condenser, m
2
K/W
R
w,c
thermal resistance of wick at condenser, m
2
K/W
R
w,e
thermal resistance of wick at evaporator, m
2
K/W
Ra Rayleigh number, Ra = Gr
∗
Pr
Re Reynolds number
S ﬁn spacing, m
T temperature,
◦
C
t
f
ﬁn thickness, m
T
i
inlet temperature at evaporator jacket,
◦
C
T
o
outlet temperature at evaporator jacket,
◦
C
t
p
heat pipe wall thickness, m
T
p,c
condenser pipe wall temperature,
◦
C
T
p,e
evaporator pipe wall temperature,
◦
C
T
pw,c
temperature at the interface of condenser pipe wall and
saturated wick,
◦
C
T
pw,e
temperature at the interface of evaporator pipe wall and
saturated wick,
◦
C
T
sw
surface temperature of wooden box,
◦
C
T
v,c
vapor temperature at condenser,
◦
C
T
v,e
vapor temperature at evaporator,
◦
C
t
w
wick thickness, m
T
∞
ambient temperature,
◦
C
U overall heat transfer coefﬁcient, W/(m
2
K)
U
HP,p
overall heat transfer coefﬁcient of heat pipe based on
outer diameter, W/(m
2
K)
V
f
volumetric ﬂow rate of heating ﬂuid, m
3
/s
v velocity, m/s
¯
X arithmetic mean of the measurement
x
i
value of the measurement at i
th
point
Greek Symbols
ρ ﬂuid density [kg/m
3
]
σ Stefan Boltzmann constant, W/(m
2
K
4
),
5.669E8 W/(m
2
K
4
)
ε emissivity, 0.77
ε
o
porosity of wick material, dimensionless, 0.65
ν kinematic viscosity, m
2
/s
β volumetric expansion coefﬁcient, 1/K
η ﬁn effectiveness
η
f
overall ﬁn surface efﬁciency
λ latent heat of vaporization, J/kg
ψ inclination angle from horizontal
heat transfer engineering vol. 28 no. 11 2007
V. KUMAR ET AL. 965
Subscripts
C convection
c condenser
fﬁn
h hot
in input
l liquid
out output
p pipe
R radiation
T total
v vapor
w wick
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Vikas Kumar is a team leader of the Compu
tational Fluid Dynamics group at the Centre for
Development of Advanced Computing, Pune, In
dia. He obtained his Ph.D. in heat transfer from
Thapar Institute of Engineering & Technology,
Patiala, India. Currently, he is working in the area
of heat transfer and ﬂuid ﬂow.
D. Gangacharyulu is an associate professor in
the Chemical Engineering Department at Thapar
Institute of Engineering & Technology, Patiala,
India. He obtained his Ph.D. in the area of heat
exchanger from Thapar Institute of Engineering
& Technology, Patiala, India. His research inter
ests are heat transfer, heat exchangers, process
simulation, and computational ﬂuid dynamics.
Ram Gopal Tathgir is a professor in the Mechan
ical Engineering Department at Thapar Institute
of Engineering & Technology, Patiala, India. He
obtained his Ph.D. in the area of energy studies
from Punjabi University, Patiala, India. His re
search interests include heat transfer, heat pipe,
and energy studies.
heat transfer engineering vol. 28 no. 11 2007