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Pressure effect on flow boiling heat transfer of water in minichannels
International Journal of Thermal Sciences 50 (2011) 280e286
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Pressure effect on flow boiling heat transfer of water in minichannels K.H. Bang a, *, K.K. Kim a, S.K. Lee a, B.W. Lee b a b
Department of Mechanical Engineering, Korea Maritime University, 1 Dongsam-dong Yeongdo-gu, Busan 606-791, Republic of Korea Department of Materials Engineering, Korea Maritime University, 1 Dongsam-dong Yeongdo-gu, Busan 606-791, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 January 2010 Received in revised form 11 March 2010 Accepted 15 March 2010 Available online 20 April 2010
The effect of pressure on the flow boiling of water in minichannels has been experimentally studied. The range of pressure was 2e16 bars in the experiment. The experimental apparatus consisted mainly of the 1.73 mm inner diameter round tube test section, gear pump, pre-heater, pressurizer, pre-evaporator, and condenser. The pre-evaporator was used for varying the vapor quality entering the test section. The pressurizer controls the desired system pressure. The test tube is made of 316 stainless steel and the test tube and the pre-evaporator tube were heated by DC electric current through the tubes. The measured flow boiling heat transfer coefficients were in the range of 10,000e35,000 W/m2 K and showed the general convection dominant trend in terms of vapor quality. The data also indicate that the pressure does not alter the heat transfer coefficient significantly. Comparisons of the experimental data to the existing correlations showed large discrepancy, implying that these correlations are not correctly accounted for pressure. A simplified annular flow model has been proposed and the model prediction shows a reasonably good agreement with the measured data. Ó 2010 Elsevier Masson SAS. All rights reserved.
Keywords: Flow boiling Minichannel Microchannel Annular flow
1. Introduction For the last several decades compact heat exchangers have shown growing interest and demand in many industrial applications such as automobile radiators, HVAC and refrigeration systems, and recently electronic equipment cooling. The interesting hydraulic diameter of the tubes and channels is continuously getting smaller and now even down to tens of micron is considered for microprocessor chip cooling. Classifying a tube or channel size as large or small seems rather vague since the heat transfer and fluid flow characteristics can be different even over the ranges of millimeter to sub-millimeter size. Recently the term “minichannel” has become a common word for tubes and channels whose hydraulic diameters are in the range of 0.3e3 mm, as proposed by Kandlikar and Balasubramanian [1]. The channel sizes over 3 mm are called conventional channel, and the channel sizes smaller than 0.3 mm are called microchannel. The main motivation of such channel size classification has come from the question that the existing knowledge of heat transfer and fluid flow, which has been documented from the data collected largely from the conventional larger size channels, can be valid for smaller channels; minichannels and microchannels. For single phase flow, the literature reporting recent work on
* Corresponding author. Tel.: þ82 51 410 4365; fax: þ82 51 405 4790. E-mail address: [email protected] (K.H. Bang). 1290-0729/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2010.03.011
microchannels including the work of present authors [2] indicates that the heat transfer and fluid flow characteristics are similar over all these three classifications of channel size. For two-phase flow boiling, however, the recent articles have reported different characteristics depending upon channel size and fluid type. The influence of the channel size in flow boiling is associated with the length scales involved; channel size and bubble size or the twophase flow patterns such as bubbly, slug and annular flow. Since early 1990s a number of experimental studies on the flow boiling heat transfer in minichannels have been reported. These include the experiments of Wambsganss et al. [3] and their coworkers Tran et al. [4] using small round and rectangular tubes of 2.4e2.9 mm inner diameter and R-12/R-113 fluids. They reported that in small tubes the evaporation heat transfer coefficients are greatly affected by the heat flux and it does not seem to be a function of vapor quality at higher heat fluxes. Bang and Choo [5] with 1.6 mm round tubes and R-22 also reported a similar trend to Wambsganss et al. [3] results such that the heat transfer coefficients are independent of vapor quality and mass flux. However, Yan and Lin [6] conducted experiments using small round tube of 2.0 mm inner diameter and R-134a refrigerant and found a trend similar to the Kandlikar [7] correlation such that the evaporation heat transfer coefficient decreases as the vapor quality increases. The major tend of flow boiling heat transfer in minichannels is that the local heat transfer coefficients are largely independent of mass flux or vapor quality, but only a function of wall heat flux. These experimental observations may indicate that the flow boiling
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
x* X We
Nomenclature Boiling number, q00 /Ghfg Convection number, ((1 x)/x)0.8 (rg/rl)0.5 diameter friction factor fluid dependent parameter for eq. (3) mass flux Graetz number, dh$Re$Pr/x heat transfer coefficient thermal conductivity pressure loss coefficient channel length Nusselt number, hd/k pressure, perimeter pressure drop Prandtl number heat input heat flux radius Reynolds number, Gd/m temperature velocity vapor quality
a d f2f m r s
void fraction liquid film thickness two-phase multiplier viscosity density surface tension
Subscripts g vapor h hydraulic i inner l liquid o outer sat saturation w wall LO liquid only NBD nucleate boiling dominant CBD convective boiling dominant
"
3000Bo0:86
Kandlikar and Balasubramanian [1]:
( h ¼
maxðhNBD ; hCBD Þ; Rel > 100 hNBD ; Rel < 100
i hNBD ¼ 0:6683Co0:2 ð1 xÞ0:8 þ1058Bo0:7 ð1 xÞ0:8 FFL hLO i h hCBD ¼ 1:136Co0:9 ð1 xÞ0:8 þ667:2Bo0:7 ð1 xÞ0:8 FFL hLO h
(3) The predictions of flow boiling of water in 1.73 mm diameter circular tube by these correlations are compared in Fig. 1 for two different pressures; 1 atm and 20 atm. The mass flux of 300 kg/m2 s in this comparison corresponds to Re ¼ 1600 at 1 atm (laminar flow) and to Re ¼ 4000 at 20 atm (turbulent flow) for both liquidonly flows. Fig. 1 shows that there are large differences between the predictions by the three correlations for both pressures. It is 50000
40000
2
in minichannels is of so-called nucleate boiling dominant regime. One notes, however, that most of the experimental work mentioned here used Freon type fluids. The work by Steinke and Kandlikar [8] and Qu and Mudawar [9] have a common in working fluid of water and in general showed a contradicting trend of heat transfer coefficient versus mass flux and heat flux to Freon cases. Convection dominant heat transfer in water system may be related to high latent heat of vaporization of water compared to hydrocarbons. The authors of this paper have been interested in flow boiling of water in minichannels and this paper is the continuing work of the article by Bang et al. [10]. Most of the information obtained in the literature for flow boiling in minichannels is the data of hydrocarbon fluids. Therefore, the first attempt was to choose three correlations of flow boiling heat transfer and to compare each prediction for water flow in minichannels at different pressures. The three correlations are Gungor and Winterton [11], Yu et al. [12], and Kandlikar and Balasubramanian [1], and are given below. The first one has been applied to conventional larger size tubes and the latter two have been tested with the data from minichannels and microchannels. It is noted that the vapor quality is not a parameter in the correlation of Yu et al. and the Kandlikar’s is basically his correlation for conventional channels with some classification for microchannels, where hLO is single phase convective heat transfer coefficient for laminar or turbulent depending on Reynolds number [7]. Gungor and Winterton [11]:
0:75 0:41 # rl x h ¼ hl 1 þ þ 1:12 rg 1x Gð1 xÞd 0:8 0:4 kl Pr l hl ¼ 0:023 ml d
dimensionless entry length, x/dh$Re$Pr Martinelli parameter Weber number, G2d/rls
Greeks
hTP (W/m K)
Bo Co d f FFL G Gz h k K L Nu P DP Pr Q q00 r Re T V x
Kandlikar (2003) Yu et al. (2002) Gungor & Winterton (1987) filled: 1 atm , open: 20 atm
30000
20000
10000
0 0.1
6:4 106
Water, D=1.73 mm 2 2 G=100 kg/m s, q"=80 kW/m
(1)
Yu et al. [12]:
h ¼
281
Bo2 We1
0:27 r l
rg
!0:2
0.2
0.3
0.4
0.5
Vapor Quality, x
(2)
Fig. 1. Comparison of flow boiling heat transfer correlations for water at pressure of 1 atm and 20 atm.
282
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
also interesting to note that the Yu et al. correlation predicts higher heat transfer coefficient for higher pressure but the other two predict in opposite trend. This observation was the motivation of the present experimental work on flow boiling of water in minichannels. 2. Experiment The design and construction of the flow boiling experiment for water at pressures from the atmospheric pressure up to 20 bars needed a special consideration of the high temperature since the saturation temperature at 20 bars is 212 C and the heating side temperature is further higher. As a heat flux source to the test tube, heating wire method has a limitation of electrical insulation material breakdown at temperature over 200 C. The Joule heating by direct DC current also requires electrically insulating tube pieces at both ends of the test tube which should withstand the high temperature and high pressure. In the present experiment, Joule heating method was chosen with PFA tube pieces at the both ends of the test tube for electrical insulation, and due to this temperature problem, the present experiment was operated up to 16 bars, although most components were designed for pressures up to 30 bars. The schematic of the experimental apparatus is shown in Fig. 2. It consists mainly of pump, pre-heater, pressurizer, evaporator, test tube, and condenser. The pump is a magnetic gear pump with variable speed and a coriolis-type flow meter is installed to measure the mass flow rate. The allowed operating temperature limit of the pump and the flow meter requires cool down of water below 90 C before entering the pump and reheat the water to the saturation temperature before the evaporator. The pre-heater is a cylindrical chamber which contains a cartridge heater to raise the water temperature to the saturation temperature of the desired operating pressure. To control the system pressure, a pressurizer is installed at the pump suction side. The pressurizer is a rectangular chamber of
which both sidewalls are made of transparent quartz plates in order to visually check the liquid water level of the loop. At the top of pressurizer is nitrogen gas tank connected to control the system pressure. To supply various vapor quality at the inlet of the test tube, an evaporator is installed before the test tube. It is a 2 m long tube of the same tube size with the test tube and heated by passing direct DC current. In the connecting part to the test tube, the same flow crosssectional area is kept to prevent two-phase flow regime change. The test tube is a 300-mm long, SS316 round tube and its inner diameter is 1.73 mm and the wall thickness is 0.72 mm. The heat flux is provided by passing direct DC current. At the both ends of the test tube a short PFA (PerFluoroAlkoxy) tube is connected to provide electrical insulation between the test tube and the rest of the loop. The temperature of the test tube wall is measured at five locations using thermocouples bonded to the outer wall using high thermal conductivity cement. The measurement error of temperature difference is within 0.2 C. The exiting two-phase water is passing the condenser which is a coiled, long tube and immersed into a constant temperature bath. The condenser capacity is designed such that the exiting liquid water temperature from the condenser is kept constant so that it helps maintaining a steady state of the system. The fluid temperature measurement at the exit of pre-heater, at the inlet of evaporator, at both the inlet and the exit of test tube, and the exit of the condenser are made by direct insertion of the thermocouples into the tube. The differential pressure across the test tube and the absolute pressure at the inlet of the test tube are measured. All the signals of flow rate, pressure and temperature are monitored and recorded using PC-based Labview system. The reduction of the measured variables to the local heat transfer coefficients is done using the equations below. One notes that the inner wall temperature is estimated from the measured outer wall temperature using the conduction heat transfer equation for round tube wall with an internal heat generation.
Fig. 2. Schematic of experimental apparatus for flow boiling in minichannels.
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
h ¼
q00 Tw;i Tsat
(4)
q00 ¼
Q Pi LH
(5)
DP ¼
rV 2 2
q00 ri ðri =ro Þ2 2 lnðri =ro Þ 1 $ 2k 1 ðri =ro Þ2
L X K f þ d
(6)
(7)
Experimental uncertainty analysis has been done with careful collection of the uncertainty in each measurement. The largest uncertainty source is found in the temperature difference between the wall and the fluid. The local saturation temperature of water is calculated using the measured pressure at the inlet and the differential pressure across the test section. The overall uncertainty analysis using an error propagation method [13] shows that the uncertainty in heat transfer coefficient is 14.8%. The summary of the uncertainty in experimental measurement is given in Table 1. 3. Results and discussions The present experiment is primarily aimed at obtaining flow boiling data of water in 1.73 mm inner-diameter minichannel. The primary experimental variables are pressure and wall heat flux. 3.1. Single phase laminar flow First, the single phase flow experiments were carried out to evaluate the measurement performance of the present experimental setup. For Reynolds number 200e2000, the measured heat transfer coefficients are shown in Fig. 3 and the measured friction factors are shown in Fig. 4. The single phase heat transfer data are compared with the analytical solution of thermally developing laminar flow. The analytical solution is written in an explicit form as [14] 0:506
Nux ¼ 4:364 þ 8:68 ð1000 x* Þ
*
e41x
(8)
The agreement between the data and equation (8) is reasonably good thus it implies that the present experimental measurement of heat transfer coefficient is in a right setup. The observation that the friction factor data well match by accuracy the 64/Re curve implies that the flow is fully-developed and the single phase laminar flow in the 1.73 mm inner-diameter tube is well described by the typical laminar flow characteristics of the regular size tubes.
Table 1 Experimental uncertainty analysis. Parameter
Uncertainty
Temperature Pressure Saturation temperature Temperature difference Flow rate Heat input Heat loss Heat flux Heat transfer coefficient
0.5 C 1% 0.5 C 0.7 C 2% 1.4% 4.5% 4.7% 14.8%
Fig. 3. Single phase laminar heat transfer measurement and comparison to Shah and London’s prediction [13].
3.2. Two-phase flow boiling heat transfer For two-phase flow boiling experiment, the data were obtained for pressures of 2 bars and 16 bars and the heat flux was varied between 50 and 160 kW/m2. The inlet vapor quality was varied by the evaporator until dry out occurred. The data collected are presented in Figs. 5 and 6. The saturation temperature of water at high pressure was as high as 201 C (16 bars) and the heat loss from the test section to the environment was sizable and cannot be neglected in the heat transfer analysis. The thermal insulation covering the test section was made heavy enough with ceramic wool but the heat loss was as high as 10% of the heat applied to the test section. In order to account for the heat loss in the wall heat flux calculation, heat losses at various wall temperatures up to 220 C were obtained from single phase runs without heat input to the test section. The temperature difference between the inlet and the outlet was used to calculate the heat loss. This measured heat loss was subtracted from the heat input of Joule heating in the test tube. For the low pressure of 2 bars, the influence of heat flux on the flow boiling heat transfer coefficient is shown in Fig. 5. The dry out
1
64 / Re Present Data
Friction Factor, f
Tw;i ¼ Tw;o
283
0.1
0.01 100
1000
Re Fig. 4. Single phase laminar friction factor measurement and comparison to fullydeveloped laminar fiction factor.
284
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286 40000
2
D=1.73 mm, 2 bars, G=100 kg/m s
2
h (W/m K)
30000
20000
2
q"=50 kW/m 2 q"=80 kW/m 2 q"=115 kW/m 2 q"=150 kW/m
10000
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
x Fig. 5. Flow boiling heat transfer coefficients of water at 2 bars.
Fig. 7. Effect of pressure on heat transfer coefficients.
occurred at about 0.6 of vapor quality. The measured flow boiling heat transfer coefficients are in the general trend of convection dominant flow boiling such that at low vapor quality the change of the heat transfer coefficient versus vapor quality is small or nearly plateau and at higher quality the heat transfer coefficient increases as the quality increases. It is interesting to observe that the higher heat flux reduces the heat transfer coefficient. For the high pressure of 16 bars as shown in Fig. 6, the heat transfer coefficients show the general convection dominant trend but the heat flux does not affect the heat transfer coefficient. The effect of pressure on heat transfer coefficient is shown in Fig. 7 in which all the data for both pressures are plotted. At present, the data for only two pressures are compared: 2 bars and 16 bars. At low vapor quality where the slug flow pattern seems to be dominant, the heat transfer coefficient is slightly higher at the higher pressure. At high vapor quality where the flow pattern is annular flow, the effect of pressure does not appear. This experimental observation of the pressure effect is much different from the predictions of the existing correlations shown in Fig. 1. The present flow boiling heat transfer data for water (Fig. 7) are compared with the predictions of the three selected correlations as shown in Figs. 8e10. First, the prediction of Gungor and Winterton correlation (Fig. 8) does not look good for both low pressure and high pressure data and this is probably because this correlation is based on the data for the conventional larger size channels.
The comparison of Yu et al. correlation (Fig. 9) shows relatively good agreement for the low pressure data, but the correlation overpredicts the high pressure data. One notes that the Yu et al. correlation is based on their own data obtained for water in 2.98 mm diameter tube and the pressure of around 2 bars and this is probably the reason for the observation in the comparison. The best prediction of lower pressure data is by Kandlikar correlation as shown in Fig. 10. This correlation has been developed based on flow boiling data for minichannels and microchannels. However, this correlation also fails to predict the high pressure data. It highly underpredicts the data for high pressure. The observed large discrepancy between the present data and the existing correlations reveals the need of fundamental understanding on flow boiling in small channels (minichannels). Among the flow boiling fundamentals the mode of nucleate boiling and the two-phase flow patterns of slug flow and annular flow seem to be the key aspects in explaining the present observations. Two-phase flow boiling in channels is characterized by two distinctive modes: nucleate boiling and convective boiling. In nucleate boiling certain amount of wall superheat is required for a bubble to be created and to grow. For a situation in which constant heat flux is applied, the increasing heat transfer coefficient reduces the wall superheat then it may suppress nucleate boiling. Such a boiling mode without bubble nucleation is called convective
Fig. 6. Flow boiling heat transfer coefficients of water at 16 bars.
Fig. 8. Comparison of present data with prediction of Gunger and Winterton correlation [11].
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
ð1 aÞ ¼
4pdd 4d ¼ d pd2
285
(9)
Following the LockharteMartinelli approach on annular flow [15], the relationship between the two-phase multiplier and the void fraction is
f2f ¼ ð1 aÞ2
(10)
And the LockharteMartinelli correlation for the two-phase multiplier is
C X
f2f ¼ 1 þ þ
1 X2
(11)
where X is the Martinelli parameter and the constant C is 12 for the case of laminar liquid flow and turbulent vapor flow which is a typical case for flow boiling in minichannels. Yu et al. proposed an empirical expression for the Martinelli parameter. Fig. 9. Comparison of present data with prediction of Yu et al. correlation [12].
0:5 X ¼ 18:65
boiling and the convective boiling is more associated with the twophase flow pattern. 3.3. Simplified annular flow model Two-phase flow pattern in minichannel or microchannel is dominated by slug flow in low vapor quality and annular flow in high vapor quality. Thome et al. [16] proposed a three-zone flow boiling model to describe evaporation of elongated bubbles of slug flow in microchannels. Their heat transfer model describes the transient variation in local heat transfer coefficient during the sequential and cyclic passage of (i) a liquid slug, (ii) an evaporating elongated bubble and (iii) a vapor slug. Besides, however, this detailed modeling of slug bubble seems to be applicable to the very short length of entry part of heated channels since the flow quickly becomes annular as the vapor quality increases, the model is strongly dependent on empirical data such as bubble frequency. In this paper, a simplified annular flow model has been constructed to predict the flow boiling heat transfer coefficient at different pressure. In annular two-phase flow the heat transfer at the inner wall is dominated by the heat transfer across the liquid film and the prediction of liquid film thickness is the key in determining the heat transfer coefficient. For annular flow with a liquid film of thickness d,
Fig. 10. Comparison of present data with prediction of Kandlikar correlation [1].
rg rl
0:1 1 x Reg x Re0:5 l
(12)
Using equations (9)e(12), the liquid film thickness can be calculated. Since the liquid film in minichannels is typically thin, the heat transfer across the liquid film can be approximated by conduction dominant with linear temperature profile. Based on this assumption, the heat transfer coefficient can be given by
h ¼
kl
d
(13)
Using the proposed annular flow model, the flow boiling heat transfer coefficients were calculated for the present experimental conditions. The calculated liquid film thickness was 20e70 mm and the calculated heat transfer coefficients were shown in Fig. 11 together with the measured data. The calculations show that the higher pressure gives lower heat transfer coefficient and the difference becomes larger as the vapor quality increases. Also the proposed model reasonably predicts the measured data in higher vapor quality where the annular flow is obvious. At lower vapor quality where slug flow seems dominant and the contribution of nucleate boiling cannot be neglected, this annular flow model underpredicts the data. For such slug flow region a dedicated model such as Thome et al. model [16] can be used.
Fig. 11. Comparison of measured flow boiling heat transfer coefficients with the prediction of proposed model (G ¼ 100 kg/m2 s, d ¼ 1.7 mm).
286
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
The effect of pressure in the proposed model appears as a counter-affecting between vapor density, liquid viscosity as well as liquid thermal conductivity. The higher vapor density at the higher pressure reduces the vapor velocity thus film thickness increases, resulting in suppression of heat transfer. However, lower liquid viscosity and higher liquid thermal conductivity at the higher pressure have an enhancing effect of heat transfer. The overall effect is found to be suppressing heat transfer as pressure increases. 4. Conclusion An experimental study on flow boiling of water in a minichannel of 1.73 mm inner diameter round tube has been conducted. The major objective of this study was to experimentally observe the effect of pressure on flow boiling heat transfer in minichannels. The range of pressure was 2e16 bars. The measured flow boiling heat transfer coefficients were in the range of 10,000e35,000 W/m2 K and showed the general convection dominant trend in terms of vapor quality. The data also indicate that the pressure does not alter the heat transfer coefficient significantly. Comparisons of the experimental data with the predictions of correlations (Gungor and Winterton; Yu et al.; Kandlikar) showed large discrepancy, especially for the high pressure data. Also a simplified annular flow model has been proposed and the model prediction of flow boiling heat transfer coefficient shows a reasonably good agreement with the measured data. Acknowledgments This work was supported by the National Research Foundation of Korea under BAERI program and the Korean Ministry of Knowledge Economy under ITRC program (NIPA-2009-C1090-0903-0007).
References [1] S.G. Kandlikar, P. Balasubramanian, Extending the applicability of the flow boiling correlation to low Reynolds number flows in microchannels, in: Proceedings of the 1st International Conference on Microchannels and Minichannels, Rochester, New York, April 2003. [2] K.H. Bang, T.Y. Yoon, Effect of operating pressure on flow boiling heat transfer in microchannels, in: Proceedings of the 3rd International Conference on Microchannels and Minichannels, Toronto, Canada, 2005. [3] M.W. Wambsganss, et al., Boiling heat transfer in a horizontal small-diameter tube. J. Heat Transf. 115 (1993) 963e972. [4] T.N. Tran, et al., Small circular- and rectangular-channel boiling with two refrigerants. Int. J. Multiphase Flow 22 (1996) 485e498. [5] K.H. Bang, W.H. Choo, Flow boiling in minichannels of brass, copper and aluminum round tubes, in: Proceedings of the 2nd International Conference on Microchannels and Minichannels, Rochester, USA, 2004. [6] Y.Y. Yan, T.F. Lin, Evaporation heat transfer and pressure drop of refrigerant R-134a in a small pipe. Int. J. Heat Mass Transf. 41 (1998) 4183e4194. [7] S.G. Kandlikar, A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. J. Heat Transf. 112 (1990) 219e228. [8] M.E. Steinke, S.G. Kandlikar, Flow boiling and pressure drop in parallel flow microchannels, in: Proceedings of the 1st International Conference on Microchannels and Minichannels, Rochester, 2003, pp. 567e579. [9] W. Qu, I. Mudawar, Flow boiling heat transfer in two-phase micro-channel heat sinks e I. Experimental investigation and assessment of correlation methods. Int. J. Heat Mass Transf. 46 (2003) 2755e2771. [10] K.H. Bang, et al., Flow boiling of water in minichannels: effect of pressure, in: Proceedings of the 5th International Conference on Nanochannels, Microchannels and Minichannels, Puebla, Mexico, 2007. [11] K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli. Int. J. Heat Mass Transf. 29 (1986) 351e358. [12] W. Yu, et al., Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int. J. Multiphase Flow 28 (2002) 927e941. [13] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiments. Mech. Eng. (January 1953) 3. [14] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, In: Advances in Heat Transfer, Suppl. 1. Academic Press, New York, 1978. [15] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, third ed. Oxford Science, 1994. [16] J.R. Thome, et al., Heat transfer model for evaporation in microchannels. Part I: presentation of the model. Int. J. Heat Mass Transf. 47 (2004) 3375e3385.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Pressure effect on flow boiling heat transfer of water in minichannels K.H. Bang a, *, K.K. Kim a, S.K. Lee a, B.W. Lee b a b
Department of Mechanical Engineering, Korea Maritime University, 1 Dongsam-dong Yeongdo-gu, Busan 606-791, Republic of Korea Department of Materials Engineering, Korea Maritime University, 1 Dongsam-dong Yeongdo-gu, Busan 606-791, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 January 2010 Received in revised form 11 March 2010 Accepted 15 March 2010 Available online 20 April 2010
The effect of pressure on the flow boiling of water in minichannels has been experimentally studied. The range of pressure was 2e16 bars in the experiment. The experimental apparatus consisted mainly of the 1.73 mm inner diameter round tube test section, gear pump, pre-heater, pressurizer, pre-evaporator, and condenser. The pre-evaporator was used for varying the vapor quality entering the test section. The pressurizer controls the desired system pressure. The test tube is made of 316 stainless steel and the test tube and the pre-evaporator tube were heated by DC electric current through the tubes. The measured flow boiling heat transfer coefficients were in the range of 10,000e35,000 W/m2 K and showed the general convection dominant trend in terms of vapor quality. The data also indicate that the pressure does not alter the heat transfer coefficient significantly. Comparisons of the experimental data to the existing correlations showed large discrepancy, implying that these correlations are not correctly accounted for pressure. A simplified annular flow model has been proposed and the model prediction shows a reasonably good agreement with the measured data. Ó 2010 Elsevier Masson SAS. All rights reserved.
Keywords: Flow boiling Minichannel Microchannel Annular flow
1. Introduction For the last several decades compact heat exchangers have shown growing interest and demand in many industrial applications such as automobile radiators, HVAC and refrigeration systems, and recently electronic equipment cooling. The interesting hydraulic diameter of the tubes and channels is continuously getting smaller and now even down to tens of micron is considered for microprocessor chip cooling. Classifying a tube or channel size as large or small seems rather vague since the heat transfer and fluid flow characteristics can be different even over the ranges of millimeter to sub-millimeter size. Recently the term “minichannel” has become a common word for tubes and channels whose hydraulic diameters are in the range of 0.3e3 mm, as proposed by Kandlikar and Balasubramanian [1]. The channel sizes over 3 mm are called conventional channel, and the channel sizes smaller than 0.3 mm are called microchannel. The main motivation of such channel size classification has come from the question that the existing knowledge of heat transfer and fluid flow, which has been documented from the data collected largely from the conventional larger size channels, can be valid for smaller channels; minichannels and microchannels. For single phase flow, the literature reporting recent work on
* Corresponding author. Tel.: þ82 51 410 4365; fax: þ82 51 405 4790. E-mail address: [email protected] (K.H. Bang). 1290-0729/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2010.03.011
microchannels including the work of present authors [2] indicates that the heat transfer and fluid flow characteristics are similar over all these three classifications of channel size. For two-phase flow boiling, however, the recent articles have reported different characteristics depending upon channel size and fluid type. The influence of the channel size in flow boiling is associated with the length scales involved; channel size and bubble size or the twophase flow patterns such as bubbly, slug and annular flow. Since early 1990s a number of experimental studies on the flow boiling heat transfer in minichannels have been reported. These include the experiments of Wambsganss et al. [3] and their coworkers Tran et al. [4] using small round and rectangular tubes of 2.4e2.9 mm inner diameter and R-12/R-113 fluids. They reported that in small tubes the evaporation heat transfer coefficients are greatly affected by the heat flux and it does not seem to be a function of vapor quality at higher heat fluxes. Bang and Choo [5] with 1.6 mm round tubes and R-22 also reported a similar trend to Wambsganss et al. [3] results such that the heat transfer coefficients are independent of vapor quality and mass flux. However, Yan and Lin [6] conducted experiments using small round tube of 2.0 mm inner diameter and R-134a refrigerant and found a trend similar to the Kandlikar [7] correlation such that the evaporation heat transfer coefficient decreases as the vapor quality increases. The major tend of flow boiling heat transfer in minichannels is that the local heat transfer coefficients are largely independent of mass flux or vapor quality, but only a function of wall heat flux. These experimental observations may indicate that the flow boiling
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
x* X We
Nomenclature Boiling number, q00 /Ghfg Convection number, ((1 x)/x)0.8 (rg/rl)0.5 diameter friction factor fluid dependent parameter for eq. (3) mass flux Graetz number, dh$Re$Pr/x heat transfer coefficient thermal conductivity pressure loss coefficient channel length Nusselt number, hd/k pressure, perimeter pressure drop Prandtl number heat input heat flux radius Reynolds number, Gd/m temperature velocity vapor quality
a d f2f m r s
void fraction liquid film thickness two-phase multiplier viscosity density surface tension
Subscripts g vapor h hydraulic i inner l liquid o outer sat saturation w wall LO liquid only NBD nucleate boiling dominant CBD convective boiling dominant
"
3000Bo0:86
Kandlikar and Balasubramanian [1]:
( h ¼
maxðhNBD ; hCBD Þ; Rel > 100 hNBD ; Rel < 100
i hNBD ¼ 0:6683Co0:2 ð1 xÞ0:8 þ1058Bo0:7 ð1 xÞ0:8 FFL hLO i h hCBD ¼ 1:136Co0:9 ð1 xÞ0:8 þ667:2Bo0:7 ð1 xÞ0:8 FFL hLO h
(3) The predictions of flow boiling of water in 1.73 mm diameter circular tube by these correlations are compared in Fig. 1 for two different pressures; 1 atm and 20 atm. The mass flux of 300 kg/m2 s in this comparison corresponds to Re ¼ 1600 at 1 atm (laminar flow) and to Re ¼ 4000 at 20 atm (turbulent flow) for both liquidonly flows. Fig. 1 shows that there are large differences between the predictions by the three correlations for both pressures. It is 50000
40000
2
in minichannels is of so-called nucleate boiling dominant regime. One notes, however, that most of the experimental work mentioned here used Freon type fluids. The work by Steinke and Kandlikar [8] and Qu and Mudawar [9] have a common in working fluid of water and in general showed a contradicting trend of heat transfer coefficient versus mass flux and heat flux to Freon cases. Convection dominant heat transfer in water system may be related to high latent heat of vaporization of water compared to hydrocarbons. The authors of this paper have been interested in flow boiling of water in minichannels and this paper is the continuing work of the article by Bang et al. [10]. Most of the information obtained in the literature for flow boiling in minichannels is the data of hydrocarbon fluids. Therefore, the first attempt was to choose three correlations of flow boiling heat transfer and to compare each prediction for water flow in minichannels at different pressures. The three correlations are Gungor and Winterton [11], Yu et al. [12], and Kandlikar and Balasubramanian [1], and are given below. The first one has been applied to conventional larger size tubes and the latter two have been tested with the data from minichannels and microchannels. It is noted that the vapor quality is not a parameter in the correlation of Yu et al. and the Kandlikar’s is basically his correlation for conventional channels with some classification for microchannels, where hLO is single phase convective heat transfer coefficient for laminar or turbulent depending on Reynolds number [7]. Gungor and Winterton [11]:
0:75 0:41 # rl x h ¼ hl 1 þ þ 1:12 rg 1x Gð1 xÞd 0:8 0:4 kl Pr l hl ¼ 0:023 ml d
dimensionless entry length, x/dh$Re$Pr Martinelli parameter Weber number, G2d/rls
Greeks
hTP (W/m K)
Bo Co d f FFL G Gz h k K L Nu P DP Pr Q q00 r Re T V x
Kandlikar (2003) Yu et al. (2002) Gungor & Winterton (1987) filled: 1 atm , open: 20 atm
30000
20000
10000
0 0.1
6:4 106
Water, D=1.73 mm 2 2 G=100 kg/m s, q"=80 kW/m
(1)
Yu et al. [12]:
h ¼
281
Bo2 We1
0:27 r l
rg
!0:2
0.2
0.3
0.4
0.5
Vapor Quality, x
(2)
Fig. 1. Comparison of flow boiling heat transfer correlations for water at pressure of 1 atm and 20 atm.
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K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
also interesting to note that the Yu et al. correlation predicts higher heat transfer coefficient for higher pressure but the other two predict in opposite trend. This observation was the motivation of the present experimental work on flow boiling of water in minichannels. 2. Experiment The design and construction of the flow boiling experiment for water at pressures from the atmospheric pressure up to 20 bars needed a special consideration of the high temperature since the saturation temperature at 20 bars is 212 C and the heating side temperature is further higher. As a heat flux source to the test tube, heating wire method has a limitation of electrical insulation material breakdown at temperature over 200 C. The Joule heating by direct DC current also requires electrically insulating tube pieces at both ends of the test tube which should withstand the high temperature and high pressure. In the present experiment, Joule heating method was chosen with PFA tube pieces at the both ends of the test tube for electrical insulation, and due to this temperature problem, the present experiment was operated up to 16 bars, although most components were designed for pressures up to 30 bars. The schematic of the experimental apparatus is shown in Fig. 2. It consists mainly of pump, pre-heater, pressurizer, evaporator, test tube, and condenser. The pump is a magnetic gear pump with variable speed and a coriolis-type flow meter is installed to measure the mass flow rate. The allowed operating temperature limit of the pump and the flow meter requires cool down of water below 90 C before entering the pump and reheat the water to the saturation temperature before the evaporator. The pre-heater is a cylindrical chamber which contains a cartridge heater to raise the water temperature to the saturation temperature of the desired operating pressure. To control the system pressure, a pressurizer is installed at the pump suction side. The pressurizer is a rectangular chamber of
which both sidewalls are made of transparent quartz plates in order to visually check the liquid water level of the loop. At the top of pressurizer is nitrogen gas tank connected to control the system pressure. To supply various vapor quality at the inlet of the test tube, an evaporator is installed before the test tube. It is a 2 m long tube of the same tube size with the test tube and heated by passing direct DC current. In the connecting part to the test tube, the same flow crosssectional area is kept to prevent two-phase flow regime change. The test tube is a 300-mm long, SS316 round tube and its inner diameter is 1.73 mm and the wall thickness is 0.72 mm. The heat flux is provided by passing direct DC current. At the both ends of the test tube a short PFA (PerFluoroAlkoxy) tube is connected to provide electrical insulation between the test tube and the rest of the loop. The temperature of the test tube wall is measured at five locations using thermocouples bonded to the outer wall using high thermal conductivity cement. The measurement error of temperature difference is within 0.2 C. The exiting two-phase water is passing the condenser which is a coiled, long tube and immersed into a constant temperature bath. The condenser capacity is designed such that the exiting liquid water temperature from the condenser is kept constant so that it helps maintaining a steady state of the system. The fluid temperature measurement at the exit of pre-heater, at the inlet of evaporator, at both the inlet and the exit of test tube, and the exit of the condenser are made by direct insertion of the thermocouples into the tube. The differential pressure across the test tube and the absolute pressure at the inlet of the test tube are measured. All the signals of flow rate, pressure and temperature are monitored and recorded using PC-based Labview system. The reduction of the measured variables to the local heat transfer coefficients is done using the equations below. One notes that the inner wall temperature is estimated from the measured outer wall temperature using the conduction heat transfer equation for round tube wall with an internal heat generation.
Fig. 2. Schematic of experimental apparatus for flow boiling in minichannels.
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
h ¼
q00 Tw;i Tsat
(4)
q00 ¼
Q Pi LH
(5)
DP ¼
rV 2 2
q00 ri ðri =ro Þ2 2 lnðri =ro Þ 1 $ 2k 1 ðri =ro Þ2
L X K f þ d
(6)
(7)
Experimental uncertainty analysis has been done with careful collection of the uncertainty in each measurement. The largest uncertainty source is found in the temperature difference between the wall and the fluid. The local saturation temperature of water is calculated using the measured pressure at the inlet and the differential pressure across the test section. The overall uncertainty analysis using an error propagation method [13] shows that the uncertainty in heat transfer coefficient is 14.8%. The summary of the uncertainty in experimental measurement is given in Table 1. 3. Results and discussions The present experiment is primarily aimed at obtaining flow boiling data of water in 1.73 mm inner-diameter minichannel. The primary experimental variables are pressure and wall heat flux. 3.1. Single phase laminar flow First, the single phase flow experiments were carried out to evaluate the measurement performance of the present experimental setup. For Reynolds number 200e2000, the measured heat transfer coefficients are shown in Fig. 3 and the measured friction factors are shown in Fig. 4. The single phase heat transfer data are compared with the analytical solution of thermally developing laminar flow. The analytical solution is written in an explicit form as [14] 0:506
Nux ¼ 4:364 þ 8:68 ð1000 x* Þ
*
e41x
(8)
The agreement between the data and equation (8) is reasonably good thus it implies that the present experimental measurement of heat transfer coefficient is in a right setup. The observation that the friction factor data well match by accuracy the 64/Re curve implies that the flow is fully-developed and the single phase laminar flow in the 1.73 mm inner-diameter tube is well described by the typical laminar flow characteristics of the regular size tubes.
Table 1 Experimental uncertainty analysis. Parameter
Uncertainty
Temperature Pressure Saturation temperature Temperature difference Flow rate Heat input Heat loss Heat flux Heat transfer coefficient
0.5 C 1% 0.5 C 0.7 C 2% 1.4% 4.5% 4.7% 14.8%
Fig. 3. Single phase laminar heat transfer measurement and comparison to Shah and London’s prediction [13].
3.2. Two-phase flow boiling heat transfer For two-phase flow boiling experiment, the data were obtained for pressures of 2 bars and 16 bars and the heat flux was varied between 50 and 160 kW/m2. The inlet vapor quality was varied by the evaporator until dry out occurred. The data collected are presented in Figs. 5 and 6. The saturation temperature of water at high pressure was as high as 201 C (16 bars) and the heat loss from the test section to the environment was sizable and cannot be neglected in the heat transfer analysis. The thermal insulation covering the test section was made heavy enough with ceramic wool but the heat loss was as high as 10% of the heat applied to the test section. In order to account for the heat loss in the wall heat flux calculation, heat losses at various wall temperatures up to 220 C were obtained from single phase runs without heat input to the test section. The temperature difference between the inlet and the outlet was used to calculate the heat loss. This measured heat loss was subtracted from the heat input of Joule heating in the test tube. For the low pressure of 2 bars, the influence of heat flux on the flow boiling heat transfer coefficient is shown in Fig. 5. The dry out
1
64 / Re Present Data
Friction Factor, f
Tw;i ¼ Tw;o
283
0.1
0.01 100
1000
Re Fig. 4. Single phase laminar friction factor measurement and comparison to fullydeveloped laminar fiction factor.
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K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286 40000
2
D=1.73 mm, 2 bars, G=100 kg/m s
2
h (W/m K)
30000
20000
2
q"=50 kW/m 2 q"=80 kW/m 2 q"=115 kW/m 2 q"=150 kW/m
10000
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
x Fig. 5. Flow boiling heat transfer coefficients of water at 2 bars.
Fig. 7. Effect of pressure on heat transfer coefficients.
occurred at about 0.6 of vapor quality. The measured flow boiling heat transfer coefficients are in the general trend of convection dominant flow boiling such that at low vapor quality the change of the heat transfer coefficient versus vapor quality is small or nearly plateau and at higher quality the heat transfer coefficient increases as the quality increases. It is interesting to observe that the higher heat flux reduces the heat transfer coefficient. For the high pressure of 16 bars as shown in Fig. 6, the heat transfer coefficients show the general convection dominant trend but the heat flux does not affect the heat transfer coefficient. The effect of pressure on heat transfer coefficient is shown in Fig. 7 in which all the data for both pressures are plotted. At present, the data for only two pressures are compared: 2 bars and 16 bars. At low vapor quality where the slug flow pattern seems to be dominant, the heat transfer coefficient is slightly higher at the higher pressure. At high vapor quality where the flow pattern is annular flow, the effect of pressure does not appear. This experimental observation of the pressure effect is much different from the predictions of the existing correlations shown in Fig. 1. The present flow boiling heat transfer data for water (Fig. 7) are compared with the predictions of the three selected correlations as shown in Figs. 8e10. First, the prediction of Gungor and Winterton correlation (Fig. 8) does not look good for both low pressure and high pressure data and this is probably because this correlation is based on the data for the conventional larger size channels.
The comparison of Yu et al. correlation (Fig. 9) shows relatively good agreement for the low pressure data, but the correlation overpredicts the high pressure data. One notes that the Yu et al. correlation is based on their own data obtained for water in 2.98 mm diameter tube and the pressure of around 2 bars and this is probably the reason for the observation in the comparison. The best prediction of lower pressure data is by Kandlikar correlation as shown in Fig. 10. This correlation has been developed based on flow boiling data for minichannels and microchannels. However, this correlation also fails to predict the high pressure data. It highly underpredicts the data for high pressure. The observed large discrepancy between the present data and the existing correlations reveals the need of fundamental understanding on flow boiling in small channels (minichannels). Among the flow boiling fundamentals the mode of nucleate boiling and the two-phase flow patterns of slug flow and annular flow seem to be the key aspects in explaining the present observations. Two-phase flow boiling in channels is characterized by two distinctive modes: nucleate boiling and convective boiling. In nucleate boiling certain amount of wall superheat is required for a bubble to be created and to grow. For a situation in which constant heat flux is applied, the increasing heat transfer coefficient reduces the wall superheat then it may suppress nucleate boiling. Such a boiling mode without bubble nucleation is called convective
Fig. 6. Flow boiling heat transfer coefficients of water at 16 bars.
Fig. 8. Comparison of present data with prediction of Gunger and Winterton correlation [11].
K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
ð1 aÞ ¼
4pdd 4d ¼ d pd2
285
(9)
Following the LockharteMartinelli approach on annular flow [15], the relationship between the two-phase multiplier and the void fraction is
f2f ¼ ð1 aÞ2
(10)
And the LockharteMartinelli correlation for the two-phase multiplier is
C X
f2f ¼ 1 þ þ
1 X2
(11)
where X is the Martinelli parameter and the constant C is 12 for the case of laminar liquid flow and turbulent vapor flow which is a typical case for flow boiling in minichannels. Yu et al. proposed an empirical expression for the Martinelli parameter. Fig. 9. Comparison of present data with prediction of Yu et al. correlation [12].
0:5 X ¼ 18:65
boiling and the convective boiling is more associated with the twophase flow pattern. 3.3. Simplified annular flow model Two-phase flow pattern in minichannel or microchannel is dominated by slug flow in low vapor quality and annular flow in high vapor quality. Thome et al. [16] proposed a three-zone flow boiling model to describe evaporation of elongated bubbles of slug flow in microchannels. Their heat transfer model describes the transient variation in local heat transfer coefficient during the sequential and cyclic passage of (i) a liquid slug, (ii) an evaporating elongated bubble and (iii) a vapor slug. Besides, however, this detailed modeling of slug bubble seems to be applicable to the very short length of entry part of heated channels since the flow quickly becomes annular as the vapor quality increases, the model is strongly dependent on empirical data such as bubble frequency. In this paper, a simplified annular flow model has been constructed to predict the flow boiling heat transfer coefficient at different pressure. In annular two-phase flow the heat transfer at the inner wall is dominated by the heat transfer across the liquid film and the prediction of liquid film thickness is the key in determining the heat transfer coefficient. For annular flow with a liquid film of thickness d,
Fig. 10. Comparison of present data with prediction of Kandlikar correlation [1].
rg rl
0:1 1 x Reg x Re0:5 l
(12)
Using equations (9)e(12), the liquid film thickness can be calculated. Since the liquid film in minichannels is typically thin, the heat transfer across the liquid film can be approximated by conduction dominant with linear temperature profile. Based on this assumption, the heat transfer coefficient can be given by
h ¼
kl
d
(13)
Using the proposed annular flow model, the flow boiling heat transfer coefficients were calculated for the present experimental conditions. The calculated liquid film thickness was 20e70 mm and the calculated heat transfer coefficients were shown in Fig. 11 together with the measured data. The calculations show that the higher pressure gives lower heat transfer coefficient and the difference becomes larger as the vapor quality increases. Also the proposed model reasonably predicts the measured data in higher vapor quality where the annular flow is obvious. At lower vapor quality where slug flow seems dominant and the contribution of nucleate boiling cannot be neglected, this annular flow model underpredicts the data. For such slug flow region a dedicated model such as Thome et al. model [16] can be used.
Fig. 11. Comparison of measured flow boiling heat transfer coefficients with the prediction of proposed model (G ¼ 100 kg/m2 s, d ¼ 1.7 mm).
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K.H. Bang et al. / International Journal of Thermal Sciences 50 (2011) 280e286
The effect of pressure in the proposed model appears as a counter-affecting between vapor density, liquid viscosity as well as liquid thermal conductivity. The higher vapor density at the higher pressure reduces the vapor velocity thus film thickness increases, resulting in suppression of heat transfer. However, lower liquid viscosity and higher liquid thermal conductivity at the higher pressure have an enhancing effect of heat transfer. The overall effect is found to be suppressing heat transfer as pressure increases. 4. Conclusion An experimental study on flow boiling of water in a minichannel of 1.73 mm inner diameter round tube has been conducted. The major objective of this study was to experimentally observe the effect of pressure on flow boiling heat transfer in minichannels. The range of pressure was 2e16 bars. The measured flow boiling heat transfer coefficients were in the range of 10,000e35,000 W/m2 K and showed the general convection dominant trend in terms of vapor quality. The data also indicate that the pressure does not alter the heat transfer coefficient significantly. Comparisons of the experimental data with the predictions of correlations (Gungor and Winterton; Yu et al.; Kandlikar) showed large discrepancy, especially for the high pressure data. Also a simplified annular flow model has been proposed and the model prediction of flow boiling heat transfer coefficient shows a reasonably good agreement with the measured data. Acknowledgments This work was supported by the National Research Foundation of Korea under BAERI program and the Korean Ministry of Knowledge Economy under ITRC program (NIPA-2009-C1090-0903-0007).
References [1] S.G. Kandlikar, P. Balasubramanian, Extending the applicability of the flow boiling correlation to low Reynolds number flows in microchannels, in: Proceedings of the 1st International Conference on Microchannels and Minichannels, Rochester, New York, April 2003. [2] K.H. Bang, T.Y. Yoon, Effect of operating pressure on flow boiling heat transfer in microchannels, in: Proceedings of the 3rd International Conference on Microchannels and Minichannels, Toronto, Canada, 2005. [3] M.W. Wambsganss, et al., Boiling heat transfer in a horizontal small-diameter tube. J. Heat Transf. 115 (1993) 963e972. [4] T.N. Tran, et al., Small circular- and rectangular-channel boiling with two refrigerants. Int. J. Multiphase Flow 22 (1996) 485e498. [5] K.H. Bang, W.H. Choo, Flow boiling in minichannels of brass, copper and aluminum round tubes, in: Proceedings of the 2nd International Conference on Microchannels and Minichannels, Rochester, USA, 2004. [6] Y.Y. Yan, T.F. Lin, Evaporation heat transfer and pressure drop of refrigerant R-134a in a small pipe. Int. J. Heat Mass Transf. 41 (1998) 4183e4194. [7] S.G. Kandlikar, A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. J. Heat Transf. 112 (1990) 219e228. [8] M.E. Steinke, S.G. Kandlikar, Flow boiling and pressure drop in parallel flow microchannels, in: Proceedings of the 1st International Conference on Microchannels and Minichannels, Rochester, 2003, pp. 567e579. [9] W. Qu, I. Mudawar, Flow boiling heat transfer in two-phase micro-channel heat sinks e I. Experimental investigation and assessment of correlation methods. Int. J. Heat Mass Transf. 46 (2003) 2755e2771. [10] K.H. Bang, et al., Flow boiling of water in minichannels: effect of pressure, in: Proceedings of the 5th International Conference on Nanochannels, Microchannels and Minichannels, Puebla, Mexico, 2007. [11] K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli. Int. J. Heat Mass Transf. 29 (1986) 351e358. [12] W. Yu, et al., Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int. J. Multiphase Flow 28 (2002) 927e941. [13] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiments. Mech. Eng. (January 1953) 3. [14] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, In: Advances in Heat Transfer, Suppl. 1. Academic Press, New York, 1978. [15] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, third ed. Oxford Science, 1994. [16] J.R. Thome, et al., Heat transfer model for evaporation in microchannels. Part I: presentation of the model. Int. J. Heat Mass Transf. 47 (2004) 3375e3385.