Measurements and simulations of transient characteristics
of heat pipes
Jaros?aw Legierski a ,Bogus?aw Wie ?cek
a,*
,Gilbert de Mey
b
a
Technical University of ?o ′dz ′,Institute of Electronics,ul.Wo ′lczanska 223,90-924?o ′dz ′,Poland
b
University of Ghent,Department of Electronics and Information Systems,Sint Pieternieuwstraat 41,9000Ghent,Belgium
Received 1April 2004;received in revised form 13May 2005
Available online 5August 2005
Abstract
The rejection of heat generated by components and circuits is a very important aspect in design of electronics sys-tems.Heat pipes are very e?ective,low cost elements,which can be used in cooling systems.This paper presents the modelling and measurements of the heat and mass transfer in heat pipes.The physical model includes the e?ects of liquid evaporation and condensation inside the heat pipe.The internal vapour ?ow was fully simulated using compu-tational ?uid dynamics.The theory has been compared with experimental measurements using thermographic camera and contact thermometers.The main purpose of this study is to determine the e?ective heat pipe thermal conductivity in transient state during start up the pipe operation and temperature increase.ó2005Elsevier Ltd.All rights reserved.
1.Introduction
The investigations of heat pipes and their applica-tions into thermal management are known for years,but lately they have become more attractive to transport and dissipate heat in electronics [2,3,6,7].It is mainly due to the high e?ectiveness,small size and compact con-struction.Most of the previous research was made for static thermal conditions,and it resulted in getting the e?ective thermal resistance [6,7,9–11].
Heat pipe is a passive heat transfer device with a high e?ective thermal conductivity.The device is built up as hermetic container that is partially ?lled with a ?uid (typically water for electronic cooling design).The inner surfaces of the heat pipe have a capillary wicking mate-
rial.The liquid in the pipe saturates the capillary wick.When one heats up the end of the pipe,the liquid at this place evaporates.Because evaporated medium in the heated section has a higher pressure than in the other part of the pipe,the vapour moves to the colder section,where it is cooled down and condensed.The condensed liquid is then transported back to the hot area thought the capillary wicks.This process causes a transport of heat and mass along the pipe [7,12].
In such a heat sink one can de?ne three sections:–evaporator,–condenser,
–adiabatic region in the middle of the pipe.
Usually,the heat pipe is modelled as a very high ther-mal conductivity
element (k =50000W/m K)[5].The purpose of the measurements and simulations presented in this paper is to determine the e?ective thermal
0026-2714/$-see front matter ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.microrel.2005.06.003
*
Corresponding author.
E-mail address:wiecek@p.lodz.pl (B.Wie ?cek).
Microelectronics Reliability 46(2006)109–115
https://www.doczj.com/doc/6f10561389.html,/locate/microrel
conductivity of the heat pipe during the transient process of temperature rise in a typical cooling system (Fig.1).
2.Measurements of transient characteristics
The experimental layout for the measurement of heat pipe e?ective thermal conductivity is presented in Fig.2.The heat pipe was placed between two containers.One of them (container 2)was ?lled with water at ambient temperature.Container 1was initially empty.The ther-mal input function was done by ?lling in container 1with hot water (about 90°C).The measurement proce-dure is started when the hot water reached the heat pipe edges.The results of the temperature measurements were saved on the hard disc in the computer as a ?lm from the thermal camera.The investigated heat pipe was insulated by low conductive material in order to keep adiabatic condition in the middle region of the heat sink and to have the considerable amount of energy
transported to the cold container.At the beginning and the end of heat pipe,the insulation has been re-moved in order to measure temperature T B and T E by the thermographic camera.Additionally,the tempera-ture of the hot and cold water was measured by two con-tact thermometers,as shown in Fig.2.
During the measurement,the temperatures of the fol-lowing characteristic thermal points at the surface of the heat pipe and in containers were recorded:T H mean temperature of a thermal source in hot water container 1
T B temperature at the beginning of the heat pipe (evaporator)
T E temperature at the end of the pipe (condenser)T C
mean temperature of water in cold container 2
Temperature results obtained from the measurement (experiment)and simulation were described with the index exp and sim ,
respectively.
Fig.1.Heat pipe construction and principle of
operation.
Fig.2.Transient thermal characteristic measurement setup.
110J.Legierski et al./Microelectronics Reliability 46(2006)109–115
A water heat pipe,of 200mm length,4mm diameter and 25mm evaporator and condenser lengths was used in the investigation [8].Two containers,hot and cold ones were insulated by foamed polystyrene of 10mm thickness.Hot and cold reservoirs were ?lled with about 2l and 250ml of water,respectively.The transient ther-mal characteristics obtained from the measurement are shown in Figs.3–5display the temperature ?elds as observed with the thermal camera.
As shown in Fig.3,during the ?rst 20s,the heat pipe is in a transient state.This period can be explained as a time constant of the heat pipe itself.During starting time the evaporation and condensing rates are rising and will reach the steady state conditions in which the heat pipe operates optimally.One can notice a certain anomaly in Fig.3.After some time (25s)from starting point,the temperatures T B,exp (t )and T E,exp (t )are slightly reduced.
It seems that the temperature pro?le gets the maximum value at time t =25s.It is due to a slight cooling of the hot water container T H,exp (t ),what is clearly visible in Fig.3(upper curve).
Water temperature in cold container was changing from T C,exp (0)=22.7°C to T C,exp (130s)=23.2°C dur-ing 130s of the experiment.In order to calculate the average power transported through the heat pipe into the cold container ?lled with 250ml of water,the tem-perature measurement was performed using digital ther-mometer equipped with thermocouples.Assuming the accuracy of the temperature readout better then 0.1°C,one can evaluate the relative accuracy of temper-ature and average power measurement at about 10%.Power transported through the pipe during the experi-ment was evaluated as P ?m ác S á
T C ;exp e130TàT C ;exp e0T
%4W
e1T
where m is the water mass in cold container,c S is the speci?c heat of water.The temperature T B,exp and T E,exp was measured with a thermographic camera,while T H,exp was recorded using digital electronic thermometer.
In steady state,temperature drop T B,exp àT E,exp along the pipe is about 0.7°C,which is an experimental proof of the high thermal conductivity of such a device.
3.Simulations of transient processes in the heat pipe The simulation of heat and mass transfer inside the pipe was performed using CFD (Computer Fluid Dynamics)software—Fluent 6.0òwith pre-processor Gambit 2.0ò.3D model of the heat pipe consists of three elements:evaporator,condenser and central adia-batic https://www.doczj.com/doc/6f10561389.html,ing C-based programming
tools—User
Fig. 3.Thermal characteristics of the heat pipe (measure-
ments).
Fig.4.Temperature ?eld for time t =8
s.
Fig.5.Temperature ?eld for time t =39s.
J.Legierski et al./Microelectronics Reliability 46(2006)109–115111
De?ne Functions (UDF),one can easily introduce evap-oration and condensation into the modelling.The sur-faces where evaporation takes place were modelled using build-in mass-?ow-inlet elements in Fluent òenvi-ronment.In the condenser,an out?ow element was implemented.The evaporation and condensation heat ?uxes (negative and positive)were placed on two small areas in the evaporator and condenser section to simu-late absorption and dissipation of energy for both ends of the heat pipe as shown in Fig.6.The thermal excita-tion function was implemented as temperature (T S )in UDF ?le,equal to the temperature of the evaporator section obtained from the measurement T B,exp .Cold water container was simulated as a box ?lled with water at T C temperature.The rectangular mesh with 10666elements (cells)was used in the simulations for all parts of the cooling system.
Wick material and its in?uence of heat transfer in a pipe were neglected.In the preliminary investigations presented in this paper,one assumed that the evapora-tion,vapour transport and condensation are phenomena of the highest signi?cance in the operation of the heat pipe,and the e?ective thermal conductivity can be eval-uated without considering the liquid return in a wick.The further more detailed research can include a wick in the simulations.
The mass transfer in the pipe was described by well-known the Navier–Stokes equations,while heat transfer was solved using Fourier–Kircho?expressions.Hertz–Knudsen model was applied to determine mass ?ux during the evaporation [1,4]
u EVAP ?e á???????????????M 2áp áR r p 0
?????T 0p àp p ??????T p p
!e2T
where u EVAP is the mass ?ux during the evaporation
[kg/m 2s];M is the molar mass of liquid [kg/mol];R =8.314is the universal gas constant [J/mol K];p 0is the saturation vapour pressure at the interface [Pa];p p is the saturation vapour pressure in the end region of a pipe [Pa];e is the evaporation coe?cient (06e 61);T 0is the temperature of the vapour at the interface
[K];T p is the temperature of the vapour in the end range of a pipe [K].
The evaporation coe?cient e describes the rate of evaporation.A smooth surface will have a low e value,while a rough surface will have a higher value because more ‘‘kernels’’for initiating evaporation are available.Because air is not presented in the simulated heat pipe,the saturation vapour pressure over the interface is equal to the static pressure at this place.The evaporating liquid absorbs a thermal heat ?ux U EVAP from the ambient:U EVAP ?u EVAP áh fg
e3T
where h fg is the latent heat,describing vaporization [J/kg].
One should assume that the entire evaporating mass ?ux is condensing in condenser section,what leads to the equation u COND ?u EVAP
e4T
The heat ?ux U COND corresponding to phase change in the condenser can be expressed as U COND ?u COND áh fg
e5T
where u COND is the condensation mass ?ux [kg/m 2s].Simulations have been performed for di?erent values of evaporation coe?cient e .Although the
adiabatic
Fig.6.Model of the heat
pipe.
Fig.7.Thermal characteristic for e =1.58·10à3and a =0.25.
112J.Legierski et al./Microelectronics Reliability 46(2006)109–115
section of the heat pipe is insulated thermally,the heat losses may not be neglected as compared to the power of 4W transported into the cold container.Therefore,a heat transfer coe?cient a along the adiabatic section has been introduced in the simulation.The coe?cient a stands both for the conduction in the insulation and the natural convection from the outer surface to the ambient.The simulation results were compared with the measurement.In Fig.7,the thermal characteristics obtained from the simulation are shown.Figs.8–10graphically present the results of the simulations (tem-perature and vapour velocity distributions).The images present only one half of the simulated area because of the cylindrical symmetry of the modelled heat pipe.
https://www.doczj.com/doc/6f10561389.html,paring simulation results with measurement The evaporation coe?cient values e used in the sim-ulations were between 10à4and 10à2.Figs.11–13pres-
ent the simulation results for increased evaporation rate.The time constant values obtained from the simu-lation agree very well with the experimental data,as shown in Figs.12and 13.The temperature values
also
Fig.8.Temperature in condenser and cold water container for e =1.58·10à3and t =90
s.
Fig.9.Velocity distribution in evaporator section [m/s]:e =1.58·10à3and t =20
s.
Fig.10.Velocity distribution in condenser section [m/s]:e =1.58·10à3and t =90
s.
https://www.doczj.com/doc/6f10561389.html,paring results of simulation with measurement for e =10à4and a =0.25(P =0.79W).
J.Legierski et al./Microelectronics Reliability 46(2006)109–115113
agree very well.The only discrepancy is for the time de-lay for T E,sim if the evaporation coe?cient is e =10à4
(Fig.11)or e =1.58·10à3(Fig.12).For e =10à2(Fig.13)this delay has disappeared but for longer times,the temperature drop T B,sim àT E,sim =0.09°C,which is much less than the experimentally found T B,exp àT E,exp =0.7°C.In this case the power transported by the heat pipe is six times higher (24W)than in the exper-iment (4W).This makes e =10à2an unacceptable va-lue.For e =1.58·10à3(Fig.12)the simulated temperature drop T B,sim àT E,sim =0.73°C is in perfect agreement with the experimental observations,as well as heat transported by the pipe (4.046W)corresponds precisely with the measurements.Hence one must con-clude that e =1.58·10à3should be the correct evapora-tion coe?cient.The delay between T B,sim and T E,sim still visible in Fig.12but it is relatively small and acceptable.Resuming the best results obtained by comparing simulation with measurement were for evaporation coef-?cient e =1.58·10à3.For e =10à4heat pipe is ‘‘too slow’’and evaporator heating time to temperature T =55°C is 50s.This result is opposite to experimental data.For evaporation coe?cient value e =10à2temper-ature gradient along the pipe is too small what results in disagreement of the power transported through the pipe.
5.E?ective thermal conductivity of the pipe
The e?ective thermal conductivity of the pipe k was determined by using the simulation result as a function of time.By de?nition the thermal conductivity can by expressed as k ?à/
L eff D T
e6T
where /is the heat ?ux along the pipe [W/m 2];D T is the temperature gradient;L e?is the e?ective heat pipe length [m].
E?ective heat pipe length can be approximated by the equation [5]
L eff ?
L C 2tL A tL E
2
e7T
where L C ,L E ,L A are condenser,evaporator and adia-batic section lengths,respectively.
Both heat ?ux /and the total power P T transferred to the cold container as well as temperature gradient D T were calculated by Fluent software.The heat ?ux and power were evaluated in the condenser section on the contact surface between the pipe and water,as shown in Fig.6.One can notice that the total power transferred to the cold reservoir includes both the power generated by the vapour condensation and the heat ?ux on the contact surface between the hot vapour to the cold water.Results are presented in Table 1.
One may argue whether a time dependent thermal conductivity is the right way to represent the phenome-non observed here.A network involving capacitances and resistors is more common to deal with transient
Table 1
E?ective thermal conductivity k (e =1.58·10à3)
t (s)1
510152030405060708090P T (W)0.39 1.41 2.27 4.25 5.54 5.15 4.34 4.20 4.02 4.38 4.23 4.10D T (°C) 4.023 2.3353 1.7582 1.2396 1.01850.60280.79860.78080.67840.63230.77060.7607U (W/m 2)7823281064517684608110129102387863908355479939871758414581508k (W/m K)
340.3
2106.2
4496.5
11944.5
18922.4
29724.3
18931.1
18726.8
20621.1
24127.1
19109.0
18751.1
https://www.doczj.com/doc/6f10561389.html,paring results of simulation with measurement for e =1.58·10à3and a =0.25(P =4.05
W).
https://www.doczj.com/doc/6f10561389.html,paring results of simulation with measurement for e =10à2and a =0.25(P =24.61W).
114J.Legierski et al./Microelectronics Reliability 46(2006)109–115
phenomena.However,in the beginning of heat pipe operation,the velocity of the vapour particles is quite small resulting in lower thermal conductivity.One must also bear in mind that the thermal capacity of the va-pour in the adiabatic section is rather small,especially at low pressure.Hence,it makes sense to represent the heat pipe by a time dependent conductor or alternatively by an equivalent time dependent thermal resistance net-work.One can remark that the maximum measured value found here is around25000W/m K which is less than the value recommended in Ref.[5].This may be due to the fact that the heat pipe was placed horizontally in our experiments.It is well known that heat pipes operate more e?ciently in the vertical position,in which the evaporating section is at the bottom.It is also clear from Fig.14that the heat pipe,or at least its adiabatic section becomes a very good conductor only after20s.
6.Conclusion
As a result of the measurements and the simulations of heat pipe,one was able to determine the evaporation coe?cient.The value is about1.58·10à3for a pipe pre-sented in this paper.The e?ective thermal conductivity of the heat pipe was found to be time dependent with a maximum value in the range:15000–30000W/m K, which is close to the value obtained from technical paper e.g.[8].The e?ective thermal conductivity reaches its steady state value after%20–30s.This result was ob-tained for the water heat pipe of200mm length and 4mm diameter,but general model and overall approach of measurement and simulation can be extended to any other heat pipe.
References
[1]Eames IW,Marr NJ,Sabir H.The evaporation coe?cient
of water:a review.Int J Heat Mass Transfer1997;40(12): 2963–73.
[2]Terpstra M,Van Veen JG.Heat pipes construction and
applications—study of patents.London,NY:Elsevier Applied Science;1987.
[3]Garner SD.Heat pipes for electronics cooling applications.
Electronics Cooling,September1996.
[4]Wajman T,Wiecek B,Felczak M.Vaporation from
capillaries in cooling electronics devices—evaporation coe?cient evaluation.Mixed Design of Integrated Cir-cuits and Systems(MIXDES),Lodz/Poland,June26–28, 2003.
[5]Thyrum G.Critical aspects of modelling heat pipe assisted
heat sinks.Thermacore Inc.,https://www.doczj.com/doc/6f10561389.html,.
[6]DeHo?R,Grubb K.Heat pipe application guidelines.
Thermacore Inc.,https://www.doczj.com/doc/6f10561389.html,.
[7]Toth J,DeHo?R,Grubb K.Heat pipes:the silent way
to manage desktop thermal problems.Thermacore Inc., I-THERM Conference Seattle,1998.
[8]Miniature Heat Pipes HP-NB Product Data Guide,
Thermacore Inc.,4/8/1998.
[9]Legierski J,Wiecek B.Steady state analysis of cooling
electronic circuits using heat pipes.IEEE Trans Comp Pack Technol2001;24(4).
[10]Wiecek B.Heat Pipe Cooling Fins for Integrated Circuits,
Workshop Microtechnology and Thermal Problems in Electronics,Microtherm?98,Zakopane,21–27September 1998.
[11]Legierski J,Wiecek B.Modelling and measurements of
power circuits cooled by heat pipes.Proc.Quantitative Infrared Thermography,Reims,July18–21,2000. [12]Legierski J,Wiecek B.Transient thermal characteristics of
heat pipes.Measurements and Simulation.Proc.Quanti-tative Infrared Thermography,Dubrovnik,September24–27,
2002.
J.Legierski et al./Microelectronics Reliability46(2006)109–115115