Experimental Thermal and Fluid Science

Experimental Thermal and Fluid Science 37 (2012) 12 18 Contents lists available at SciVerse ScienceDirect Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs Heat transfer and friction characteristics of air flow in microtubes Chien-Yuh Yang a,, Chia-Wei Chen a, Ting-Yu Lin b, Satish G. Kandlikar b a National Central University, Jhong-Li, Taoyuan, Taiwan b Rochester Institute of Technology, Rochester, NY, USA article info abstract Article history: Received 6 May 2011 Received in revised form 6 September 2011 Accepted 6 September 2011 Available online 29 September 2011 Keywords: Microtube Heat transfer Liquid Crystal Thermography Several researches dealing with the single-phase forced convection heat transfer inside microchannels have been published in the past decades. The performance of liquid flow has been proved that agrees with the conventional correlations very well. However, owing to the low heat transfer coefficient of gaseous flow, it is more difficult to eliminate the effects of thermal shunt and heat loss than water flow while measuring its heat transfer performance. None of the heat transfer performance experimental results have been published in the literature. This study provides an experimental investigation on the pressure drop and heat transfer performance of air flow through microtubes with inside diameter of 86, 308 and 920 lm. The Liquid Crystal Thermography method was used to measure the tube surface temperature for avoiding the thermocouple wire thermal shunt effect. The experimental results show that the frictional coefficient of gas flow in microtube is the same as that in the conventional larger tubes if the effect of gaseous flow compressibility was well taken consideration. The conventional heat transfer correlation for laminar and turbulent flow can be well applied for predicting the fully developed gaseous flow heat transfer performance in microtubes. There is no significant size effect for air flow in tubes within this diameter range. Ó 2011 Elsevier Inc. All rights reserved. 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 for increasing 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. However, the conventional forced convection heat transfer correlations were derived from tubes with diameter much larger than those used in microchannels. They have not been verified to work well for predicting the heat transfer coefficient for flow inside small diameter tubes. The study on heat transfer performance in microchannels has become more important due to the rapid growth of the application for high heat flux electronic devices cooling. Several researches dealing with the single-phase friction and forced convection heat transfer in microtubes have been published in the past years. Wu and Little [1,2] measured the flow friction and heat transfer characteristics of gases flowing through trapezoid silicon and glass microchannels of hydraulic diameters from 45 to 165 lm. They observed that the friction coefficients for silicon channels are in agreement with that for smooth tubes shown Corresponding author. Tel.: +886 3 4267347; fax: +886 3 4254501. E-mail address: cyyang@ncu.edu.tw (C.-Y. Yang). in the Moody chart but the results for glass channels are not. They concluded that for microchannels, the relative surface roughness is high for so-called smooth channels. The methods of manufacture and shape of the channels are all factors which affect the value of the friction coefficient in small channels. Choi et al. [3] measured the friction factors and convective heat transfer coefficients for flow of nitrogen gas in microtubes with inside diameters ranged from 3 to 81 lm in both laminar and turbulent flow regime. The experimental results indicated significant departures from the thermofluid correlations used for conventional sized tubes. They concluded that the Colburn analogy was not applied for microtubes having inside diameters less than 80 lm. Yu et al. [4] 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. [5] investigated turbulent single-phase forced convection of water in circular microchannels 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 obtained, along with earlier data for small circular channels by 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.09.003

C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 13 Nomenclature A heat transfer area (m 2 ) c p specific heat (J/kg K) d i tube inside diameter (m) d o tube outside diameter (m) D h hydraulic diameter (m) f friction coefficient, dimensionless G mass velocity (kg/m 2 s) h heat transfer coefficient (W/m 2 C) k f water conductivity (W/m C) L tube length L h tube heating length (m) L m wall temperature measuring position (m) LCT Liquid Crystal Thermography _m mass flow rate (kg/s) Nu d Nusselt number, dimensionless p pressure (Pa) q heat transfer rate (W) q 00 heat flux (W/m 2 ) R specific gas constant (J/kg K) R a average roughness (m) reynolds number, dimensionless T temperature ( C) T i inlet water temperature ( C) T x local water temperature ( C) T wx local tube inside wall temperature ( C) TLC thermochromic liquid crystal x axial position of tubes (m) l viscosity (N/m 2 s) q density (kg/m 3 ) Dp pressure drop (Pa) Yu et al. [4], they developed a correlation for the Nusselt number for turbulent, single-phase, forced convection in circular microchannels with diameters range from 0.102 mm to 1.09 mm. Mala and Li [6] 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. [7] 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. [8] 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 f in rough tubes is 15 37% higher than 64. Yang et al. [9] 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 friction coefficients are lower than the values predicted by Blasius equation. The discrepancy increased with increasing Reynolds number. Yen et al. [10] 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 (Nu d = 4.36). However, the Nusselt number data have a very high scattering distribution from around 2 5. Lelea et al. [11] 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 conventional or classical theories are applicable for water flow through microtubes of the sizes tested. Grohmann [12] measured the heat transfer coefficient of liquid argon at around 120 K in microchannels with diameter 250 and 500 lm. The results revealed that there is no physical difference in heat transfer mechanisms between macrotubes and microtubes. The enhancement of heat transfer coefficients in small tubes compared to conventional correlations was explained with the increased influence of surface roughness. Lin and Yang [13] proposed a non-contacted Liquid Crystal Thermography (LCT) method to measure the surface temperature of microtubes. It is successfully avoid the thermal shunt and contact problem caused by using thermocouple. Yang and Lin [14] used this method to measure the heat transfer performance of water flow in microtubes with inside diameters from 123 to 962 lm. The test results showed 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 from laminar to turbulent flow 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. Celata et al. [15] presented the work deals with the compressible flow of nitrogen gas inside microtubes ranging from 30 to 500 lm and with different values of the surface roughness (<1%), for different flow regimes. Their results showed that classic correlations can predict friction factor in laminar flow without revealing any evident influence of the surface roughness. The laminar turbulent transition starts for Reynolds number not lower than 2000 for smooth pipes. In the fully developed turbulent regime, an agreement between experimental data and the Blasius correlation has been verified for smooth pipes. In summarizing the above literature review, we may find that most of the early studies showed significant discrepancy between the experimental results and convention correlations prediction values. However, in the recent years, the friction factors test results for both liquid and gas in microtubes can be adequately predicted by the conventional correlations. The heat transfer test results for liquid can also be well predicted by the traditional forced convection heat transfer correlations. But owing to the measurement difficulties, none of the heat transfer test results for gas flow in microtubes have been published in the literature. The conventional heat transfer correlations have not been verified to be applied for flow in microtubes. This study provides an experimental investigation on laminar and turbulent forced convective heat transfer characteristics of air flow in microtubes. The LCT method proposed by Lin and Yang [13] was used in this study to measure the surface temperature of microtubes. 2. Experimental method 2.1. Tubes size measurement and experiment system setup Three steel tubes with inside diameter of 920.1, 308.4 and 85.6 lm were tested in the present study. The tubes inner diameters were measured from the enlarged photographs taken by scanning electron microscope (SEM) for tube with inner diameter of 85.6

14 C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 Fig. 1. Enlarged photographs of the microtubes. Table 1 Detail dimensions and surface roughness of the tubes tested. Tube notation Tube length, L (mm) Average outside diameter, d o (lm) Average inside diameter, d i (lm) Standard deviation (lm) Surface roughness, R a (lm) Heating length, L h (mm) 920 181.5 1260 920.1 3.02 0.704 78.14 28.6 308 179.3 550 308.4 2.74 0.685 82.67 19.5 86 96.3 270 85.6 1.28 0.135 32.55 9.2 Temperature measuring position, L m (mm) and 308.4 lm, and optical microscope (OM) for tube with inner diameter of 920.1 lm. Fig. 1 shows the sample enlarged photographs of the cross-section view of the tubes. For reducing the measurement uncertainties, seven tubes were bundled together, cut and ground to have smooth cross section surface. Each tube diameter was measured and all values were averaged to obtain the average tube diameter. The tubes inside surface roughness were measured by atomic force microscope (AFM) for 85.6 lm tube and by surface texture measuring instrument for 308.4 lm and 920.1 lm tubes. Table 1 gives the detail dimensions and surface roughness of these tubes. The Detail drawing of the corresponding tube dimensions is shown in Fig. 2. The schematic diagram of the test facilities is shown in Fig. 3. High pressure air flows from a storage tank through a regulator to the test section. The inlet air temperature was measured by a resistance temperature detector (RTD). A differential pressure transducer was installed on both ends of the test tube to measure the flow pressure drop. A mass flow meter was connected after the test tube to measure the flow rate of the working fluid. DC power was clapped on both ends of the test tube to heat the tube wall. The DC voltage and current were measured by connecting an ampere and a volt meter to the electrodes directly. The power input was calculated by the product of measured current and voltage. Tube surface temperature was measured by the LCT method that proposed by Lin and Yang [13] for avoiding the thermocouple wire thermal shunt effect and will be described in the next section. The heating length and temperature measuring positions are shown in Fig. 2 for each tube and there values are also listed in Table 1. The measuring position was designed to be longer than the maximum theoretical laminar flow entrance length. But because of the experimental space limitation, the length for 920 lm tube is slightly shorter than its theoretical entrance length. The experimental apparatus and derived parameters uncertainties are listed in Table 2. Since the heat transfer coefficient of gaseous flow is low, the heat loss by natural convection from outside of the test section may be important in the heat transfer measurement. For minimizing the heat loss, the test section was enclosed in a vacuum chamber. The chamber was evacuated by a vacuum pump before test to maintain the inside pressure below 13 mtorr. The heat loss was calibrated for each tube before its heat transfer performance test. The test tube was heated inside the vacuum chamber without working fluid through it. It was maintained at the temperature that same as it was expected for the heat transfer performance test by adjusting the power input. The power input thus can be treated as the heat loss that would be resulted in the heat transfer performance test. 2.2. LCT temperature measurements Fig. 2. Detail drawing of the test tube. The LCT method that proposed by Lin and Yang [13] was used in this study to measure the surface temperature of microtubes. For

C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 15 Fig. 3. Schematic diagrams of the test facilities. Table 2 Uncertainties of the experimental apparatus and derived parameters. Apparatus Uncertainties Calibration range RTD ( C) ±0.1 0 100 T type thermocouple ( C) ±0.2 0 100 Differential pressure transducers ±0.075% 0 10 kpa, 0 500 kpa and 0 9 MPa Pressure transducer ±0.4% 0 2 MPa Mass flow meter ±0.6% 0 100 SCCM, 0 5 SLM, 0 50 SLM T wx (LCT) ( C) 0.5 28 43 Derived parameters 86 lm 308 lm 920 lm Friction coefficient (f) (%) 2.0 8.0 0.9 6.1 0.8 10.0 Nusselt number (Nu d ) (%) 7.3 27.0 6.4 26.5 6.0 14.4 Reynolds number ( ) (%) 0.7 4.0 0.3 3.0 0.3 4.8 increasing the accuracy of temperature measurement, two thermochromic liquid crystals (TLCs) with 5 C band width from 28 33 C and 38 43 C were used. The diameters of the encapsulated TLCs are from 5 to 15 microns. 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. Electrical heating wires were attached on inside surfaces of the box to maintain the entire box space at the 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 [13]. The standard deviation for the calibrated temperature-hue curve was evaluated within ±0.5 C. 2.3. Data reduction The heat transfer rate q, was measured from the DC power input deducted by the corresponding heat loss calibrated. It equals to the increased enthalpy of air flow. Since the electrical power was added uniformly on the tube surface, the local air temperature, T x, at the position x from the heating entrance can be estimated by: q x L h ¼ _mc p ðt x T i Þ where _m is the air flow rate, L h is the tube heating length and T i is the air inlet temperature. From the Newton s Law of cooling, q 00 ¼ q A ¼ hðt wx T x Þ The local heat transfer coefficient h can be derived as: ð1þ ð2þ q h ¼ AðT wx T x Þ where A is the heat transfer area, A = pd i L h, d i is the tube inside diameter. T wx 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 temperature difference between the inside and the outside wall was calculated as less than 0.03 C which is among the experimental uncertainty range. The Reynolds number and Nusselt number are defined as the following: ¼ Gd i l and Nu d ¼ hd i k f where G is the air mass flux, G ¼ _m=a c, A c is the tube 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. [16]. The results show that the ratio of axial conduction to the tube inside convection is less than 0.02 for all tubes and thus can be neglected. 3. Results and discussions 3.1. Friction coefficients The total flow pressure drop, Dp t was measured at the condition of no heating power added. The frictional pressure drop Dp f was evaluated by deducted the inlet (Dp i ), exit (Dp e ) and acceleration (Dp a ) terms from the measured total pressure drop (Dp t ). Dp f ¼ Dp t Dp i Dp e Dp a Dp i, Dp e and Dp a were calculated by following those suggested by Kays and London [16]: Dp i ¼ G2 2q i ð1 r 2 þ K c Þ Dp e ¼ G2 2q e ð1 r 2 K e Þ Dp a ¼ G2 q i 1 q i q o where G is the air mass velocity, r is the test section connectors contraction ratio and K c and K e are the entrance and exit loss coefficients which can also be obtained from Kays and London [17]. Since the Kn numbers range in the present study, 2.8 10 5 to 2.28 10 6, is far below the slip-continuum flow boundary (10 3 ) that suggested by Beskok and Karniadakis [18], continuum flow condition was considered in the present study. The friction coefficients can be derived directly from the Darcy s equation listed below. ð3þ ð4þ ð5þ ð6þ ð7þ ð8þ

16 C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 f 1 0.1 0.01 0.001 f ¼ Dp f 2q d i G 2 4L Laminar (16/ ) Turbulent (Blasius) Fig. 4. Variation of friction coefficients versus Reynolds number. Fig. 4 shows the variation of friction coefficients versus Reynolds number for each tube. It clearly shows that the laminar to turbulent transition Reynolds number is around of 2200 for all tubes. This is the same as that for conventional larger tubes. In laminar flow regime, the friction coefficients can be well predicted by Poiseuille theory (f = 16/ ). In turbulent flow regime, the friction coefficients for 920 lm tube still agree well with those predicted by the Blasius equation. However, for 308 lm tube, the friction factor departed from the Blasius prediction values while Reynolds higher than 10,000. The discrepancy increases with increasing Reynolds number. For the smallest tube, 86 lm, the friction factors are significantly lower than those predicted by Blasius equation. These results are the same as those tested by Yang et al. [9]. Since the pressure drop was tested under no heating condition, and the viscous shear heating was much lower than the possible ð9þ heat loss by natural convection from outside of the tube for long tubes with L d i, the flow can be considered as on the isothermal condition. Shapiro [19] proposed a theoretical equation for calculating friction coefficient that includes the effect of flow compressibility as: f ¼ D h p 2 i p 2 o 4L G 2 RT 2lnp i ð10þ p o The friction coefficients evaluated by the above equation are shown in Fig. 5. It shows that the friction coefficients in turbulent flow regime for all tubes agree reasonably with those predicted by the Blasius equation. The above comparison shows that the acceleration (Dp a ) terms from Kays and London [17] (Eq. (8)) over estimated the effect of momentum change for a large pressure variation flow condition. The frictional coefficient of gas flow in microtube is the same as that in the conventional larger tubes if the compressibility effect is evaluated by the method that proposed by Shapiro [19]. 3.2. Effect of heat loss Since the heat transfer coefficient of air flow is low, the heat loss by natural convection from outside of the test tube may not be neglected in the heat transfer measurement. The ratio of heat loss to the input heating power at various flow rates for each tube has been measured and shown in Fig. 6. The ratios varied from 0.76% to 46.6% depending on the air flow rate and the tube size. From the fundamentals of convective heat transfer, the in-tube forced convection heat transfer coefficient increases with increasing Reynolds number but with decreasing tube diameter. The outside natural convection heat transfer coefficient is almost independent of tube diameter. Therefore, the heat loss ratio is smaller for smaller tube and decreases with increasing Reynolds number as that shown in Fig. 6. 3.3. Heat transfer coefficients The heat transfer rate was measured from the DC power input deducted by the corresponding heat loss calibrated. The derived Nusselt numbers for each tube at various Reynolds number are 1 0.1 Laminar (16/ ) Turbulent (Blasius) 1.0 0.1 f q loss /q 0.01 0.0 0.001 Fig. 5. Friction factors in microtubes evaluated by the Shapiro [19] equation. Fig. 6. Ratio of heat loss to total heat transfer.

C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 17 Nu d 100 10 Laminar (Nu d = 4.36) Turbulent (Gnielinski [1976]) Turbulent (Gnielinski [1995]) taken consideration. The conventional heat transfer correlation for laminar and turbulent flow can be well applied for predicting the fully developed air flow heat transfer performance in microtubes. If we combine the present results and the results by Yang and Lin [14] for water flow, we may conclude that the conventional friction and heat transfer correlations can be well applied for both gas and liquid flow in microtubes ranged from 86 to 920 lm. There is no significant size effect for air flow in tubes within this diameter range. Furthermore, since the heat transfer coefficient of gaseous flow is low, the heat loss by natural convection from outside of the test tube is not negligible in the heat transfer measurement. The heat loss percentage is smaller for smaller tube and decreases with increasing Reynolds number. Acknowledgment shown in Fig. 7. Morini et al. [20] suggested that for flow in microchannels, the low values of the inner diameter limit the significance of the Grashof number (which depends on the third power of the inner diameter) and, hence, of mixed convection. Gnielinski, [21] proposed a series of correlations for the prediction of the Nusselt number for pure forced convection. The prediction values by Gnielinski [21] and the original Gnielinski correlation [22] for conventional sized tubes were also plotted in Fig. 7 for comparison. The result shows that in the turbulent regime, the conventional Gnielinski [22] correlation is able to well predict the present test results for the 920 lm tube. However, for the 86 lm tube, the Gnielinski [21] correlation for pure force convection provides a better prediction. This agrees with that suggested by Morini et al. [20]. For the flow in laminar regime, Nusselt numbers agree 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 is longer than that estimated by the correlation from Incropera et al. [23]. This is in agreement with those tested by Yang and Lin [14] for water flow. The above test results show that the conventional heat transfer correlation for large tubes can be well applied for predicting the heat transfer performance of air flow in microtubes in both laminar and turbulent flow regime. Furthermore, if we combine the test results by Yang and Lin [14] for water flow, we may conclude that the conventional heat transfer correlation can be well applied for predicting the heat transfer performance of both air and water flow in microtubes ranged from 86 to 920 lm. There is no significant size effect for air flow in tubes within this diameter range. 4. Conclusions 1 Fig. 7. Nusselt number versus Reynolds number for all tubes. This study provides an experimental investigation on the pressure drop and heat transfer performance of air flow through microtubes with inside diameter of 86 920 lm. The experimental results show that the frictional coefficient of gas flow in microtube is the same as that in the conventional larger tubes if the effect of gaseous flow compressibility that proposed by Shapiro [19] was The study was financially supported by the National Science Council under Grant No. NSC 98-2221-E-008-088-MY3. References [1] P. Wu, W.A. 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18 C.-Y. Yang et al. / Experimental Thermal and Fluid Science 37 (2012) 12 18 [21] V. Gnielinski, Ein Neues Berechnungsverfahren fur die Warmeubertragung im Ubergangsbereich Zwischen Laminaren und Turbulenter Rohstromung, Forschung im Ingenieurwesen Engineering Research 61 (1995) 240 248 (quote in Mirini et al. [19]). [22] V. Gnielinski, New equation for heat and mass transfer in turbulent pipe and channel flow, International Journal of Chemical Engineering 16 (1976) 359 368. [23] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2007. pp. 492.