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Heat transfer characteristics of water flow in microtubes
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Experimental Thermal and Fluid Science 32 (2007) 432–439 www.elsevier.com/locate/etfs
Heat transfer characteristics of water flow in microtubes C.-Y. Yang *, T.-Y. Lin Department of Mechanical Engineering, Institute of Energy Engineering, National Central University, Chung-Li 32054, Taiwan Received 23 March 2007; received in revised form 31 May 2007; accepted 31 May 2007
Abstract This study provides an experimental investigation on forced convective heat transfer performance of water flowing through six microtubes with inner diameters ranging from 123 to 962 lm. A non-contacted liquid crystal thermography (LCT) temperature measurement method that proposed by Lin and Yang [T.-Y. Lin, C.-Y. Yang, An experimental investigation on forced convection heat transfer performance in microtubes by the method of liquid crystal thermography, International Journal of Heat and Mass Transfer (2007), doi:10.1016/j.ijheatmasstransfer.2007.03.038] was used in this study to measure the surface temperature of microtubes. The test results show that the conventional heat transfer correlations for laminar and turbulent flow can be well applied for predicting the fully developed heat transfer performance in microtubes. The transition occurs at Reynolds number from 2300 to 3000. This is also the same range as that for conventional tubes. There is no significant size effect for water flow in tubes within this diameter range. The laminar thermal entrance length for microtubes is longer than that estimated by the conventional correlation. The developing Nusselt numbers for 962 lm tube agree well with those predicted by the Shah and Bhatti [R.K. Shah, M.S. Bhatti, Laminar convective heat transfer in ducts, in: S. Kakac, R.K. Shah, W. Aung, (Eds.), Handbook of Single-Phase Convective Heat Transfer, Willy, New York, 1987] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. 2007 Elsevier Inc. All rights reserved. Keywords: Forced convective heat transfer; Microtubes; Liquid crystal thermography (LCT); Thermally developing heat transfer
1. Introduction Owing to the fabrication technology development during the past decades, the so-called microtubes with internal diameters smaller than 1 mm can be easily made and used to increase the compactness of heat exchangers. These kinds of heat exchangers are able to attain extremely high heat transfer surface area per unit volume, high heat transfer coefficient and low thermal resistance. The study on heat transfer performance in microtubes has become more important due to the rapid growth of the application for high heat flux electronic devices cooling. However, the conventional forced convection heat transfer correlations were derived from tubes with diameter much larger than those used in micro-channels. They have not been verified to
*
Corresponding author. Tel.: +886 3 4267347; fax: +886 3 4254501. E-mail address: [email protected] (C.-Y. Yang).
0894-1777/$ - see front matter 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.05.006
work well for predicting the heat transfer coefficient inside small diameter tubes. Several researches dealing with the single-phase forced convection heat transfer in microtubes have been published in the past years. Yu et al. [3] studied the fluid flow and heat transfer characteristics of nitrogen gas and water in circular tubes with diameters of 19, 52 and 102 lm and Reynolds numbers ranging from 250 to near 20,000. The measured friction factors were slightly lower than the Moody chart values for both laminar and turbulent regimes. However, the Nusselt numbers for cooling of water in the turbulent regime were considerably higher than those would be predicted for larger tubes, suggesting that the Reynolds analogy does not hold for micro-channel flow. Adams et al. [4] investigated turbulent single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. Their data suggested that the extent of enhancement increases as the channel diameter decreases and Reynolds number increases. Based on the data they
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Nomenclature A Ac cp di do f G Gz h kf L Lfd Lm LCT
heat transfer area (m2) tube cross-section area (m2) specific heat (J/kg K) tube inside diameter (m) tube outside diameter (m) friction factor, dimensionless mass velocity (kg/m2 s) Graetz number, dimensionless heat transfer coefficient (W/m2 C) water conductivity (W/m C) tube heating length (m) thermal entrance length (m) wall temperature measuring position (m) liquid crystal thermography
obtained, along with earlier data for small circular channels by Yu et al. [3], they developed a correlation for the Nusselt number for turbulent, single-phase, forced convection in circular micro-channels with diameters range from 0.102 to 1.09 mm. Mala and Li [5] investigated water flow through microtubes with diameters ranging from 50 to 254 lm. The experimental results indicate that at high Reynolds number laminar flow condition, the friction factor is higher than that given by the conventional Poiseuille flow theory. Celata et al. [6] reported the results of refrigerant R-114 flowing in capillary tubes with a diameter of 130 lm. They found that the friction factor was in good agreement with the Poiseuille theory for Reynolds number below 600 but higher than that for higher Reynolds number. Li et al. [7] tested the frictional characteristic of water flowing in glass, silicon and stainless steel microtubes with diameters ranging from 79.9 to 205.3 lm. They concluded that for smooth tubes, the friction factor is consistent with the results in macro tubes, while the value of Red in rough tubes is 15– 37% higher than 64. Yang et al. [8] provided a systematic test of friction characteristic for air, water, and liquid refrigerant R-134a in 10 tubes with inside diameters from 0.173 to 4.01 mm including the laminar and turbulent flow regime. The test results show that the conventional correlations for large tubes may be adequately used to estimate the friction factors for water, refrigerant, and laminar air flow in microtubes. For turbulent airflow, however, the flow Mach number is too high to be treated as incompressible flow. Yen et al. [9] measured heat transfer performance of laminar refrigerant R-123 flow in 0.3 mm diameter tube by direct attaching K-type thermocouple on the tube wall. The results are in reasonable agreement with the analytical laminar constant heat flux value (Nud = 4.36). However, the data have a very high Nusselt number scattering distribution from around 2–5. Lelea et al. [10] investigated developing and laminar distilled water flow in microtubes with diameter 0.1, 0.3 and 0.5 mm. The experimental results confirm that, including the entrance effects, the conven-
m_ Nud Pr q q00 Ra Red Ti Tx Twx TLC x l
mass flow rate (kg/s) Nusselt number, dimensionless Prandtl number, dimensionless heat transfer rate (W) heat flux (W/m2) average roughness (m) Reynolds number, dimensionless inlet water temperature (C) local water temperature (C) local tube inside wall temperature (C) thermochromic liquid crystal axial position of tubes (m) viscosity (N/m2 s)
tional or classical theories are applicable for water flow through microtubes of the sizes tested. Agostini et al. [11] measured liquid flow friction factor and heat transfer coefficient in rectangular and circular mini-channels with hydraulic diameters from 0.77 to 2.01 mm. They obtained very good agreement between the Gnielinski [12] correlation and their experimental heat transfer results in the turbulent regime. However no accurate prediction was found in the laminar regime. They concluded that this discrepancy is probably due to longitudinal conduction. To summarize the above literature review, friction factors in microtubes can be adequately predicted by the conventional correlations. However, most of the heat transfer test results are significantly dissimilar from those predicted by the traditional forced convection heat transfer correlations. Some researchers attributed their different results to the effect of shape, surface roughness and size of the channels. This seems in conflict with to the friction measurement results. For heat transfer tests, the measurement accuracy of microtube wall temperature may be the most important factor that causes this discrepancy. Since the diameter of the sensors for measuring microtube surface temperature is comparable to the size of the microtube itself, the tube surface temperature cannot be accurately measured due to the effect of sensor wire thermal shunt. Furthermore, since the size of the thermocouple is extremely small, it is very difficult to have it firmly in contact with on the tube wall. Lin and Yang [1] proposed a noncontacted liquid crystal thermography (LCT) method to measure the surface temperature of microtubes. It successfully avoids the thermal shunt and contact problem caused by using thermocouple. This study provides an experimental investigation on laminar and turbulent forced convective heat transfer characteristics of water flowing through micro stainless steel tubes with inside diameter from 123 to 962 lm. The LCT method proposed by Lin and Yang [1] was used in this study to measure the surface temperature of microtubes.
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test space limitation, the length of the 962 lm tube is slightly shorter than its estimated entrance length.
2. Experimental method 2.1. Tubes size measurement and experiment system setup
2.2. LCT temperature measurements Six stainless steel tubes with inner diameter ranging from 123 to 962 lm were tested in the present study. The tubes inner diameters were measured from the enlarged photographs taken by scanning electron microscope (SEM) for tubes with inner diameter from 123 to 416 lm, and optical microscope (OM) for tubes with inner diameter 764 and 962 lm. Fig. 1 shows the sample enlarged photographs of the cross-section view of the tubes with inner diameters 220 lm and 764 lm. To reduce the measurement uncertainties, several tubes were bundled together, cut and ground to have smooth cross-section surface. For each size of tube, each tube diameter was measured and all values were averaged to obtain the average tube diameter. Table 1 gives the detail dimensions and surface roughness of these tubes. The schematic diagram of the test facilities is shown in Fig. 2. A pressure vessel connected to high-pressure nitrogen was used to push the water through microtube. The inlet water temperature was measured by a resistance temperature detector (RTD). DC power was applied via clamps on both ends of the test tube to heat the tube wall. The flow rate was measured by a programmable electronic microbalance. The experimental apparatus and derived parameters uncertainties are listed in Table 2. The heating length and temperature measuring position shown in Fig. 3 for each tube are also listed in Table 1. The measuring position was designed to be longer than the maximum theoretical laminar flow entrance length. However, because of the
The LCT method that proposed by Lin and Yang [1] was used in this study to measure the surface temperature of microtubes. To increase the accuracy of temperature measurement, four thermochromic liquid crystals (TLCs) with 5 C band width from 28 to 33, 33 to 38, 38 to 43 and 45 to 50 C and one TLC with 3 C band width from 75 to 78 were used in this study. The diameters of the encapsulated TLCs are from 5 to 15 lm. The TLCs was painted on the tested surface with thickness of approximately 30 lm. A black paint was also painted under the TLCs as the background for improving the color resolution by absorbing un-reflected light. The relation between the hue value and temperature was calibrated in a constant temperature box. During the calibration process, electrical heating wires were attached on inside surfaces of the box to maintain the entire box space at designated temperatures. Seven T-type thermocouples were evenly placed near the test tube in the box to measure its temperature distribution. The liquid crystal thermograph and temperature measured by thermocouples were recorded simultaneously. The temperature uniformity in the constant box at different temperature can be maintained within ±0.2 C. The detail process and uncertainty of the LCT temperature measurement was described in Lin and Yang [1]. the standard deviation for the calibrated temperature–hue curve was evaluated within ±0.4 C.
Fig. 1. Enlarged photographs of the 220 lm and 764 lm microtubes (a) di = 220 lm (by SEM) (b) di = 764 lm (by OM).
Table 1 Detail dimensions and surface roughness of the tubes tested Tube notation
123 220 308 416 764 962
Tube length (mm)
140 190 260 320 406 356
Number of tubes measured
15 13 14 7 14 14
Average outer diameter do (lm)
282 472 579 743 1110 1318
Average inner diameter di (lm)
123.0 220.4 308.3 416.1 763.5 962.0
Standard deviation (lm)
1.00 1.09 3.53 2.39 1.11 1.28
Surface roughness, Ra (lm)
1.40 1.48 1.34 1.46 1.16 1.40
Wall temperature measuring position, Lm (mm) Fully developed
Developing
75 126 190 210 279 287
33 30 50 50 102 35,107
Heating length, L (mm)
120 171 237 290 340 327
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Power + Test tube
High perssure N2 Filter Water reservoir
P T
Pressure vessel
CCD
Balance
Pump Fig. 2. Schematic diagrams of the test facilities.
Table 2 Uncertainties of the experimental apparatus and derived parameters Apparatus
Uncertainties
Calibrated range
RTD T type Thermocouple Balance (A) Balance (B) Twx (LCT) Derived parameters Friction coefficient (f) Heat transfer coefficient (h) _ Mass flow rate (m) 1/Gz Red Nud Nud
±0.1 C ±0.2 C ±0.015 g ±0.005 g ±0.4 C
10–70 C 0–70 C 4200 g 850 g 28–78 C
0.2–5.3% 1.9–52% 0.02–0.2% 0.5–4.0% 0.4–3.9% 2.0–12% 2.0–53%
for 1/Gz < 0.1 for 1/Gz > 0.1
copper block heating length
measuring position
test tube
where A is the heat transfer area, A = pdiL, di is the tube inner diameter. Twx is the local inside tube surface temperature that can be derived from the LCT measured outside surface temperature by the method of one-dimensional heat conduction analysis. The Reynolds number and Nusselt number are defined as the following: Red ¼
Gd i hd i and Nud ¼ ; l kf
ð4Þ
_ c , Ac is the tube where G is the water mass flux, G ¼ m=A cross-section area. Since the tubes are small, the tube wall thickness is comparable with the inside diameter, the heat conduction in the wall along axis direction may be important. This axial conduction was estimated by the method of Maranzana et al. [13]. The results show that the ratio of axial conduction to the tube inside convection is less than 8.9 · 105 and 1.1 · 105 for 123 lm tube and 962 lm tube, respectively, and thus can be neglected. 3. Results and discussion
tube length
Fig. 3. Detail sketch of the test section.
2.3. Data reduction The heat transfer rate was measured from the DC power input and it equals the increase of the enthalpy in the flow of water. Since the electrical power was distributed uniformly on the tube surface, the local bulk water temperature, Tx, at position x from the heating entrance can be estimated by x _ p ðT x T i Þ; ð1Þ q ¼ mc L where m_ is the water flow rate, L is the tube heating length and Ti is the water inlet temperature. From the Newton’s law of cooling, q ð2Þ q00 ¼ ¼ hðT wx T x Þ: A The local heat transfer coefficient h can be derived as: q ; ð3Þ h¼ AðT wx T x Þ
3.1. Friction factors Yang et al. [8] measured the friction factors of water flow in tubes with diameter ranging from 0.5 to 4.0 mm. They found that there is no significant discrepancy for water flow in these range tubes in comparing with larger tubes. The present study measured friction factors of water flows in the tubes smaller than 500 lm and shown in Fig. 4. The Yang et al. [8] data of tubes with diameters of 798 lm and 1100 lm were also plotted for comparison. All of those test results agree very well with the conventional Blasius f ¼ 0:079Re0:25 and Poiseuille (f = 16/Red) equations d in turbulent and laminar flow regime, respectively. This figure shows clearly that there is no significant physical difference for water flows in tubes larger than 100 lm. The conventional theories are applicable for flow in this size range. 3.2. Fully developed heat transfer Fig. 5 shows the measured Nusselt numbers versus Reynolds numbers for water heated in the six microtubes. In low Reynolds numbers laminar flow regime, the measured
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1000
Hagen-Poiseuille Blasius [1913] Filonenko [1954]
0.1
di = 123 μm di = 220 μm di = 308 μm di = 416 μm f
Nud
100
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36 Lm = 46 mm Lm = 75 mm Lm = 145 mm
0.01
10
di = 798 μm [Yang et al. 2003] di = 1,100 μm [Yang et al. 2003] 100
1000
10000
1 1000
Red
Red
Fig. 4. Friction factors of water in microtubes.
Nusselt numbers agree very well with the theoretical constant heat flux value, 4.36. For Reynolds numbers greater than 1000, the heat transfer coefficients increase with increasing Reynolds numbers. This shows that the tubes length is not long enough for fully developed flow at high Reynolds number conditions and the flow is still in the developing regime. The thermal entrance length, Lfd, must be longer than the test section design value that estimated by the correlation, Lfd = 0.05RedPr Æ di, from Incropera et al. [14]. To verify this test results, two new test sections with longer and shorter length 123 lm tubes were tested. The test results are shown in Fig. 6. For the shorter tube
1000 di = 123 μm di = 220 μm di = 308 μm
di = 416 μm di = 764 μm di = 962 μm
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36
Nud
100
10
1 100
1000
10000
10000
Red Fig. 5. Measured Nusselt number versus Reynolds number.
Fig. 6. Laminar heat transfer performance varies with Reynolds for different length 123 lm tubes.
with measuring position length of 46 mm, the Nusselt numbers are higher than those of the original tube (Lm = 75 mm) at Reynolds from 1000 to transition. Contrarily, the Nusselt number of the longer tube (Lm = 145 mm) kept close to 4.36 until transition. This shows that the entrance length for microtubes is longer than that of conventional sized tubes. Starting from Reynolds number around 2300–3000, the flow regime changed to turbulent. The turbulent Nusselt numbers perfectly agree with those predicted by the Gnielinski [12] correlation. This shows that the conventional heat transfer correlation for large tubes can be well applied for predicting the heat transfer performance in microtubes. There is no significant size effect for water flow in tubes within this diameter range. Attributed to the advantage of the fast time response of the TLCs, the tube surface temperature variation can be easily observed. Fig. 7 records the transient temperature variation in different flow regimes within the interval of one second. In laminar and turbulent flow regimes, the surface temperatures varied within a range of 0.1–0.3 C, respectively, which is lower than the uncertainties of LCT temperature measurements. However, while it is in transition regime, the surface temperature fluctuated drastically as high as 2.3 C. The fluctuating behavior did not change with longer time interval from the real-time observation. The LCT temperature measurement method can be used to precisely justify the onset of flow regime transition. 3.3. Effect of heat loss Since the tubes are small, the heat loss by natural convection may be important compared to the heat input. In
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1000
44
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36
Recording frequency: 30 frames/second Red = 1884 (Laminar) Red = 2394 (Transition) Red = 12078 (Turbulent) 100
42
41
without heat loss with heat loss
Nud
Temperature (oC)
43
437
10
40
39
1
38 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Time (s)
the present study, the heat loss from the tube outer surface was determined by a separate experiment without water flow inside the tube. The test tube was heated to keep at a uniform temperature which is the same as the measuring point temperature of the heat transfer test. The heating rate was recorded. Since during the heat transfer test, the tube surface temperature varied nearly linearly from the inlet water temperature to the measuring point temperature, the heat loss can be estimated as the half of the heating rate recorded in the heat loss test times the fraction of measuring position length to the heating length. The measured heat loss is less than 4% and 1% of the total heat input for 123 lm tube and 962 lm tube, respectively. The most significant heat loss appears at the lowest Reynolds condition. For a constant heat flux heating condition, the water temperature rise increases with decreasing Reynolds. Since for a small tube, the local liquid-wall temperature difference is very small (Twx Tx = 3.6 C for 123 lm tube at Red = 424.4) and the water temperature rise at the measuring point is large (Tx Ti = 23.2 C), a very low heat loss will cause significant heat transfer coefficient estimation error. Fig. 8 shows that at the lowest Reynolds number in the 123 lm tube, a 4% heat loss will cause 25% heat transfer coefficient overestimated. The tube outside natural convection heat loss effect is not negligible for small tubes.
10000 Red
Fig. 8. Effect of heat loss on heat transfer coefficient calculation for 123 lm tube at Red = 424.4.
the theoretical value of fully developed constant heat flux condition, 4.36. Shah and Bhatti [2] proposed a set of correlations for representing the local Nusselt number of thermally developing laminar flow in a circular tube at various Graetz number (Gz) region. The Graetz number is defined as Gz ¼ RedxPrd i , where x is the axial position of tubes. For 1=Gz 6 0:00005 Nud ¼ 1:302Gz1:3 1
ð5Þ 1:3
0:00005 6 1=Gz 6 0:0015 Nud ¼ 1:302Gz 0:5 1=Gz P 0:0015 Nud ¼ 4:364 þ 8:68ð103 GzÞ
0:506
ð6Þ
expð41=GzÞ ð7Þ
10 Shah and Bhatti [1987]
9
di = 123 μm di = 220 μm di = 308 μm di = 416 μm di = 764 μm di = 962 μm
8
7
Nud
Fig. 7. Surface temperature fluctuation on 764 lm tube in different flow regime.
1000
6
5
4
3.4. Thermally developing heat transfer Fig. 9 illustrates the local Nusselt number inside the tubes at various Reynolds number in laminar flow regime. The figure shows that the local Nusselt number decreases along the flow direction and approaches asymptotically
0.01
0.1 1/Gz
1
Fig. 9. Comparison of tested developing Nusselt number and Shah and Bhatti [2] prediction results.
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Shah and Bhatti [1987]
10
di = 123μm di = 220μm di = 308μm di = 416μm di = 764μm di = 962μm
9 8
Nud
7 6
5
4
0.01
0.1 1/Gz
Fig. 10. Nusselt number variation in the entrance region with error bar.
A prediction curve calculated from the above correlations was also plotted in the figure for comparison. It shows that the present test results can be predicted reasonably by the Shah and Bhatti [2] correlations for 1/Gz larger than 0.1. For 1/Gz smaller than 0.1, it is found that the developing Nusselt numbers for 962 lm tube still agree well with those predicted by the Shah and Bhatti [2] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. To examine that if this result was caused by experimental uncertainty, a closer view of the entrance region for 1/Gz less than 0.2 with error bar is shown in Fig. 10. It is apparently that the experimental uncertainties are much lower than the discrepancy between different size tubes. There is no published literature that discussed about the entrance heat transfer in microtubes. The axial conduction effect has been estimated that may be neglected for the present cases. Any other reason that may cause this result is still not clear. Several researches (Guo and Li [15]) have discussed about the effects that may alter the laminar flow heat transfer in microtube. But none of them noticed the variation in the developing flow regime. More study is necessary for the entrance thermal phenomenon in microtubes. 4. Conclusions This study measured the heat transfer coefficients for water flow through six microtubes with inner diameters ranging from 123 to 962 lm by the method of liquid crystal thermography. The test results show that the conventional heat transfer correlations for laminar and turbulent flow can be well applied for predicting the fully developed heat transfer performance in microtubes. The transition occurs at Reynolds number from 2300 to 3000. This is also the
same range as that for conventional tubes. There is no significant size effect for water flow in tubes within this diameter range. The laminar-turbulent transition flow regime can be easily observed from the tube wall temperature variations. The surface temperature fluctuation in transition flow regime is much larger than that in laminar and turbulent flow regimes. The LCT temperature measurement method can be used to precisely justify the onset of flow regime transition. The measured heat loss for the present study is less than 4% and 1% of the total heat input for 123 lm tube and 962 lm tube, respectively. However, at the lowest Reynolds number in the 123 lm tube, a 4% heat loss will cause 25% heat transfer coefficient overestimate. The tube outside natural convection heat loss effect is not negligible for microtubes. For developing flow, the laminar thermal entrance length for microtubes is longer than that estimated by the conventional correlation, Lfd = 0.05RedPr Æ di. The developing Nusselt numbers for 962 lm tube agree well with those predicted by the Shah and Bhatti [2] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. None of the published literatures have noticed the size effect of heat transfer performance variation in the developing flow regime. More study is necessary for the entrance thermal phenomenon in microtubes. References [1] T.-Y. Lin, C.-Y. Yang, An experimental investigation on forced convection heat transfer performance in micro tubes by the method of liquid crystal thermography, International Journal of Heat and Mass Transfer (2007), doi:10.1016/j.ijheatmasstransfer.2007.03.038. [2] R.K. Shah, M.S. Bhatti, Laminar convective heat transfer in ducts, in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single-Phase Convective Heat Transfer, Willy, New York, 1987. [3] D. Yu, R. Warrington, R. Barron, T. Ameel, An experimental and theoretical investigation of fluid flow and heat transfer in microtubes, ASME/JSME Thermal Engineering Conference 1 (1995) 523–530. [4] T.M. Adams, S.I. Abdel-Khalik, S.M. Jeter, Z.H. Qureshi, An experimental investigation of single-phase forced convection in microchannels, International Journal of Heat and Mass Transfer 41 (1998) 851–857. [5] Gh.M. Mala, D.Q. Li, Flow characteristics in microtubes, International Journal of Heat and Fluid Flow 20 (1999) 142–148. [6] G.P. Celata, M. Cumo, M. Guglielmi, G. Zummo, Experimental investigation of hydraulic and single phase heat transfer in 0.130 mm capillary tube, Microscale Thermophysical Engineering 6 (2002) 85– 97. [7] Z.X. Li, D.X. Du, Z.Y. Guo, Experimental study on flow characteristics of liquid in circular microtubes, Microscale Thermophysical Engineering 7 (2003) 253–265. [8] C.-Y. Yang, J.-C. Wu, H.-T. Chien, S.-R. Lu, Friction characteristics of water, R-134a, and air in small tubes, Microscale Thermophysical Engineering 7 (2003) 335–348. [9] T.-H. Yen, N. Kasagi, Y. Suzuki, Forced convective boiling heat transfer in microtubes at low mass and heat fluxes, International Journal of Multiphase Flow 29 (2003) 1771–1792.
C.-Y. Yang, T.-Y. Lin / Experimental Thermal and Fluid Science 32 (2007) 432–439 [10] D. Lelea, S. Nishio, K. Yakano, The experimental research on microtube heat transfer and fluid flow of distilled water, International Journal of Heat and Mass Transfer 47 (2004) 2817–2830. [11] B. Agostini, A. Bontemps, B. Thonon, Effects of geometrical and thermophysical parameters on heat transfer measurements in small diameter channels, Heat Transfer Engineering 27 (2006) 14–24. [12] V. Gnielinski, New equation for heat and mass transfer in turbulent pipe and channel flow, International Journal of Chemical Engineering 16 (1976) 359–368.
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[13] G. Maranzana, I. Perry, D. Maillet, Mini- and micro-channels: influence of axial conduction in the walls, International Journal of Heat and Mass Transfer 47 (2004) 3993–4004. [14] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2007. [15] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer 46 (2003) 149–159.
Experimental Thermal and Fluid Science 32 (2007) 432–439 www.elsevier.com/locate/etfs
Heat transfer characteristics of water flow in microtubes C.-Y. Yang *, T.-Y. Lin Department of Mechanical Engineering, Institute of Energy Engineering, National Central University, Chung-Li 32054, Taiwan Received 23 March 2007; received in revised form 31 May 2007; accepted 31 May 2007
Abstract This study provides an experimental investigation on forced convective heat transfer performance of water flowing through six microtubes with inner diameters ranging from 123 to 962 lm. A non-contacted liquid crystal thermography (LCT) temperature measurement method that proposed by Lin and Yang [T.-Y. Lin, C.-Y. Yang, An experimental investigation on forced convection heat transfer performance in microtubes by the method of liquid crystal thermography, International Journal of Heat and Mass Transfer (2007), doi:10.1016/j.ijheatmasstransfer.2007.03.038] was used in this study to measure the surface temperature of microtubes. The test results show that the conventional heat transfer correlations for laminar and turbulent flow can be well applied for predicting the fully developed heat transfer performance in microtubes. The transition occurs at Reynolds number from 2300 to 3000. This is also the same range as that for conventional tubes. There is no significant size effect for water flow in tubes within this diameter range. The laminar thermal entrance length for microtubes is longer than that estimated by the conventional correlation. The developing Nusselt numbers for 962 lm tube agree well with those predicted by the Shah and Bhatti [R.K. Shah, M.S. Bhatti, Laminar convective heat transfer in ducts, in: S. Kakac, R.K. Shah, W. Aung, (Eds.), Handbook of Single-Phase Convective Heat Transfer, Willy, New York, 1987] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. 2007 Elsevier Inc. All rights reserved. Keywords: Forced convective heat transfer; Microtubes; Liquid crystal thermography (LCT); Thermally developing heat transfer
1. Introduction Owing to the fabrication technology development during the past decades, the so-called microtubes with internal diameters smaller than 1 mm can be easily made and used to increase the compactness of heat exchangers. These kinds of heat exchangers are able to attain extremely high heat transfer surface area per unit volume, high heat transfer coefficient and low thermal resistance. The study on heat transfer performance in microtubes has become more important due to the rapid growth of the application for high heat flux electronic devices cooling. However, the conventional forced convection heat transfer correlations were derived from tubes with diameter much larger than those used in micro-channels. They have not been verified to
*
Corresponding author. Tel.: +886 3 4267347; fax: +886 3 4254501. E-mail address: [email protected] (C.-Y. Yang).
0894-1777/$ - see front matter 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.05.006
work well for predicting the heat transfer coefficient inside small diameter tubes. Several researches dealing with the single-phase forced convection heat transfer in microtubes have been published in the past years. Yu et al. [3] studied the fluid flow and heat transfer characteristics of nitrogen gas and water in circular tubes with diameters of 19, 52 and 102 lm and Reynolds numbers ranging from 250 to near 20,000. The measured friction factors were slightly lower than the Moody chart values for both laminar and turbulent regimes. However, the Nusselt numbers for cooling of water in the turbulent regime were considerably higher than those would be predicted for larger tubes, suggesting that the Reynolds analogy does not hold for micro-channel flow. Adams et al. [4] investigated turbulent single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. Their data suggested that the extent of enhancement increases as the channel diameter decreases and Reynolds number increases. Based on the data they
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Nomenclature A Ac cp di do f G Gz h kf L Lfd Lm LCT
heat transfer area (m2) tube cross-section area (m2) specific heat (J/kg K) tube inside diameter (m) tube outside diameter (m) friction factor, dimensionless mass velocity (kg/m2 s) Graetz number, dimensionless heat transfer coefficient (W/m2 C) water conductivity (W/m C) tube heating length (m) thermal entrance length (m) wall temperature measuring position (m) liquid crystal thermography
obtained, along with earlier data for small circular channels by Yu et al. [3], they developed a correlation for the Nusselt number for turbulent, single-phase, forced convection in circular micro-channels with diameters range from 0.102 to 1.09 mm. Mala and Li [5] investigated water flow through microtubes with diameters ranging from 50 to 254 lm. The experimental results indicate that at high Reynolds number laminar flow condition, the friction factor is higher than that given by the conventional Poiseuille flow theory. Celata et al. [6] reported the results of refrigerant R-114 flowing in capillary tubes with a diameter of 130 lm. They found that the friction factor was in good agreement with the Poiseuille theory for Reynolds number below 600 but higher than that for higher Reynolds number. Li et al. [7] tested the frictional characteristic of water flowing in glass, silicon and stainless steel microtubes with diameters ranging from 79.9 to 205.3 lm. They concluded that for smooth tubes, the friction factor is consistent with the results in macro tubes, while the value of Red in rough tubes is 15– 37% higher than 64. Yang et al. [8] provided a systematic test of friction characteristic for air, water, and liquid refrigerant R-134a in 10 tubes with inside diameters from 0.173 to 4.01 mm including the laminar and turbulent flow regime. The test results show that the conventional correlations for large tubes may be adequately used to estimate the friction factors for water, refrigerant, and laminar air flow in microtubes. For turbulent airflow, however, the flow Mach number is too high to be treated as incompressible flow. Yen et al. [9] measured heat transfer performance of laminar refrigerant R-123 flow in 0.3 mm diameter tube by direct attaching K-type thermocouple on the tube wall. The results are in reasonable agreement with the analytical laminar constant heat flux value (Nud = 4.36). However, the data have a very high Nusselt number scattering distribution from around 2–5. Lelea et al. [10] investigated developing and laminar distilled water flow in microtubes with diameter 0.1, 0.3 and 0.5 mm. The experimental results confirm that, including the entrance effects, the conven-
m_ Nud Pr q q00 Ra Red Ti Tx Twx TLC x l
mass flow rate (kg/s) Nusselt number, dimensionless Prandtl number, dimensionless heat transfer rate (W) heat flux (W/m2) average roughness (m) Reynolds number, dimensionless inlet water temperature (C) local water temperature (C) local tube inside wall temperature (C) thermochromic liquid crystal axial position of tubes (m) viscosity (N/m2 s)
tional or classical theories are applicable for water flow through microtubes of the sizes tested. Agostini et al. [11] measured liquid flow friction factor and heat transfer coefficient in rectangular and circular mini-channels with hydraulic diameters from 0.77 to 2.01 mm. They obtained very good agreement between the Gnielinski [12] correlation and their experimental heat transfer results in the turbulent regime. However no accurate prediction was found in the laminar regime. They concluded that this discrepancy is probably due to longitudinal conduction. To summarize the above literature review, friction factors in microtubes can be adequately predicted by the conventional correlations. However, most of the heat transfer test results are significantly dissimilar from those predicted by the traditional forced convection heat transfer correlations. Some researchers attributed their different results to the effect of shape, surface roughness and size of the channels. This seems in conflict with to the friction measurement results. For heat transfer tests, the measurement accuracy of microtube wall temperature may be the most important factor that causes this discrepancy. Since the diameter of the sensors for measuring microtube surface temperature is comparable to the size of the microtube itself, the tube surface temperature cannot be accurately measured due to the effect of sensor wire thermal shunt. Furthermore, since the size of the thermocouple is extremely small, it is very difficult to have it firmly in contact with on the tube wall. Lin and Yang [1] proposed a noncontacted liquid crystal thermography (LCT) method to measure the surface temperature of microtubes. It successfully avoids the thermal shunt and contact problem caused by using thermocouple. This study provides an experimental investigation on laminar and turbulent forced convective heat transfer characteristics of water flowing through micro stainless steel tubes with inside diameter from 123 to 962 lm. The LCT method proposed by Lin and Yang [1] was used in this study to measure the surface temperature of microtubes.
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test space limitation, the length of the 962 lm tube is slightly shorter than its estimated entrance length.
2. Experimental method 2.1. Tubes size measurement and experiment system setup
2.2. LCT temperature measurements Six stainless steel tubes with inner diameter ranging from 123 to 962 lm were tested in the present study. The tubes inner diameters were measured from the enlarged photographs taken by scanning electron microscope (SEM) for tubes with inner diameter from 123 to 416 lm, and optical microscope (OM) for tubes with inner diameter 764 and 962 lm. Fig. 1 shows the sample enlarged photographs of the cross-section view of the tubes with inner diameters 220 lm and 764 lm. To reduce the measurement uncertainties, several tubes were bundled together, cut and ground to have smooth cross-section surface. For each size of tube, each tube diameter was measured and all values were averaged to obtain the average tube diameter. Table 1 gives the detail dimensions and surface roughness of these tubes. The schematic diagram of the test facilities is shown in Fig. 2. A pressure vessel connected to high-pressure nitrogen was used to push the water through microtube. The inlet water temperature was measured by a resistance temperature detector (RTD). DC power was applied via clamps on both ends of the test tube to heat the tube wall. The flow rate was measured by a programmable electronic microbalance. The experimental apparatus and derived parameters uncertainties are listed in Table 2. The heating length and temperature measuring position shown in Fig. 3 for each tube are also listed in Table 1. The measuring position was designed to be longer than the maximum theoretical laminar flow entrance length. However, because of the
The LCT method that proposed by Lin and Yang [1] was used in this study to measure the surface temperature of microtubes. To increase the accuracy of temperature measurement, four thermochromic liquid crystals (TLCs) with 5 C band width from 28 to 33, 33 to 38, 38 to 43 and 45 to 50 C and one TLC with 3 C band width from 75 to 78 were used in this study. The diameters of the encapsulated TLCs are from 5 to 15 lm. The TLCs was painted on the tested surface with thickness of approximately 30 lm. A black paint was also painted under the TLCs as the background for improving the color resolution by absorbing un-reflected light. The relation between the hue value and temperature was calibrated in a constant temperature box. During the calibration process, electrical heating wires were attached on inside surfaces of the box to maintain the entire box space at designated temperatures. Seven T-type thermocouples were evenly placed near the test tube in the box to measure its temperature distribution. The liquid crystal thermograph and temperature measured by thermocouples were recorded simultaneously. The temperature uniformity in the constant box at different temperature can be maintained within ±0.2 C. The detail process and uncertainty of the LCT temperature measurement was described in Lin and Yang [1]. the standard deviation for the calibrated temperature–hue curve was evaluated within ±0.4 C.
Fig. 1. Enlarged photographs of the 220 lm and 764 lm microtubes (a) di = 220 lm (by SEM) (b) di = 764 lm (by OM).
Table 1 Detail dimensions and surface roughness of the tubes tested Tube notation
123 220 308 416 764 962
Tube length (mm)
140 190 260 320 406 356
Number of tubes measured
15 13 14 7 14 14
Average outer diameter do (lm)
282 472 579 743 1110 1318
Average inner diameter di (lm)
123.0 220.4 308.3 416.1 763.5 962.0
Standard deviation (lm)
1.00 1.09 3.53 2.39 1.11 1.28
Surface roughness, Ra (lm)
1.40 1.48 1.34 1.46 1.16 1.40
Wall temperature measuring position, Lm (mm) Fully developed
Developing
75 126 190 210 279 287
33 30 50 50 102 35,107
Heating length, L (mm)
120 171 237 290 340 327
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Power + Test tube
High perssure N2 Filter Water reservoir
P T
Pressure vessel
CCD
Balance
Pump Fig. 2. Schematic diagrams of the test facilities.
Table 2 Uncertainties of the experimental apparatus and derived parameters Apparatus
Uncertainties
Calibrated range
RTD T type Thermocouple Balance (A) Balance (B) Twx (LCT) Derived parameters Friction coefficient (f) Heat transfer coefficient (h) _ Mass flow rate (m) 1/Gz Red Nud Nud
±0.1 C ±0.2 C ±0.015 g ±0.005 g ±0.4 C
10–70 C 0–70 C 4200 g 850 g 28–78 C
0.2–5.3% 1.9–52% 0.02–0.2% 0.5–4.0% 0.4–3.9% 2.0–12% 2.0–53%
for 1/Gz < 0.1 for 1/Gz > 0.1
copper block heating length
measuring position
test tube
where A is the heat transfer area, A = pdiL, di is the tube inner diameter. Twx is the local inside tube surface temperature that can be derived from the LCT measured outside surface temperature by the method of one-dimensional heat conduction analysis. The Reynolds number and Nusselt number are defined as the following: Red ¼
Gd i hd i and Nud ¼ ; l kf
ð4Þ
_ c , Ac is the tube where G is the water mass flux, G ¼ m=A cross-section area. Since the tubes are small, the tube wall thickness is comparable with the inside diameter, the heat conduction in the wall along axis direction may be important. This axial conduction was estimated by the method of Maranzana et al. [13]. The results show that the ratio of axial conduction to the tube inside convection is less than 8.9 · 105 and 1.1 · 105 for 123 lm tube and 962 lm tube, respectively, and thus can be neglected. 3. Results and discussion
tube length
Fig. 3. Detail sketch of the test section.
2.3. Data reduction The heat transfer rate was measured from the DC power input and it equals the increase of the enthalpy in the flow of water. Since the electrical power was distributed uniformly on the tube surface, the local bulk water temperature, Tx, at position x from the heating entrance can be estimated by x _ p ðT x T i Þ; ð1Þ q ¼ mc L where m_ is the water flow rate, L is the tube heating length and Ti is the water inlet temperature. From the Newton’s law of cooling, q ð2Þ q00 ¼ ¼ hðT wx T x Þ: A The local heat transfer coefficient h can be derived as: q ; ð3Þ h¼ AðT wx T x Þ
3.1. Friction factors Yang et al. [8] measured the friction factors of water flow in tubes with diameter ranging from 0.5 to 4.0 mm. They found that there is no significant discrepancy for water flow in these range tubes in comparing with larger tubes. The present study measured friction factors of water flows in the tubes smaller than 500 lm and shown in Fig. 4. The Yang et al. [8] data of tubes with diameters of 798 lm and 1100 lm were also plotted for comparison. All of those test results agree very well with the conventional Blasius f ¼ 0:079Re0:25 and Poiseuille (f = 16/Red) equations d in turbulent and laminar flow regime, respectively. This figure shows clearly that there is no significant physical difference for water flows in tubes larger than 100 lm. The conventional theories are applicable for flow in this size range. 3.2. Fully developed heat transfer Fig. 5 shows the measured Nusselt numbers versus Reynolds numbers for water heated in the six microtubes. In low Reynolds numbers laminar flow regime, the measured
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1000
Hagen-Poiseuille Blasius [1913] Filonenko [1954]
0.1
di = 123 μm di = 220 μm di = 308 μm di = 416 μm f
Nud
100
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36 Lm = 46 mm Lm = 75 mm Lm = 145 mm
0.01
10
di = 798 μm [Yang et al. 2003] di = 1,100 μm [Yang et al. 2003] 100
1000
10000
1 1000
Red
Red
Fig. 4. Friction factors of water in microtubes.
Nusselt numbers agree very well with the theoretical constant heat flux value, 4.36. For Reynolds numbers greater than 1000, the heat transfer coefficients increase with increasing Reynolds numbers. This shows that the tubes length is not long enough for fully developed flow at high Reynolds number conditions and the flow is still in the developing regime. The thermal entrance length, Lfd, must be longer than the test section design value that estimated by the correlation, Lfd = 0.05RedPr Æ di, from Incropera et al. [14]. To verify this test results, two new test sections with longer and shorter length 123 lm tubes were tested. The test results are shown in Fig. 6. For the shorter tube
1000 di = 123 μm di = 220 μm di = 308 μm
di = 416 μm di = 764 μm di = 962 μm
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36
Nud
100
10
1 100
1000
10000
10000
Red Fig. 5. Measured Nusselt number versus Reynolds number.
Fig. 6. Laminar heat transfer performance varies with Reynolds for different length 123 lm tubes.
with measuring position length of 46 mm, the Nusselt numbers are higher than those of the original tube (Lm = 75 mm) at Reynolds from 1000 to transition. Contrarily, the Nusselt number of the longer tube (Lm = 145 mm) kept close to 4.36 until transition. This shows that the entrance length for microtubes is longer than that of conventional sized tubes. Starting from Reynolds number around 2300–3000, the flow regime changed to turbulent. The turbulent Nusselt numbers perfectly agree with those predicted by the Gnielinski [12] correlation. This shows that the conventional heat transfer correlation for large tubes can be well applied for predicting the heat transfer performance in microtubes. There is no significant size effect for water flow in tubes within this diameter range. Attributed to the advantage of the fast time response of the TLCs, the tube surface temperature variation can be easily observed. Fig. 7 records the transient temperature variation in different flow regimes within the interval of one second. In laminar and turbulent flow regimes, the surface temperatures varied within a range of 0.1–0.3 C, respectively, which is lower than the uncertainties of LCT temperature measurements. However, while it is in transition regime, the surface temperature fluctuated drastically as high as 2.3 C. The fluctuating behavior did not change with longer time interval from the real-time observation. The LCT temperature measurement method can be used to precisely justify the onset of flow regime transition. 3.3. Effect of heat loss Since the tubes are small, the heat loss by natural convection may be important compared to the heat input. In
C.-Y. Yang, T.-Y. Lin / Experimental Thermal and Fluid Science 32 (2007) 432–439
1000
44
Dittus-Boelter (heating) Petukhov Gnielinski Nud = 4.36
Recording frequency: 30 frames/second Red = 1884 (Laminar) Red = 2394 (Transition) Red = 12078 (Turbulent) 100
42
41
without heat loss with heat loss
Nud
Temperature (oC)
43
437
10
40
39
1
38 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Time (s)
the present study, the heat loss from the tube outer surface was determined by a separate experiment without water flow inside the tube. The test tube was heated to keep at a uniform temperature which is the same as the measuring point temperature of the heat transfer test. The heating rate was recorded. Since during the heat transfer test, the tube surface temperature varied nearly linearly from the inlet water temperature to the measuring point temperature, the heat loss can be estimated as the half of the heating rate recorded in the heat loss test times the fraction of measuring position length to the heating length. The measured heat loss is less than 4% and 1% of the total heat input for 123 lm tube and 962 lm tube, respectively. The most significant heat loss appears at the lowest Reynolds condition. For a constant heat flux heating condition, the water temperature rise increases with decreasing Reynolds. Since for a small tube, the local liquid-wall temperature difference is very small (Twx Tx = 3.6 C for 123 lm tube at Red = 424.4) and the water temperature rise at the measuring point is large (Tx Ti = 23.2 C), a very low heat loss will cause significant heat transfer coefficient estimation error. Fig. 8 shows that at the lowest Reynolds number in the 123 lm tube, a 4% heat loss will cause 25% heat transfer coefficient overestimated. The tube outside natural convection heat loss effect is not negligible for small tubes.
10000 Red
Fig. 8. Effect of heat loss on heat transfer coefficient calculation for 123 lm tube at Red = 424.4.
the theoretical value of fully developed constant heat flux condition, 4.36. Shah and Bhatti [2] proposed a set of correlations for representing the local Nusselt number of thermally developing laminar flow in a circular tube at various Graetz number (Gz) region. The Graetz number is defined as Gz ¼ RedxPrd i , where x is the axial position of tubes. For 1=Gz 6 0:00005 Nud ¼ 1:302Gz1:3 1
ð5Þ 1:3
0:00005 6 1=Gz 6 0:0015 Nud ¼ 1:302Gz 0:5 1=Gz P 0:0015 Nud ¼ 4:364 þ 8:68ð103 GzÞ
0:506
ð6Þ
expð41=GzÞ ð7Þ
10 Shah and Bhatti [1987]
9
di = 123 μm di = 220 μm di = 308 μm di = 416 μm di = 764 μm di = 962 μm
8
7
Nud
Fig. 7. Surface temperature fluctuation on 764 lm tube in different flow regime.
1000
6
5
4
3.4. Thermally developing heat transfer Fig. 9 illustrates the local Nusselt number inside the tubes at various Reynolds number in laminar flow regime. The figure shows that the local Nusselt number decreases along the flow direction and approaches asymptotically
0.01
0.1 1/Gz
1
Fig. 9. Comparison of tested developing Nusselt number and Shah and Bhatti [2] prediction results.
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Shah and Bhatti [1987]
10
di = 123μm di = 220μm di = 308μm di = 416μm di = 764μm di = 962μm
9 8
Nud
7 6
5
4
0.01
0.1 1/Gz
Fig. 10. Nusselt number variation in the entrance region with error bar.
A prediction curve calculated from the above correlations was also plotted in the figure for comparison. It shows that the present test results can be predicted reasonably by the Shah and Bhatti [2] correlations for 1/Gz larger than 0.1. For 1/Gz smaller than 0.1, it is found that the developing Nusselt numbers for 962 lm tube still agree well with those predicted by the Shah and Bhatti [2] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. To examine that if this result was caused by experimental uncertainty, a closer view of the entrance region for 1/Gz less than 0.2 with error bar is shown in Fig. 10. It is apparently that the experimental uncertainties are much lower than the discrepancy between different size tubes. There is no published literature that discussed about the entrance heat transfer in microtubes. The axial conduction effect has been estimated that may be neglected for the present cases. Any other reason that may cause this result is still not clear. Several researches (Guo and Li [15]) have discussed about the effects that may alter the laminar flow heat transfer in microtube. But none of them noticed the variation in the developing flow regime. More study is necessary for the entrance thermal phenomenon in microtubes. 4. Conclusions This study measured the heat transfer coefficients for water flow through six microtubes with inner diameters ranging from 123 to 962 lm by the method of liquid crystal thermography. The test results show that the conventional heat transfer correlations for laminar and turbulent flow can be well applied for predicting the fully developed heat transfer performance in microtubes. The transition occurs at Reynolds number from 2300 to 3000. This is also the
same range as that for conventional tubes. There is no significant size effect for water flow in tubes within this diameter range. The laminar-turbulent transition flow regime can be easily observed from the tube wall temperature variations. The surface temperature fluctuation in transition flow regime is much larger than that in laminar and turbulent flow regimes. The LCT temperature measurement method can be used to precisely justify the onset of flow regime transition. The measured heat loss for the present study is less than 4% and 1% of the total heat input for 123 lm tube and 962 lm tube, respectively. However, at the lowest Reynolds number in the 123 lm tube, a 4% heat loss will cause 25% heat transfer coefficient overestimate. The tube outside natural convection heat loss effect is not negligible for microtubes. For developing flow, the laminar thermal entrance length for microtubes is longer than that estimated by the conventional correlation, Lfd = 0.05RedPr Æ di. The developing Nusselt numbers for 962 lm tube agree well with those predicted by the Shah and Bhatti [2] correlations. However, as the tube size decreases, the discrepancy between the test results and the predicting value increases. None of the published literatures have noticed the size effect of heat transfer performance variation in the developing flow regime. More study is necessary for the entrance thermal phenomenon in microtubes. References [1] T.-Y. Lin, C.-Y. Yang, An experimental investigation on forced convection heat transfer performance in micro tubes by the method of liquid crystal thermography, International Journal of Heat and Mass Transfer (2007), doi:10.1016/j.ijheatmasstransfer.2007.03.038. [2] R.K. Shah, M.S. Bhatti, Laminar convective heat transfer in ducts, in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single-Phase Convective Heat Transfer, Willy, New York, 1987. [3] D. Yu, R. Warrington, R. Barron, T. Ameel, An experimental and theoretical investigation of fluid flow and heat transfer in microtubes, ASME/JSME Thermal Engineering Conference 1 (1995) 523–530. [4] T.M. Adams, S.I. Abdel-Khalik, S.M. Jeter, Z.H. Qureshi, An experimental investigation of single-phase forced convection in microchannels, International Journal of Heat and Mass Transfer 41 (1998) 851–857. [5] Gh.M. Mala, D.Q. Li, Flow characteristics in microtubes, International Journal of Heat and Fluid Flow 20 (1999) 142–148. [6] G.P. Celata, M. Cumo, M. Guglielmi, G. Zummo, Experimental investigation of hydraulic and single phase heat transfer in 0.130 mm capillary tube, Microscale Thermophysical Engineering 6 (2002) 85– 97. [7] Z.X. Li, D.X. Du, Z.Y. Guo, Experimental study on flow characteristics of liquid in circular microtubes, Microscale Thermophysical Engineering 7 (2003) 253–265. [8] C.-Y. Yang, J.-C. Wu, H.-T. Chien, S.-R. Lu, Friction characteristics of water, R-134a, and air in small tubes, Microscale Thermophysical Engineering 7 (2003) 335–348. [9] T.-H. Yen, N. Kasagi, Y. Suzuki, Forced convective boiling heat transfer in microtubes at low mass and heat fluxes, International Journal of Multiphase Flow 29 (2003) 1771–1792.
C.-Y. Yang, T.-Y. Lin / Experimental Thermal and Fluid Science 32 (2007) 432–439 [10] D. Lelea, S. Nishio, K. Yakano, The experimental research on microtube heat transfer and fluid flow of distilled water, International Journal of Heat and Mass Transfer 47 (2004) 2817–2830. [11] B. Agostini, A. Bontemps, B. Thonon, Effects of geometrical and thermophysical parameters on heat transfer measurements in small diameter channels, Heat Transfer Engineering 27 (2006) 14–24. [12] V. Gnielinski, New equation for heat and mass transfer in turbulent pipe and channel flow, International Journal of Chemical Engineering 16 (1976) 359–368.
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[13] G. Maranzana, I. Perry, D. Maillet, Mini- and micro-channels: influence of axial conduction in the walls, International Journal of Heat and Mass Transfer 47 (2004) 3993–4004. [14] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2007. [15] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer 46 (2003) 149–159.