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Experimental study on thermosyphon boiling in 3-D micro-channels
International Journal of Heat and Mass Transfer 131 (2019) 1260–1269
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Experimental study on thermosyphon boiling in 3-D micro-channels Jia-Hui Huang, Shuang-fei Li, Zhen-Hua Liu ⇑ School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e
i n f o
Article history: Received 24 August 2018 Received in revised form 11 November 2018 Accepted 27 November 2018
Keywords: Thermosyphon Boiling Micro-channel 3-D chip cooling
a b s t r a c t An experimental study on thermosyphon boiling in 3-D micro-channels with inclined angle changed from 90° to 0° was carried out, to develop a new passive cooling technology for 3-D chip cooling. The specific micro-channel structure of actual 3-D chip was simulated as evaporating section of thermosyphon, and the critical heat flux and heat transfer coefficient of 3-D micro-channel thermosyphon boiling in different inclined angles were studied in detail. Experiments were carried out using two kinds of working liquids of deionized water and R113. The length and gap (the distance between two heated walls) of test channels with a rectangular section were in the range of 30–100 mm and 30–50 lm, respectively. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction for forming change in width of micro-channel. The width of rectangular section changed from 0.4 mm to 4 mm. The study results show that the boiling characteristics in 3-D micro-channels thermosyphon can be predicted through the extension of the correlations used for 2-D micro-channels. The present 3-D micro-channel thermosyphon boiling is a promising passive technology for 3-D chip cooling. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction 3-D chip is a new technology that vertically integrates several chips. The chips are no longer connected side by side, but the upper and lower parallel connection. In this way, the distribution area of the cable is extended to the surface of the entire processor, and the parallel structure also effectively shortens the length of the cable between the processors. Researches have shown that the length of global wires can be reduced by as much as 50% in 3-D chip [1]. 3-D integration technology is also considered as the preferred option to achieve miniaturization. However, the higher the integration of the 3-D chip is, the greater the power consumption per unit area of the chip is. If the heat generated by the chip cannot be dissipated in time, it will cause temperature drift, which will not only affect the normal operation of the computer, but also reduce the life of the chip. Long term reliability drops by 50% for each 10 degree rise in junction temperature [2]. For the 2-D chip cooling, many studies have proposed various cooling methods [3–8]. Micro-channel cooling methods for 2-D chip is a rapidly developing cooling technology in recent years that was firstly proposed by Tucherman and Peace [9] in 1981. Because micro-channels have large surface area, and fluid in the channels has a thin boundary layer, high heat transfer coefficient (HTC) ⇑ Corresponding author. E-mail address: [email protected] (Z.-H. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.147 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
can be obtained. For the 3-D chip cooling, because the horizontal chips are stacked in vertical direction and the adjacent gaps are as small as a few microns, it cannot simply apply the cooling methods of traditional 2-D chips where the cooling channels are mounted in the substrate. However, the most 3-D chip cooling technologies are still the simple extension of 2-D chip cooling technologies. Up to now, most of the 3-D stacked chip’s cooling design conceptions have been active methods that micro-channels are installed in encapsulation, and working fluid driven by external power flows through the micro-channels to take away heat [10–15]. In view of the defects of active type of micro-channel cooling method, the authors provided a new passive cooling conception for 3-D chips cooling and carried out some experimental results [16,17]. In these studies, 2-D micro-channels with rectangular section were used for simply simulating chip structure. The length and gap of the channels were changed and the width was fixed at 4 mm. In the first-step study [16], a predicting correlation of the critical heat flux (CHF) in vertical micro-channels was proposed which can be well fitted with the experimental results. In the further study [17], a predictive formula was proposed to predict the boiling CHF for inclined and horizontal micro-channels. However, in these studies, the width effect is not taken into account in the predictive formula, which means that the predictive formula belongs to the 2-D scale. These researches have also revealed that the thermosyphon boiling mode and the boiling heat transfer
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Nomenclature b d D De f g G h Hfg L I p P q qmax S T DT u U x z
width of channel (m) gap of channel (m) gap (m) hydrodynamic equivalent diameter (m) friction coefficient local acceleration of gravity (m/s2) mass flow rate per unit area (kg=ðm2 sÞ) heat transfer coefficient (W=ðm2 KÞ) latent heat of evaporation (J/kg) height of channel (m) electric current (A) pressure (Pa) power (W) heat flux (W/m2) critical heat flux (W/m2) surface area (m2) temperature (°C) mean super-heating (K) velocity (m/s) voltage (V) dryness height (m)
mechanism in micro channels are different from that of traditional thermosyphon [18–20]. In traditional thermosyphon, the governing force is only buoyancy, but in the micro-channel thermosyphon, the governing forces are both buoyancy and capillarity. In other hand, the present concept of micro-channel thermosyphon is also different from that of traditional micro heat pipes that were designed as small tubes and channels with various grooves or small triangle tubes for providing capillary force [21– 25]. In this study, as a further development of the studies mentioned above, boiling heat transfer characteristics in 3-D micro-channels with different inclined angles are studied. And a series of basic experiments were conducted to verify the technical feasibility. A set of apparatus was designed to simulate the 3-D chip structure to investigate the cooling capacity of this novel 3-D chip cooling technology. The research particularly focused on the exploration of the maximum heat flux of the micro scale thermosyphon boiling heat transfer, since the main obstacle to 3-D chip cooling is that the intermediate chip may be overheated without adequate cooling. Spaced apart nickel heating elements were used to simulate 3-D chips as fever ends. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction to change the width of micro-channels. In the experiment, both deionized water and R113 were applied as the working fluids. The equipment reliability, the effect of micro-channel width and inclination on the CHF, and the heat transfer coefficient of thermosyphon boiling are discussed respectively. Furthermore, based on the 2-D predictive formula for the CHF in micro-channels, the new 3-D predictive correlations for the CHF and heat transfer coefficient (HTC) where the effect of width is considered are respectively given out, both of which agree well with the experimental results. 2. Experimental apparatus and procedure 2.1. Experimental apparatus Fig. 1 is a schematic diagram of the experimental system. The whole system can be divided into four parts: 3-D chip simulation experiment piece, thermal insulation container, working fluid cool-
Greek letters dimensionless heat flux b contact angle ( ) q density (kg/m3) l dynamic viscosity (Pa s) t specific volume (m3/kg) r surface tension coefficient (N/m) s frictional shear stress (Pa) x mass fraction
U
Subscripts buo buoyancy cap capillarity v vapor phase l liquid phase m average value s saturated state w heating surface loss heat loss
ing system and data acquisition system. The 3-D chip simulation experiment piece includes the micro-channel main device where the micro-channels with different thicknesses and widths are constructed by the splints, and the support frame that is used for supporting the micro-channel main device immersed in the liquid heat transfer medium and can adjust the inclination angle of microchannels according to requirements. The thermal insulation container is a glass thermostatic tank wrapped with insulation where the glass cover is separated from the tank and is drilled two holes for electric wire and steam to get through, respectively. An auxiliary heating rod is mounted on the bottom of the tank for preheating the working fluid and it is switched off during formal test. After putting the wire through the hole and connecting the steam hole with the glass condenser, the glass cover is simply sealed on the glass tank to prevent the working fluids from escaping. In addition, a viewing window is opened on both sides of the glass container. A computer and data acquisition system including voltmeters, ammeters and thermocouples etc. are used for power and temperature measurements. A silicon rectifier provides steady direct current for heating the test pieces. Fig. 2 shows the structure of the fixture for test piece installation which simulates actual 3-D chip structure. In each test piece, three vertical channel structures are arranged parallel, middle of which is tested and measured to evaluate the heat transfer performance of the channels. The two side channels are used for constitution of a symmetrical geometry and reducing heat dissipation of the middle channel. The length of micro-channels used in the experiment includes 30 mm, 60 mm and 100 mm. The thickness includes 0.1 mm and 0.05 mm which is realized by changing the thickness of copper electrodes and PTFE gasket. And the width changed from 4 mm to 0.4 mm which is realized by the different amounts of wire. Fig. 3 shows a single test piece structure. Each test piece includes four epoxy resin lamina (FR4) substrate plates separated by PTFE gaskets, an I-shaped nickel foil pasted on the FR4 substrate plate by a thin glue layer to form the heating surface of the channel, and four thin copper plates attached to the tail of the nickel foil as electrodes. As is shown in Fig. 3, two pieces of symmetrical PTFE gaskets are pasted on two sides of the nickel foil as the spacers to
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Inlet of cooling water
Outlet of cooling water
16
1.Auxiliary heating rod, 2.glass tank, 3.LED lamp, 4.working fluid, 5.insulation, 6.steam outlet, 7.rubber hose, 8.condenser, 9.power source, 10.data acquisition system, 11.silicon rectifier. 12.current meter. 13.wire tube, 14.glass cover, 15.fixture and channel, 16.viewing window, 17.holder, 18.organic glass base, 19.voltage measurement line, 20.thermocouple, 21.earth wire Fig. 1. A schematic view of experimental system.
Fig. 2. Structure diagram of a fixture for test piece installation.
form an empty rectangular channel between nickel foils with two heating walls. In the present study, the widths of channel are changed by the following method. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction. The diameter of the stainless steel wires is the same as the gap of the channel. Here, the width of channel is defined as the interval between the two stainless steel wires. Fig. 4 shows the Schematic diagram of wire fixation.
Fig. 4 shows how the wires are fixed in the micro-channel and how they are positioned to prevent displacement during the experiment. The diameter of the wire passing through the micro-channel is the same as the thickness of the corresponding micro-channel to ensure that the wire can function as a dividing channel. The uniform distribution of the wires in the micro-channel mainly depends on the wire positioning grooves opened on both sides of the epoxy resin substrate, and positioning grooves are processed by a precision wire cutting machine with a dimensional accuracy of 0.02 mm. The fastening of the wire mainly depends on the friction between the wire and upper & lower splints. The center of the upper and lower splints has a raised chopping board surface which is used to increase the friction between the splints and the wire to ensure that the wire won’t slip. Two countersunk through holes are formed on both sides of the upper splint, meanwhile, threaded holes are formed at corresponding positions on both sides of the lower splint. In addition, the lower splint is directly adhered to the back surface of the epoxy resin substrate with heat resistant glue. The wire was assembled by the following steps: Firstly, one side of the wire was clamped by the upper and lower splints and pressed against the chopping board surface on the splints, in addition, the fastening bolts were screwed. Secondly, each wire was tensioned in the positioning groove on the side of substrate, and the wire was also positioned in the positioning groove on the other side of substrate through the entire channel. Thirdly, the wire passed through the chopping board surface on the other side of the splint and was wound around the drum tool, then it was brought into a tight state by rotating the tool. Finally, tighten the bolts on the other side of splint and cut off the excess wire with scissors.
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1. PTFE gaskets, 2.FR4 substrate, 3.thermocouple mounting slits, 4.heating surface, 5.copper electrode Fig. 3. Structure diagram of a single test piece.
Fig. 4. Schematic diagram of wire fixation.
A section diagram of 3-D channel with 0.8 mm width along the flow direction is shown in Fig. 5. The thickness of the nickel foil is 0.05 mm. To illustrate the cross-sectional shape of the channel, an epoxy substrate at the top is added and displayed as empty white. As is shown in Fig. 5, the gap of channel is determined by the thickness of copper electrode, which can be measured precisely. The dimensions of PTFE gaskets are precisely processed as well. To measure the wall temperature distribution along the height direction (flow direction), three GG-K-30 thermocouples are installed in substrate plate by three slits on substrate plate as
shown in Fig. 3. Thermocouples are posted in the slits, and the indirect contact of thermocouples and the heating surface leads to an extra thermal contact resistance and position offset, which cause a temperature measurement error with a maximum of 0.9 K by a numerical simulation evaluation. 2.2. Working fluids In the present study, deionized water and R113 were used as the working fluids at first. The deionized water used had an electrical conductivity of 1.005 lS/cm which was measured before the formal experiment. 2.3. Experimental process Four main parameters are considered during the test, including input power, effective heat flux, wall super-heating and HTC, which are calculated as follows:
P ¼UI qw ¼ q qloss ¼
Fig. 5. Top view of glass fiber cloth laminate (W = 0.8 mm).
ð1Þ P Ploss S
ð2Þ
DT ¼ T w T s
ð3Þ
qw DT
ð4Þ
hw ¼
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where P is the electric power, I is the total current flowing through the heating surface, S is the total heating area in a channel. Before every test, the value calculated by the existing CHF prediction formula was used as an experimental reference. The region from 0 to predicted CHF was roughly divided into 10 nodes. The first half span was larger, however the second half span was smaller, ensuring that the heating chip and substrate couldn’t be burnt when the CHF occurred. Calculate the voltage value corresponding to each node, gradually increase the voltage across the copper electrode, and the voltage was raised to the next node when the three wall temperatures were stable for 2 min. Immediately turn off the power and stop the experiment when the wall temperatures measured by the instrument were observed to rise sharply. At this time, it can be determined that the CHF was between the front and rear heat flux, but the experimental precision was not sufficient. In order to improve the accuracy of the experiment, the heating experiment was restarted, and the heat flux density was increased by 1% of the previous experimental value. If the wall temperatures rise sharply again, stop the experiment. The heat flux density in the previous steady state was the CHF. Thus, the cut-off error of input power corresponding to CHF is 1%. 2.4. Uncertainty analysis The physical quantities obtained by the measuring instruments in the experiment include the voltage (U), the current (I), the width (W) and height (L) of the micro-channel, and the temperature (T). The errors of these physical quantities are mainly caused by the accuracy of the measuring instruments, which are listed in the Table 1. According to the transfer function theory of the relative standard deviation, the maximum relative deviation of input power, wall effective heat flux, wall super-heating and heat transfer coefficient can be derived from Eqs. (1)–(4) as follows:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @ ln P @ ln P r2U þ r2I ¼ @U @I P
rP
rqeff qeff
ð5Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @ ln DT @ ln DT r2T w þ r2T l ¼ @T w @T l DT
hw
Parameters
Relative errors
P qeff DT hw CHF
2% 5.3% 2.4% 7.1% 11.3%
3. Results and discussion 3.1. Reliability analysis Because the experimental device requires frequent disassembly and assembly, moreover, the micro-channel size is extremely small, if the device structure is unreasonable, it is highly likely that the data obtained in different experiments are very different. In addition, whether the inlet, outlet and interior of the microchannel will be blocked by steam drums is also the key observation target of reliability analysis. In order to verify the reliability of the micro-channel thermosyphon boiling experiment device used in this paper, the repetitive experiments were carried out on different micro-channels to confirm whether there was steam blockage and the instability of the experimental results due to assembly problems. The experimental device was separately disassembled, cleaned and installed for each set of repetitive experiments, which ensured the independence of the experiment. Fig. 6 shows the experimental results of a vertical micro-channel (L = 30 mm, W = 2 mm, and d = 0.05 mm) with deionized water as working medium under two identical experimental conditions. The CHF recorded in the two experiments were 6831.5 W/m2 and 7052.8 W/m2 respectively. The relative error of the two experiment results was 3.1% and no bubble blockage occurred in the micro-channel during the experiment. Similarly, the repeated experiments were performed on the series of micro-channels with different widths. The results show that the errors of the repetitive
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 @ ln qeff @ ln qeff @ ln qeff @ ln qeff @ ln qeff ¼ r2U þ r2I þ r2L þ r2eff þ r2qloss @U @I @L @b @qloss
rDT rhw
Table 2 Errors of calculated parameters.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 @ ln hw @ ln hw @ ln hw ¼ r2qb þ r2T w þ r2T l @qb @T w @T l
ð7Þ
ð8Þ
When calculating the relative deviation of CHF, it is necessary to take into account the experimental repeatability error (±5%) and the error (±1%) caused by the jump increase of power. The relative errors of the important physical quantities calculated from the experimental data are listed in the Table 2. Table 1 Error of measured parameters. Parameters U, I L, W T Tw qloss
Errors ±0.2% ±0.01 mm ±0.1 K ±2% ±1%
ð6Þ
experiment results are all within 5%, which proves the reliability of the experimental device, furthermore, in each independent experiment, the CHF did not appear in advance due to micro-channel blockage. 3.2. The CHF of 3-D micro-channel thermosyphon boiling 3.2.1. The proposed CHF formula for 2-D micro-channel For the vertical and inclined 2-D micro-channel thermosyphon boiling, our laboratory has done a lot of research that reveal effect of both the micro-channel length and thickness on the heat transfer when the channel width is greater than 4 mm. The previous study has proposed a dimensionless prediction formula for the thermosyphon boiling CHF of 2-D micro-channels [16,17]:
q =h q
fg v c U2D ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4
rg ql qv =q2v
¼ 0:25
2 !12 1 1 L f L þ Bo2 ðsin hÞ4 h ¼ maxð5 ; hÞ 2d 4 2d
ð9Þ
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130 Temp of water Temp in the upper part Temp in the middle part Temp in the bottom part Actual boiling heat flux
125
1.2
12500
1.0
120
Experiment condition: water, 90° L=30mm W=4mm d=0.05mm
7500
5000 105
CHF3D/CHF2D
110
10000
q(W/m2)
115
0.8
0.6
Experiment condition: water, 90°
0.4
2500
100
0
10
20
30
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm
0.2
0
95 40
t (min)
0.0 1
a) The first experiment results 15000
130
3
4
(a) Water
Temp of water Temp in the upper part Temp in the middle part Temp in the bottom part Actual boiling heat flux
125
2
W(mm)
12500
1.2
120
Experiment condition: water, 90° L=30mm W=4mm d=0.05mm
7500
1.1
5000 105 2500
100 95
1.0
CHF3D/CHF2D
110
10000
q(W/m2)
115
0.9 0.8
Experiment condition: R113, 90°
0.7
0 0
10
20
30
40
0.6
t (min)
b) The second experiment results
0.5
Fig. 6. Test measuring results for a vertical micro-channel using water with L = 30 mm, W = 4 mm, d = 0.05 mm.
0.4
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm 1
2
3
4
W(mm) Bo ¼
2d ðr=gðql qv ÞÞ1=2
ð10Þ
where f is the friction coefficient, which varies little over a large Reynolds number range for micro-channels and can be taken as a fixed value of 0.1 [16]. Hence, the modified semi-theoretical-semiempirical prediction formula is:
U2D ¼ 0:25
2 !12 1 1 L L þ 0:025 Bo2 ðsin hÞ4 ; h ¼ maxð5 ; hÞ 2d 2d
ð11Þ
where h is the inclined angle of micro-channel, for the 2-D microchannel, the CHF dimensionless number is proportional to the 0.25th power of the sinusoidal value of the inclined angle, furthermore, the CHF remains essentially unchanged when the inclined angle is less than 5°. 3.2.2. The effect of the width of the vertical micro-channel on the CHF Because the influence of micro-channel length and gap on CHF has been mastered, the focus of this paper is on the effect of microchannel width (W) on the thermosyphon boiling heat transfer. Fig. 7 shows the results of comparative data for water and R113 where the 2-D data as the denominator is a predictive value obtained according to the aforementioned 2-D prediction formula. The width and length of the micro-channel in each image are changing, however the gap remains unchanged. For the micro-
(b) R113 Fig. 7. Relationship between the relative value of CHF and the channel width for vertical channels.
channels with width of 4 mm and 2 mm, the CHF value is basically the same as that of the 2-D channel, indicating that when the width is close to 4 mm, the effect of width disappears basically, and the micro-channel can be regarded as 2-D channel. When the width is less than 2 mm, the effect of width is very significant. The CHF decreases rapidly with the decrease of width, reducing 22% for the micro-channel with a width of 1.33 mm, by 30% for the micro-channel with a width of 1 mm and by 44% for the micro-channel with a width of 0.8 mm. In addition, there is no difference in the effect of the working fluid type on the width. The CHF variation of the 3-D microchannel for the two kinds of working fluid is almost the same. Meanwhile, the effect of length doesn’t appear, indicating that the effects of length and width are independent and there is no coupling relationship. After the CHF is processed by the relative value, although the length of 3-D micro-channels and the working fluid are different, the three independent curves are almost coincident. And for the same width, the upper and lower errors of the relative value don’t exceed 15%, which can basically be described by a curve.
J.-H. Huang et al. / International Journal of Heat and Mass Transfer 131 (2019) 1260–1269
7000
qCHF, =qCHF,90°(sin )0.25
6500 6000 5500 2
Fig. 8 is a comparison of the CHF experimental data for vertical 3-D micro-channel and CHF calculated values for 2-D vertical micro-channel. The ratio of the 3-D vertical micro-channel CHF to the calculated value of the 2-D vertical micro-channel CHF is taken as the ordinate, and the dimensionless form of W/d is taken as the abscissa. The data points can be described by one curve and the error is within 15%. For the case of W/d > 40, the CHF ratios remain unchanged, and the micro-channel can be regarded as 2D micro-channel. When W/d < 40, the micro-channel must be considered as 3-D micro-channel. As the W/d increases, the vertical micro-channel thermosyphon boiling CHF gradually increases, and the turning point occurs at W/d = 40.
CHF(W/m )
1266
5000 4500 4000 3500
Experiment condition: water L=30mm d=0.05mm
3000
(
U3D;h ¼
0:25
U3D;0 ðsin 5 Þ
h 6 5
U3D;0 ðsinhÞ0:25
h > 5
W=1.33mm W=4mm
2500 2000 0
10
20
30
2
2500
CHF3D/CHF2D
100
2000
W=1mm W=4mm 1000 10
20
30
40
50
60
70
80
90
100
°
(b) R113 Fig. 9. Influence of tilt angle to CHF.
1.2 R113 1.1 90° 1
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.1mm
0.8
0.8
90
Experiment condition: R113 L=30mm d=0.05mm
0.9
Φ3D/Φ2D
0.9
80
1500
3.2.4. The dimensionless formula of CHF After investigating the influence of the three-dimensional size of the micro-channels on CHF and verifying that the inclined 3-D micro-channel thermosyphon boiling CHF still obeys the formula (12), the experimental results are organized into a form similar to the formula (11). Fig. 10 shows the results in both extreme cases
1
70
3000
0
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.1mm
60
qCHF, =qCHF,90°(sin )0.25
ð12Þ
R113 90°
50
(a) Water
where U3D;0 is the dimensionless number of CHF for the vertical 3-D micro-channel thermosyphon boiling.
1.2 1.1
40
°
CHF(W/m)
3.2.3. The effect of inclined angle on the CHF for the inclined 3-D micro-channels In our previous study, a prediction formula (11) has been proposed for 2-D inclined micro-channel thermosyphon boiling CHF. For the 2-D micro-channels, the CHF dimensionless number is proportional to the 0.25th power of the sinusoid of the inclined angle, and the CHF remains basically unchanged when the inclined angle is less 5°. In this study, a verification experiment was carried out on the 3D micro-channels, where a 3-D chip simulation experiment piece with adjustable inclined angle was designed. Experiments were carried out in the inclined angle of 0°, 5°, 10°, 30°, 45°, 60° and 90° respectively. Fig. 9(a) and (b) show the effect of inclined angle on the CHF with water and R113 as working fluids, respectively. It can be found from the figure that the influence of the inclined angle on the 3-D micro-channel CHF is the same as that in the 2-D case, and can also be organized into the following relationship:
0°
0.7
L=60mm d=0.05mm L=100mm d=0.1mm
0.6 water 90°
+15%
0.5
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=100mm d=0.1mm
0.7
-15%
0.4
0.6 0°
0.5
L=30mm d=0.05mm L=30mm d=0.1mm
0.3 water 90°
0.4
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=100mm d=0.1mm
0.3 6
7 8 9 10
20
30
40
50 60 70 80 90100
W/d Fig. 8. Relationship between relative value of CHF and W/d for vertical channels.
6
7 8 9 10
20
30
40
50 60 70 80 90100
W/d Fig. 10. Relationship between relative value of dimensionless CHF and W/d.
of vertical and horizontal. The data of other inclined angles are basically coincident with the two sets of data and are not placed into the figure where the ordinate is the ratio of the dimensionless number of the 3-D micro-channel thermosyphon boiling CHF to
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that of the 2-D micro-channel and the abscissa is in the form of W/d. Because L d in the experiment, further simplification of Eq. (11) can be done as follows:
1 1 d Bo2 ðsin hÞ4 L
350 300 250
As can be seen from Fig. 10 where U3D is the dimensionless number of the thermosyphon boiling CHF for the 3-D microchannels with different widths and U2D is the dimensionless number of the thermosyphon boiling CHF for the 2-D micro-channels with the same inclination obtained according to the formula (13) where the CHF is not affected by the width, the thermosyphon boiling CHF is basically the same when W/d > 40, at this time, the CHF of 3-D micro-channel is indistinguishable from that of 2D micro-channel, however, the CHF of 3-D micro-channel increases with the increase of W/d when W/d < 40. This relationship also applies to inclined 3-D micro-channels, as the effect of the inclined angle is also eliminated by the ratio form. By fitting the data in Fig. 10, the following empirical formula is obtained:
200
(
1 0:098
W 0:6407 d
W d
P 40
W d
< 40
U3D
100
0 0
P 40
W d
< 40
ð15Þ
Although the error between the formula (14) and the experimental value is within 15%, since the predictive formula (12) itself has an error, the error between the formula (15) that is compounded and the experimental value is still 30%.
10
15
20
(a) R113 1000 900 800
W d
5
ΔT
ð14Þ
Eq. (14) is suitable for 3-D micro-channel thermosyphon boiling with any inclined angles. Furthermore, the dimensionless formula for the 3-D micro-channel thermosyphon boiling can be obtained by combining Eq. (12) as follows:
8 < 3:162dBo12 ðsin hÞ14 L ¼ : 0:31dW 0:6407 Bo12 ðsin hÞ14 L d
150
50
d=0.05mm d=0.1mm water° w=4mm w=4mm L=30mm w=2mm w=2mm w=1.33mm w=1.33mm Vertical w=1mm w=1mm w=0.8mm w=0.8mm
700
h(W/(m2.K))
U3D ¼ U2D
h(W/(m2.K))
ð13Þ
U2D ¼ 3:162
d=0.05mm d=0.1mm R113 w=4mm w=4mm L=30mm w=2mm w=2mm w=1.33mm w=1.33mm Vertical w=1mm w=1mm w=0.8mm w=0.8mm
600 500 400 300 200 100 0
3.3. The HTC of 3-D micro-channel thermosyphon boiling Fig. 11(a) and (b) give out the curves of HTC versus wall average super-heating during vertical 3-D micro-channel thermosyphon boiling with water and R113 as working fluids, respectively. The last data point of each curve corresponds to the wall super-heat of CHF. The micro-channel length is uniform to 30 mm, the gap has two types which are 0.1 mm and 0.05 mm respectively, and the width is gradually reduced from 4 mm that belongs to 2-D micro-channel to 0.8 mm. The results show that the HTC of thermosyphon boiling in the 3-D micro-channels increase rapidly with the increase of wall super-heat at the early stage, and no longer increase after the average super-heating degree reach 10 K, but remains at a relatively stable value until the CHF occurs. Comparing the HTC between deionized water and R113, the HTC of deionized water is 1–3 times larger than that of R113 under the same micro-channel. The difference is the same as conventional pool or thermosyphon boiling. Comparing the experimental data of micro-channels with different gaps, the HTC of d = 0.1 mm is much larger than that of d = 0.05 mm, which is consistent with the conclusion of the 2-D micro-channel. Fig. 12 shows the effect of width on HTC in the horizontal variation region of the HTC and the HTC can be divided into two regional discussions. In 3-D micro-channel region (W/d < 40), the HTC will increase with the increase of width, however, in 2-D microchannel region (W/d 40), HTC is basically unchanged and even slightly reduced, which shows that the effect of width is different
0
5
10
15
20
25
ΔT (b) Water Fig. 11. Relationship between HTC and average super-heating.
for the 2-D micro-channel and 3-D micro-channel. The complex morphology that the effect of width on the HTC should be due to the complexity of bubble generation, growth and flow with in the micro-channels. In the 3-D region, the bubbles are also strongly suppressed in the channel width direction. Therefore, when the width increases, the cross-section area of flow path increases and restraint of bubbles in the width direction decreases, which leads to the decrease of bubble flow resistance. Furthermore, the HTC increases, which is approximately proportional to the square root of width. After entering the 2-D region, the bubbles are not restrained in the width direction, so the influence of width becomes weaker and disappears. For the horizontal change regions of the HTC (from the position of super-heating 10 K to the CHF point), the HTC can be roughly estimated by the following data processing method. It is noticed that the super-heating of CHF occurrence points is concentrated in a narrow region of 20–25 K under various working fluids and micro-channel geometries. As an estimated value, the superheating of all CHF points can be regarded as an average constant (such as 22.5 K), then the HTC of the CHF point can be calculated simply by the quotient of the critical heat flux calculated by the
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Eq. (15) and the average super-heating. Further, in the whole horizontal region of the HTC, the HTC at any super-heating can be approximately equal to the HTC at CHF points, i.e.: 1000 850 700 550
superheat at 15K
h=CW0.6407
2
h( W/(m .K))
ð16Þ
The minimum super-heating in the HTC horizontal region is approximately 10 K. The optimal value of the average superheating of the CHF points can be obtained by data processing. Fig. 13 and formula (17) show the illustration and collation formula of the optimization results where the average superheating of the CHF points is 21.8 K, whose applicable superheating range is greater than 10 K, and the error range of h is within 30%.
400 250
hfg qv =DT c h ¼ hc ¼ qc =DT c ¼ U3D qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 rg ql qv =q2v
100 85 70 55 R113, 90° L=30mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.05mm water, 90° L=30mm d=0.05mm L=100mm d=0.1mm
40 25
1
2
3
4
h3D
8 < 4:472h ðg q q Þ12 d1:5 ðsin hÞ14 1 fg v l L DT ¼ : 0:438h ðg q q Þ12 d0:8593 W 0:6407 ðsin hÞ14 fg
v
l
L
1 DT
W d
P 40
W d
< 40
ð17Þ
4. Conclusions
W(mm)
a super-heating at 15 K 1000 850 700 550
A new passive cooling technology for 3-D chip is proposed utilizing 3-D chip’s specific micro-channels structure to form a 3-D thermosyphon boiling in micro-channels. The critical heat flux and heat transfer coefficient of thermosyphon boiling in 3-D micro-channels were experimentally studied. Both deionized water and R113 were applied as the working fluids. The equipment reliability, the effect of micro-channel width and inclination on the CHF, and the HTC of thermosyphon boiling are discussed respectively. The experimental results are given as:
CHF point
400
h( W/(m2.K))
250
h=CW0.6407
100 85 70 55
R113 L=30mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.05mm water L=30mm d=0.05mm L=100mm d=0.1mm
40 25 1
2
3
4
W(mm)
(b) CHF point Fig. 12. Relationship between HTC to channel width.
800 700
+30%
h(Calculated value)
600 500 400
-30% 300 R113 L=30mm d=0.05mm R113 L=30mm d=0.1mm
200
(1) The effect of micro-channel width on the CHF at different scales is different. When the value of W/d is larger than 40 that belongs to 2 dimensional scale, the effect of width disappears basically. However, when this value is less than 40 that belongs to 3 dimensional scale, the effect of width is very significant and the CHF decreases rapidly with the decrease of width. (2) The effect of sizes of 3-D micro-channel on the CHF for the two kinds of working fluid (Water and R113) is almost the same. Both the CHF and HTC of deionized water are 1–3 times larger than that of R113 under the same microchannel. (3) The influence of the inclined angle on the 3-D micro-channel CHF is the same as that in the 2-D case, and the corresponding equation has been given out which agrees well with the experimental results. (4) The predictive formulas of the CHF and the HTC for 3-D micro-channel thermosyphon boiling at arbitrary inclination angles are given out. And both of them are in good agreement with the experimental results. (5) Based on the experimental results, it is concluded that the thermosyphon heat pipe utilizing 3-D chip’s specific micro structure and driven by buoyancy and capillary force is a feasible new technology for 3-D ship cooling. Several valuable heat transfer prediction formulas are given out and the research results indicate that this new conception has high industrial application prospect for 3-D ship cooling.
R113 L=60mm d=0.05mm water L=30mm d=0.05mm
100
water L=30mm d=0.1mm water L=100mm d=0.1mm
0 0
100
200
300
400
500
600
700
800
h(Experimental value) Fig. 13. The comparison between calculated and experimental values of HTC.
Conflict of interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
J.-H. Huang et al. / International Journal of Heat and Mass Transfer 131 (2019) 1260–1269
Acknowledgement This work was supported by the National Natural Science Foundation of China under grant No. 51876121. References [1] N.H. Khan, S.M. Alam, S. Hassoun, System-level comparison of power delivery design for 2D and 3D ICs, in: 2009 IEEE International Conference on 3D System Integration, 2009 3DIC, IEEE, 2009, pp. 1–7. [2] J. Frenkil, Tools and methodologies for low power design, in: Proceedings of the 34th annual Design Automation Conference, ACM, 1997, pp. 76–81. [3] K. Cheon, Water Cooling Type Cooling System for Electronic Device, Google Patents, 2002. [4] J. Wang, X.-J. Zhao, Y.-X. Cai, C. Zhang, W.-W. Bao, Experimental study on the thermal management of high-power LED headlight cooling device integrated with thermoelectric cooler package, Energy Convers. Manage. 101 (2015) 532– 540. [5] I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, et al., On-chip cooling by superlattice-based thin-film thermoelectrics, Nat. Nanotechnol. 4 (2009) 235–238. [6] R.L. Webb, Next generation devices for electronic cooling with heat rejection to air, J. Heat Transfer 127 (2005) 2–10. [7] D. Enescu, E.O. Virjoghe, A review on thermoelectric cooling parameters and performance, Renew. Sustain. Energy Rev. 38 (2014) 903–916. [8] H.-C. Chien, J.H. Lau, Y.-L. Chao, M.-J. Dai, R.-M. Tain, L. Li, et al., Thermal evaluation and analyses of 3D IC integration SiP with TSVs for network system applications, in: 2012 IEEE 62nd Electronic Components and Technology Conference, IEEE, 2012, pp. 1866–1873. [9] D.B. Tuckerman, R. Pease, High-performance heat sinking for VLSI, IEEE Electr. Dev. Lett. 2 (1981) 126–129. [10] N. Khan, L.H. Yu, T.S. Pin, S.W. Ho, V. Kripesh, D. Pinjala, et al., 3-D packaging with through-silicon via (TSV) for electrical and fluidic interconnections, IEEE Trans. Compon. Packag. Manuf. Technol. 3 (2013) 221–228. [11] S. Tan, K.C. Toh, N. Khan, D. Pinjala, V. Kripesh, Development of single phase liquid cooling solution for 3-D silicon modules, IEEE Trans. Compon. Packag. Manuf. Technol. 1 (2011) 536–544. [12] A. Sridhar, A. Vincenzi, D. Atienza, T. Brunschwiler, 3D-ICE: A compact thermal model for early-stage design of liquid-cooled ics, IEEE Trans. Comput. 63 (2014) 2576–2589.
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[13] H. Mizunuma, C.-L. Yang, Y.-C. Lu, Thermal modeling for 3D-ICs with integrated microchannel cooling, in: Proceedings of the 2009 International Conference on Computer-Aided Design, ACM, 2009, pp. 256–263. [14] Z. Feng, P. Li, Fast thermal analysis on GPU for 3D ICs with integrated microchannel cooling, IEEE Trans. Very Large Scale Integr. VLSI Syst. 21 (2013) 1526–1539. [15] J.-M. Koo, S. Im, L. Jiang, K.E. Goodson, Integrated microchannel cooling for three-dimensional electronic circuit architectures, J. Heat Transfer 127 (2005) 49–58. [16] Kai-lun Zhang, Zhen-Hua Liu, Bao-chen Zheng, A new 3D chip cooling technology using micro-channels thermosyphon with moist fluids and nanofluids, Energy Convers. Manage. 128 (2016) 44–56. [17] Ping-yang Wang, Shuang-fei Li, Zhen-hua Liu, Natural convective boiling in horizontal and inclined micro-channels structure using super-moist fluids for cooling 3D stacked chip, Int. J. Heat Mass Transf. 107 (2017) 479–487. [18] M.M. Sarafraz, F. Hormozi, S.M. Peyghambarzadeh, Thermal performance and efficiency of a thermosyphon heat pipe working with a biologically ecofriendly nanofluid, Int. Commun. Heat Mass Transfer 57 (2014) 297–303. [19] M.M. Sarafraz, F. Hormozi, S.M. Peyghambarzadeh, Role of nanofluid fouling on thermal performance of a thermosyphon: Are nanofluids reliable working fluid?, Appl Therm. Eng. 82 (2015) 212–224. [20] M.M. Sarafraz, F. Hormozi, S.M. Peyghambarzadeh, Pool boiling heat transfer to aqueous alumina nano-fluids on the plain and concentric circular microstructured (CCM) surfaces, Exp. Therm. Fluid Sci. 72 (2016) 125–139. [21] Wang Xiaowu, Tang Yong, Chen Ping, Investigation into performance of a heat pipe with micro grooves fabricated by extrusion–ploughing process, Energy Convers. Manage. 50 (2009) 1384–1388. [22] Wael I.A. Aly, Moustafa A. Elbalshouny, H.M. Abd El-Hameed, M. Fatouh, Thermal performance evaluation of a helically-micro-grooved heat pipeworking with water and aqueous Al2O3 nanofluid at different inclinationangle and filling ratio, Appl. Therm. Eng. 110 (2017) 1294–1304. [23] Mehdi Famouri, Gerardo Carbajal, Chen Li, Transient analysis of heat transfer and fluid flow in a polymer-based Micro Flat Heat Pipe with hybrid wicks, Int. J. Heat Mass Transf. 70 (2014) 545–555. [24] M.M. Rahman, M. Saha, M.M.K. Bhuiya, A. Biswas, Md.H. Alam, C.Md. Feroz, Heat transfer characteristics of a parallel miniature heat pipe system, Int. Commun. Heat Mass Transfer 79 (2016) 1–8. [25] Y.P. Chen, F.W. Yu, C.B. Zhang, X.D. Liu, Experimental study on thermohydrodynamic behaviors in miniaturized two-phase thermosyphons, Int. J. Heat Mass Transf. 100 (2016) 550–558.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental study on thermosyphon boiling in 3-D micro-channels Jia-Hui Huang, Shuang-fei Li, Zhen-Hua Liu ⇑ School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e
i n f o
Article history: Received 24 August 2018 Received in revised form 11 November 2018 Accepted 27 November 2018
Keywords: Thermosyphon Boiling Micro-channel 3-D chip cooling
a b s t r a c t An experimental study on thermosyphon boiling in 3-D micro-channels with inclined angle changed from 90° to 0° was carried out, to develop a new passive cooling technology for 3-D chip cooling. The specific micro-channel structure of actual 3-D chip was simulated as evaporating section of thermosyphon, and the critical heat flux and heat transfer coefficient of 3-D micro-channel thermosyphon boiling in different inclined angles were studied in detail. Experiments were carried out using two kinds of working liquids of deionized water and R113. The length and gap (the distance between two heated walls) of test channels with a rectangular section were in the range of 30–100 mm and 30–50 lm, respectively. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction for forming change in width of micro-channel. The width of rectangular section changed from 0.4 mm to 4 mm. The study results show that the boiling characteristics in 3-D micro-channels thermosyphon can be predicted through the extension of the correlations used for 2-D micro-channels. The present 3-D micro-channel thermosyphon boiling is a promising passive technology for 3-D chip cooling. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction 3-D chip is a new technology that vertically integrates several chips. The chips are no longer connected side by side, but the upper and lower parallel connection. In this way, the distribution area of the cable is extended to the surface of the entire processor, and the parallel structure also effectively shortens the length of the cable between the processors. Researches have shown that the length of global wires can be reduced by as much as 50% in 3-D chip [1]. 3-D integration technology is also considered as the preferred option to achieve miniaturization. However, the higher the integration of the 3-D chip is, the greater the power consumption per unit area of the chip is. If the heat generated by the chip cannot be dissipated in time, it will cause temperature drift, which will not only affect the normal operation of the computer, but also reduce the life of the chip. Long term reliability drops by 50% for each 10 degree rise in junction temperature [2]. For the 2-D chip cooling, many studies have proposed various cooling methods [3–8]. Micro-channel cooling methods for 2-D chip is a rapidly developing cooling technology in recent years that was firstly proposed by Tucherman and Peace [9] in 1981. Because micro-channels have large surface area, and fluid in the channels has a thin boundary layer, high heat transfer coefficient (HTC) ⇑ Corresponding author. E-mail address: [email protected] (Z.-H. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.147 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
can be obtained. For the 3-D chip cooling, because the horizontal chips are stacked in vertical direction and the adjacent gaps are as small as a few microns, it cannot simply apply the cooling methods of traditional 2-D chips where the cooling channels are mounted in the substrate. However, the most 3-D chip cooling technologies are still the simple extension of 2-D chip cooling technologies. Up to now, most of the 3-D stacked chip’s cooling design conceptions have been active methods that micro-channels are installed in encapsulation, and working fluid driven by external power flows through the micro-channels to take away heat [10–15]. In view of the defects of active type of micro-channel cooling method, the authors provided a new passive cooling conception for 3-D chips cooling and carried out some experimental results [16,17]. In these studies, 2-D micro-channels with rectangular section were used for simply simulating chip structure. The length and gap of the channels were changed and the width was fixed at 4 mm. In the first-step study [16], a predicting correlation of the critical heat flux (CHF) in vertical micro-channels was proposed which can be well fitted with the experimental results. In the further study [17], a predictive formula was proposed to predict the boiling CHF for inclined and horizontal micro-channels. However, in these studies, the width effect is not taken into account in the predictive formula, which means that the predictive formula belongs to the 2-D scale. These researches have also revealed that the thermosyphon boiling mode and the boiling heat transfer
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Nomenclature b d D De f g G h Hfg L I p P q qmax S T DT u U x z
width of channel (m) gap of channel (m) gap (m) hydrodynamic equivalent diameter (m) friction coefficient local acceleration of gravity (m/s2) mass flow rate per unit area (kg=ðm2 sÞ) heat transfer coefficient (W=ðm2 KÞ) latent heat of evaporation (J/kg) height of channel (m) electric current (A) pressure (Pa) power (W) heat flux (W/m2) critical heat flux (W/m2) surface area (m2) temperature (°C) mean super-heating (K) velocity (m/s) voltage (V) dryness height (m)
mechanism in micro channels are different from that of traditional thermosyphon [18–20]. In traditional thermosyphon, the governing force is only buoyancy, but in the micro-channel thermosyphon, the governing forces are both buoyancy and capillarity. In other hand, the present concept of micro-channel thermosyphon is also different from that of traditional micro heat pipes that were designed as small tubes and channels with various grooves or small triangle tubes for providing capillary force [21– 25]. In this study, as a further development of the studies mentioned above, boiling heat transfer characteristics in 3-D micro-channels with different inclined angles are studied. And a series of basic experiments were conducted to verify the technical feasibility. A set of apparatus was designed to simulate the 3-D chip structure to investigate the cooling capacity of this novel 3-D chip cooling technology. The research particularly focused on the exploration of the maximum heat flux of the micro scale thermosyphon boiling heat transfer, since the main obstacle to 3-D chip cooling is that the intermediate chip may be overheated without adequate cooling. Spaced apart nickel heating elements were used to simulate 3-D chips as fever ends. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction to change the width of micro-channels. In the experiment, both deionized water and R113 were applied as the working fluids. The equipment reliability, the effect of micro-channel width and inclination on the CHF, and the heat transfer coefficient of thermosyphon boiling are discussed respectively. Furthermore, based on the 2-D predictive formula for the CHF in micro-channels, the new 3-D predictive correlations for the CHF and heat transfer coefficient (HTC) where the effect of width is considered are respectively given out, both of which agree well with the experimental results. 2. Experimental apparatus and procedure 2.1. Experimental apparatus Fig. 1 is a schematic diagram of the experimental system. The whole system can be divided into four parts: 3-D chip simulation experiment piece, thermal insulation container, working fluid cool-
Greek letters dimensionless heat flux b contact angle ( ) q density (kg/m3) l dynamic viscosity (Pa s) t specific volume (m3/kg) r surface tension coefficient (N/m) s frictional shear stress (Pa) x mass fraction
U
Subscripts buo buoyancy cap capillarity v vapor phase l liquid phase m average value s saturated state w heating surface loss heat loss
ing system and data acquisition system. The 3-D chip simulation experiment piece includes the micro-channel main device where the micro-channels with different thicknesses and widths are constructed by the splints, and the support frame that is used for supporting the micro-channel main device immersed in the liquid heat transfer medium and can adjust the inclination angle of microchannels according to requirements. The thermal insulation container is a glass thermostatic tank wrapped with insulation where the glass cover is separated from the tank and is drilled two holes for electric wire and steam to get through, respectively. An auxiliary heating rod is mounted on the bottom of the tank for preheating the working fluid and it is switched off during formal test. After putting the wire through the hole and connecting the steam hole with the glass condenser, the glass cover is simply sealed on the glass tank to prevent the working fluids from escaping. In addition, a viewing window is opened on both sides of the glass container. A computer and data acquisition system including voltmeters, ammeters and thermocouples etc. are used for power and temperature measurements. A silicon rectifier provides steady direct current for heating the test pieces. Fig. 2 shows the structure of the fixture for test piece installation which simulates actual 3-D chip structure. In each test piece, three vertical channel structures are arranged parallel, middle of which is tested and measured to evaluate the heat transfer performance of the channels. The two side channels are used for constitution of a symmetrical geometry and reducing heat dissipation of the middle channel. The length of micro-channels used in the experiment includes 30 mm, 60 mm and 100 mm. The thickness includes 0.1 mm and 0.05 mm which is realized by changing the thickness of copper electrodes and PTFE gasket. And the width changed from 4 mm to 0.4 mm which is realized by the different amounts of wire. Fig. 3 shows a single test piece structure. Each test piece includes four epoxy resin lamina (FR4) substrate plates separated by PTFE gaskets, an I-shaped nickel foil pasted on the FR4 substrate plate by a thin glue layer to form the heating surface of the channel, and four thin copper plates attached to the tail of the nickel foil as electrodes. As is shown in Fig. 3, two pieces of symmetrical PTFE gaskets are pasted on two sides of the nickel foil as the spacers to
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Inlet of cooling water
Outlet of cooling water
16
1.Auxiliary heating rod, 2.glass tank, 3.LED lamp, 4.working fluid, 5.insulation, 6.steam outlet, 7.rubber hose, 8.condenser, 9.power source, 10.data acquisition system, 11.silicon rectifier. 12.current meter. 13.wire tube, 14.glass cover, 15.fixture and channel, 16.viewing window, 17.holder, 18.organic glass base, 19.voltage measurement line, 20.thermocouple, 21.earth wire Fig. 1. A schematic view of experimental system.
Fig. 2. Structure diagram of a fixture for test piece installation.
form an empty rectangular channel between nickel foils with two heating walls. In the present study, the widths of channel are changed by the following method. Stainless steel wires with different numbers were evenly laid in the channel along the flow direction. The diameter of the stainless steel wires is the same as the gap of the channel. Here, the width of channel is defined as the interval between the two stainless steel wires. Fig. 4 shows the Schematic diagram of wire fixation.
Fig. 4 shows how the wires are fixed in the micro-channel and how they are positioned to prevent displacement during the experiment. The diameter of the wire passing through the micro-channel is the same as the thickness of the corresponding micro-channel to ensure that the wire can function as a dividing channel. The uniform distribution of the wires in the micro-channel mainly depends on the wire positioning grooves opened on both sides of the epoxy resin substrate, and positioning grooves are processed by a precision wire cutting machine with a dimensional accuracy of 0.02 mm. The fastening of the wire mainly depends on the friction between the wire and upper & lower splints. The center of the upper and lower splints has a raised chopping board surface which is used to increase the friction between the splints and the wire to ensure that the wire won’t slip. Two countersunk through holes are formed on both sides of the upper splint, meanwhile, threaded holes are formed at corresponding positions on both sides of the lower splint. In addition, the lower splint is directly adhered to the back surface of the epoxy resin substrate with heat resistant glue. The wire was assembled by the following steps: Firstly, one side of the wire was clamped by the upper and lower splints and pressed against the chopping board surface on the splints, in addition, the fastening bolts were screwed. Secondly, each wire was tensioned in the positioning groove on the side of substrate, and the wire was also positioned in the positioning groove on the other side of substrate through the entire channel. Thirdly, the wire passed through the chopping board surface on the other side of the splint and was wound around the drum tool, then it was brought into a tight state by rotating the tool. Finally, tighten the bolts on the other side of splint and cut off the excess wire with scissors.
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1. PTFE gaskets, 2.FR4 substrate, 3.thermocouple mounting slits, 4.heating surface, 5.copper electrode Fig. 3. Structure diagram of a single test piece.
Fig. 4. Schematic diagram of wire fixation.
A section diagram of 3-D channel with 0.8 mm width along the flow direction is shown in Fig. 5. The thickness of the nickel foil is 0.05 mm. To illustrate the cross-sectional shape of the channel, an epoxy substrate at the top is added and displayed as empty white. As is shown in Fig. 5, the gap of channel is determined by the thickness of copper electrode, which can be measured precisely. The dimensions of PTFE gaskets are precisely processed as well. To measure the wall temperature distribution along the height direction (flow direction), three GG-K-30 thermocouples are installed in substrate plate by three slits on substrate plate as
shown in Fig. 3. Thermocouples are posted in the slits, and the indirect contact of thermocouples and the heating surface leads to an extra thermal contact resistance and position offset, which cause a temperature measurement error with a maximum of 0.9 K by a numerical simulation evaluation. 2.2. Working fluids In the present study, deionized water and R113 were used as the working fluids at first. The deionized water used had an electrical conductivity of 1.005 lS/cm which was measured before the formal experiment. 2.3. Experimental process Four main parameters are considered during the test, including input power, effective heat flux, wall super-heating and HTC, which are calculated as follows:
P ¼UI qw ¼ q qloss ¼
Fig. 5. Top view of glass fiber cloth laminate (W = 0.8 mm).
ð1Þ P Ploss S
ð2Þ
DT ¼ T w T s
ð3Þ
qw DT
ð4Þ
hw ¼
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where P is the electric power, I is the total current flowing through the heating surface, S is the total heating area in a channel. Before every test, the value calculated by the existing CHF prediction formula was used as an experimental reference. The region from 0 to predicted CHF was roughly divided into 10 nodes. The first half span was larger, however the second half span was smaller, ensuring that the heating chip and substrate couldn’t be burnt when the CHF occurred. Calculate the voltage value corresponding to each node, gradually increase the voltage across the copper electrode, and the voltage was raised to the next node when the three wall temperatures were stable for 2 min. Immediately turn off the power and stop the experiment when the wall temperatures measured by the instrument were observed to rise sharply. At this time, it can be determined that the CHF was between the front and rear heat flux, but the experimental precision was not sufficient. In order to improve the accuracy of the experiment, the heating experiment was restarted, and the heat flux density was increased by 1% of the previous experimental value. If the wall temperatures rise sharply again, stop the experiment. The heat flux density in the previous steady state was the CHF. Thus, the cut-off error of input power corresponding to CHF is 1%. 2.4. Uncertainty analysis The physical quantities obtained by the measuring instruments in the experiment include the voltage (U), the current (I), the width (W) and height (L) of the micro-channel, and the temperature (T). The errors of these physical quantities are mainly caused by the accuracy of the measuring instruments, which are listed in the Table 1. According to the transfer function theory of the relative standard deviation, the maximum relative deviation of input power, wall effective heat flux, wall super-heating and heat transfer coefficient can be derived from Eqs. (1)–(4) as follows:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @ ln P @ ln P r2U þ r2I ¼ @U @I P
rP
rqeff qeff
ð5Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @ ln DT @ ln DT r2T w þ r2T l ¼ @T w @T l DT
hw
Parameters
Relative errors
P qeff DT hw CHF
2% 5.3% 2.4% 7.1% 11.3%
3. Results and discussion 3.1. Reliability analysis Because the experimental device requires frequent disassembly and assembly, moreover, the micro-channel size is extremely small, if the device structure is unreasonable, it is highly likely that the data obtained in different experiments are very different. In addition, whether the inlet, outlet and interior of the microchannel will be blocked by steam drums is also the key observation target of reliability analysis. In order to verify the reliability of the micro-channel thermosyphon boiling experiment device used in this paper, the repetitive experiments were carried out on different micro-channels to confirm whether there was steam blockage and the instability of the experimental results due to assembly problems. The experimental device was separately disassembled, cleaned and installed for each set of repetitive experiments, which ensured the independence of the experiment. Fig. 6 shows the experimental results of a vertical micro-channel (L = 30 mm, W = 2 mm, and d = 0.05 mm) with deionized water as working medium under two identical experimental conditions. The CHF recorded in the two experiments were 6831.5 W/m2 and 7052.8 W/m2 respectively. The relative error of the two experiment results was 3.1% and no bubble blockage occurred in the micro-channel during the experiment. Similarly, the repeated experiments were performed on the series of micro-channels with different widths. The results show that the errors of the repetitive
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 @ ln qeff @ ln qeff @ ln qeff @ ln qeff @ ln qeff ¼ r2U þ r2I þ r2L þ r2eff þ r2qloss @U @I @L @b @qloss
rDT rhw
Table 2 Errors of calculated parameters.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 @ ln hw @ ln hw @ ln hw ¼ r2qb þ r2T w þ r2T l @qb @T w @T l
ð7Þ
ð8Þ
When calculating the relative deviation of CHF, it is necessary to take into account the experimental repeatability error (±5%) and the error (±1%) caused by the jump increase of power. The relative errors of the important physical quantities calculated from the experimental data are listed in the Table 2. Table 1 Error of measured parameters. Parameters U, I L, W T Tw qloss
Errors ±0.2% ±0.01 mm ±0.1 K ±2% ±1%
ð6Þ
experiment results are all within 5%, which proves the reliability of the experimental device, furthermore, in each independent experiment, the CHF did not appear in advance due to micro-channel blockage. 3.2. The CHF of 3-D micro-channel thermosyphon boiling 3.2.1. The proposed CHF formula for 2-D micro-channel For the vertical and inclined 2-D micro-channel thermosyphon boiling, our laboratory has done a lot of research that reveal effect of both the micro-channel length and thickness on the heat transfer when the channel width is greater than 4 mm. The previous study has proposed a dimensionless prediction formula for the thermosyphon boiling CHF of 2-D micro-channels [16,17]:
q =h q
fg v c U2D ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4
rg ql qv =q2v
¼ 0:25
2 !12 1 1 L f L þ Bo2 ðsin hÞ4 h ¼ maxð5 ; hÞ 2d 4 2d
ð9Þ
1265
J.-H. Huang et al. / International Journal of Heat and Mass Transfer 131 (2019) 1260–1269 15000
130 Temp of water Temp in the upper part Temp in the middle part Temp in the bottom part Actual boiling heat flux
125
1.2
12500
1.0
120
Experiment condition: water, 90° L=30mm W=4mm d=0.05mm
7500
5000 105
CHF3D/CHF2D
110
10000
q(W/m2)
115
0.8
0.6
Experiment condition: water, 90°
0.4
2500
100
0
10
20
30
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm
0.2
0
95 40
t (min)
0.0 1
a) The first experiment results 15000
130
3
4
(a) Water
Temp of water Temp in the upper part Temp in the middle part Temp in the bottom part Actual boiling heat flux
125
2
W(mm)
12500
1.2
120
Experiment condition: water, 90° L=30mm W=4mm d=0.05mm
7500
1.1
5000 105 2500
100 95
1.0
CHF3D/CHF2D
110
10000
q(W/m2)
115
0.9 0.8
Experiment condition: R113, 90°
0.7
0 0
10
20
30
40
0.6
t (min)
b) The second experiment results
0.5
Fig. 6. Test measuring results for a vertical micro-channel using water with L = 30 mm, W = 4 mm, d = 0.05 mm.
0.4
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm 1
2
3
4
W(mm) Bo ¼
2d ðr=gðql qv ÞÞ1=2
ð10Þ
where f is the friction coefficient, which varies little over a large Reynolds number range for micro-channels and can be taken as a fixed value of 0.1 [16]. Hence, the modified semi-theoretical-semiempirical prediction formula is:
U2D ¼ 0:25
2 !12 1 1 L L þ 0:025 Bo2 ðsin hÞ4 ; h ¼ maxð5 ; hÞ 2d 2d
ð11Þ
where h is the inclined angle of micro-channel, for the 2-D microchannel, the CHF dimensionless number is proportional to the 0.25th power of the sinusoidal value of the inclined angle, furthermore, the CHF remains essentially unchanged when the inclined angle is less than 5°. 3.2.2. The effect of the width of the vertical micro-channel on the CHF Because the influence of micro-channel length and gap on CHF has been mastered, the focus of this paper is on the effect of microchannel width (W) on the thermosyphon boiling heat transfer. Fig. 7 shows the results of comparative data for water and R113 where the 2-D data as the denominator is a predictive value obtained according to the aforementioned 2-D prediction formula. The width and length of the micro-channel in each image are changing, however the gap remains unchanged. For the micro-
(b) R113 Fig. 7. Relationship between the relative value of CHF and the channel width for vertical channels.
channels with width of 4 mm and 2 mm, the CHF value is basically the same as that of the 2-D channel, indicating that when the width is close to 4 mm, the effect of width disappears basically, and the micro-channel can be regarded as 2-D channel. When the width is less than 2 mm, the effect of width is very significant. The CHF decreases rapidly with the decrease of width, reducing 22% for the micro-channel with a width of 1.33 mm, by 30% for the micro-channel with a width of 1 mm and by 44% for the micro-channel with a width of 0.8 mm. In addition, there is no difference in the effect of the working fluid type on the width. The CHF variation of the 3-D microchannel for the two kinds of working fluid is almost the same. Meanwhile, the effect of length doesn’t appear, indicating that the effects of length and width are independent and there is no coupling relationship. After the CHF is processed by the relative value, although the length of 3-D micro-channels and the working fluid are different, the three independent curves are almost coincident. And for the same width, the upper and lower errors of the relative value don’t exceed 15%, which can basically be described by a curve.
J.-H. Huang et al. / International Journal of Heat and Mass Transfer 131 (2019) 1260–1269
7000
qCHF, =qCHF,90°(sin )0.25
6500 6000 5500 2
Fig. 8 is a comparison of the CHF experimental data for vertical 3-D micro-channel and CHF calculated values for 2-D vertical micro-channel. The ratio of the 3-D vertical micro-channel CHF to the calculated value of the 2-D vertical micro-channel CHF is taken as the ordinate, and the dimensionless form of W/d is taken as the abscissa. The data points can be described by one curve and the error is within 15%. For the case of W/d > 40, the CHF ratios remain unchanged, and the micro-channel can be regarded as 2D micro-channel. When W/d < 40, the micro-channel must be considered as 3-D micro-channel. As the W/d increases, the vertical micro-channel thermosyphon boiling CHF gradually increases, and the turning point occurs at W/d = 40.
CHF(W/m )
1266
5000 4500 4000 3500
Experiment condition: water L=30mm d=0.05mm
3000
(
U3D;h ¼
0:25
U3D;0 ðsin 5 Þ
h 6 5
U3D;0 ðsinhÞ0:25
h > 5
W=1.33mm W=4mm
2500 2000 0
10
20
30
2
2500
CHF3D/CHF2D
100
2000
W=1mm W=4mm 1000 10
20
30
40
50
60
70
80
90
100
°
(b) R113 Fig. 9. Influence of tilt angle to CHF.
1.2 R113 1.1 90° 1
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.1mm
0.8
0.8
90
Experiment condition: R113 L=30mm d=0.05mm
0.9
Φ3D/Φ2D
0.9
80
1500
3.2.4. The dimensionless formula of CHF After investigating the influence of the three-dimensional size of the micro-channels on CHF and verifying that the inclined 3-D micro-channel thermosyphon boiling CHF still obeys the formula (12), the experimental results are organized into a form similar to the formula (11). Fig. 10 shows the results in both extreme cases
1
70
3000
0
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.1mm
60
qCHF, =qCHF,90°(sin )0.25
ð12Þ
R113 90°
50
(a) Water
where U3D;0 is the dimensionless number of CHF for the vertical 3-D micro-channel thermosyphon boiling.
1.2 1.1
40
°
CHF(W/m)
3.2.3. The effect of inclined angle on the CHF for the inclined 3-D micro-channels In our previous study, a prediction formula (11) has been proposed for 2-D inclined micro-channel thermosyphon boiling CHF. For the 2-D micro-channels, the CHF dimensionless number is proportional to the 0.25th power of the sinusoid of the inclined angle, and the CHF remains basically unchanged when the inclined angle is less 5°. In this study, a verification experiment was carried out on the 3D micro-channels, where a 3-D chip simulation experiment piece with adjustable inclined angle was designed. Experiments were carried out in the inclined angle of 0°, 5°, 10°, 30°, 45°, 60° and 90° respectively. Fig. 9(a) and (b) show the effect of inclined angle on the CHF with water and R113 as working fluids, respectively. It can be found from the figure that the influence of the inclined angle on the 3-D micro-channel CHF is the same as that in the 2-D case, and can also be organized into the following relationship:
0°
0.7
L=60mm d=0.05mm L=100mm d=0.1mm
0.6 water 90°
+15%
0.5
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=100mm d=0.1mm
0.7
-15%
0.4
0.6 0°
0.5
L=30mm d=0.05mm L=30mm d=0.1mm
0.3 water 90°
0.4
L=30mm d=0.05mm L=60mm d=0.05mm L=100mm d=0.05mm L=30mm d=0.1mm L=100mm d=0.1mm
0.3 6
7 8 9 10
20
30
40
50 60 70 80 90100
W/d Fig. 8. Relationship between relative value of CHF and W/d for vertical channels.
6
7 8 9 10
20
30
40
50 60 70 80 90100
W/d Fig. 10. Relationship between relative value of dimensionless CHF and W/d.
of vertical and horizontal. The data of other inclined angles are basically coincident with the two sets of data and are not placed into the figure where the ordinate is the ratio of the dimensionless number of the 3-D micro-channel thermosyphon boiling CHF to
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that of the 2-D micro-channel and the abscissa is in the form of W/d. Because L d in the experiment, further simplification of Eq. (11) can be done as follows:
1 1 d Bo2 ðsin hÞ4 L
350 300 250
As can be seen from Fig. 10 where U3D is the dimensionless number of the thermosyphon boiling CHF for the 3-D microchannels with different widths and U2D is the dimensionless number of the thermosyphon boiling CHF for the 2-D micro-channels with the same inclination obtained according to the formula (13) where the CHF is not affected by the width, the thermosyphon boiling CHF is basically the same when W/d > 40, at this time, the CHF of 3-D micro-channel is indistinguishable from that of 2D micro-channel, however, the CHF of 3-D micro-channel increases with the increase of W/d when W/d < 40. This relationship also applies to inclined 3-D micro-channels, as the effect of the inclined angle is also eliminated by the ratio form. By fitting the data in Fig. 10, the following empirical formula is obtained:
200
(
1 0:098
W 0:6407 d
W d
P 40
W d
< 40
U3D
100
0 0
P 40
W d
< 40
ð15Þ
Although the error between the formula (14) and the experimental value is within 15%, since the predictive formula (12) itself has an error, the error between the formula (15) that is compounded and the experimental value is still 30%.
10
15
20
(a) R113 1000 900 800
W d
5
ΔT
ð14Þ
Eq. (14) is suitable for 3-D micro-channel thermosyphon boiling with any inclined angles. Furthermore, the dimensionless formula for the 3-D micro-channel thermosyphon boiling can be obtained by combining Eq. (12) as follows:
8 < 3:162dBo12 ðsin hÞ14 L ¼ : 0:31dW 0:6407 Bo12 ðsin hÞ14 L d
150
50
d=0.05mm d=0.1mm water° w=4mm w=4mm L=30mm w=2mm w=2mm w=1.33mm w=1.33mm Vertical w=1mm w=1mm w=0.8mm w=0.8mm
700
h(W/(m2.K))
U3D ¼ U2D
h(W/(m2.K))
ð13Þ
U2D ¼ 3:162
d=0.05mm d=0.1mm R113 w=4mm w=4mm L=30mm w=2mm w=2mm w=1.33mm w=1.33mm Vertical w=1mm w=1mm w=0.8mm w=0.8mm
600 500 400 300 200 100 0
3.3. The HTC of 3-D micro-channel thermosyphon boiling Fig. 11(a) and (b) give out the curves of HTC versus wall average super-heating during vertical 3-D micro-channel thermosyphon boiling with water and R113 as working fluids, respectively. The last data point of each curve corresponds to the wall super-heat of CHF. The micro-channel length is uniform to 30 mm, the gap has two types which are 0.1 mm and 0.05 mm respectively, and the width is gradually reduced from 4 mm that belongs to 2-D micro-channel to 0.8 mm. The results show that the HTC of thermosyphon boiling in the 3-D micro-channels increase rapidly with the increase of wall super-heat at the early stage, and no longer increase after the average super-heating degree reach 10 K, but remains at a relatively stable value until the CHF occurs. Comparing the HTC between deionized water and R113, the HTC of deionized water is 1–3 times larger than that of R113 under the same micro-channel. The difference is the same as conventional pool or thermosyphon boiling. Comparing the experimental data of micro-channels with different gaps, the HTC of d = 0.1 mm is much larger than that of d = 0.05 mm, which is consistent with the conclusion of the 2-D micro-channel. Fig. 12 shows the effect of width on HTC in the horizontal variation region of the HTC and the HTC can be divided into two regional discussions. In 3-D micro-channel region (W/d < 40), the HTC will increase with the increase of width, however, in 2-D microchannel region (W/d 40), HTC is basically unchanged and even slightly reduced, which shows that the effect of width is different
0
5
10
15
20
25
ΔT (b) Water Fig. 11. Relationship between HTC and average super-heating.
for the 2-D micro-channel and 3-D micro-channel. The complex morphology that the effect of width on the HTC should be due to the complexity of bubble generation, growth and flow with in the micro-channels. In the 3-D region, the bubbles are also strongly suppressed in the channel width direction. Therefore, when the width increases, the cross-section area of flow path increases and restraint of bubbles in the width direction decreases, which leads to the decrease of bubble flow resistance. Furthermore, the HTC increases, which is approximately proportional to the square root of width. After entering the 2-D region, the bubbles are not restrained in the width direction, so the influence of width becomes weaker and disappears. For the horizontal change regions of the HTC (from the position of super-heating 10 K to the CHF point), the HTC can be roughly estimated by the following data processing method. It is noticed that the super-heating of CHF occurrence points is concentrated in a narrow region of 20–25 K under various working fluids and micro-channel geometries. As an estimated value, the superheating of all CHF points can be regarded as an average constant (such as 22.5 K), then the HTC of the CHF point can be calculated simply by the quotient of the critical heat flux calculated by the
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Eq. (15) and the average super-heating. Further, in the whole horizontal region of the HTC, the HTC at any super-heating can be approximately equal to the HTC at CHF points, i.e.: 1000 850 700 550
superheat at 15K
h=CW0.6407
2
h( W/(m .K))
ð16Þ
The minimum super-heating in the HTC horizontal region is approximately 10 K. The optimal value of the average superheating of the CHF points can be obtained by data processing. Fig. 13 and formula (17) show the illustration and collation formula of the optimization results where the average superheating of the CHF points is 21.8 K, whose applicable superheating range is greater than 10 K, and the error range of h is within 30%.
400 250
hfg qv =DT c h ¼ hc ¼ qc =DT c ¼ U3D qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 rg ql qv =q2v
100 85 70 55 R113, 90° L=30mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.05mm water, 90° L=30mm d=0.05mm L=100mm d=0.1mm
40 25
1
2
3
4
h3D
8 < 4:472h ðg q q Þ12 d1:5 ðsin hÞ14 1 fg v l L DT ¼ : 0:438h ðg q q Þ12 d0:8593 W 0:6407 ðsin hÞ14 fg
v
l
L
1 DT
W d
P 40
W d
< 40
ð17Þ
4. Conclusions
W(mm)
a super-heating at 15 K 1000 850 700 550
A new passive cooling technology for 3-D chip is proposed utilizing 3-D chip’s specific micro-channels structure to form a 3-D thermosyphon boiling in micro-channels. The critical heat flux and heat transfer coefficient of thermosyphon boiling in 3-D micro-channels were experimentally studied. Both deionized water and R113 were applied as the working fluids. The equipment reliability, the effect of micro-channel width and inclination on the CHF, and the HTC of thermosyphon boiling are discussed respectively. The experimental results are given as:
CHF point
400
h( W/(m2.K))
250
h=CW0.6407
100 85 70 55
R113 L=30mm d=0.05mm L=30mm d=0.1mm L=60mm d=0.05mm water L=30mm d=0.05mm L=100mm d=0.1mm
40 25 1
2
3
4
W(mm)
(b) CHF point Fig. 12. Relationship between HTC to channel width.
800 700
+30%
h(Calculated value)
600 500 400
-30% 300 R113 L=30mm d=0.05mm R113 L=30mm d=0.1mm
200
(1) The effect of micro-channel width on the CHF at different scales is different. When the value of W/d is larger than 40 that belongs to 2 dimensional scale, the effect of width disappears basically. However, when this value is less than 40 that belongs to 3 dimensional scale, the effect of width is very significant and the CHF decreases rapidly with the decrease of width. (2) The effect of sizes of 3-D micro-channel on the CHF for the two kinds of working fluid (Water and R113) is almost the same. Both the CHF and HTC of deionized water are 1–3 times larger than that of R113 under the same microchannel. (3) The influence of the inclined angle on the 3-D micro-channel CHF is the same as that in the 2-D case, and the corresponding equation has been given out which agrees well with the experimental results. (4) The predictive formulas of the CHF and the HTC for 3-D micro-channel thermosyphon boiling at arbitrary inclination angles are given out. And both of them are in good agreement with the experimental results. (5) Based on the experimental results, it is concluded that the thermosyphon heat pipe utilizing 3-D chip’s specific micro structure and driven by buoyancy and capillary force is a feasible new technology for 3-D ship cooling. Several valuable heat transfer prediction formulas are given out and the research results indicate that this new conception has high industrial application prospect for 3-D ship cooling.
R113 L=60mm d=0.05mm water L=30mm d=0.05mm
100
water L=30mm d=0.1mm water L=100mm d=0.1mm
0 0
100
200
300
400
500
600
700
800
h(Experimental value) Fig. 13. The comparison between calculated and experimental values of HTC.
Conflict of interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
J.-H. Huang et al. / International Journal of Heat and Mass Transfer 131 (2019) 1260–1269
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