Proceedings of the 14th International Heat Transfer ConferenceIHTC14

August 8-13, 2010, Washington D.C., USA

IHTC14-22647

EXPLORATION OF EXPERIMENTAL TECHNIQUES TO DETERMINE THE CONDENSATION HEAT FLUX IN MICROCHANNELS AND MINICHANNELS

Melanie M. Derbya, Hee Joon Leea, Rose C. Craftb, Gregory J. Michnac, Yoav Pelesa, Michael K. Jensena

aDepartment of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic InstituteTroy, NY, USA

bHeat Transfer Research, Inc., College Station, TX, USAcMechanical Engineering Department, South Dakota State University, Brookings, SD, USA

ABSTRACTThis study seeks to analyze and explore experimental

methods to study condensation heat transfer in micro- and mini-channel. Following, an experimental setup was built and initial results are presented. Several experimental techniques were reviewed, while two, thermoelectric coolers and a copper-heat-flux-sensor were analyzed in detail for condensation heat flux. It was concluded that thermoelectric coolers were not suitable as heat flux sensors for single-phase validation, but the copper-heat-flux-sensor was appropriate to measure heat transfer coefficients at the mini-scale. Condensation heat transfer coefficients were obtained experimentally in seven parallel square minichannels of diameter 1mm. Existing condensation correlations were applied to these data; micro- and mini-scale correlations captured the appropriate trends but underpredicted the data.

INTRODUCTION Most current electronic cooling systems use air as a working fluid. However, as transistor and power densities increase, more aggressive cooling schemes, such as the use of vapor-compression cycles, are needed in high power density systems. The entire vapor-compression cycle needs to be optimized to be compact and lightweight. Boiling heat transfer in small diameter channels has received significant attention in the last decade. Good boiling heat transfer and pressure drop correlations are available for design because heat flux in mini- and microchannel boiling experiments can be easily obtained by measuring heater power. However, significantly less literature is available for condensation heat transfer, with a lack of fundamental knowledge on governing processes and accurate correlations. Difficulty in measuring both the heat flux and wall temperature at the mini- and micro-scales yields high uncertainties in heat transfer coefficients.

Because of the low heat duties encountered in mini- and microscale condensation, researchers have adapted macro-scale experimental methods and created new experimental techniques to measure heat flux and wall temperature, and ultimately condensation heat transfer coefficients. To increase the measured heat duties, some studies used fluid-to-fluid heat exchangers comprising of parallel microchannels. Fernandez-Seara et al. [1] reviewed the Wilson plot— a method frequently used for macro-scale heat exchangers. The condensation heat transfer coefficient can be inferred through a series of resistances without direct measurement of the wall temperature. However, Garimella and Bandhauer [2] estimated in an uncertainty analysis that a 1:6 resistance ratio of condensation to coolant was needed to obtain the heat transfer coefficient within ± 15%. Webb and Ermis [3] used the Modified Wilson plot to determine the condensation heat transfer coefficient in multi-port channels with hydraulic diameters of 0.44 - 1.56 mm. The test section was designed to produce cooling water heat transfer coefficients higher than the refrigerant. Measured condensation heat transfer coefficients were reported to be within ± 10.6%. The Wilson plot method and its derivatives at the micro and mini-scale required sufficiently high coolant heat transfer coefficients, which in turn created low log mean temperature differences. Therefore, temperature measurement error could increase heat transfer coefficient uncertainty. Rather than using resistances to find the condensation heat transfer coefficient as in the Wilson plot method, the heat flux was measured by conducting an energy balance on a test section’s coolant. Cavallini et al. [4] utilized a test section with three fluid-to-fluid heat exchangers. The first fluid-to-fluid heat exchanger superheated the refrigerant, the second partially condensed to the desired inlet quality, and the third was the cooled measurement section. The measurement section had thirteen square 1.4 mm channels,

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DRAFT

although there was no flow in the outer two channels because thermocouples were inserted in them to measure the wall temperatures. Uncertainties in heat transfer coefficients of ±7% were reported. But it is important to note that a large cooling water temperature difference is necessary for the temperature measurement’s uncertainty to be small compared to the measured temperature difference. Aside from conducting an energy balance on the test section, one could conduct an energy balance before and after the test section to get the heat transfer rate. Wang et al. [5] studied the effects of stratified and annular flow regimes on condensation of R134a in ten 1.46-mm diameter channels cooled in a cross flow air heat exchanger. Two methods of calculating heat duty, an air-side energy balance and the pre- and post-heater energy balance, were compared; the difference of ± 10% between the methods was concluded to be heat losses. This work shows the effect of heat losses on the measured heat duty, but also the difference between two methods for obtaining the heat duty, possibly resulting from measurement uncertainty. Condensation heat transfer coefficients were determined from seven cross flow heat exchangers. Reported uncertainties for the heat transfer coefficient are ± 8.2%. However, these fluid-to-fluid heat exchangers had some drawbacks, including low temperature differences across coolant flows and difficulty measuring wall temperature in some parallel channel geometries. As a result of measurement issues associated with fluid-to-fluid heat exchangers, other studies modified the standard fluid-to-fluid heat exchangers. Garimella and Bandhauer [2] adopted the Wilson plot method and modified it to be more suitable at the micro and mini-scales. First they studied a square multi-port channel of 0.76-mm hydraulic diameter, and then Bandhauer et al. [6] expanded it to other shapes and diameters. Their test section consisted of a counterflow fluid-to-fluid heat exchanger. A low quality change was desirable across the test section, thus low heat duties needed to be measured, which resulted in a very low temperature rise across the test section coolant. The researchers decoupled this problem by using a “thermal amplification” loop, separating the cooling portion into two loops; the primary loop cooled the test section and the secondary loop measured heat duty in the primary loop, but had a larger temperature change. Using this technique, the total uncertainty of heat duty was estimated to be ± 10%, and the condensation heat transfer coefficient was estimated on average within ± 21%. Still others utilized experimental techniques that measured the heat transfer coefficient via electrical means. Shin and Kim [7, 8] compared an air-cooled test section to an electrically heated test section. This innovative approach measured heat transfer rates of 10 W or less in circular and rectangular single channels of diameters ranging from 0.493 to 1.067 mm. Two identical copper tubes with attached fins were placed in a crossflow air-cooled heat exchanger. Refrigerant flowed through one tube, while the other tube contained a resistive heater, controlled by a DC power supply. The heat transfer rate

was assumed to be the same in both tubes when comparable surface temperatures were read by thermocouples at identical fin positions, although the tube boundary conditions differed. Therefore, this technique was not dependent on an air side energy balance. Uncertainties in the heat transfer coefficient of ±3.5-19.9% were reported. Two practical barriers to implementing this method were measuring extremely low mass flow rates and manufacturing two identical finned copper test sections. Alternatively, thermoelectric coolers (TECs) provided an electrical method to determine heat flux. Baird et al. [9] studied condensation in single channels, 0.92 and 1.95 mm in diameter. Thermoelectric coolers (TECs) provided an electrical method to determine heat flux. Ten TECs were arranged along the channel for cooling, dividing the channel into ten “quasi-local” energy balances. Applied voltages created temperature differences across each TEC, producing a cold side attached to a load, and hot side that rejected heat to a heat sink. Each TEC was tested by placing the TEC between two copper blocks whose temperatures were controlled by circulating water. Because the TECs were checked against the manufacturer’s equation, but not calibrated, the uncertainties in the heat flux could be greater than their claimed ±5% and, therefore, some TECs may have been accepted that, in reality, were outside of the acceptable range. Additionally, the wall temperatures were measured 2 mm away from the channel in a copper block to obtain heat transfer coefficients. Baird et al. [9] reported uncertainties in the heat transfer coefficient of ±20%. The TEC method showed promise due to the ability to measure quasi-local heat transfer coefficients in several positions along a single channel, but appropriate calibration is a concern. Since simultaneous measurement of the heat transfer rate and wall temperature presented difficulty in condensation, boiling heat transfer literature was investigated for experimental methods that could be applied to condensation. One such method was a heat flux sensor developed by Kedzierski and Worthington [10]. Oxygen-free copper was selected because of high thermal conductivity, thus reducing the overall uncertainty resulting from the thermal conductivity. Embedded thermocouples in the copper block were used to obtain the wall temperature and heat flux from the temperature gradient in the block. Therefore, the dominant uncertainty in the heat flux was the contribution from the temperature gradient. In the pool boiling experiments conducted by Kedzierski [11] using R123 and hydrocarbon mixtures, the measured heat flux by the copper-heat-flux sensor was estimated to be ± 10% at a flux of 10 kW/m2, and ± 3 - 6% for fluxes above 30 kW/m2. These low uncertainties showed that this method was promising to consider for condensation heat transfer experiments. Existing experimental methods for measuring condensation heat transfer coefficients were identified in this study. Among those, TECs and conduction in a copper block were examined further because they do not rely on measuring a cooling water temperature differences as in a fluid-to-fluid heat exchanger, and exhibit potential to

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accurately measure the condensation heat transfer coefficient.

NOMENCLATUREA Area [m2]D Diameter [m2]G Mass flux [kg/m2s]I Current [A]k Theraml conductivity [W/m2K]Nu Nusselt numberq Heat flux [W/m2K]Q̇ Heat transfer rate [W]ℜ Reynolds numberT Temperature [oC]w Uncertaintyy Position [m]

Subscriptsb Blockc ColdCu CopperD Diameterexp Experimentalf Fluidg Gradienth Hotpred Predictedw Predicted

EXPERIMENTAL APPARATUS - TEST FACILITY The same basic refrigerant loop (Fig. 1) was used for two experimental test sections: thermoelectric-cooled and copper-heat-flux-sensor test sections. The loop was designed to accommodate a wide range of mass fluxes and qualities. A pump produced flow rates range from 10 to 180 mL/min, measured by a four tube rotameter. Pressure in the loop was controlled by adjusting the pressure in a bladder accumulator. A preheater set the test section inlet quality and an upstream throttling valve was added to suppress boiling instabilities. Temperature and pressure probes at the inlet and outlet of the test section yielded an energy balance during single-phase validation. An air-cooled post condenser was added for use with the copper-heat-flux-sensor test sections.

THERMOELECTRIC COOLERS - TEST SECTION The goals of the thermoelectric-cooled test section were to obtain quasi-local heat transfer coefficients in a wide range of circular tube diameters. As shown in Figure 2, the complete test section assembly consisted of an instrumented tube in which condensation occurred.

Thermoelectric coolers were mounted

Figure 1 Loop schematic

to copper blocks which provided an interface between the TEC and the tube. To maintain good thermal contact between the copper and TEC interface as well as the TEC and heat sink interface, thermal grease was used along with thermal pads to fill in air gaps. Thermal grease also surrounded the tube to provide good thermal contact with the copper blocks. The test section was separated into ten modules insulated from each other by a sheet of 0.4 mm Teflon. Each module consisted of a TEC and two copper blocks, which surrounded the tube. Each of these copper blocks had a 1.5 mm diameter cutout to allow the tube to pass through. The tube was centered inside the copper blocks by rubber o-rings, which allowed for tubes of diameters up to approximately 3 mm to be used. All ten TECs shared one water-cooled aluminum heat sink to which the TECs rejected heat. Bolts provided vertical compression to reduce contact resistances. The modules were held in place by a combination of a Lexan end block, a Lexan locator tray and a slider block, which provided horizontal compression, shown in Fig. 3. The test section was insulated with plastic and balsa wood.

THERMOELECTRIC COOLERS - DATA ANALYSIS The test section was instrumented to determine the heat flux, wall temperature, and, ultimately, the heat transfer coefficient. The necessary variables for the heat flux were the TEC hot side temperatures, cold side temperatures, voltages and currents. Type T, 36-gauge thermocouples were installed on the hot and cold sides of the TECs and attached to the tube wall using thermal epoxy. The thermocouples were calibrated to ±0.2 oC

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Figure 2 Cross section view of the test section

Figure 3 TEC test section

using a National Instruments Data Acquisition system and LabVIEW and a reference thermometer accurate to ±0.01oC. The TECs were connected to a power supply in parallel. Ten TEC voltages, maximum of 2.3 V, were measured directly via LabVIEW. Individual currents, maximum of 8.5 A, were measured by a 15 A current shunt. The TECs required calibration to determine the heat flux, as the manufacturer’s curves were only for ideal cases. A calibration apparatus was constructed, similar to Figure 2, but an electric heater replaced the tube. Therefore, the heat transfer rate was measured via the heater voltage and current, and this could be correlated to cold side temperature, hot side temperature, TEC voltage and current. Additionally 40 V, 80 A, and 3.5 mΩ transistors acted as a switch for each TEC. Feedback control implemented in LabVIEW controlled TEC cold side temperatures around a set point. The hot side temperature was controlled by the temperature of the water-filled heat sink. The calibration was conducted over a range of 0 – 6 W heater power and 0-2 V TEC voltage. The cold side temperature was maintained at 10°C. The data were then correlated in a form similar to Baird [9],

Q̇=( T c−(0.607 I 2−8.22 I+T h−1.42)4.96 ) (1

This calibration equation predicted most of the calibration data within 10%, with better agreement at higher heat transfer rates. Heat flux was then the heat transfer rate divided by the tube segment’s surface area. With the heat

flux determined from the TEC calibration in Eq. (), the wall temperature measured from the local wall thermocouple, and the fluid temperature for single-phase flow determined from an energy balance, the heat transfer coefficient could be obtained through Newton’s law of cooling.

THERMOELECTRIC COOLERS - RESULTS AND DISCUSSIONS The heat flux calibrations were evaluated using laminar and turbulent single-phase flows in the test section shown in Figure 2. At a Reynolds number of 5420, without feedback control of the cold side temperature, the measured Nusselt numbers exhibited wide variation. Although the Gnielinski’s Correlation [12] predicted a Nusselt Number of 33, the measured values ranged from 3 to 51 with an average of 13.1, as shown in Figure 4. Similarly when the cold side temperature was computer-controlled, Eq. (1) did not adequately determine the heat flux. The significant difference in TEC performance could be a combination of variation in thermal contact resistance and TEC performance. Nagy and Buist [13] developed a technique to determine the variation in thermal contact. Once the TECs were turned off, the decay of the Seebeck voltage indicated quality of the thermal contact. If the thermal contact was consistent between TECs, the slope of the voltage versus time curve would be the same. Using this technique, the slopes were similar, suggesting that thermal contact is consistent between TECs. Differences in the individual TECs explain the poor validation of the heat flux in Eq. (1). In conclusion,

Figure 4 Turbulent Nusselt Numbers using TECs

thermoelectric coolers were suitable for cooling, but not as an accurate heat flux sensors in condensation experiments. COPPER HEAT FLUX SENSOR - TEST SECTION Because the thermoelectric-cooled test section was not an accurate heat flux sensor, the copper-heat-flux test section, shown in Figure 5, was designed. The test section consisted of seven parallel square minichannels 1 mm in diameter machined in an oxygen-free copper block of

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dimensions 20 mm by 38.1 mm by 140 mm. A Lexan plate, clear for future flow visualization, was sealed to the copper block with an o-ring. During condensation, a two-phase R134a mixture entered through a 4.7-mm hole in the Lexan cover plate, flowed into the inlet header, through the channels, and exited through a symmetric exit header. To limit heat transfer in the header region, the total header area accounted for 6.8% of the total heat transfer area. For heat flux measurements, the copper block was divided into three measuring segments, with nominal lengths of 28, 38 and 28 mm and separated by 1.59-mm slots, for reporting the heat transfer coefficient at average qualities. A water-filled serpentine cold plate was attached to the bottom of the copper-heat-flux sensor. The coolant water temperature, controlled by a thermal bath, created a temperature difference in the block proportional to heat flux. To measure the heat flux and wall temperature, 1 mm diameter, 10 mm deep thermocouple wells were drilled for T-type sheathed thermocouples, 3, 14, 19, 24, 29 and 34 mm from the bottom of the channel.

Figure 5 Copper test section

COPPER HEAT FLUX SENSOR - DATA ANALYSIS The average heat flux and wall temperature were measured in three measuring segments along the channel. For validation, the data reduction method was applied to FLUENT data and the results were compared. First, the heat transfer rate in each segment was expressed assuming Fourier’s Law in one dimension,

Q̇=−kcu AbdTdy

(2

Subsequently, the channel heat flux was determined by dividing the segment’s heat transfer rate by its channel area. The assumption of one-dimensional Fourier’s Law required a linear temperature gradient. Therefore, FLUENT simulations were conducted that predicted the linear temperature gradient, shown in Figure 6, and, in each segment, the five thermocouples located 14, 19, 24,

29, and 34 mm from the bottom of the channels measured the temperature gradient. The uncertainty in the temperature gradient, therefore, was the slope of the temperature versus position line. Kedzierski and Worthington [10] developed an expression for the uncertainty in the temperature gradient, wg,

wg=√wT2 +¿¿¿ (3)

The first term in Eq. (3) represented the uncertainty in the temperature sensors and the uncertainty in the position of the thermocouple in the drilled thermocouple well, although the thermocouple well diameter was selected to minimize this contribution to the gradient uncertainty. The second term represented the distribution of the thermocouple wells in the block, as increasing the distance between thermocouple wells will reduce the uncertainty in the temperature gradient.

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Also, axial conduction along the channel and between segments contributed to uncertainty in the temperature gradient. This was more important when the fluid temperature changed along the channel length, as in single-phase validation. FLUENT simulations utilized single phase flow, and showed the insertion of air-filled slots between the measuring segments reduced the axial conduction in a segment. The temperature distribution in the copper block on two lines parallel and 17.1 mm and 27.1 mm from the bottom of the channels is shown in Figure 7. Due to two-dimensional conduction, the axial temperature changed greatly in segments without separating slots, but the two-dimensional conduction effects decreased with the insertion of slots between the channels. Thus, one-dimensional conduction was an appropriate assumption when the measuring segments were separated by air-filled slots. In addition to the heat flux in each segment, a measured wall temperature was needed to determine the heat transfer coefficient, and the header heat transfer coefficient was also needed to determine fluid temperature in single-phase

Figure 6 Temperature Gradient in FLUENT Simulations

Figure 7 Effect of Slots on Axial Conduction

experiments and quality in condensation experiments. The wall temperature was extrapolated with a second order polynomial curve fit, using the five thermocouples for measuring the temperature gradient and sixth “near wall” thermocouple, located 3 mm from the bottom of the channel. The y-intercept of the polynomial fit was then the wall temperature. Additionally, the inlet header heat transfer coefficient was needed to determine the single-phase fluid temperature or two-phase inlet quality. FLUENT simulations showed the inlet header heat transfer coefficient was approximately twice that of the middle measuring segment, and the outlet heat transfer coefficient the same as the middle measuring segment. All these assumptions were validated by inputing FLUENT simulation data into the developed data reduction program, and comparing the results of FLUENT and the data reduction program. The FLUENT simulations incorporated both fluid motion and conduction in the test section. In the fluid, a very fine structured hexagonal grid solved the steady incompressible Navier-Stokes equations using k-ε turbulent modeling, while unstructured tetrahedron grids solved the conduction equation. A constant temperature boundary condition was prescribed on the bottom surface of the copper block. A wide range of single-phase Reynolds numbers was tested, as higher Reynolds numbers exhibited high heat transfer coefficients and low fluid temperature changes along the channel, akin to condensation. As shown in Table 1, there was good agreement between the wall to fluid temperature difference, especially at lower Reynolds numbers, and outside of the laminar range, the difference in heat flux was less than 4%.

COPPER HEAT FLUX SENSOR- RESULTS AND DISCUSSIONS Single-phase experiments validated the determination of wall temperature and heat flux. Nusselt and Reynolds numbers were calculated at local fluid properties and

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plotted in Figure 8. The first segment Nusselt numbers were corrected for turbulent developing flow using the Al-Arabi [14] correlation. To obtain the turbulent entrance length for a rectangular channel, Hartnett et. al. [15] proposed the developing length over diameter ratios were 40 for a Reynolds number of 3000 and less than 20 for Reynolds numbers greater than 4000. Therefore, a turbulent entrance length to diameter ratio of thirty was assumed because the flow was in the transitional regime. The experimental data changed with Reynolds number to the power of 1.08, close to the power of one used in the Gnielinski’s correlation [12]. As these Reynolds numbers were at the lower end of the correlation’s range, and the Gnielinski’s correlation was not developed for the micro/mini-scales and three-side cooling, a higher value of Nusselt number was reasonable. Additionally, a single-phase energy balance and the heat transfer rate calculated from the temperature gradient and headers agreed within 3.5-8%. Good agreements in Nusselt number and energy balance showed this approach is valid for determining the condensation heat transfer coefficient.

Condensation data were graphed in Figure 9 for a mass flux of 250 kg/m2s and a saturation temperature of 45 oC. The trend of increasing heat transfer coefficient with increasing average quality was expected. In addition, the uncertainties in the condensation heat transfer coefficient are lower than in single phase because a larger temperature gradient occurred at the higher condensation heat fluxes. In Figure 10, the data were compared with various existing condensation correlations. The Shah [16] and Akers et al. [17] macro-scale correlations, both did not capture the trend of the data. However, the Bandhauer [6] and Agarwal [18] correlations, developed for micro and mini-scale circular and non-circular channels, respectively, underpredicted the data. The behavior of these correlations may be explained by differences in boundary conditions, as the correlations were developed for four sided cooling, and the experimental apparatus utilizes three sided cooling. Additionally, the Soliman [19] correlation, developed for the conventional scale condensation mist flow regime, also predicts the appropriate trend of the data. Therefore, the trends of the data were best fit by micro and mini-scale correlations, but difference could be caused by the different boundary conditions.

Table 1 Mean Average Errors Between FLUENT and Data Reduction Program

Re 930 3,200 6,475 32,000 63,000MAETf - Tw

3.0% 2.4% 4.0% 8.6% 9.5%

MAEHeat Flux 8.3% 2.7% 3.9% 3.5% 3.2%

Figure 8 Nu Versus Re Using Copper Test Section

Figure 9 Condensation Data, G = 257 kg/m2s

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Figure 10 Comparison of Data with Correlations

CONCLUSIONS Existing experimental techniques for measuring condensation heat transfer have been reviewed. In this study, thermoelectric coolers and a copper-heat-flux sensor were built and analyzed as potential approaches for studying flow condensation in micro and minichannels. Single-phase validation experiment results and condensation data were presented for these two methods. The main conclusions of this study are as follows:1. Thermoelectric coolers were suitable for cooling but are not appropriate as a heat flux sensors. 2. The single-phase heat transfer coefficient results from the copper block heat flux sensor experiments agreed well with the nGnielinski’s correlation [12] for transitional flows. An uncertainty analysis showed that this approach can yield high accuracy heat transfer coefficient measurements.3. The copper block heat flux sensor was used to determine the condensation heat flux in mini-channels. The measured heat transfer coefficient indicated that the trend is physically correct. The existing mini-scale correlations were the best predictor for current measured condensation heat transfer coefficient. Therefore, this method is promising for accurately measuring the heat transfer coefficient.

ACKNOWLEDGEMENTS This work was supported in part by the Office of Naval Research (ONR) under the Multidisciplinary University Research Initiative (MURI) Award GG10919 entitled "System-Level Approach for Multi-Phase, Nanotechnology-Enhanced Cooling of High-Power Microelectronic Systems."

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Heat Exchanger Devices,” Applied Thermal Engineering, 27 (17-18) , pp. 2745-2757.[2] Garimella, S., Bandhauer, T. M., 2001, “Measurement of Condensation Heat Transfer Coefficients in Microchannel Tubes,” Proc. ASME International Mechanical Engineering Congress and Exposition, New York, NY, pp. 1-7.[3] Webb, R. W., Ermis, K., 2001, “Effect of Hydraulic Diameter on Condensation of R-134a in Flat, Extruded Aluminum Tubes,” Enhanced Heat Transfer, 8 (2), pp. 77-90.[4] Cavallini, A., Censi, G., Del Col, D., Doretti, L., Longo, G. A., Rossetto, L., 2003, “Experimental Investigation on Condensation Heat Transfer Coefficient Inside Multi-port Minichannels,” First International Conference on Microchannels and Minichannels , Rochester, NY, pp. 691-698.[5] Wang, W. W., Radcliff, T. D., Christensen, R. N., 2002, “A Condensation Heat Transfer Correlation for Millimeter-scale Tubing with Flow Regime Transition,” Experimental Thermal and Fluid Science, 26 (5), pp. 473-485.[6] Bandhauer, T. M., Akhil, A., Garimella, S., 2006, “Measurement and Modeling of Condensation Heat Transfer Coefficients in Circular Microchannels,” Journal of Heat Transfer 128 (10), 1050-1059.[7] Shin, J. S., Kim, M. H., 2004, “An Experimental Study of Flow Condensation Heat Transfer Inside Circular and Rectangular Mini-channels,” Second International Conference on Microchannels and Minichannels, Rochester, NY, pp. 633-640.[8] Shin, J. S., Kim, M. H., 2004, “An Experimental Study of Condensation Heat Transfer Inside a Mini-channel with a New Measurement Technique,” International Journal of Multiphase Flow 30 (3), pp. 311-325.[9] Baird, J. R., Fletcher, D. F., Haynes, B. S., 2003, “Local Condensation Heat Transfer Rates in Fine Passages,” International Journal of Heat and Mass Transfer 46 (23), pp. 4453-4466.[10] Kedzierski, M. A., Worthington III, J. L., 1993, “Design and Machining of Copper Specimens with Micro Holes for Accurate Heat Transfer Measurements,” Experimental Heat Transfer 6 (4), pp. 329-344.[11] Kedzierski, M., 2000, “Enhancement of R123 Pool Boiling by the Addition of Hydrocarbons,” International Journal of Refrigeration 23 (2), pp. 89-100.[12] Gnielinski, V., 1995, “New method to calculate heat transfer in the transition region between laminar and turbulent tube flow,” Forschung im Ingenieurwesen 61 (9), pp. 240.[13] Nagy, M. J., Buist, R. J., 1996, “Transient Analysis of Thermal Junctions Within a Thermoelectric Cooling Assembly. 15th International Conference on Thermoelectrics,” pp. 288-292.[14] Al-Arabi, M., 1982, “Turbulent Heat Transfer in the Entrance Region of a Tube,” Heat Transfer Engineering 3 (3-4), pp. 76-83.[15] Hartnett, J. P., Koh, J. Y., McComas, S. T., 1962, “A Comparison of Predicted and Measured Friction Factors

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for Turbulent Flow through Rectangular Ducts,” Journal of Heat Transfer 84, pp. 82-88.[16] Shah, M. M., 1979, “General Correlation for Heat Transfer During Film Condensation Inside Pipes,” International Journal of Heat and Mass Transfer 22, pp. 547-556.[17] Akers, W. W., Deans, H. A., Crosser, O. K., 1959, “Condensation Heat Transfer within Horizontal Tubes,” Chemical Engineering Prograss Symposium Series 55(29), pp. 171-176.[18] Agarwal, A., Bandhauer, T. M., Garimella, S., 2007, “Heat Transfer Model for Condensation in Non-circular

Microchannels,” Proceedings of the Fifth International Conference on Nanochannels, Microchannels and Minichannels, Puebla, Mexico, pp. 117-126.[19] Soliman, H. M., 1986, “The Mist-annular Transition During Condensation and its Influence on the Heat Trans-fer Mechanism,” International Journal of Multiphase Flow 12 (2), pp. 277-288.

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