Modeling and Simulation of the Heat Transfer Behaviour
of a Shell-and-Tube Condenser for a Moderately High-Temperature Heat Pump

79
The estimation procedures for sizing a shell-and-tube condenser is shown as follows:
• Input design parameters:
• Input design parameters include: refrigerant inlet/outlet temperatures, refrigerant inlet
pressure, water inlet/outlet temperatures, water and refrigerant mass flow rates,
condensing temperature, number of copper tubes, tube inner/outer diameters, shell
inner diameter, baffle spacing, and copper tube spacing.
• Give a tube length and shell-side outlet temperature to be initial guess values for
Section-I calculation.
• Calculate the physical properties for Section-I and Section-II.
• Calculate the overall heat transfer rates by present model.
• Check the percent error between model predicting and experimental data for overall
heat transfer rates. If the percent error is less than the value of 0.01%, then output the
tube length and end the estimation process; if it is larger than the percent error, then set
a new value for
L and return to the second step.
In accordance with the above estimation procedures, the resulting length is 0.694 m when
input the experimental data set, Case 1, as the design parameters for sizing. The same
estimation procedures are utilizing to another 26 cases, and the results are shown in Figure
10. Fig. 10. Estimation results for sizing condensers
Comparisons between the estimating values length for all the cases and the experimental
data (0.7 m) indicats that the relative error were within ± 10 % with an average CV value of
3.16 %. In summary, the results from the application of present model on heat exchanger
sizing calculation are satisfactory.
5.2 Rating problem (Estimation of thermal performance)

r
) as an initial guess for Section-I.
• Calculate the properties for Section-I and Section-II.
• Calculate the overall heat transfer rates by present model.
• Check the percent error between model predicting and experimental data for overall
heat transfer rates. If the percent error is less than the value of 0.01%, then output the
refrigerant outlet temperature, water outlet temperature, and heat transfer rate; if it is
larger than the percent error, then reset a new refrigerant outlet temperature, and
return to the second step.
In accordance with the above calculation process, the experimental data of Case 1 can be
used as input into the present model for rating calculations. The calculation results give the
water outlet temperature is 74.84°C, refrigerant outlet temperature is 64.35°C, and heat
transfer rate was is 33.01 kW. Experimental data of Case 2 were used as input into the rating
calculation process, and another set of result tell: water outlet water temperature is 45.16 °C,
refrigerant outlet temperature is 39.04 °C, and heat transfer rate is 35.03 kW. Repeat the
same procedures for the remaining 26 sets of experimental data, the calculation results for
rating are displayed in Figures 11.
As depicted in Figure 11, comparison of the model predicting and the experimental data for
water outlet temperature, refrigerant outlet temperature and heat transfer rates show that
the average CV values are 0.63%, 0.36%, and 1.02% respectively. In summary, the predicting
accuracies of present model on shell-and-tube condenser have satisfactory results.
6. Conclusion
This study investigated the modelling and simulation of thermal performance for a shell-
and-tube condenser with longitude baffles, designed for a moderately high-temperature
heat pump. Through the validation of experimental data, a heat transfer model for
predicting heat transfer rate of condenser was developed, and then used to carry out size
estimation and performance rating of the shell-and-tube condenser for cases study. In
summary, the following conclusions were obtained:
• A model for calculation, size estimation, and performance rating of the shell-and-tube
condenser has been developed, varified, and modified. A good agreement is observed

＆ Mirgolbabaei, H. (2010). An experimental study of
thermal performance of shell-and-coil heat exchangers.
International communications
in Heat and Mass Transfer
, Vol. 37, pp. 775-781.
Hewitt, G.F. (1998).
Heat Exchanger Design Handbook, ISBN 1-56700-097-5, Begell House, New
York.
Holman, J.P. (2000).
Heat Transfer, ISBN 957-493-199-4, McGraw-Hill, New York.
Kakac, S.,
＆ Liu, H. (2002). Design correlations for condensers and Evaporators, In:Heat
Exchangers, pp. 229-236, CRC press, ISBN 0-8493-0902-6, United Ststes of America.
Kara, Y.A.,
＆ Güraras, Ö. (2004). A computer program for designing of shell-and-tube heat
exchangers.
Applied Thermal Engineering, Vol. 24, pp. 1797-1805.
Karlsson, T., & Vamling, L. (2005). Flow fields in shell-and-tube condensers: comparison of a
pure refrigerant and a binary mixture.
International Journal of Refrigeration , Vol. 28,
pp. 706-713.
Karno, A., & Ajib, S. (2006). Effect of tube pitch on heat transfer in shell-and-tube heat
exchangers—new simulation software.
Springer-Verlag, Vol. 42, pp. 263-270.
Kern, D.Q. (1950).
Process Heat Transfer, ISBN 0070341907, McGraw-Hill, New York.
Li, Y., Jiang, X., Huang, X., Jia, J., & Tong, J. (2010). Optimization of high-pressure shell-and-
tube heat exchanger for syngas cooling in an IGCC.
International Journal of Heat and
Mass Transfer

Iran
1. Introduction
In every system, if Knudsen number is larger than 0.1, the Navier-Stokes equation will not
be satisfied for investigation of flow patterns. In this condition, the Boltzmann equation,
presented by Ludwig Boltzmann in 1872, can be useful. The conditions that this equation
can be used were investigted by Cercignani in 1969. The most successful method for solving
Boltzmann equation for a rarefied gas system is Direct Simulation Monte Carlo (DSMC)
method. This method was suggested by Bird in 1974. The cylindrical Couette flow and
occurrence of secondry flow (Taylor vortex flow) in a annular domin of two coaxial rotating
cylinders is a classical problem in fluid mechanics. Because this type of gas flow can occur in
many industrical types of equipment used in chemical industries, Chemical engineers are
interested in this problem. In 2000, De and Marino studied the effect of Knudsen number on
flow patterns and in 2006 the effect of temperature gradient between two cylinders was
investigated by Yoshio and his co-workers. The aim of the present paper is investigation of
understanding of the effect of different conditions of rotation of the cylinders on the vortex
flow and flow patterns.
2. Mathematical model
In the Boltzmann equation, the independent variable is the proption of molecules that are in
a specific situation and dependent variables are time, velocity components and molecules
positions. We consider the Boltzmann equation as follow:

fff
FQff
tKn
x
1
(,)
δδδ
ν
δ

f

is zero, we can rewrite
equation 2 as:

Two Phase Flow, Phase Change and Numerical Modeling

84

RS RS
Qf f f fd d ffd d
32 32
****
**
(,) ( ,) ( ,)
σν ν ω ων σν ν ω ων
′′
=− −−
 


(3)
The sign ‘ is refered to values of distribution function after collision. The value of above
integral is not related on
V

, then we have

RS RS
Q f f f fd d f fd d

()
μ
ν

as

m
()
κ
ρ
μν μ
==

(6)
Then the Boltzmann equation can be written as

ff
Pf f f
tKn
x
1
.(,)()
δδ
νμ
ν
δ
δ


+= −



== −



(9)
Equation 8 describes the movement of the particles and equation 9 explains the collision of
the particles. For estimation of new position of a mobile particle, we use following
realationship

new old
xx t.
ν
=+Δ


(10)
For solving equation 9 by a numerical method, we can write it as

nn
nn n
ff
Pf f f
tKn
1
1
(,)
μ
+

Equation (12) is solved using the DSMC method. DSMC is a molecule-based statistical
simulation method for rarefied gas introduced by Bird (2). It is a numerical solution method
to solve the dynamic equation for gas flow by at least thousands of simulated molecules.
Under the assumption of molecular chaos and gas rarefaction, the binary collisions are only
considered. Therefore, the molecules' motion and their collisions are uncoupling if the
computational time step is smaller than the physical collision time. After some steps, the
macroscopic flow characteristics should be obtained statistically by sampling molecular
properties in each cell and mean value of each property should be recorded. For estimation
of macroscopic characteristics we used following realationship

f
d
3
ρ
ν
ℜ
=


(13)
u
f
d
3
ρ
νν
ℜ
=



cylindrical domin R1<R2
، 02
π
≤Θ≤ and zL0 ≤≤. Two cylinders are rotating around z-
axes at surfac velocities
V
1Θ
and
V
2Θ
in the Θ direction. We will investigate the behavior of
the gas numerically on the basis of Kinetic theory. The flow field is symmetric and the gas
molecules are Hard-Sphere undergo diffuse reflection on the surface of the cylinders and
specular reflection on the bottom and top boundaries. Here
Kn R
00
/
λ
=Δ
is the Knudsen
number with
0
λ
being the mean free path of the gas molecules in the equilibrium state at rest
with temerature
T
0
and density
0
ρ

temperature plot at pressure 4, 40 and 400 Pa. It can be seen when the outlet cylinder is
stagnant, the maximum amount of the temperature gradient occurs at the middle section
and near the walls of the inlet cylinder. Fig. 6 shows density contour at pressure 4 Pa then
maximum amount of density is near the walls of the outlet cylinder. Fig. 7 shows density
contour at VRT
1/2
10
/(2 )
Θ
= 0.26

and

VRT
1/2
20
/(2 )
Θ
= 0.52. Fig. 8 shows the flow field of
single vortex flow at VRT
1/2
10
/(2 )
Θ
= 0.81 and VRT
1/2
20
/(2 )
Θ
= -0.237.

1/2
10
/(2 )
Θ
= 0.26 VRT
1/2
20
/(2 )
Θ
0.52=

Simulation of Rarefied Gas Between Coaxial Circular Cylinders by DSMC Method

89

Fig. 8. Flow filed of single-vortex Flow VRT
1/2
10
/(2 )
Θ
= 0.81 VRT
1/2
20
/(2 )
Θ
=-0.237 Fig. 9. Flow filed of double-vortex Flow VRT
1/2

Θ
= -0.311. It can be seen from these figures when
pressure increases, we have weaker vortex flow. Figure 11 shows density when
V
1Θ
= 1000
m/s is constant and
V
2Θ
is 200, 500 and 1000 m/s. According to this figure, if the velocity of

Two Phase Flow, Phase Change and Numerical Modeling

90
the outlet cylinder increases, density changes rapidly. Figure 12 shows temperature changes
when
V
1Θ
= 1000 m/s is constant and V
2Θ
is 200, 500 and 1000 m/s. It can be seen that
maximum temperature occurs when the velocity of the outlet cylinder is 200 m/s. Figure 13
shows radial velocity at 4, 40 and 400 Pa. The results show different flow patterns at
different temperature and pressure. Fig. 10. Flow filed of single-vortex Flow VRT
1/2
10
/(2 )

4. Conclusions
In this work, The Couette-Taylor flow for a rarefied gas is supposed to be contained in an
annular domain, bounded by two coaxial rotating circular cylinders. The Boltzmann
equation was solved with DSMC method. The results showed different type of flow
patterns, as Couette-Taylor flow or single and double vortex flow, can be created in a wide

Two Phase Flow, Phase Change and Numerical Modeling

92
range of speed of rotation of inner and outer cylinders. This work shows if size or number
of cells is not proper, we cannot obtain reasonable results by using DSMC method.
5. Nomenclature
f = density distribution function
F = external forces filed
K = Boltzmann constant
K
n
=Knudsen number
m = molecular wieght
p = pressure
Q = collision integral
T = temperature
R1 =radius of the inlet cylinder
R2 =radius of the outlet cylinder
T
tr
=translational temperature
u = free stream velocity

v = molecular velocity

Including Grooved Capillary Structures
Zaghdoudi Mohamed Chaker, Maalej Samah and Mansouri Jed
University of Carthage – Institute of Applied Sciences and technology
Research Unit Materials, Measurements, and Applications
Tunisia
1. Introduction
Thermal management of electronic components must solve problems connected with the
limitations on the maximum chip temperature and the requirements of the level of
temperature uniformity. To cool electronic components, one can use air and liquid coolers as
well as coolers constructed on the principle of the phase change heat transfer in closed
space, i.e. immersion, thermosyphon and heat pipe coolers. Each of these methods has its
merits and draw-backs, because in the choice of appropriate cooling one must take into
consideration not only the thermal parameters of the cooler, but also design and stability of
the system, durability, technology, price, application, etc.
Heat pipes represent promising solutions for electronic equipment cooling (Groll et al.,
1998). Heat pipes are sealed systems whose transfer capacity depends mainly on the fluid
and the capillary structure. Several capillary structures are developed in order to meet
specific thermal needs. They are constituted either by an integrated structure of
microchannels or microgrooves machined in the internal wall of the heat spreader, or by
porous structures made of wire screens or sintered powders. According to specific
conditions, composed capillary structures can be integrated into heat pipes.
Flat Miniature Heat Pipes (FMHPs) are small efficient devices to meet the requirement of
cooling electronic components. They are developed in different ways and layouts, according
to its materials, capillary structure design and manufacturing technology. The present study
deals with the development of a FMHP concept to be used for cooling high power
dissipation electronic components. Experiments are carried out in order to determine the
thermal performance of such devices as a function of various parameters. A mathematical
model of a FMHP with axial rectangular microchannels is developed in which the fluid flow
is considered along with the heat and mass transfer processes during evaporation and
condensation. The numerical simulations results are presented regarding the thickness

l
c
Condenser width, m
L
c
Condenser length, m
l
e
Evaporator width, m
L
e
Evaporator length, m
m

Mass flow rate, kg/s
m
1
Constant in Eq. (8)
m
2
Constant in Eq. (8)
m
3
Constant in Eq. (8)
N
g
Number of grooves
Nu Nüsselt number
P Pressure, N/m²
Pr Prandtl number

T
sf
Heat sink temperature, °C

T
w
Wall temperature, °C
V Voltage, V
V
e
Velocity, m/s
w Axial velocity, m/s
W FMHP width, m
W
g
Groove width, m
z Coordinate, m
Greek Symbols
α Contact angle, °
β Tilt angle, °
ΔT Temperature difference = T
ev
–T
c
, K
Δh
v
Latent heat of vaporization, J/kg
ΔP Pressure drop, N/m²
λ Thermal conductivity, W/m.K

within Flat Mini Heat Pipe Including Grooved Capillary Structures

95
3. Literature survey on mini heat pipes prototyping and testing
This survey concerns mainly the FMHPs made in metallic materials such as copper,
aluminum, brass, etc. For the metallic FMHPs, the fabrication of microgrooves on the heat
pipe housing for the wick structure has been widely adopted as means of minimizing the
size of the cooling device. Hence, FMHPs include axial microgrooves with triangular,
rectangular, and trapezoidal shapes. Investigations into FMHPs with newer groove designs
have also been carried out, and recent researches include triangular grooves coupled with
arteries, star and rhombus grooves, microgrooves mixed with screen mesh or sintered metal.
The fabrication of narrow grooves with sharp corner angle is a challenging task for
conventional micromachining techniques such as precision mechanical machining.
Accordingly, a number of different techniques including high speed dicing and rolling
method (Hopkins et al., 1999), Electric-Discharge-Machining (EDM) (Cao et al., 1997; Cao
and Gao, 2002; Lin et al., 2002), CNC milling process (Cao and Gao, 2002; Gao and Cao,
2003; Lin et al., 2004; Zaghdoudi and Sarno, 2001, Zaghdoudi et al., 2004; Lefèvre et al.,
2008), drawing and extrusion processes (Moon et al., 2003, 2004; Romestant et al., 2004;
Xiaowu, 2009), metal forming process (Schneider et al., 1999a, 1999b, 2000; Chien et al.,
2003), and flattening (Tao et al., 2008) have been applied to the fabrication of microgrooves.
More recently, laser-assisted wet etching technique was used in order to machine fan-shaped
microgrooves (Lim et al., 2008). A literature survey of the micromachining techniques and
capillary structures that have been used in metallic materials are reported in table 1.
It can be seen from this overview that three types of grooved metallic FMHP are developed:
i. Type I: FMHPs with only axial rectangular, triangular or trapezoidal grooves
(Murakami et al., 1987; Plesh et al., 1991; Sun and Wang, 1994; Ogushi and Yamanaka.,
1994; Cao et al., 1997; Hopkins et al., 1999; Schneider et al., 1999a, 1999b, 2000; Avenas et
al., 2001, Cao and Gao, 2002, Lin et al., 2002; Chien et al., 2003; Moon et al., 2003, 2004;
Soo Yong and Joon Hong, 2003; Lin et al., 2004; Romestant et al., 2004; Zhang et al.,
2004; Popova et al., 2006; Lefevre et al., 2008; Lim et al., 2008; Tao et al., 2008, Zhang et

Triangular and
rectangular grooves
Plesh et al. (1991) __
a
Copper
Axial and transverse
rectangular grooves
Sun and Wang (1994) __
a
Aluminum V-shaped axial grooves
Ogushi and
Yamanaka (1994)
__
a
Brass
Triangular and
trapezoidal axial
grooves
Cao et al. (1997)
Electric-discharge-machining
(EDM)
Copper
Rectangular axial
grooves
Hopkins et al. (1999)
Rolling method
High-speed dicing saw
Copper
Trapezoidal diagonal
grooves

(EDM)
Copper
Rectangular axial
grooves
Chien et al. (2003) Metal forming process Aluminum
Radial rectangular
grooves
Gao and Cao (2003) Milling process Aluminum
Waffle-like cubes
(protrusions)
Moon et al. (2003)
Drawing and extrusion
process
Copper
Triangular and
rectangular axial
grooves with curved
walls
Soo Yong and Joon
Hong (2003)
__
a
__
a

Rectangular axial
grooves with half circle
shape at the bottom
Lin et al. (2004)
Etching, CNC milling, and

Rectangular axial
grooves
Trapezoidal axial
grooves
Iavona et al. (2005)
Direct Bounded Copper
technology
Copper/Al
umina
Fiber mixed material of
Al
2
O
3
and SiO
2

Popova et al. (2005) __
a
Copper
Rectangular grooves
machined in sintered
copper structure
Popova et al. (2006) __
a
Copper
Rectangular grooves
machined in sintered
copper structure
Lefèvre et al. (2008) Milling process Copper

degradation, can be avoided.
ii. The choice and the quantity of the introduced fluid in the microchannel play a
primordial role for the good operation of the FMHP.
iii. Although the heat flux rates transferred by FMHPs with integrated capillary structure
are low, these devices permit to transfer very important heat fluxes avoiding the
formation of hot spots. Their major advantage resides in their small dimensions that
permit to integrate them near the heat sources.
4. Literature survey on micro/mini heat pipe modeling
For FMHPs constituted of an integrated capillary structure including microchannels of
different shapes, the theoretical approach consists of studying the flow and the heat transfer

Two Phase Flow, Phase Change and Numerical Modeling

98
in isolated microchannels. The effect of the main parameters, of which depends the FMHP
operation, can be determined by a theoretical study. Hence, the influence of the liquid and
vapor flow interaction, the fill charge, the contact angle, the geometry, and the hydraulic
diameter of the microchannel can be predicted by models that analyze hydrodynamic aspect
coupled to the thermal phenomena.
Khrustalev and Faghri (1995) developed a detailed mathematical model of low-temperature
axially grooved heat pipes in which the fluid circulation is considered along with the heat
and mass transfer processes during evaporation and condensation. The results obtained are
compared to existing experimental data. Both capillary and boiling limitations are found to
be important for the flat miniature copper-water heat pipes, which is capable of
withstanding heat fluxes on the order of 40 W/cm² applied to the evaporator wall in the
vertical position. The influence of the geometry of the grooved surface on the maximum
heat transfer capacity of the miniature heat pipe is demonstrated.
Faghri and Khrustalev (1997) studied an enhanced flat miniature heat pipes with capillary
grooves for electronics cooling systems, They survey advances in modeling of important
steady-state performance characteristics of enhanced and conventional flat miniature

An improved model is suggested and it is compared with the simulation and experimental
Theoretical and Experimental Analysis of Flows and Heat Transfer
within Flat Mini Heat Pipe Including Grooved Capillary Structures

99
results. The improved model implements a different analytically derived form of the friction
factor-Reynolds number product (Poiseuille number). The simulated results with the
proposed model demonstrate better coherence to the experiment showing the importance of
accurate physical modeling to heat conduction behavior of the FMHP.
Shi et al. (2006) carried out a performance evaluation of miniature heat pipes in LTCC by
numerical analysis, and the optimum miniature heat pipe design was defined. The effect of
the groove depth, width and vapor space on the heat transfer capacity of miniature heat
pipes was analyzed.
Do et al. (2008) developed a mathematical model for predicting the thermal performance of
a FMHP with a rectangular grooved wick structure. The effects of the liquid-vapor
interfacial shear stress, the contact angle, and the amount of liquid charge are accounted for
in the present model. In particular, the axial variations of the wall temperature and the
evaporation and condensation rates are considered by solving the one-dimensional
conduction equation for the wall and the augmented Young-Laplace equation, respectively.
The results obtained from the proposed model are in close agreement with several existing
experimental data in terms of the wall temperatures and the maximum heat transport rate.
From the validated model, it is found that the assumptions employed in previous studies
may lead to significant errors for predicting the thermal performance of the heat pipe.
Finally, the maximum heat transport rate of a FMHP with a grooved wick structure is
optimized with respect to the width and the height of the groove by using the proposed
model. The maximum heat transport rate for the optimum conditions is enhanced by
approximately 20%, compared to existing experimental results.
Do and Jang (2010) investigated the effect of water-based Al2O3 nanofluids as working fluid
on the thermal performance of a FMHP with a rectangular grooved wick. For the purpose,
the axial variations of the wall temperature, the evaporation and condensation rates are

indicated in table 2 and in Fig. 1. A view of the microchannels is shown in Fig. 2.
Filling the FMHP presents one of the greatest challenges. In this study, a boiling method is
used for the filling purpose. The filling assembly includes a vacuum system, a boiler filled
with distilled water, vacuum tight electrovalves, a burette for a precise filling of the FMHP
and a tubular adapter. The degassing and charging procedure consists of the following
steps: (i) degassing water by boiling process, (ii) realizing a vacuum in the complete set-up,
(iii) charging of the burette, and (iv) charging of the FMHP. An automatic process controls
the whole steps. After charging the FMHP, the open end (a 2 mm diameter charging tube) is
sealed. The amount of liquid is controlled by accurate balance. Indeed, the FMHP is
weighed before and after the fill charging process and it is found that the optimum fill
charge for the FMHP developed in this study is 1.2 ml. Fig. 1. Sketch of the FMHPs Fig. 2. View of the microchannels
Theoretical and Experimental Analysis of Flows and Heat Transfer
within Flat Mini Heat Pipe Including Grooved Capillary Structures

101
FMHP width, W 50
FMHP overall length, L
t
100
FMHP thickness, t 3
Microchannel height, D
g
0.5
Microchannel width W

FMHP and the copper plate is obtained using 6 type-J surface mounted thermocouples. The
thermocouples are located, respectively at 5, 15, 27, 42, 60, and 90 mm from the end cap of the
evaporator section. In order to measure the evaporator and condenser temperatures, grooves
are practiced on the FMHP wall and thermocouples are inserted along the grooves. The
thermocouples locations and the experimental set-up are shown in Figs. 3 and 4. Fig. 3. Thermocouple locations
The experimental investigation focuses on the heat transfer characteristics of the FMHP at
various heat flux rates, Q, and operating temperatures, T
sf
. Input power is varied in
increments from a low value to the power at which the evaporator temperature starts to
increase rapidly. In the process, the temperature distribution of the heat pipe along the
longitudinal axis is observed and recorded. All experimental data are obtained with a
systematic and consistent methodology that is as follows. First, the flat miniature heat pipe is
positioned in the proper orientation and a small heat load is applied to the evaporator section.
Secondly, the heat sink operating temperature is obtained and maintained by adjusting the
cooling water flow to the aluminum heat sink. Once the heat sink temperature is obtained, the

Two Phase Flow, Phase Change and Numerical Modeling

102
system is allowed to reach steady-state over 10-15 minutes. After steady-state is reached,
temperature readings at all thermocouples are recorded and power to the evaporator is
increased by a small increment. This cycle is repeated until the maximum capillary limit is
reached which is characterized by a sudden and steady rise of the evaporator temperature. Fig. 4. Experimental set-up

= 40 °C, at an input power of 60 W, the maximum steady-state evaporator
temperature for the FMHP is nearly 100 °C, while for the copper plate the maximum
evaporator temperature is 160°C. This results in a decrease in temperature gradients of
approximately 60 °C. The heat source-heat sink temperature difference, ΔT = T
ev
- T
c
, for
T
sf
= 40 °C when the FMHP is oriented horizontally, are plotted as a function of the applied
heat flux rate in Fig. 6. Also shown for comparison is the heat source-heat sink temperature
difference for a copper plate. The maximum evaporator temperature and temperature
gradients for the FMHP are considerably smaller than those obtained for the copper plate.
As shown in Fig. 6, the heat pipe operation reduces the slope of the temperature profile for
the FMHP. This gives some indication of the ability of such FMHP to reduce the thermal
gradients or localized hot spots. The size of the source-sink temperature difference for the
FMHP increases in direct proportion of the input heat flux rate and varies from almost 10 °C
at low power levels to approximately 50 °C at input power levels of approximately 60 W.
Theoretical and Experimental Analysis of Flows and Heat Transfer
within Flat Mini Heat Pipe Including Grooved Capillary Structures

103
This plot again shows the effectiveness of the enhanced FMHP and clearly indicates the
temperature reduction level that can be expected at higher heat flux rates prior to dry-out.
The effective end cap to end cap thermal resistance of the FMHP is given in Fig. 7. Effective
end cap to end cap thermal resistance, R
tht
, defined here as the overall en cap to end cap
temperature drop divided by the total applied heat load, Q. A common characteristic of the

z (mm)
T (°C)
10 W
20 W
30 W
40 W
50 W
60 W
Evaporator Adiabatic
Condenser
T
sf
= 10 °C - Horizontal
0
10
20
30
40
50
60
70
80
90
100
110
0 102030405060708090100
z (mm)
T (°C)
Q=10
Q=20

20 W
30 W
40 W
50 W
60 W
T
sf
= 40 °C - Horizontal position
Evaporator
Adiabatic Condenser
0
20
40
60
80
100
120
140
160
0 102030405060708090100
z (mm)
T (°C)
10 W
20 W
30 W
40 W
50 W
60 W
T
sf