- Email: [email protected]
Experimental study on local heat transfer with liquid impingement flow in two-dimensional micro-channels
ht.
J. Heor Mass
Vol. 40, No. 17, pp. 405HO59, 1997 Transfer. 1997 Ekvier Science Ltd. All rights reserved F’rinted in Great Britain 0017~9310/97 s17.ca+o.oo
0
Pergamon
PI1 : sao17-9310(97)ooo39-2
ExDerimental studv on local heat transfer with Ii&id impingemebt flow in two-dimensional micro-channels Y. ZHUANG,
C. F. MAT and M. QIN
Department of Thermal Science and Engineering, Beijing Polytechnic University, Beijing 100022, China (Received 9 February 1997)
Abstract-E:xperiments were performed to investigate the heat transfer characteristics of impingement flow of transformer oil and 3M fluorinert liquid FC-72 in two-dimensional micro-channels. Jet impingement technique was used in this research for its high heat transfer rate and large potential in industrial applications. Local heat transfer coefficients were recorded both at stagnation and parallel flow regions in the range of Reynolds number from 70 to 170, and 911 to 4807, for oil and FC-72, respectively. The influences of different parameters, such as liquid velocity, channel size and fluid Prandtl number, on heat transfer behavior were examined. Empirical correlations of local heat transfer were developed for the whole channels. Very significant enhancement of heat transfer was observed and recorded. 0 1997 Elsevier Science Ltd.
approach to create unique heat transfer performance. This study was performed with emphasis on the fundamental aspect of heat transfer mechanism. The result indicated that the heat transfer pattern proposed by the present work would be a good candidate for high-density energy dissipation.
INTRODUCTION Rapidly tigation serious field of
increasing attention has focused on the invesof micro-scale heat transfer, which poses new challenges 1.0the scientists and engineers in the thermal engineering. The pioneer work on heat
transfer in microstructures was stimulated by cooling techniques for microelectronic components [l-3]. It is expected that the continuing rise in heat dissipation of microelectronic chips will result in maximum surface heat flux up to lo6 W me2 in the latter part of this decade [4]. In consequence, electronic cooling is still the main promoter for the development in this area [3, 5, 61. However, new applications or potential applications of micro-scale heat transfer are also found in other fields such as bioengineering, astronautics, material processing and manufacturing, and mini heaters and heat exchangers. Recent work has contributed to the fundamental understanding of heat, mass and momentum transport in microstructures with or without phase change [7-91, but the investigations concerning the data and knowledge bases of heat transfers at micro-scale level are still relatively scarce in open literature. It is also noted that all the available investigations are related to parallel flow in micro-channels. In the present work, our attention focused on the local heat transfer characteristics in microstructure by applying liquid jet impingement technique. Impinging liquid jets can produce very high heat transfer rates [lo]. The novel combination of micro-structure and impingement liquid flow should provide a new t Author to whom correspondence should be addressed.
EXPERIMENTAL APPARATUS AND PROCEDURE Experimental apparatus
The test facility is shown schematically in Fig. 1. Transformer oil (Pr = 200400) and FC-72 (Pr x 15) were used as the working fluids. The test liquid was circulated in a closed loop which had provision for filtering, metering, preheating and cooling. The test chamber was constructed of stainless steel with three visual ports. The test section assembly was vertically fixed on one side of the chamber. The details of the test section are illustrated in Fig. 2. The main part was a strip of 10 pm thick constantan foil with a heated section of 5 x 10 mm (nominal) exposed to the coolant. The strip on either side of this active section was soldered to copper bus blocks which were, in turn, connected to power leads. The heated section of the foil was cemented to a bakelite block inserted between the copper blocks. The assembly was cemented in a Plexiglas disk fixed in a brass housing with a screwed flange. The test section was thermally insulated by fiberglass to minimize heat loss. The temperature at the center of the inner surface of the heater was measured with a 40 gage iron-constantan thermocouple, which was electrically insulated from the foil, yet in close thermal contact. The active section of the constantan foil was used as an electrically heating element
4055
Y. ZHUANG
4056
et al.
NOMENCLATURE
A B
GZ H h
t7 I k NU 4 Pr
R Re
area of test section slot width Graetz number channel height local heat transfer coefficient average local heat transfer coefficient current intensity thermal conductivity of the fluid Nusselt number heat flux Prandtl number (v/a) electrical resistance Reynolds number
u
mean fluid velocity width of test section lateral distance from the stagnation point.
W X
Greek symbols CI thermal diffusivity V kinematic viscosity. Subscripts 0 X
stagnation point local values in parallel flow zone.
-
Targkt
Fig. 1. Schematic layout of flow loop. 1. Cooler; 2. filter; 3. liquid rotameter; 4. test section; 5. auxillary heater ; 6. filter ; 7. spillage valve ; 8. pump.
Fig. 2. Test section assembly. 1. Power lead; 2. voltage tap; 3. thermocouple; 4. tank wall; 5. fiberglass; 6. epoxy; 7. plexiglass; 8. Bakelite; 9. constantan foil ; 10. copper block ; 11. rubber sealing.
as well as a heat transfer surface. AC power to the test section was provided by a 50 A power supply. The fluid was supplied from a vertical delivery tube to the jet nozzle passing a plenum box. Their axes were perpendicular with each other in avertical plane. The jet nozzle-delivery assembly was fixed on a three-
Fluid flow
surface
Fig. 3. The configuration
of slot nozzle.
dimensional coordinate rack and could be adjusted with respect to the test section with placements accomplished within fO.O1 mm. By recording this measured wall temperature for various locations of the jet nozzles, the local temperature distributions along the flow channel could be obtained for given flow conditions and surface heat flux. The jet temperature was measured with a 40 gage iron-constantan thermocouple placed inside the plenum box close to the entrance of the jet nozzle. The fluid temperature in the test chamber was also monitored by a thermocouple of the same type. The nozzles employed in the present study were made of Plexiglass. Figure 3 shows the configuration of the jet nozzles. The nozzles have the same streamwise length of 35 mm and different dimensions of the cross-sections : 0.146, 0.210 and 0.234 mm in width, respectively, and 12 mm in height. The large aspect ratio of height to width eliminates the edge effect and leads to a situation of truly two-dimensional flow. Great efforts were made to control the parallelism of the two larger walls of the rectangular tubes. The shape and size of the nozzles were precisely measured with the tool maker’s microscope of 0.001 mm resolution. The liquid velocity in channels varied from 0.54
Local heat transfer with liquid impingement flow
4057
to 8.45 m s-‘. Details of the experimental apparatus were presented in ref. [ 11. 0 0.46
Data reduction
Oil
Heat flux was calculated from the electrical power supplied to the test section and the area of the heated surface by the following formula : q = I=R/A
(1)
where the resistance R was measured accurately with direct current before experiments. It was verified in preliminary tests that the variation of resistance with temperature could be neglected (less than + 0.1%)) as the heater temperature variation was less than 40 K in the present stu’dy and the variation in resistance with temperature is extremely small for constantan. The current intensity was measured by an ampermeter. Properties of the working fluid were evaluated at the film temperature by averaging the wall and jet temperatures. The experimental data were finally reduced in terms of Nusselt number and Reynolds number : Nu
0
JWH k
or
h*x
Nu, = _
k
(2)
u *2H Re = v .
EXPERIMENTAL
RESULTS
AND
DISCUSSION
As different patterns of fluid Ilow existing in stagnation and parallel flow zones, heat transfer data in the two regions should be correlated, respectively. In the stagnation region the axial flow strongly decelerates and the lateral flow accelerates associated with negative pressure gradients which tend to stabilize the laminar flow. On the other hand, the velocity in paraIIe1 flow zone is nearly constant. Consequently, heat transfer in the two regions exhibits very different characteristics and will be discussed in detail, respectively. Heat transfer at stagnation zone
Nusselt number was found to be determined by the Reynolds number, Prandtl number of test liquid and the geometry of the flow channel. The local heat transfer coefficients at the stagnation point were measured and collected at various channel heights and mean flow velocities in channels. The experimental result is presented in Fig. 4. Accounting for the effects of Reynolds number, Prandtl number and channel geometry, an effort was made to develop a correlation as follows :
where the Prandtl number power m = l/3 was adopted for large Prandtl number liquid based on the
Re Fig. 4. Heat transfer at stagnation point.
results of previous studies [lo, 111. Coefficient C and exponents n and q were obtained from the experimental data by a least-squares technique. The values were determined to be C = 22.184, n = 0.515 and q = - 1.021. With these constants, the correlation presents 87% of the experimental data points within k 10% with an average error of f 5.7% and a mean absolute deviation of 7.6% for all the data. Good agreement is seen from Fig. 4 between the predicted curve by equation (4) and the experimental data of both PC-72 and transformer oil. It is noteworthy that the power of Reynolds number n = 0.515 is almost equal to the analytical value of 0.5 for laminar flows, indicating the laminar characteristic of the heat transfer at stagnation zone due to the existence of favorable pressure gradient in this area. It is also noted that, with the increasing of channel height, the heat transfer is augmented for the same working fluid as shown in the figure. Higher convective heat transfer rates were observed for larger channels. However, the mechanism for this phenomenon is not clear yet and further investigation is needed. Lateral distribution of local heat transfer coefficients in parallel flow zone
Measurements were made to determine the lateral variation of local heat transfer coefficients along the flow direction for transformer oil and FC-72 in the five micro-channels. In total, 23 distribution curves were collected in the range of velocity from 0.54 to 8.45 m s-‘. The measured local heat transfer coefficient was expressed in Nusselt number based on the lateral distance x. Figure 5(a, b) gives the local Nusselt numbers for the liquid flow between the parallel plates plotted against the dimensionless parameter (x/ 2H)/(Re* Pr). The inverse of this dimensionless parameter is called the Graetz number : Gz = Re. Pr/ (x/2@). In Fig. 5 two predicted curves are also presented. One is calculated from the equation presented by Naito [12] for simultaneously developing laminar flow between two parallel flat plates : NM, = 0.209062. Gz’.‘( 1 + 76.6826
Y. ZHUANG et al.
4058
(a)
H = 0.4 mm Methane: Peng and Wang V Oil H = 0.2 mm 0 Methane: Peng and Wang A FC12
1ooot Re
Transformer Oil A
*
:z
o
H
058-
103 * 154 v 82 0.46 mm . 120 150 ??
14000
??
v.
12000
A
V A
7
10000
V
1 8000
A x
6000
A
I
4OOOl2000,&-I
_
x/2H ReF’r
0
0 2.5
I 1.0
0
00 t 1.5
I 2.0
I 2.5
I 3.0
I 3.5
I 4.0
4.5
u [m s-l]
(b)
1000
Fig. 6. Comparison of average heat transfer between the present work and ref. [12].
liquid flow in micro-channels of similar size. A remarkable increase in heat transfer is also observed from the figure. This fact testifies the enhancement effects of jet impingement on heat transfer in downstream flow. The heat transfer augmentation can also be ascribed to the fact that the present data are collected for tiny size channels (H = O.lCM.58 mm), which are very different from the normal size channels Shah / usually studied. Examination of the local heat transfer 5 x 10-4 1 x 10-4 distributions in Fig. 5(b) for large Reynolds number Gz-l _ x/21+ flows of FC-72 liquid indicates the transition from Re Pr Fig. 5. Local heat transfer distribution in the parallel flow laminar to turbulent flow. If comparison is made among the three curves with Reynolds number zone. (a) Transformer oil ; (b) FC-72. between 4680 and 4807 for the three different channel heights, different transition trends may be observed. For the case of H = 0.10 mm the local Nusselt number declines with the lateral distance until a minimum (5) appears around Gz-’ = 2.4 x 10m4, then the Nusselt -9.869 x lo6 *Gz-‘). number will evaluate along the flow direction due to This equation was obtained by using the numerical the transition to turbulent flow. For the channel of solution of integral equation for constant heat flux H = 0.21 mm significant slope change of the diswall. Presented in the figures are also the predicted tribution curve is observed around Gz-’ = 7.0 x 10p5, curves by an empirical correlation proposed by Shah but for the largest channel (H = 0.32 mm) there is no [ 131 for thermally developing, hydrodynamically considerable evidence of transition recorded in this developed laminar flow between parallel plates study. However, more investigation is required for clarifying the transition phenomenon and mechanism. Nu * = 149.G~“‘. . (f-5) A general empirical correlation was developed of the two liquids. It can be expressed by : The predicted curves by equation (6) are expectantly lower, in the main, than those proposed by Naito as = 0 429. R&589 . &‘I’ Nu shown in the figures. It is seen from the two figures x f that the experimental data are 40-120% and 75-225% higher for transformer oil and FC-72, respectively, in (7) comparison with the predicted curves by Naito. The great increase in heat transfer can be attributed to the strong turbulence intensity induced by jet impingement. Figure 6 exhibits the comparison of the average heat transfer coefficients, which were obtained from the local heat transfer rates collected in this work, with those reported by Peng and Wang [ 14] for parallel
with this correlation, 97% of the experimental data are within k 10% with an average error of +5.92% and a mean absolute deviation of 8.64% of all the data. The experimental data can be collapsed to a single line by plotting the result in the term of the ratio 3Nu x *(B/2H)“.494/(Pr’/3 - Z&0.583), as shown in Fig.
Local heat transfer with liquid impingement flow
4059
National Natural Foundation of China. Generous donations of the Fluorinert liquid (FC-72) from the 3M Company are gratefully appreciated. REFERENCES 1. Tuckermann, D. B. and Pease, R. F., Optimized convective cooling using micromachined structure. Journal of Electrochemical Society, 1982,129(3), C98. 2. Koh, J. C. Y. and Colony, R., Heat transfer of microstructures for integrated circuits. International Communications in Heat and Mass Transfer, 1986,13,89-98. 3. Peterson, G. P. and Ortega, A., Thermal control of electronic equipment and devices. In Advances in Heat Transfer, Vol. 17. Pergamon Press, 1990, pp. 181-314.
1
10
x/2H Fig. 7. Correlation of local heat transfer in the parallel flow zone.
7. It can be found the general decreasing trend of local heat transfer rates along with the lateral distance from the stagnation point. This trend is apparently resulted from the thickening of boundary layer along the micro-channel.
Transfer, 1993,36(14), 3421-3427. 8. Wu, P. Y. and Little, W. A., Measurement
CONCLUSION
This paper has reported a study on convective heat transfer with impingement flow in two-dimensional micro-channels. The local heat transfer characteristics were investigated in experimental details. Transformer oil and FC-72 were chosen as the test liquid covering quite a wide range of Prandtl number. Empirical correlations were developed both for the stagnation zone and parallel flow ztone. To the best knowledge of the present authors, the present work is the first paper dealing with the heat transfer to impingement flow in two-dimensional micro-channels. It was found that this cooling technique may provide excellent heat transfer performance in comparison with the conventional parallel flow in channels. Significant enhancement of convective heat transfer was testified in a wide range of Reynolds number between 70 and 4807. The experimental data and empirical correlations presented in this paper laid a foundation for the potential applications of this new cooling method in high technology and industry. Acknowledgements-This
study was supported
4. Tuckermann, D. B. and Pease, R. F., High-performance heat sinking for VLSI. IEEE Electronic Device Letters, 1991, EDG2, 126-129. 5. Choi, S. B., Barron, R. F., Warrington, R. O., Liquid flow and heat transfer in microtubes. In Micromechanical Sensors, Actuators and Systems, ASME DSC-32, eds D. Choi et al. 1991, pp. 123-134. 6. Yang, X. and Zhang, N. L., Micro- and nano-scale heat transfer phenomena research trends. In Transport Phenomena Science and Technology 1992, ed. B. X. Wang. Higher Education Press, Beijing, 1992, pp. 1-15. 7. Peng, X. F. and Wang, B. X., Forced convection and flow boiling heat transfer for liquid flowing through microchannels. International Journal of Heat and Mass
by the
of friction factor for the flow of gases in very fme channels used for microminiature Joule-Thompson refrigerators. Cryogenics, 1983,24(8), 273-277. 9. Mallik. A. K.. Peterson. G. P. and Weichold. H. M.. On the use micro he& pipes as an integral part ok semiconductor devices. Proceedings of the ASMEIJSMS Thermal Engineering Joint Conference, Reno, Nevada, Vol. 2., 1991, pp. 393-401. 10. Webb, B. W. and Ma, C. F., Single-phase liquid jet impingement heat transfer. In Advances in Heat Transfer, Vol. 26 Academic Press, New York, 1995, pp. 105-217. 11. Ma, C. F., Zhuang, Y. and Lei, D. H., Impingement heat transfer and recovery effect with submerged jets of large Prandtl number liquid-II. Initially laminar confined slot jets. International Journal of Heat and Mass
of
Transfer, 1997,40(6),
1491-1500.
12. Naito, E., Laminar heat transfer in the entrance region between parallel plates---the case of uniform heat flux. Heat Transfer-Japanese
Research, 1975,4(2),
63-14.
13. Shah, R. K., Thermal entry length solutions for the circular tube and parallel plates. Proceedings of the 3rd National Heat and Mass Transfer Conference, Indian Institute of Technology, Bombay, Vol. 1, No. HMT-1 l75, 1975. 14. Peng, X. F. and Wang, B. X., Forced-flow convection for liquid methanol flowing through microchannels. Journal of Thermal Science, 1993,2(3), 18&189.
J. Heor Mass
Vol. 40, No. 17, pp. 405HO59, 1997 Transfer. 1997 Ekvier Science Ltd. All rights reserved F’rinted in Great Britain 0017~9310/97 s17.ca+o.oo
0
Pergamon
PI1 : sao17-9310(97)ooo39-2
ExDerimental studv on local heat transfer with Ii&id impingemebt flow in two-dimensional micro-channels Y. ZHUANG,
C. F. MAT and M. QIN
Department of Thermal Science and Engineering, Beijing Polytechnic University, Beijing 100022, China (Received 9 February 1997)
Abstract-E:xperiments were performed to investigate the heat transfer characteristics of impingement flow of transformer oil and 3M fluorinert liquid FC-72 in two-dimensional micro-channels. Jet impingement technique was used in this research for its high heat transfer rate and large potential in industrial applications. Local heat transfer coefficients were recorded both at stagnation and parallel flow regions in the range of Reynolds number from 70 to 170, and 911 to 4807, for oil and FC-72, respectively. The influences of different parameters, such as liquid velocity, channel size and fluid Prandtl number, on heat transfer behavior were examined. Empirical correlations of local heat transfer were developed for the whole channels. Very significant enhancement of heat transfer was observed and recorded. 0 1997 Elsevier Science Ltd.
approach to create unique heat transfer performance. This study was performed with emphasis on the fundamental aspect of heat transfer mechanism. The result indicated that the heat transfer pattern proposed by the present work would be a good candidate for high-density energy dissipation.
INTRODUCTION Rapidly tigation serious field of
increasing attention has focused on the invesof micro-scale heat transfer, which poses new challenges 1.0the scientists and engineers in the thermal engineering. The pioneer work on heat
transfer in microstructures was stimulated by cooling techniques for microelectronic components [l-3]. It is expected that the continuing rise in heat dissipation of microelectronic chips will result in maximum surface heat flux up to lo6 W me2 in the latter part of this decade [4]. In consequence, electronic cooling is still the main promoter for the development in this area [3, 5, 61. However, new applications or potential applications of micro-scale heat transfer are also found in other fields such as bioengineering, astronautics, material processing and manufacturing, and mini heaters and heat exchangers. Recent work has contributed to the fundamental understanding of heat, mass and momentum transport in microstructures with or without phase change [7-91, but the investigations concerning the data and knowledge bases of heat transfers at micro-scale level are still relatively scarce in open literature. It is also noted that all the available investigations are related to parallel flow in micro-channels. In the present work, our attention focused on the local heat transfer characteristics in microstructure by applying liquid jet impingement technique. Impinging liquid jets can produce very high heat transfer rates [lo]. The novel combination of micro-structure and impingement liquid flow should provide a new t Author to whom correspondence should be addressed.
EXPERIMENTAL APPARATUS AND PROCEDURE Experimental apparatus
The test facility is shown schematically in Fig. 1. Transformer oil (Pr = 200400) and FC-72 (Pr x 15) were used as the working fluids. The test liquid was circulated in a closed loop which had provision for filtering, metering, preheating and cooling. The test chamber was constructed of stainless steel with three visual ports. The test section assembly was vertically fixed on one side of the chamber. The details of the test section are illustrated in Fig. 2. The main part was a strip of 10 pm thick constantan foil with a heated section of 5 x 10 mm (nominal) exposed to the coolant. The strip on either side of this active section was soldered to copper bus blocks which were, in turn, connected to power leads. The heated section of the foil was cemented to a bakelite block inserted between the copper blocks. The assembly was cemented in a Plexiglas disk fixed in a brass housing with a screwed flange. The test section was thermally insulated by fiberglass to minimize heat loss. The temperature at the center of the inner surface of the heater was measured with a 40 gage iron-constantan thermocouple, which was electrically insulated from the foil, yet in close thermal contact. The active section of the constantan foil was used as an electrically heating element
4055
Y. ZHUANG
4056
et al.
NOMENCLATURE
A B
GZ H h
t7 I k NU 4 Pr
R Re
area of test section slot width Graetz number channel height local heat transfer coefficient average local heat transfer coefficient current intensity thermal conductivity of the fluid Nusselt number heat flux Prandtl number (v/a) electrical resistance Reynolds number
u
mean fluid velocity width of test section lateral distance from the stagnation point.
W X
Greek symbols CI thermal diffusivity V kinematic viscosity. Subscripts 0 X
stagnation point local values in parallel flow zone.
-
Targkt
Fig. 1. Schematic layout of flow loop. 1. Cooler; 2. filter; 3. liquid rotameter; 4. test section; 5. auxillary heater ; 6. filter ; 7. spillage valve ; 8. pump.
Fig. 2. Test section assembly. 1. Power lead; 2. voltage tap; 3. thermocouple; 4. tank wall; 5. fiberglass; 6. epoxy; 7. plexiglass; 8. Bakelite; 9. constantan foil ; 10. copper block ; 11. rubber sealing.
as well as a heat transfer surface. AC power to the test section was provided by a 50 A power supply. The fluid was supplied from a vertical delivery tube to the jet nozzle passing a plenum box. Their axes were perpendicular with each other in avertical plane. The jet nozzle-delivery assembly was fixed on a three-
Fluid flow
surface
Fig. 3. The configuration
of slot nozzle.
dimensional coordinate rack and could be adjusted with respect to the test section with placements accomplished within fO.O1 mm. By recording this measured wall temperature for various locations of the jet nozzles, the local temperature distributions along the flow channel could be obtained for given flow conditions and surface heat flux. The jet temperature was measured with a 40 gage iron-constantan thermocouple placed inside the plenum box close to the entrance of the jet nozzle. The fluid temperature in the test chamber was also monitored by a thermocouple of the same type. The nozzles employed in the present study were made of Plexiglass. Figure 3 shows the configuration of the jet nozzles. The nozzles have the same streamwise length of 35 mm and different dimensions of the cross-sections : 0.146, 0.210 and 0.234 mm in width, respectively, and 12 mm in height. The large aspect ratio of height to width eliminates the edge effect and leads to a situation of truly two-dimensional flow. Great efforts were made to control the parallelism of the two larger walls of the rectangular tubes. The shape and size of the nozzles were precisely measured with the tool maker’s microscope of 0.001 mm resolution. The liquid velocity in channels varied from 0.54
Local heat transfer with liquid impingement flow
4057
to 8.45 m s-‘. Details of the experimental apparatus were presented in ref. [ 11. 0 0.46
Data reduction
Oil
Heat flux was calculated from the electrical power supplied to the test section and the area of the heated surface by the following formula : q = I=R/A
(1)
where the resistance R was measured accurately with direct current before experiments. It was verified in preliminary tests that the variation of resistance with temperature could be neglected (less than + 0.1%)) as the heater temperature variation was less than 40 K in the present stu’dy and the variation in resistance with temperature is extremely small for constantan. The current intensity was measured by an ampermeter. Properties of the working fluid were evaluated at the film temperature by averaging the wall and jet temperatures. The experimental data were finally reduced in terms of Nusselt number and Reynolds number : Nu
0
JWH k
or
h*x
Nu, = _
k
(2)
u *2H Re = v .
EXPERIMENTAL
RESULTS
AND
DISCUSSION
As different patterns of fluid Ilow existing in stagnation and parallel flow zones, heat transfer data in the two regions should be correlated, respectively. In the stagnation region the axial flow strongly decelerates and the lateral flow accelerates associated with negative pressure gradients which tend to stabilize the laminar flow. On the other hand, the velocity in paraIIe1 flow zone is nearly constant. Consequently, heat transfer in the two regions exhibits very different characteristics and will be discussed in detail, respectively. Heat transfer at stagnation zone
Nusselt number was found to be determined by the Reynolds number, Prandtl number of test liquid and the geometry of the flow channel. The local heat transfer coefficients at the stagnation point were measured and collected at various channel heights and mean flow velocities in channels. The experimental result is presented in Fig. 4. Accounting for the effects of Reynolds number, Prandtl number and channel geometry, an effort was made to develop a correlation as follows :
where the Prandtl number power m = l/3 was adopted for large Prandtl number liquid based on the
Re Fig. 4. Heat transfer at stagnation point.
results of previous studies [lo, 111. Coefficient C and exponents n and q were obtained from the experimental data by a least-squares technique. The values were determined to be C = 22.184, n = 0.515 and q = - 1.021. With these constants, the correlation presents 87% of the experimental data points within k 10% with an average error of f 5.7% and a mean absolute deviation of 7.6% for all the data. Good agreement is seen from Fig. 4 between the predicted curve by equation (4) and the experimental data of both PC-72 and transformer oil. It is noteworthy that the power of Reynolds number n = 0.515 is almost equal to the analytical value of 0.5 for laminar flows, indicating the laminar characteristic of the heat transfer at stagnation zone due to the existence of favorable pressure gradient in this area. It is also noted that, with the increasing of channel height, the heat transfer is augmented for the same working fluid as shown in the figure. Higher convective heat transfer rates were observed for larger channels. However, the mechanism for this phenomenon is not clear yet and further investigation is needed. Lateral distribution of local heat transfer coefficients in parallel flow zone
Measurements were made to determine the lateral variation of local heat transfer coefficients along the flow direction for transformer oil and FC-72 in the five micro-channels. In total, 23 distribution curves were collected in the range of velocity from 0.54 to 8.45 m s-‘. The measured local heat transfer coefficient was expressed in Nusselt number based on the lateral distance x. Figure 5(a, b) gives the local Nusselt numbers for the liquid flow between the parallel plates plotted against the dimensionless parameter (x/ 2H)/(Re* Pr). The inverse of this dimensionless parameter is called the Graetz number : Gz = Re. Pr/ (x/2@). In Fig. 5 two predicted curves are also presented. One is calculated from the equation presented by Naito [12] for simultaneously developing laminar flow between two parallel flat plates : NM, = 0.209062. Gz’.‘( 1 + 76.6826
Y. ZHUANG et al.
4058
(a)
H = 0.4 mm Methane: Peng and Wang V Oil H = 0.2 mm 0 Methane: Peng and Wang A FC12
1ooot Re
Transformer Oil A
*
:z
o
H
058-
103 * 154 v 82 0.46 mm . 120 150 ??
14000
??
v.
12000
A
V A
7
10000
V
1 8000
A x
6000
A
I
4OOOl2000,&-I
_
x/2H ReF’r
0
0 2.5
I 1.0
0
00 t 1.5
I 2.0
I 2.5
I 3.0
I 3.5
I 4.0
4.5
u [m s-l]
(b)
1000
Fig. 6. Comparison of average heat transfer between the present work and ref. [12].
liquid flow in micro-channels of similar size. A remarkable increase in heat transfer is also observed from the figure. This fact testifies the enhancement effects of jet impingement on heat transfer in downstream flow. The heat transfer augmentation can also be ascribed to the fact that the present data are collected for tiny size channels (H = O.lCM.58 mm), which are very different from the normal size channels Shah / usually studied. Examination of the local heat transfer 5 x 10-4 1 x 10-4 distributions in Fig. 5(b) for large Reynolds number Gz-l _ x/21+ flows of FC-72 liquid indicates the transition from Re Pr Fig. 5. Local heat transfer distribution in the parallel flow laminar to turbulent flow. If comparison is made among the three curves with Reynolds number zone. (a) Transformer oil ; (b) FC-72. between 4680 and 4807 for the three different channel heights, different transition trends may be observed. For the case of H = 0.10 mm the local Nusselt number declines with the lateral distance until a minimum (5) appears around Gz-’ = 2.4 x 10m4, then the Nusselt -9.869 x lo6 *Gz-‘). number will evaluate along the flow direction due to This equation was obtained by using the numerical the transition to turbulent flow. For the channel of solution of integral equation for constant heat flux H = 0.21 mm significant slope change of the diswall. Presented in the figures are also the predicted tribution curve is observed around Gz-’ = 7.0 x 10p5, curves by an empirical correlation proposed by Shah but for the largest channel (H = 0.32 mm) there is no [ 131 for thermally developing, hydrodynamically considerable evidence of transition recorded in this developed laminar flow between parallel plates study. However, more investigation is required for clarifying the transition phenomenon and mechanism. Nu * = 149.G~“‘. . (f-5) A general empirical correlation was developed of the two liquids. It can be expressed by : The predicted curves by equation (6) are expectantly lower, in the main, than those proposed by Naito as = 0 429. R&589 . &‘I’ Nu shown in the figures. It is seen from the two figures x f that the experimental data are 40-120% and 75-225% higher for transformer oil and FC-72, respectively, in (7) comparison with the predicted curves by Naito. The great increase in heat transfer can be attributed to the strong turbulence intensity induced by jet impingement. Figure 6 exhibits the comparison of the average heat transfer coefficients, which were obtained from the local heat transfer rates collected in this work, with those reported by Peng and Wang [ 14] for parallel
with this correlation, 97% of the experimental data are within k 10% with an average error of +5.92% and a mean absolute deviation of 8.64% of all the data. The experimental data can be collapsed to a single line by plotting the result in the term of the ratio 3Nu x *(B/2H)“.494/(Pr’/3 - Z&0.583), as shown in Fig.
Local heat transfer with liquid impingement flow
4059
National Natural Foundation of China. Generous donations of the Fluorinert liquid (FC-72) from the 3M Company are gratefully appreciated. REFERENCES 1. Tuckermann, D. B. and Pease, R. F., Optimized convective cooling using micromachined structure. Journal of Electrochemical Society, 1982,129(3), C98. 2. Koh, J. C. Y. and Colony, R., Heat transfer of microstructures for integrated circuits. International Communications in Heat and Mass Transfer, 1986,13,89-98. 3. Peterson, G. P. and Ortega, A., Thermal control of electronic equipment and devices. In Advances in Heat Transfer, Vol. 17. Pergamon Press, 1990, pp. 181-314.
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x/2H Fig. 7. Correlation of local heat transfer in the parallel flow zone.
7. It can be found the general decreasing trend of local heat transfer rates along with the lateral distance from the stagnation point. This trend is apparently resulted from the thickening of boundary layer along the micro-channel.
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CONCLUSION
This paper has reported a study on convective heat transfer with impingement flow in two-dimensional micro-channels. The local heat transfer characteristics were investigated in experimental details. Transformer oil and FC-72 were chosen as the test liquid covering quite a wide range of Prandtl number. Empirical correlations were developed both for the stagnation zone and parallel flow ztone. To the best knowledge of the present authors, the present work is the first paper dealing with the heat transfer to impingement flow in two-dimensional micro-channels. It was found that this cooling technique may provide excellent heat transfer performance in comparison with the conventional parallel flow in channels. Significant enhancement of convective heat transfer was testified in a wide range of Reynolds number between 70 and 4807. The experimental data and empirical correlations presented in this paper laid a foundation for the potential applications of this new cooling method in high technology and industry. Acknowledgements-This
study was supported
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