- Email: [email protected]
Miniature heat-pipe thermal performance prediction tool – software development
Applied Thermal Engineering 21 (2001) 559±571
www.elsevier.com/locate/apthermeng
Miniature heat-pipe thermal performance prediction tool ± software development V. Maziuk a, A. Kulakov a, M. Rabetsky a, L. Vasiliev a,*, M. Vukovic b a
Luikov Heat and Mass Transfer Institute, Academy of Science, P. Brovka 15, 220072 Minsk, Belarus, Russian Federation b Nortel Networks, Ottawa, Ont., Canada Received 26 October 1999; accepted 12 May 2000
Abstract The software for ¯at miniature heat-pipe parameters (Qmax , Rhp , temperature ®eld along the pipe surface, heat transfer coecients in the evaporator and condenser zones he , hc , etc.) prediction and numerical modeling was developed. The experimental data received for the ¯at miniature heat pipe (2.5±4 mm thickness, 50±250 mm length, 8±11 mm width) with a copper sintered powder wick saturated with water were compared with the data of numerical analysis and results showed that experimental veri®cation testi®es the validity of the software application. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Miniature heat pipe; Metal powder wick; Two-dimensional numerical analysis
1. Introduction The recent design of desktop and notebook computer performance necessitates higher performance processors to be developed. The miniature ¯at heat-pipe applications for cooling telecom boots and notebook computers were started in the last ten years. Conventional miniature heat pipes and miniature ¯at heat pipes now are used in 80% of notebook PCs. Heat pipes have been appreciated by thermal designers for their small size and eective cooling capacity. In notebook PCs, several applications of the heat pipe cooling technology are put to practical use in large quantities [1,2]. The high heat ¯uxes typical for the electronic equipment need to use the eective heat pipes with high heat transfer capabilities at any inclination. Hence, we need to use *
Corresponding author. Tel.: +375-17-284-2133; fax: +375-17-284-2133. E-mail addresses: [email protected] (L. Vasiliev), [email protected] (M. Vukovic).
1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 0 ) 0 0 0 6 6 - 1
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Nomenclature
r d kcs ql ll qv lv Tv A dT dTe g k K0 L, l l mHP pc pv Q R
liquid surface tension wick thickness eective thermal conductivity of the wick liquid density liquid viscosity vapor density vapor viscosity vapor temperature at the end of the evaporator vapor channel thickness temperature dierence at the mHP ends temperature dierence of the evaporator end and the adiabatic zone gravity constant wick permeability coecient speci®c capacity ratio Cp =Cv heat-pipe length heat-pipe eective length miniature heat pipe maximal capillary pressure vapor pressure heat ¯ow mHP thermal resistance, calculated using the temperature dierence between the mHP ends r* latent heat of evaporation vapor bubble radius (near 2:54 10ÿ7 m) Rb Rc , Re the thermal resistance of the condenser and evaporator, calculated using the mean temperature of the condenser and the evaporator eective mHP thermal resistance, calculated using the mean temperature dierence of Reff the evaporator and the condenser gas constant Rg meniscus radius Rm the square of a heat-pipe wick cross-section Scs evaporator cross-section square Se vapor channel cross-section square Sv T1 , T2 , . . ., Tn temperature of mHP surface (thermocouples data) Te , Tc , Ta temperature of the evaporator, condenser and adiabatic zone vapor temperature Tv Tw;in temperature of the cooling water at the entrance Tw;out temperature of the cooling water at the exit W vapor channel width X coordinate (mm)
V. Maziuk et al. / Applied Thermal Engineering 21 (2001) 559±571
Index a amb avg c e
561
adiabatic zone ambiance temperature average condenser evaporator
miniature heat pipes with improved wick structures due to their operation at top heating mode typical for most of the notebook manufacturers with a decrease of 30±40% of the thermal resistance over conventional cooling systems. High speed CPUs with a heat loading of 35 W are used in notebook PCs [3±8]. The eciency of the developed software tool was compared with the experimental data received during the experiments with a ¯at miniature heat pipe made from copper (copper sintered powder wick). The ¯at miniature heat pipes with thickness 2±4 mm are used on electronic components cooling in small cabinets. The evaporating section is installed between each package, and condenser section is attached to the cabinet wall directly. The cabinet wall is used as a cooling heat sink. The main advantage of the ¯at miniature heat pipes as the electronic components cooler is a possibility to ensure a good thermal contact with the chips and have a symmetric heat input from both sides of the heat pipe, like in the cylindrical heat pipes. In both cases, the liquid motion inside the capillary wick and the temperature distribution along the heat pipe can be considered as onedimensional. If the heat input to the ¯at miniature heat pipe is ensured from one side, the liquid and temperature distribution in the heat pipe is considered as two-dimensional and we need to modify the software to calculate the heat transfer coecients in the evaporator and condenser zones, the heat pipe thermal resistance, temperature distribution along the heat pipe and to determine Qmax along the heat pipe. The goal of this work is to develop a software to calculate the ¯at miniature heat-pipe parameters and experimentally validate this software [9±11]. 2. Experimental setup The experimental setup (Fig. 1) to determine the miniature heat-pipe's (¯at and cylindrical) parameters was designed and made. The general goal of this setup application was to · determine the temperature distribution along the heat pipe for dierent heat loads, · estimate the heat-pipe's maximum capacity in horizontal and vertical, and inverted position, and · evaluate the dependency between a heat-pipe thermal resistance and heat dissipation. This setup was done in a way as to reproduce the mode of heat-pipe applications close to realistic. Heat-pipe heating was done by the electric heaters (¯at or circular), and heat-pipe cooling by the air ¯ow (forced or natural convection) and water ¯ow. Three small fans were installed inside the experimental setup. Heat-pipes thermal control was done with the help of the
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Fig. 1. Experimental setup schematic: 1. heat pipe disposed inside the reinforced polymer chamber, 2. electric cartridge heater, 3. the platform for the heat pipe inclination, 4. wattmeter, 5. electric source of energy, 6. electric signals recorder with the thermocouples, 7. electric tension meter, 8. IBM PC computer, 9. thermostat, 10. water rate recorder, and 11. ampermeter.
heat ¯ow measurements in the evaporator (qmax 40±50 W/cm2 , Qmax 100 W), heat-pipe surface temperature measurements were performed by thermocouples and heat-pipe tilt measurements (90° to 0° to ÿ90°) were performed by an automatic system of the tilt deviation. A miniature heat pipe is disposed in a thermally insulated chamber inside the experimental setup. This chamber is divided into three zones and comprises four components ± the basement to which heat pipe is attached, two lids covering the bottom, the chamber and one movable partition (wall). This thermally insulated chamber is ®xed on the turning device to ensure heat-pipe tilt changing. The heat ¯ux in the evaporator is regulated following the computer program. Thus, the length of the evaporator, adiabatic zone and the condenser zone of the heat pipe can also be regulated following the program of testing. The most typical case is when the length of the heat-pipe evaporator is 15±30% and the length of the heat-pipe condenser is 40±60% of the heat-pipe's total length. To measure the temperature ®eld along the heat pipe some thermocouples d 0:2 mm are soldered on the heat-pipe surface. Three thermocouples were ®xed on the evaporator surface, two on the adiabatic zone surface and three on the condenser zone surface (Fig. 2). The heat ¯ux qmax can be determined as follows: the heat ¯ow supplied to the heat-pipe evaporator increases step by step with the temperature ®eld measurements. The heat ¯ow increases in steps of 1±2 W.
Fig. 2. Heat pipe schematic with the thermocouples on its surface.
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Fig. 3. Heat transfer limits for the ¯at miniature heat pipe with a sintered metal powder as a wick.
The miniature heat-pipe thermal resistance RHP (and the heat transfer coecients in the evaporator and condenser zones) is calculated when the temperature drops in the evaporator and condenser zones and the heat ¯ow transfer through the heat pipe are known: RHP Te ÿ Tc =Q: The computer program is developed to determine the heat ¯ow Q, heat-pipe temperature drop DT and heat transfer coecient in the evaporator zone: he q= Te ÿ Tsat ; and heat transfer coecient in the condensation zone, hc q= Tsat ÿ Tc : The graphic data and ®gures of qmax , Qmax , RHP , he and hc as a function of heat-pipe tilt are received for dierent heat load and heat-pipe orientation in the space. A computer program was developed to determine Qmax for the ¯at miniature heat pipes (Fig. 3).
3. The methodology of the experiment The heat load of the heat pipe is guided by the computer program depending on the electric heater electric resistance. Qmax is determined as follows. After the ®xed heat-pipe orientation in space, the electric heater is switched-on when the temperature ®eld along a heat pipe is stationary and recorded in the ®le. Then, the heat-pipe heat load increases on DQ and the temperature ®eld along a heat pipe is measured once more. The Qmax value is ®xed when there is a non-proportional dependency between the temperature change (thermocouples data disposed below the electric heater) and the
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heat load change. In this case, we could see a sharp increase of the temperature. For the precise measurement of the heat-pipe crisis Qmax value, a small step of heat load DQ 1 W increasing was ensured. Heat-pipe thermal resistance is determined using the data of the vapor temperature in the adiabatic zone, and the mean temperature value in the evaporator and in the condenser. Two dierent modes of heat-pipe cooling were used during these experiments. Initially, we used the air forced convection cooling (by fans), but this mode of cooling did not give us an opportunity to approach the critical situation (Qmax ) due to a high heat-pipe temperature (more than 120°C). For the second set of experiments, we were obliged to use a water forced convection cooling of the heat-pipe condenser (thermostat application with the temperature measurements accuracy less than 1°C). The liquid motion was directed from the heat-pipe condenser end to the adiabatic zone at a constant rate. During the experiments, the temperature of the adiabatic zone and of the cooling water were maintained constant. A special computer program for the miniature heat-pipe experimental data analysis was developed and tested, which permits ®xing and analyzing of all the experimental data in a steady state and transitional mode. The ®rst ®le is developed for a steady state heat ¯ow along the heat pipe. The second ®le is used to analyze the experimental data in the transitional mode (®xed time intervals). This program guarantees automatic de®nition of the stationary heat transfer in the heat pipe. After this, the next command is sent (electric heater is switched-on) to change the heat ¯ow value transferred through a heat pipe. The experimental data of the temperature ®eld along the heat pipe are automatically visualized on the display screen (Fig. 4). The heat-pipe physical model is based on some assumptions: (1) The evaporation of the working liquid from the capillary structure of the wick occurs only where the wick temperature is higher than the vapor temperature. The condensation of the vapor on the wick structure occurs only where the wick temperature is lower than the vapor temperature.
Fig. 4. Temperature distribution along the heat pipe.
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(2) The liquid motion occurs through the whole capillary structure (wick) under the capillary action. Due to one side heat-pipe heating, the evaporation zone is also situated on one side of a ¯at heat pipe and the liquid movement inside the wick is considered as two-dimensional. (3) The heat and mass transfer eciency in the heat pipe is mostly dependent on the wick properties and the wick saturation by liquid. When the liquid saturation in the evaporation zone reaches a critical value, there is a limit of the capillary suction by the wick and for further decreasing of the liquid saturation inside the wick a strong increase of the heat-pipe thermal resistance takes place. The heat-pipe heat load increase is also a reason for its thermal resistance increasing. When a wick is completely dry the heat transfer is realized only by thermal conductivity of the heat-pipe envelope and the wick. In this case, the heat-pipe thermal resistance of this part of the heat pipe increases several times. The heat transfer coecients in the evaporators and condensers of heat pipes are directly related with a wick thermal conductivity. The ratio between the axial heat ¯ow transferred along the heat-pipe envelope and radial heat ¯ow transferred as a liquid evaporation in the pores is dierent for dierent heat pipes. For the heat pipes with a metal sintered powder wick, the heat ¯ow transferred in the radial direction by the liquid evaporation up to Qmax is several times more than the heat ¯ow transferred along the heat-pipe envelope, because the eective thermal conductivity of the wick is high (up to 40 W/m K). As a result, we have an isothermal temperature pro®le along the evaporator. These heat-pipe features are included in the software through the wick eective thermal conductivity. The heat transfer coecient in the condenser zone depends on the wick eective thermal conductivity, wick thickness and the liquid ®lm thickness under the wick surface. This liquid ®lm thickness is varied along the condenser ± the heat transfer coecient also varies along the condenser length.
Fig. 5. Cross-section of the ¯attened copper miniature heat pipe with sintered metal powder wick (received from the cylindrical heat pipe ¯attening): 1. HP envelope (3:7 8 mm), 2. porous wick, and 3. vapor channel.
Fig. 6. Cross-section of the copper±water ¯at miniature heat pipe with sintered metal powder wick (rectangular crosssection): 1. HP envelope (2:2 9 mm), 2. porous wick, and 3. vapor channel.
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Fig. 7. Heat ¯ow Qmax as a function of saturated vapor temperature inside the copper±water ¯attened miniature heat pipe with copper sintered powder wick.
Fig. 8. Temperature distribution along the ¯at miniature heat pipe: 1. experimental data and 2. numerical modeling of the heat pipe data.
Experimental samples of the ¯at miniature heat pipe were chosen as copper/water heat pipe with a copper sintered powder as a wick. Two dierent samples were tested. The ®rst sample was a ¯attened cylindrical heat pipe (Figs. 5, 7±13). The second sample was a heat pipe with a rectangular cross-section (Figs. 6 and 14). Heat-pipe heat transfer limit is Qmax . Usually, the heat transfer limit in heat pipes is determined experimentally as a fast temperature rise in the evaporator. This temperature rise is not proportional to the heat ¯ow increase. In our experiments, the temperature on the surface of the evaporator was controlled by the thermocouple disposed on the opposite side of the electric heater (electric heater was joined to the opposite side of a ¯at heat pipe). Basically, the temperature rise on the surface of a heat pipe in contact with an electric heater was dierent from the temperature rise on the opposite side of heat-pipe evaporator (a faster temperature increase occurred).
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Fig. 9. Temperature distribution along the ¯attened mHP for various powers supplied (Le 20 mm, Lc 100 mm, La 30 mm, experimental data, horizontal position).
Fig. 10. Temperature distribution along the ¯attened mHP for various powers supplied (Le 20 mm, Lc 100 mm, La 30 mm, experimental data, vertical, inverted position).
The calculations show that the temperature drop between these ¯at surfaces of the evaporator could be essential (Fig. 13), so a real heat transfer limit starts earlier, when Qmax is few watts less than that we can estimate by the thermocouple no. 1 temperature data. Analyzing the data of Qmax (Fig. 14), we can conclude that the heat transfer limit for two dierent orientations of a heat pipe in space (vertical and horizontal) is essentially dierent. To verify the reliability of the computer program, we need to compare the computer data with some of the experimental data ± the temperature ®eld along the heat pipe for dierent heat ¯ows transferred. We can conclude that the theoretical and experimental data coincides within the limit of 10% for large range of heat ¯ow transferred through a heat pipe.
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Fig. 11. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal sintered powder): horizontal position, 20°C cooling water, experimental data, Le 20 mm, Lc 100 mm, La 30 mm.
Fig. 12. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal powder): vertical, inverted position, 20°C cooling water, experimental data, Le 20 mm, Lc 100 mm, La 30 mm.
Fig. 13. 1. Non-heated opposite side of the evaporator and 2. heated surface of the evaporator, theoretical data.
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Fig. 14. Capillary limit Q of a miniature rectangular heat pipe with dimensions 2:2 9 150 mm and Le /La /Lc ± 20/70/ 60 mm.
The equation to calculate heat-pipe limit Qmax due to capillary forces limitation is Q
pc ÿ ql gl : ll l 12lv l ql r Scs k qv r A3 W
The ®rst part of this equation is the liquid pressure drop and the second part of this equation is the vapor pressure drop in the heat pipe. Heat-pipe boiling limit Qcr and sonic limit Qcr were analyzed following [1±3]. The heat-pipe boiling limit Qcr is determined as kcs Se Rg Tv2 2r 1 1 2rqv ÿ : Qcr ln 1 pv Rb Rm d r p v Rb q1 Heat-pipe sonic limit is determined as 0 0:5 K Rg Tv Qcr Sv qv r : 2 K 0 1 A ¯at long miniature heat pipe is considered for the numerical analysis of its action. A comprehensive two-dimensional steady-state mathematical model for predicting thermal performances (maximum transport capacity, thermal resistance, heat-pipe temperature axial pro®le, temperature drop between a heat source and heat sink) is the goal of this research program. This model needs to predict a heat-pipe performance within =ÿ10%. Actually, we analyze a ¯at heat pipe which has an isotropic capillary structure (metal sintered powder wick) on the inner heat-pipe surface. The heat-pipe orientation in space is in the limits of ÿ90° to 90°. A long heat-pipe axis is constantly in a horizontal position and we consider the heat-pipe rotation on its axis. Heat-pipe performance depends upon a heat-pipe thermal resistance, while the thermal resistance depends upon the heat-pipe ¯uid transport limit, wick structure, permeability limitation, input power and operating temperature, etc.
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The main (principal) particularity of the metal sintered powder wick is the possibility of functioning with a partially dry porous structure in the heat-pipe evaporator. The degree of wick saturation with the liquid has an in¯uence on the heat transfer across the wick. For such sintered powder wicks, the heat transfer crisis (Qmax ) beginning is soft and the heat-pipe works in a certain range of DQmax (from Qmax1 up to Qmax2 ). Within this DQmax range, the wick capillary properties change: liquid permeability decreases (some pores are occupied by the vapor), and capillary pressure increases (small pores are responsible for a liquid capillary suction). The heat-pipe evaporator works as the porous structure with the ``inverted'' meniscus of the evaporation and the heat transfer increases. When Qmax2 is reached full drying in the evaporator's wick occurs and the heat pipe stops functioning [10]. Therefore, the heat transfer coecient in the evaporator basically is a function of the wick eective thermal conductivity, wick thickness and the degree of the wick saturation with the liquid. Therefore, in such cases, the surface of the liquid ®lm evaporation in the pores increases and the wick eective thickness decreases. These two phenomena are the reasons for the heat transfer coecient he increase. Evidently, he is a function of the evaporator length and the heat-pipe tilt. The heat transfer coecient in the heat-pipe condenser zone depends on the wick eective thermal conductivity, wick thickness and the liquid ®lm thickness on the wick surface. During the evaporator partial drying (Qmax ), the excess of the liquid is accumulated on the wick surface in the heat-pipe condenser. The liquid ®lm thickness increases and the heat transfer coecient in the condenser zone decreases. The local value of the heat transfer in the condenser zone is a function of the condenser length which can be estimated [11]. The vapor channel thickness inside the ¯at miniature heat pipes usually does not exceed 1 mm and the vapor pressure drop is comparable with the liquid pressure drop inside the wick. This vapor pressure drop DPv can be determined as the pressure drop for the gas ¯ow in the thin rectangular channel [12]: DPv
12lv l : qv r A3 W
The heat and mass transfer analysis in the ¯at miniature heat pipe gives the possibility of determining the meniscus diameter distribution along the wick surface, wick saturation, capillary permeability and heat transfer coecients in the evaporator and condenser zones. To utilize the software for the ¯at miniature heat-pipe numerical modeling, we need to use some experimental data related with the real pore distribution in the wick (mercury pore distribution check technology).
4. Conclusion Heat transfer coecients in the evaporator and condenser of the ¯at miniature heat pipe depend on two-dimensional hydraulic (pore saturation, capillary permeability, capillary pressure) and thermal (temperature distribution along the heat-pipe envelope) parameters of such devices.
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(1) The temperature in the middle of the heated surface of the envelope (evaporator) can exceed the symmetric point temperature on the opposite (non-heated) surface of the envelope (evaporator) by nearly 10°C. (2) The technology of heat pipes with the metal sintered powder wick development strongly in¯uences the heat-pipe parameters (¯attened heat pipe or rectangular heat pipe). (3) Experimental veri®cation of the ¯at miniature heat-pipe parameters testi®es the validity of the software application.
Acknowledgements The authors would like to show their appreciation to Nortel Networks Ltd. for ®nancing software development, Contract No. 642817, ``Thermal performance prediction algorithm for ¯at miniature heat pipe''.
References [1] A. Faghri, Heat Pipe Science and Technology, Taylor and Francis, Washington, DC, 1995. [2] Y. Cao, M. Gao, J.E. Beam, B. Donovan, Experiments and analyses of ¯at miniature heat pipes, J. Thermophys. Heat Transfer 11 (2) (1997) 158±164. [3] A. Basilius, H. Tanzer, S. McCabe, Heat pipes for cooling of high density printed wiring board, in: Proc. Sixth Int. Heat Pipe Conf., Grenoble, France, 1987, pp. 531±536. [4] M. Adami, B. Yimer, Development and evaluation of a planar heat pipe for cooling electronic systems, Chem. Eng. Comm. 10 (1990) 57±74. [5] G.P. Peterson, An Introduction to Heat Pipes-Modelling, Testing and Applications, Wiley, New York, 1994. [6] M. Murakami, T. Ogushi, Y. Sakurai, H. Masumoto, M. Furukawa, R. Imai, Heat pipe heat sink, in: Proc. Sixth Int. Heat Pipe Conf., Grenoble, France, 1987, pp. 257±226. [7] J. Sotani, M. Yamamoto, S. Tanaka, K. Nanba, K. Yamamori, Y. Susa, N. Yamazaki, Y. Kojima, Feasability study of printed circuit board using ¯at plate heat pipes, Adv. Electron. Packag. 1 (1992) 83±88. [8] O. Plesch, W. Rier, D. Seidel, K. Schubert, Miniature heat pipes for heat removal from microelectronic circuits, micromechanical sensors, actuators and systems, ASME-DSC 32C (1991) 303±314. [9] V.V. Maziuk, V.K. Sheleg, Computation of Transport Capacity of Heat Pipe Powder Capillary Structure taking into account the Dewatering, Proc. of Ninth Int. Heat Pipe Conf., Albuquerque, 1995. [10] V.V. Maziuk, V.K. Sheleg, Proc. Calculation of the Heat Transfer coecient in Heat Pipe Evaporation Zone with Regard to Partial Capillary Structure Drying, Proc. 10th Int. Heat Pipe Conf., Stuttgart, 1997, pp. 142±144. [11] L.L.Vasiliev, L.P. Grakovich, D.K. Khrustalev, Heat pipes in the alternative sources of energy, Minsk, Science and Technology, 1988, p. 159. [12] F. Kreith, W.Z. Black, Basic Heat Transfer, Harper and Row, New York, 1980.
www.elsevier.com/locate/apthermeng
Miniature heat-pipe thermal performance prediction tool ± software development V. Maziuk a, A. Kulakov a, M. Rabetsky a, L. Vasiliev a,*, M. Vukovic b a
Luikov Heat and Mass Transfer Institute, Academy of Science, P. Brovka 15, 220072 Minsk, Belarus, Russian Federation b Nortel Networks, Ottawa, Ont., Canada Received 26 October 1999; accepted 12 May 2000
Abstract The software for ¯at miniature heat-pipe parameters (Qmax , Rhp , temperature ®eld along the pipe surface, heat transfer coecients in the evaporator and condenser zones he , hc , etc.) prediction and numerical modeling was developed. The experimental data received for the ¯at miniature heat pipe (2.5±4 mm thickness, 50±250 mm length, 8±11 mm width) with a copper sintered powder wick saturated with water were compared with the data of numerical analysis and results showed that experimental veri®cation testi®es the validity of the software application. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Miniature heat pipe; Metal powder wick; Two-dimensional numerical analysis
1. Introduction The recent design of desktop and notebook computer performance necessitates higher performance processors to be developed. The miniature ¯at heat-pipe applications for cooling telecom boots and notebook computers were started in the last ten years. Conventional miniature heat pipes and miniature ¯at heat pipes now are used in 80% of notebook PCs. Heat pipes have been appreciated by thermal designers for their small size and eective cooling capacity. In notebook PCs, several applications of the heat pipe cooling technology are put to practical use in large quantities [1,2]. The high heat ¯uxes typical for the electronic equipment need to use the eective heat pipes with high heat transfer capabilities at any inclination. Hence, we need to use *
Corresponding author. Tel.: +375-17-284-2133; fax: +375-17-284-2133. E-mail addresses: [email protected] (L. Vasiliev), [email protected] (M. Vukovic).
1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 0 ) 0 0 0 6 6 - 1
560
V. Maziuk et al. / Applied Thermal Engineering 21 (2001) 559±571
Nomenclature
r d kcs ql ll qv lv Tv A dT dTe g k K0 L, l l mHP pc pv Q R
liquid surface tension wick thickness eective thermal conductivity of the wick liquid density liquid viscosity vapor density vapor viscosity vapor temperature at the end of the evaporator vapor channel thickness temperature dierence at the mHP ends temperature dierence of the evaporator end and the adiabatic zone gravity constant wick permeability coecient speci®c capacity ratio Cp =Cv heat-pipe length heat-pipe eective length miniature heat pipe maximal capillary pressure vapor pressure heat ¯ow mHP thermal resistance, calculated using the temperature dierence between the mHP ends r* latent heat of evaporation vapor bubble radius (near 2:54 10ÿ7 m) Rb Rc , Re the thermal resistance of the condenser and evaporator, calculated using the mean temperature of the condenser and the evaporator eective mHP thermal resistance, calculated using the mean temperature dierence of Reff the evaporator and the condenser gas constant Rg meniscus radius Rm the square of a heat-pipe wick cross-section Scs evaporator cross-section square Se vapor channel cross-section square Sv T1 , T2 , . . ., Tn temperature of mHP surface (thermocouples data) Te , Tc , Ta temperature of the evaporator, condenser and adiabatic zone vapor temperature Tv Tw;in temperature of the cooling water at the entrance Tw;out temperature of the cooling water at the exit W vapor channel width X coordinate (mm)
V. Maziuk et al. / Applied Thermal Engineering 21 (2001) 559±571
Index a amb avg c e
561
adiabatic zone ambiance temperature average condenser evaporator
miniature heat pipes with improved wick structures due to their operation at top heating mode typical for most of the notebook manufacturers with a decrease of 30±40% of the thermal resistance over conventional cooling systems. High speed CPUs with a heat loading of 35 W are used in notebook PCs [3±8]. The eciency of the developed software tool was compared with the experimental data received during the experiments with a ¯at miniature heat pipe made from copper (copper sintered powder wick). The ¯at miniature heat pipes with thickness 2±4 mm are used on electronic components cooling in small cabinets. The evaporating section is installed between each package, and condenser section is attached to the cabinet wall directly. The cabinet wall is used as a cooling heat sink. The main advantage of the ¯at miniature heat pipes as the electronic components cooler is a possibility to ensure a good thermal contact with the chips and have a symmetric heat input from both sides of the heat pipe, like in the cylindrical heat pipes. In both cases, the liquid motion inside the capillary wick and the temperature distribution along the heat pipe can be considered as onedimensional. If the heat input to the ¯at miniature heat pipe is ensured from one side, the liquid and temperature distribution in the heat pipe is considered as two-dimensional and we need to modify the software to calculate the heat transfer coecients in the evaporator and condenser zones, the heat pipe thermal resistance, temperature distribution along the heat pipe and to determine Qmax along the heat pipe. The goal of this work is to develop a software to calculate the ¯at miniature heat-pipe parameters and experimentally validate this software [9±11]. 2. Experimental setup The experimental setup (Fig. 1) to determine the miniature heat-pipe's (¯at and cylindrical) parameters was designed and made. The general goal of this setup application was to · determine the temperature distribution along the heat pipe for dierent heat loads, · estimate the heat-pipe's maximum capacity in horizontal and vertical, and inverted position, and · evaluate the dependency between a heat-pipe thermal resistance and heat dissipation. This setup was done in a way as to reproduce the mode of heat-pipe applications close to realistic. Heat-pipe heating was done by the electric heaters (¯at or circular), and heat-pipe cooling by the air ¯ow (forced or natural convection) and water ¯ow. Three small fans were installed inside the experimental setup. Heat-pipes thermal control was done with the help of the
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Fig. 1. Experimental setup schematic: 1. heat pipe disposed inside the reinforced polymer chamber, 2. electric cartridge heater, 3. the platform for the heat pipe inclination, 4. wattmeter, 5. electric source of energy, 6. electric signals recorder with the thermocouples, 7. electric tension meter, 8. IBM PC computer, 9. thermostat, 10. water rate recorder, and 11. ampermeter.
heat ¯ow measurements in the evaporator (qmax 40±50 W/cm2 , Qmax 100 W), heat-pipe surface temperature measurements were performed by thermocouples and heat-pipe tilt measurements (90° to 0° to ÿ90°) were performed by an automatic system of the tilt deviation. A miniature heat pipe is disposed in a thermally insulated chamber inside the experimental setup. This chamber is divided into three zones and comprises four components ± the basement to which heat pipe is attached, two lids covering the bottom, the chamber and one movable partition (wall). This thermally insulated chamber is ®xed on the turning device to ensure heat-pipe tilt changing. The heat ¯ux in the evaporator is regulated following the computer program. Thus, the length of the evaporator, adiabatic zone and the condenser zone of the heat pipe can also be regulated following the program of testing. The most typical case is when the length of the heat-pipe evaporator is 15±30% and the length of the heat-pipe condenser is 40±60% of the heat-pipe's total length. To measure the temperature ®eld along the heat pipe some thermocouples d 0:2 mm are soldered on the heat-pipe surface. Three thermocouples were ®xed on the evaporator surface, two on the adiabatic zone surface and three on the condenser zone surface (Fig. 2). The heat ¯ux qmax can be determined as follows: the heat ¯ow supplied to the heat-pipe evaporator increases step by step with the temperature ®eld measurements. The heat ¯ow increases in steps of 1±2 W.
Fig. 2. Heat pipe schematic with the thermocouples on its surface.
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Fig. 3. Heat transfer limits for the ¯at miniature heat pipe with a sintered metal powder as a wick.
The miniature heat-pipe thermal resistance RHP (and the heat transfer coecients in the evaporator and condenser zones) is calculated when the temperature drops in the evaporator and condenser zones and the heat ¯ow transfer through the heat pipe are known: RHP Te ÿ Tc =Q: The computer program is developed to determine the heat ¯ow Q, heat-pipe temperature drop DT and heat transfer coecient in the evaporator zone: he q= Te ÿ Tsat ; and heat transfer coecient in the condensation zone, hc q= Tsat ÿ Tc : The graphic data and ®gures of qmax , Qmax , RHP , he and hc as a function of heat-pipe tilt are received for dierent heat load and heat-pipe orientation in the space. A computer program was developed to determine Qmax for the ¯at miniature heat pipes (Fig. 3).
3. The methodology of the experiment The heat load of the heat pipe is guided by the computer program depending on the electric heater electric resistance. Qmax is determined as follows. After the ®xed heat-pipe orientation in space, the electric heater is switched-on when the temperature ®eld along a heat pipe is stationary and recorded in the ®le. Then, the heat-pipe heat load increases on DQ and the temperature ®eld along a heat pipe is measured once more. The Qmax value is ®xed when there is a non-proportional dependency between the temperature change (thermocouples data disposed below the electric heater) and the
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heat load change. In this case, we could see a sharp increase of the temperature. For the precise measurement of the heat-pipe crisis Qmax value, a small step of heat load DQ 1 W increasing was ensured. Heat-pipe thermal resistance is determined using the data of the vapor temperature in the adiabatic zone, and the mean temperature value in the evaporator and in the condenser. Two dierent modes of heat-pipe cooling were used during these experiments. Initially, we used the air forced convection cooling (by fans), but this mode of cooling did not give us an opportunity to approach the critical situation (Qmax ) due to a high heat-pipe temperature (more than 120°C). For the second set of experiments, we were obliged to use a water forced convection cooling of the heat-pipe condenser (thermostat application with the temperature measurements accuracy less than 1°C). The liquid motion was directed from the heat-pipe condenser end to the adiabatic zone at a constant rate. During the experiments, the temperature of the adiabatic zone and of the cooling water were maintained constant. A special computer program for the miniature heat-pipe experimental data analysis was developed and tested, which permits ®xing and analyzing of all the experimental data in a steady state and transitional mode. The ®rst ®le is developed for a steady state heat ¯ow along the heat pipe. The second ®le is used to analyze the experimental data in the transitional mode (®xed time intervals). This program guarantees automatic de®nition of the stationary heat transfer in the heat pipe. After this, the next command is sent (electric heater is switched-on) to change the heat ¯ow value transferred through a heat pipe. The experimental data of the temperature ®eld along the heat pipe are automatically visualized on the display screen (Fig. 4). The heat-pipe physical model is based on some assumptions: (1) The evaporation of the working liquid from the capillary structure of the wick occurs only where the wick temperature is higher than the vapor temperature. The condensation of the vapor on the wick structure occurs only where the wick temperature is lower than the vapor temperature.
Fig. 4. Temperature distribution along the heat pipe.
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(2) The liquid motion occurs through the whole capillary structure (wick) under the capillary action. Due to one side heat-pipe heating, the evaporation zone is also situated on one side of a ¯at heat pipe and the liquid movement inside the wick is considered as two-dimensional. (3) The heat and mass transfer eciency in the heat pipe is mostly dependent on the wick properties and the wick saturation by liquid. When the liquid saturation in the evaporation zone reaches a critical value, there is a limit of the capillary suction by the wick and for further decreasing of the liquid saturation inside the wick a strong increase of the heat-pipe thermal resistance takes place. The heat-pipe heat load increase is also a reason for its thermal resistance increasing. When a wick is completely dry the heat transfer is realized only by thermal conductivity of the heat-pipe envelope and the wick. In this case, the heat-pipe thermal resistance of this part of the heat pipe increases several times. The heat transfer coecients in the evaporators and condensers of heat pipes are directly related with a wick thermal conductivity. The ratio between the axial heat ¯ow transferred along the heat-pipe envelope and radial heat ¯ow transferred as a liquid evaporation in the pores is dierent for dierent heat pipes. For the heat pipes with a metal sintered powder wick, the heat ¯ow transferred in the radial direction by the liquid evaporation up to Qmax is several times more than the heat ¯ow transferred along the heat-pipe envelope, because the eective thermal conductivity of the wick is high (up to 40 W/m K). As a result, we have an isothermal temperature pro®le along the evaporator. These heat-pipe features are included in the software through the wick eective thermal conductivity. The heat transfer coecient in the condenser zone depends on the wick eective thermal conductivity, wick thickness and the liquid ®lm thickness under the wick surface. This liquid ®lm thickness is varied along the condenser ± the heat transfer coecient also varies along the condenser length.
Fig. 5. Cross-section of the ¯attened copper miniature heat pipe with sintered metal powder wick (received from the cylindrical heat pipe ¯attening): 1. HP envelope (3:7 8 mm), 2. porous wick, and 3. vapor channel.
Fig. 6. Cross-section of the copper±water ¯at miniature heat pipe with sintered metal powder wick (rectangular crosssection): 1. HP envelope (2:2 9 mm), 2. porous wick, and 3. vapor channel.
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Fig. 7. Heat ¯ow Qmax as a function of saturated vapor temperature inside the copper±water ¯attened miniature heat pipe with copper sintered powder wick.
Fig. 8. Temperature distribution along the ¯at miniature heat pipe: 1. experimental data and 2. numerical modeling of the heat pipe data.
Experimental samples of the ¯at miniature heat pipe were chosen as copper/water heat pipe with a copper sintered powder as a wick. Two dierent samples were tested. The ®rst sample was a ¯attened cylindrical heat pipe (Figs. 5, 7±13). The second sample was a heat pipe with a rectangular cross-section (Figs. 6 and 14). Heat-pipe heat transfer limit is Qmax . Usually, the heat transfer limit in heat pipes is determined experimentally as a fast temperature rise in the evaporator. This temperature rise is not proportional to the heat ¯ow increase. In our experiments, the temperature on the surface of the evaporator was controlled by the thermocouple disposed on the opposite side of the electric heater (electric heater was joined to the opposite side of a ¯at heat pipe). Basically, the temperature rise on the surface of a heat pipe in contact with an electric heater was dierent from the temperature rise on the opposite side of heat-pipe evaporator (a faster temperature increase occurred).
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Fig. 9. Temperature distribution along the ¯attened mHP for various powers supplied (Le 20 mm, Lc 100 mm, La 30 mm, experimental data, horizontal position).
Fig. 10. Temperature distribution along the ¯attened mHP for various powers supplied (Le 20 mm, Lc 100 mm, La 30 mm, experimental data, vertical, inverted position).
The calculations show that the temperature drop between these ¯at surfaces of the evaporator could be essential (Fig. 13), so a real heat transfer limit starts earlier, when Qmax is few watts less than that we can estimate by the thermocouple no. 1 temperature data. Analyzing the data of Qmax (Fig. 14), we can conclude that the heat transfer limit for two dierent orientations of a heat pipe in space (vertical and horizontal) is essentially dierent. To verify the reliability of the computer program, we need to compare the computer data with some of the experimental data ± the temperature ®eld along the heat pipe for dierent heat ¯ows transferred. We can conclude that the theoretical and experimental data coincides within the limit of 10% for large range of heat ¯ow transferred through a heat pipe.
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Fig. 11. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal sintered powder): horizontal position, 20°C cooling water, experimental data, Le 20 mm, Lc 100 mm, La 30 mm.
Fig. 12. Relationship between the thermal resistance R and power dissipation Q in the ¯attened mHP (metal powder): vertical, inverted position, 20°C cooling water, experimental data, Le 20 mm, Lc 100 mm, La 30 mm.
Fig. 13. 1. Non-heated opposite side of the evaporator and 2. heated surface of the evaporator, theoretical data.
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Fig. 14. Capillary limit Q of a miniature rectangular heat pipe with dimensions 2:2 9 150 mm and Le /La /Lc ± 20/70/ 60 mm.
The equation to calculate heat-pipe limit Qmax due to capillary forces limitation is Q
pc ÿ ql gl : ll l 12lv l ql r Scs k qv r A3 W
The ®rst part of this equation is the liquid pressure drop and the second part of this equation is the vapor pressure drop in the heat pipe. Heat-pipe boiling limit Qcr and sonic limit Qcr were analyzed following [1±3]. The heat-pipe boiling limit Qcr is determined as kcs Se Rg Tv2 2r 1 1 2rqv ÿ : Qcr ln 1 pv Rb Rm d r p v Rb q1 Heat-pipe sonic limit is determined as 0 0:5 K Rg Tv Qcr Sv qv r : 2 K 0 1 A ¯at long miniature heat pipe is considered for the numerical analysis of its action. A comprehensive two-dimensional steady-state mathematical model for predicting thermal performances (maximum transport capacity, thermal resistance, heat-pipe temperature axial pro®le, temperature drop between a heat source and heat sink) is the goal of this research program. This model needs to predict a heat-pipe performance within =ÿ10%. Actually, we analyze a ¯at heat pipe which has an isotropic capillary structure (metal sintered powder wick) on the inner heat-pipe surface. The heat-pipe orientation in space is in the limits of ÿ90° to 90°. A long heat-pipe axis is constantly in a horizontal position and we consider the heat-pipe rotation on its axis. Heat-pipe performance depends upon a heat-pipe thermal resistance, while the thermal resistance depends upon the heat-pipe ¯uid transport limit, wick structure, permeability limitation, input power and operating temperature, etc.
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The main (principal) particularity of the metal sintered powder wick is the possibility of functioning with a partially dry porous structure in the heat-pipe evaporator. The degree of wick saturation with the liquid has an in¯uence on the heat transfer across the wick. For such sintered powder wicks, the heat transfer crisis (Qmax ) beginning is soft and the heat-pipe works in a certain range of DQmax (from Qmax1 up to Qmax2 ). Within this DQmax range, the wick capillary properties change: liquid permeability decreases (some pores are occupied by the vapor), and capillary pressure increases (small pores are responsible for a liquid capillary suction). The heat-pipe evaporator works as the porous structure with the ``inverted'' meniscus of the evaporation and the heat transfer increases. When Qmax2 is reached full drying in the evaporator's wick occurs and the heat pipe stops functioning [10]. Therefore, the heat transfer coecient in the evaporator basically is a function of the wick eective thermal conductivity, wick thickness and the degree of the wick saturation with the liquid. Therefore, in such cases, the surface of the liquid ®lm evaporation in the pores increases and the wick eective thickness decreases. These two phenomena are the reasons for the heat transfer coecient he increase. Evidently, he is a function of the evaporator length and the heat-pipe tilt. The heat transfer coecient in the heat-pipe condenser zone depends on the wick eective thermal conductivity, wick thickness and the liquid ®lm thickness on the wick surface. During the evaporator partial drying (Qmax ), the excess of the liquid is accumulated on the wick surface in the heat-pipe condenser. The liquid ®lm thickness increases and the heat transfer coecient in the condenser zone decreases. The local value of the heat transfer in the condenser zone is a function of the condenser length which can be estimated [11]. The vapor channel thickness inside the ¯at miniature heat pipes usually does not exceed 1 mm and the vapor pressure drop is comparable with the liquid pressure drop inside the wick. This vapor pressure drop DPv can be determined as the pressure drop for the gas ¯ow in the thin rectangular channel [12]: DPv
12lv l : qv r A3 W
The heat and mass transfer analysis in the ¯at miniature heat pipe gives the possibility of determining the meniscus diameter distribution along the wick surface, wick saturation, capillary permeability and heat transfer coecients in the evaporator and condenser zones. To utilize the software for the ¯at miniature heat-pipe numerical modeling, we need to use some experimental data related with the real pore distribution in the wick (mercury pore distribution check technology).
4. Conclusion Heat transfer coecients in the evaporator and condenser of the ¯at miniature heat pipe depend on two-dimensional hydraulic (pore saturation, capillary permeability, capillary pressure) and thermal (temperature distribution along the heat-pipe envelope) parameters of such devices.
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(1) The temperature in the middle of the heated surface of the envelope (evaporator) can exceed the symmetric point temperature on the opposite (non-heated) surface of the envelope (evaporator) by nearly 10°C. (2) The technology of heat pipes with the metal sintered powder wick development strongly in¯uences the heat-pipe parameters (¯attened heat pipe or rectangular heat pipe). (3) Experimental veri®cation of the ¯at miniature heat-pipe parameters testi®es the validity of the software application.
Acknowledgements The authors would like to show their appreciation to Nortel Networks Ltd. for ®nancing software development, Contract No. 642817, ``Thermal performance prediction algorithm for ¯at miniature heat pipe''.
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