Abstract
This article experimentally investigates the thermal resistance of a heat sink with horizontal embedded heat pipes. Heat sink with embedded heat pipes disperses heat from CPU to both the base plate and the heat pipes, and then removes heat from fins to the surrounding. This experimental approach measures the thermal resistances of interface between CPU and base plate, base plate, CPU to heat pipes, heat pipes and fins through the thermal resistance analysis. It can be divided into two steps. The first step is to measure the thermal performance of a heat pipe and the next step is the measurement for the thermal performance of heat sink with and without the function of heat pipes. These results are limited to the case of sink-processor assemblies installed horizontally and two U-shaped embedded heat pipes inserted into the heat sink in the paper. The results show that two heat pipes embedded in the base plate carry 36% of the total dissipated heat from CPU, while 64% of heat is delivered from the base plate to the fins. Furthermore, when the CPU power is 140 W, the total thermal resistance is at its minimum 0.27 °C/W and the thermal resistances of CPU to heat pipes and heat pipes are 0.32 °C/W and 0.12 °C/W respectively.
© 2007 Elsevier Ltd. All rights reserved.
Keywords: Thermal performance; Heat sink with embedded heat pipes; Thermal resistance analysis
1. Introduction
The performance in electronic components has been increasing, resulting in the problem of increased operating wattage and power[1]. The normal operating temperature of a silicon chip is below 70 °C. Bar-Cohen et al[2]pointed out that the reliability of electronic components decreases by 10% for increasing every 2 °C above normal operating temperature. If the operating temperature of the chip is too high, the stability and performance of electronic components decreases. This is the principal reason for the failure and reduced durability of electronic components. Thus, it is necessary to quickly remove heat generated by electronic components for normal operation.
Typical thermal solution of electronic components heat dissipation is to install a heat sink with a fan, as shown in Fig. 1a. Heat is transferred from the base plate to the fins and removed from fin surfaces to environment through forced
☆Communicated by A.R. Balakrishnan and S. Jayanti.
⁎ Corresponding author. Tel.: +886 2 23631808; fax: +886 2 23631755. E-mail address:[email protected](S.-L. Chen).
0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.03.015
convection. Currently, increasing the fin surface area and raising fan speed are keys to solve the high heat power problems. The total thermal resistance is used to evaluate the thermal performance of a heat sink. Duan and Muzychka [3]investigated four different sizes of heat sinks and show that increasing the fin surface area reduces the total thermal
Nomenclature
A area, m2
Ae contact surface area of the solder paste, m2
h heat transfer coefficient, W/m2K
H height from base plate to condensation section of heat pipes, m Hf fin height, m
H1 height from base plate to adiabatic line, m
H2 height from adiabatic line to condensation section of heat pipes, m
k thermal conductivity, W/mK kf fin thermal conductivity, W/mK
n number of heat pipes Q total heat transfer rate, W
Q1 heat transfer rate from base plate to fins, W
Q2 heat transfer rate from heat pipes to fins, W
Q3 heating power of single heat pipe, W
R thermal resistance, K/W Rt total thermal resistance, K/W
Rc thermal contact resistance, K/W
Rn fin-base convective thermal resistance, K/W
Rh base to heat pipes thermal resistance, K/W
Rp heat pipes thermal resistance, K/W
Rf fin-pipe convective thermal resistance, K/W
Rs spreading thermal resistance, K/W
Rm conduction thermal resistance, K/W
R3 single heat pipe thermal resistance, K/W
t thickness, m tf fin thickness, m
th thickness from CPU to heat pipes, m
T temperature, K
Tu mean upper surface temperature of base plate, K
Tb one-dimensional temperature of adiabatic line, K
Greek symbols
α modified base plate β modified base to heat pipes Subscripts
a ambient
b base plate
c condensation section of heat pipes d lower surface of base plate e evaporation section of heat pipes g thermal grease
h heat source s solder paste
resistance from 0.55 °C/W to 0.35 °C/W. Lin et al. [4,5] studied the effect of fan speed on thermal resistance. The results show that a heat sink with a maximum fan speed of 4000 RPM has an optimum total thermal resistance value of 0.33 °C/W. However, increasing the surface area results in an increase in cost and boosting the fan speed results in noise, vibration and more power consumptions, which increase the probability of failure to electronic components.
Fig. 1b shows a longitudinally-finned heat sink with embedded heat pipes which uses two heat pipes, one end of the heat pipes inserted into the base plate which wrap around 180° as the evaporation section and the other end protrude and incline about 30° angle through the upper portion of the fins as the condensation section. It disperses heat from heat source to both the base plate and the heat pipes embedded in the base plate, and then removes heat from fins to the surrounding. The heat pipe is composed of a container making up highly pure oxygen-free copper pipe; it includes a wick structure and working fluid[6–8]. The working fluid evaporates when heating, and then condenses through cooling. The wick structure can offer capillary force for working fluid flow to oppose gravity[9]. And the maximum heat dissipation is affected by the inclinations of embedded heat pipes reduced about 20% between + 90 to 0° opposition gravity[10,11]. Due to high thermal conductivity and so-named gravity-assistance of the heat pipes, the heat sink with embedded heat pipes can reduce the total thermal resistance to under 0.3 °C/W[12,13]. Xie et al.[14] conducted an experiment combining a 4-mm diameter heat pipe and a heat sink, achieving an optimum total thermal resistance of 0.29 °C/W. Gernert et al.[15]employed an experiment on a heat sink with embedded heat pipes with a 25.4-mm diameter, 156 mm long heat pipe. At a maximum heat flux of 285 W/cm2, it has the lowest total thermal resistance 0.23 °C/W. Therefore, the heat sink with embedded heat pipes is one of the best solutions for thermal problems in electronic components.
Previous research only measures the interface, base plate and total thermal resistances of a heat sink with embedded heat pipes and fails to provide the proportion of the heat borne by the heat pipes. In light of this, present research examined the thermal performance of the heat sink with and without the function of heat pipes and calculated the amount of heat transferred from the base plate to the fins and from the embedded heat pipes to the fins respectively. The individual thermal resistances of contact, base plate, base to heat pipes, heat pipes, fins and the total thermal resistance can be obtained through thermal resistance analysis. The ratio of heat transferred through the heat pipes to the fins can be also acquired.
2. Thermal resistance analysis
This study consider heat sink with embedded heat pipes as steady one-dimensional heat flow which CPU surface temperature and air environment temperature maintained constant as Thand Tarespectively. The rate of heat transfer Q
from the CPU (heat source) to the surrounding air can be expressed as Q¼DT
Rt ð1Þ
where Rtdenotes the total thermal resistance of heat sink with embedded heat pipes.Fig. 2a shows that heat transfer
rate Q transfers heat from the heat source to the fins through the base plate and the heat pipes. The base plate transfers heat to fins is Q1and the heat pipes transfer heat to fins is Q2. Then
Q¼ Q1þ Q2 ð2Þ
The temperature profile along the fins is shown in Fig. 2b. The region where temperature gradient equals to zero appearing between these two heat transfer pathways is called adiabatic line. The fins in the adiabatic line are similar to be insulated. It means that no heat flow across the adiabatic line. If the temperatures are assumed uniform both on the upper surface of base plate and on the condensation section of heat pipes, the steady one-dimensional energy balance equation for fins is[16]
d2T dY2 m 2 T T a ð Þ ¼ 0 ð3Þ and m¼ ffiffiffiffiffiffiffi 2h kjtf s ; ð4Þ
where h represents the convective heat transfer coefficient, kfis the fin conductivity and tfis the fin thickness. The
specified boundary conditions can be expressed as T ¼ Tu at Y ¼ 0 and
T ¼ Tc at Y ¼ H; ð5Þ
In Eq. (5) Tcis the temperature of the condensation section of heat pipes, Tuis the average temperature of the upper
surface of base plate and H denotes the length between base plate and condensation section of heat pipes. The temperature profile for the fins can be obtained from Eq. (3) as
T Yð Þ ¼ Taþ ðTu TaÞe mH emH emH Tc Ta emH emH emYþ ðTc TaÞ emH emH ðTu TaÞemH emH emH emY ð6Þ
From the definition of adiabatic line, BT
BY ¼ 0 at Y ¼ H1; ð7Þ
The location of adiabatic line can be shown as H1¼ 1 2mln ðTu TaÞemH ðTc TaÞ ðTc TaÞ ðTu TaÞemH ð8Þ Since there is no heat across the adiabatic line, the thermal resistance network for heat transfer through the heat sink with embedded heat pipes can be shown inFig. 3. The Q1path includes the base plate resistance Rband fin-base
convection resistance Rn; the Q2path includes the base to heat pipes resistance Rh, heat pipes resistance Rpand
fin-pipe convection resistance Rf. The total thermal resistance can be expressed as the sum of the thermal contact resistance
and those thermal resistances on the heat flow paths of Q1and Q2, which is
Rt¼ Rcþ 1 1 ðRbþ RnÞþ 1 ðRhþ Rpþ RfÞ ð9Þ In Eq. (9), contact resistance Rcis defined as the effective temperature difference at the interface (the temperature of
heat source Thminus the temperature at the center of the lower surface of the base plate Td) divided by total Q. The
thermal contact resistance can be minimized by applying thermal grease, such as silicon oil, on the contact surface before they are pressed against each other. The thickness of the thermal grease is tg, the thermal conductivity is kgand
the contact surface area is Ag, which are related to the thermal contact resistance by
Rc¼
tg
kgAg ð10Þ
Base plate resistance is defined as the temperature difference between the center of the lower surface of base plate (Td) and the average temperature of the upper surface of base plate (Tu) divided by Q1. This thermal resistance is
produced by the thickness of base plate and the thermal properties of the material. If the base plate is assumed as a plate with no heat pipes embedded, the base plate resistance including the spreading resistance Rs, the conduction resistance
Rmand the modified base resistance Rα can be expressed as
Rb¼ Rmþ Rsþ 2d Ra ð11Þ
Conduction resistance can be determined from equation below Rm¼
tb
kbAb ð12Þ
where tbis the thickness of the base plate, kbis the thermal conductivity of base plate and Abis the plate area. The
spreading resistance from Lee et al.[17]can be used as Rs¼ ffiffiffiffiffi Ab p ffiffiffiffiffiAh p kb ffiffiffiffiffiffiffiffiffiffiffiffiffi pAbAh p kkbAbRnþ tanhðktbÞ 1þ kkbAbRntanhðktbÞ ð13Þ k ¼ p1ffiffiffiffiffi:5 Ab p þ 1ffiffiffiffiffi Ah p ð14Þ
where Ahis the heat source area.
The 2.Rα is a fixed value that equals to the thermal resistance difference between the base plate resistance and the sum of the conduction resistance and spreading resistance. And it will be zero when the base plate had not been inserted in the heat pipes.
Fin-base convective resistance is defined as the average temperature of the upper surface of base plate (Tu) minus the
ambient temperature (Ta), divided by the heat transfer rate Q1, which can be determined from
Rn¼ 1 hg1A1 ð15Þ g1¼tanhðmH1Þ mH1 ð16Þ In Eq. (16) h is the convective heat transfer coefficient,η1is the surface efficiency at fin length H1and A1is the fin
area up to the height of H1.
Base to heat pipes resistance is defined as the temperature difference between the center of the lower surface of base plate (Td) and the evaporation section (Te) of heat pipes divided by the heat transfer rate Q2. This thermal resistance
includes the conduction resistance of the medium from the heat source to the heat pipes and the contact interface between the base plate and the heat pipes. Solder paste is applied to affix the heat pipes within the base plate at the surface contact. It is the material of commercial solder silver with 42 °W/mK. Thus the base to heat pipes resistance can be expressed as Rh¼ th kbAhþ tS kSAeþ R b ð17Þ
where tsis the thickness of the solder paste, ksis the solder paste's thermal conductivity, Aeis the contact surface area
of the solder paste, this the distance from CPU to heat pipes and Rβis the modified base to heat pipes resistance.
The variable value of Rβis the thermal resistance difference between the base to heat pipes resistance and the sum of
the conduction resistance of the medium from the heat source to the heat pipes and the contact interface resistance between the base plate and the heat pipes. It will be change with the performance of embedded heat pipes and the embedded distance between the two heat pipes.
Heat pipes resistance is defined as the temperature differences between the evaporation section (Te) and the
condensation section (Tc) divided by Q2, which can be determined from the thermal performance of single heat pipe
experiments[18]. Fin-pipe convective resistance is defined as the temperature differences between the condensation section of heat pipes (Tc) and the ambient temperature (Ta) divided by Q2. Similar to fin-pipe convective resistance, it
can be expressed as Rf ¼ 1 hg2A2 ð18Þ g2¼tanhðmH2Þ hg2A2 ð19Þ
In Eq. (19) h is the convective heat transfer coefficient along the region of fin length H2,η2is the corresponding
surface efficiency and A2is the fin surface area for the height of (Hf–H1–dhp), where dhpis the diameter of the heat
so on up to 55 W, until the evaporation section is dried out.
Fig. 5 shows the experimental apparatus for the heat sink with embedded heat pipes. The upper surface of the dummy heater is coated with thermal grease to reduce contact resistance. A thermocouple is attached to the upper surface of the dummy heater to measure the temperature (Th). Six thermocouples are attached to the center of the lower
surface of base plate and five points along the diagonal of the upper surface of base plate, measuring the temperatures at the center of the lower surface of the base plate (Td) and the average temperature of the upper surface of the base plate
(Tu). Computational Fluid Dynamic (CFD) software (Icepak software) is used to calculate the average temperature of
Tu, which compares with the experimental measurement of five-point average value and develops a correlation between
them within an error of ± 3%. A fan with 4200 RPM and 46 CFM is placed to the top of heat sink to disperse heat through forced convection. A thermocouple is placed to the top of the fan to measure the ambient temperature (Ta).
Thermocouples are attached to the evaporation and condensation sections of heat pipes to measure the temperatures of Te and Tc. All thermocouples are T-type. This experiment starts with a heating power of 60 W and stops 200 W
increasing it by increments of 20 W.
After completing the above experiment with function of heat pipes, let these two heat pipes in heat sink fail to function. The method for letting these two heat pipes fail to function is to split the middle position between evaporation and condensation section of two embedded heat pipes. After splitting heat pipes, the heat sink with embedded heat pipes would be heated over 100°C, and the working fluid escaped from these pipes. The heat sink experiments without the function of heat pipes are performed as same as that with the function of heat pipes. Then the corresponding thermal resistances can be determined from this experimental analysis.
The thermocouples used in the experiment have a measurement error of ± 0.5 °C. The cooling circulator manufactured by Firstek Scientific Ltd., Co. has a measurement error of ± 0.5 °C. The data recorder manufactured by
Yokogawa Ltd., Co. has a measurement error of ± 1%. The power supply unit has a measurement error of ± 0.5%. The maximum error for the thermal resistance is within ± 5%.
4. Results and discussion
Fig. 6shows the thermal resistance of a heat pipe with different power input. The heat pipe is unable to operate effectively at low heating power of 5 watts or less, resulting in a high thermal resistance. The thermal resistance has dropped from 0.49 °C/W to 0.33 °C/W at 7 W, signifying that the working fluid within the heat pipe has started to operate. From a heating power of 15 to 30 W, the working fluid within the heat pipe is operating efficiently, lowering the thermal resistance to below 0.3 °C/W. The total thermal resistance reaches a minimum of 0.24 °C/W when the heating power is 25 W. The heat pipe is considered to have a possible local dry-out limit for heat inputs higher than 30 to 35 W. At high heating power of 35 to 50 W, it results in higher vapor temperature and
Fig. 6. Performance curve for heat pipe total thermal resistance under various heating power. Fig. 5. Experimental apparatus for Heat sink with embedded heat pipes.
pressure, and the noncondensable gas is compressed more toward the end of the condensation section. Thus the thermal resistance increases from 0.35 °C/W to 0.94 °C/W. The temperature at the evaporation section surpasses 100 °C when the heating power is over 55 W. At this time the heat pipe has burned out and lost its effectiveness. From above-mentioned, the thermal load higher than 40 W does not consider long-term or tilted application in this study. From the experimental results we can derive the correlation between heating power and heat pipe resistance as
R3¼ 0:324 þ 0:013ðQ3Þ 0:002ðQ3Þ2þ 8:079 105ðQ3Þ3 8:776 107ðQ3Þ4 ð20Þ
Fig. 7shows the experimental results of thermal performance lines for a heat sink with and without the function of heat pipes. As the heating power is increasing, the temperature difference (Tu−Ta) between the upper surface of the base plate and the surrounding
air is also increasing no matter with or without the function of heat pipes. The slopes of these two lines represent the thermal resistances. Because the slope of the upper line is greater than that of the lower, the thermal resistance without function of heat pipes is greater than that with function of heat pipes. It means that the temperature difference (Tu−Ta) is higher without the function of heat
pipes than that with the function of heat pipes. This is because of having an extra path transfer's heat from heat pipes to surrounding and thus the temperature difference is smaller. As the temperature difference for the two lines is fixed as shown inFig. 7, it reaches the thermal performance lines with two points at the power input with and without function of heat pipes. The corresponding heating power represents the Q1in the heat sink without the function of heat pipes and the total Q with the function of two embedded heat
pipes. Heat transfer rate Q2is equal to the total Q minus the Q1. As indicated inFig. 7, the temperature difference is 13.3 °C, the
heating power for Q is 140 W, and the power for Q1is 88.2 W. Therefore Q2equals 51.8 W.Table 1shows the ratio of bypass
Fig. 7. Illustration for bypass heating power.
Table 1
Ratio of bypass heating power and to total heating power
Q (W) Q1/Q (%) Q1(W) Q2/Q (%) Q2(W) 60 67 40.2 33 19.8 80 64 51.2 36 28.8 100 65 65 35 35 120 63 75.6 37 44.4 140 63 88.2 37 51.8 160 64 102.4 36 57.6 180 64 115.2 36 64.8 200 65 130 35 70
heating power to total heating power. The average ratio Q1/Q is 64% and the average ratio Q2/Q is 36% for such a heat sink with two
embedded heat pipes between 60 and 200 W.
Fig. 8shows the total thermal resistance and thermal contact resistance with heating power Q. The experimental total thermal resistance falls from 0.30 °C/W to 0.27 °C/W when the heating power is 60 to 140 W and reaches its minimum of 0.27 °C/W at 140 W. The reason is when the heating power increases to the point that the two embedded heat pipes are starting to function, the total thermal resistance shows a decreasing trend. The two embedded heat pipes are unable to withstand higher heat at heating powers of above 200 W, causing the higher vapor temperature and pressure, and the noncondensable gas is compressed more toward the end of the condensation section, resulting in the heat pipes losing performance, thereby increasing total thermal resistance. The theoretical total thermal resistance has the same curve trend with the experimental total thermal resistance. The value of total thermal resistance changes with power [19]because the heat sink with two embedded heat pipes includes two-phase heat dissipation device as heat pipe. Fig. 8 also shows the theoretical results from thermal resistance analysis and experimental measurements. The experimental contact resistance is approximately 0.03 °C/W when the heating power is between 60 and 200 W and is close to the theoretical predictions; therefore the contact resistance in this experiment can be considered a constant.
The ratios of bypass heating power Q1/Q and Q2/Q are changed with the total thermal resistance. As shown inTable 2, when the
value of the theoretical Q1-path thermal resistances (e.g. Rb+ Rn) is 0.4 °C/W, the ratio of bypass heating power Q1/Q changes with
the total thermal resistance. But the ratio of bypass heating power Q2/Q changes not only with the total thermal resistance but the
theoretical Q2-path thermal resistances (e.g. Rh+ Rp+ Rf). The Q2-path thermal resistances affect the total thermal resistance because
of two embedded heat pipes inserted into the heat sink. If there is a very good thermal performance of heat pipe using in this
Fig. 8. Relationship of the total thermal resistance and contact resistance with the heating power Q.
Table 2
Thermal resistances versus the ratio of bypass heating power
Rt(°C/W) Q1/Q (%) Rb+ Rn(°C/W) Q2/Q (%) Rh+ Rp+ Rf(°C/W) Rβ(°C/W) 0.3 67 0.4 33 0.77 0.12 0.29 64 0.4 36 0.7 0.079 0.28 65 0.4 35 0.69 0.075 0.27 63 0.4 37 0.65 0.045 0.27 63 0.4 37 0.64 0.036 0.27 64 0.4 36 0.67 0.041 0.28 64 0.4 36 0.71 0.056 0.29 65 0.4 35 0.7 0.068
experiment, the ratio of bypass heating power Q2/Q will be over 36% under fixed value of Q1-path thermal resistances. The
maximum Q2/Q is 46% while Rpand Rβare zero respectively in the paper. This means that using a perfect heat pipe with zero
thermal resistance embedded in base plate of heat sink will reach their maximum Q2/Q and minimum Q1/Q in this study. Fig. 9indicates the base plate resistance and fin-base convective resistance with heating power Q1. The experimental base plate
resistance and fin-base convective resistance are approximately 0.25 °C/W and 0.15 °C/W respectively when Q1is between 40 and
129.5 W, not changing as heating power increases. Thus the base plate resistance and fin-base convective resistance in this experiment can be considered constants. The sum of Rmand Rsis 0.16 °C/W from Eqs. (12) and (13), thus the Rα equals 0.045 °C/
W. And the theoretical and experimental base plate resistances become closer as shown inFig. 9. The reason is that the components transferring heat through this path of heating power Q1transferred from the base plate without function of heat pipes to the fins are
Fig. 9. Relationship of the base plate resistance and the fin-base convective resistance with the heating power Q1.
all solid. The thermal physical properties of these components are the same when there is not much change in temperature. Thus the base plate resistance and fin-base convective resistance should remain constant. The base plate resistance and base-fin convective resistance obtained in this experiment are both constant, proving that the experimental results are correct.
Fig. 10indicates the base to heat pipes resistance and fin-pipe convective resistance with heating power Q2. The experimental
base to heat pipes resistance drops from 0.41 °C/W to 0.33 °C/W under heating power of 20 to 44 W. When Q2is 51.4 W, it reaches a
minimum value of 0.32 °C/W. Because the theoretical base to heat pipes resistance takes into account the value of Rβas shown in
Table 2and the thermal performance of the embedded base plate heat pipe, the theoretical base to heat pipes resistance is consistent with the experimental result. The experimental fin-pipe convective resistance is approximately 0.20 °C/W when the Q2is 20 to
70.5 W and does not change much as the heating power increases. Moreover, the theoretical and the experimental fin-pipe convective resistances are close, so the convective resistance Rfcan be considered a constant in this experiment.
Fig. 11indicates the relationship between the heat pipes resistance and heating power Q2. The experimental heat pipes resistance
drops from 0.16 °C/W to 0.13 °C/W when Q2is between 20 and 44 W. It reaches its minimum value of 0.12 °C/W when Q2is
51.4 W. The experimental heat pipes resistance rises from 0.15 °C/W to 0.19 °C/W when Q2is between 58.3 and 70.5 W, increasing
as the heating power increases. The dummy heater was placed at the center of the base plate and these two embedded heat pipes in the heat sink were laid out symmetrically on the left and right, so it can be assumed that these two heat pipes embedded in base plate each loaded an equal amount of heat. In other words, the Q2is twice the Q3using in the Eq. (20). When Q2is 51.4 W, Q3is 25.7 W. The
experimental results of single heat pipe show that this value is within the heating power range of 20 to 27 W which it is at minimum thermal resistance value, proving the validity of this experiment. The theoretical and experimental heat pipes resistances coincide with each other closely, meaning that the heat pipes resistance of heat sink with embedded heat pipes can be obtained from the thermal resistance of the parallel single heat pipe.
5. Conclusions
The present analysis is only valid for the sink-processor assemblies installed horizontally. The two embedded heat pipes used in the paper consisted of pure copper container and sintered copper powder with water as the working fluid. Through the experimental method and thermal resistance analysis of this study, it can be obtained that heat transfer rate Q1and Q2account for 64% and 36% of the total Q respectively. But if it is considered in different orientations with
respect to gravity or different performance (e.g. wick structure, working fluid), the results may be different. Moreover, the total thermal resistance of the heat sink with embedded heat pipes is only affected by changes in the base to heat pipes resistance and heat pipes resistance over the heat flow path of the Q2; that is, the total thermal resistance changes
with the quality of the performance of heat pipes.
[1] S. Hamilton, Intel research expands Moore's law, IEEE Computer Society 36 (1) (2003) 31–40.
[2] A. Bar-Cohen, A.D. Kraus, S.F. Davidson, Thermal frontiers in the design and packaging microelectronic equipment, Mechanical Engineering 105 (6) (1983) 53–59.
[3] Z. Duan, Y.S. Muzychka, Impingement air cooled plate fin heat sinks Part II— Thermal resistance model, Int. Society Conference on Thermal Phenomena, 2004, pp. 436–443.
[4] S.C. Lin, F.S. Chuang, C.A. Chou, Experimental study of the heat sink assembly with oblique straight fins, Experimental Thermal and Fluid Science 29 (2005) 591–600.
[5] S.C. Lin, C.A. Chou, Blockage effect of axial-flow fans applied on heat sink assembly, Applied Thermal Engineering 24 (2004) 2375–2389. [6] G.M. Grover, Evaporation-condensation heat transfer device, US Patent No.3229759, 1966.
[7] A. Faghri, Heat Pipe Science and Technology, Taylor and Francis Ltd, 1995. [8] P.D. Dunn, D.A. Reay, Heat Pipe, 3rd edition, Pergamon Press Ltd, 1982.
[9] D. Sugumar, K.K. Tio, Thermal analysis of inclined micro heat pipes, Journal of Heat Transfer 128 (2006 (February)) 198–202.
[10] V. Maziuk, A. Kulakov, M. Rabetsky, L. Vasiliev, M. Vukovic, Miniature heat-pipe thermal performance prediction tool-software development, Applied Thermal Engineering 21 (2001) 559–571.
[11] Salem A. Said, Bilal A. Akash, Experimental performance of a heat pipe, Int. Comm. Heat Mass Transfer 26 (5) (1999) 679–684. [12] T. Nguyen, et al., Advanced cooling system using miniature heat pipes in mobile PC, IEEE Transactions on Components and Packaging
Technologies 23 (1) (2000) 4516–4521.
[13] J. Legierski, B. Wiecek, Steady state analysis of cooling electronic circuits using heat pipes, IEEE Transactions on Components and Packaging Technologies 24 (4) (2001) 549–553.
[14] X. Hong, A. Ali, R. Bhatia, The use of heat pipes in personal computers, Int. Society Conference on Thermal Phenomena, 1998, pp. 442–448. [15] N.J. Gernert, J. Toth, J. Hartenstine, 100 W/cm2and higher heat flux dissipation using heat pipes, 13th International Heat Pipe Conference,
2004, pp. 256–262.
[16] W.M. Rohsenow, J.P. Hartnett, Y.I. Cho, Handbook of Heat Transfer, 3rd ed., McGraw-Hill, 1998.
[17] Seri Lee, S. Song, V. Au, K.P. Moran. Constriction/Spreading Resistance Model for Electronic Packaging, Proceedings of the 4th ASME/JSME Thermal Engineering Joint Conference (4), 1995, pp. 199–206.
[18] G.P. Peterson, L.S. Fletcher, Effective thermal conductivity of sintered heat pipe wicks, Journal of Thermophysics 1 (4) (1987) 343–347. [19] H.B. Ma, et al., An experimental investigation of a high flux heat sink heat pipe, Journal of Electronic Packaging 128 (2006 (March)) 19–22.
