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Flow-pattern-based correlations for pressure drop during flow boiling of ethanol–water mixtures in a microchannel
International Journal of Heat and Mass Transfer 61 (2013) 332–339
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Flow-pattern-based correlations for pressure drop during flow boiling of ethanol–water mixtures in a microchannel Ben-Ran Fu a, Meng-Shan Tsou a, Chin Pan a,b,c,⇑ a
Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC c Low Carbon Energy Research Center, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC b
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 1 February 2013 Accepted 3 February 2013 Available online 5 March 2013 Keywords: Flow-pattern-based correlation Pressure drop Flow boiling Mixtures
a b s t r a c t This paper constitutes an experimental investigation into the pressure drop during flow boiling of ethanol–water mixtures in a diverging microchannel with artificial cavities. Similar to boiling curves, the experimental results reveal that the single-phase and boiling two-phase flow pressure drops are significantly influenced by the molar fraction. The single-phase pressure drop for water demonstrates the smallest as the water viscosity is smaller than that of ethanol–water mixtures. During flow boiling, in general, two-phase flow pressure drop at a given wall superheat for the mixture with molar fraction of 0.1 is the highest, due to the higher boiling heat flux resulted from the Marangoni effect. Based on the correlation development of boiling heat transfer coefficient in the previous study, two flow-patternbased empirical correlations for the two-phase frictional pressure drop are proposed in the terms of nondimensional parameters, such as boiling number, Weber number, and Marangoni number. The proposed correlations are similar to the empirical correlation for boiling heat transfer coefficient with different numerical values of the coefficients and exponents. Different values of flow-pattern-based constant are obtained for different flow patterns. The constants for annular flow and liquid film breakup are the same. It may be due to the major mechanism of the two-phase flow is liquid film evaporation for these two flow types. The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively. More than 90% of the experimental data can be predicted within a ±25% error band. Such an excellent agreement confirms that the proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Boiling of multi-component mixture is of importance and interest for many applications such as in chemical engineering, in process industries, and for refrigeration systems. Studies on pool boiling of mixtures are widely available in the literature. For example, some up-to-date studies on pool boiling of mixtures are reported by Inoue and Monde [1], Sathyabhama and Ashok Babu [2], Peyghambarzadeh et al. [3], and Sarafraz and his co-workers [4–7]. In addition, there are also many studies on flow boiling of mixtures, mostly mixed refrigerants, in small channels [8–17]. However, there are few researches on flow boiling of mixtures in a microchannel. The flow boiling characteristics of multi-
⇑ Corresponding author at: Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC. Tel.: +886 3 571 5131x34320; fax: +886 3 572 0724. E-mail addresses: [email protected] (B.-R. Fu), [email protected] (C. Pan). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.02.012
component mixture in a microchannel are more complicated than that of pure component. The concentration of mixtures is expected as one of the most important factors during boiling process. In Lin et al. [18], the convective boiling heat transfer and critical heat flux (CHF) of methanol–water mixtures in a diverging microchannel with artificial cavities was investigated. They found that at the same mass flux, the CHF increases slightly as the molar fraction (xm) ranges from 0 (pure water) to 0.3 (methanol–water mixtures) and then decreases as the molar fraction ranges from 0.3 to 1 (pure methanol). The maximum CHF is reached at a molar fraction of 0.3, especially for the highest mass flux (G) of 175 kg/m2 s, owing to the Marangoni effect. A mechanism of Marangoni effect is due to differences in surface tension and may induce an additional liquid restoring force to the three-phase contact line [19]. The flow pattern of liquid film breakup at the molar fraction of 0.3 persists up to a higher heat flux than that at other molar fractions. The Marangoni effect drives the liquid flow toward the contact line, resulting in a higher heat flux and a higher critical heat flux. An empirical CHF correlation, involving the Marangoni number, for flow boiling of binary mixtures has been proposed as follows [18]:
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Nomenclature total heated area of the channel (m2) boiling number (–) contraction coefficient (–) flow-pattern-based constant in the corresponding equation, i = 0, 1, 2, 3 (–) mean hydraulic diameter (m) friction factor (–) mass flux (kg/m2 s) gravitational acceleration (m/s2) heat transfer coefficient (kW/m2 K) latent heat of vaporization (kJ/kg) channel length (m) Marangoni number (–) total mass flow rate (kg/s) Prandtl number (–) heat flux (kW/m2) Reynolds number (–) temperature (K) liquid kinematic viscosity (m2/s) channel width (m) Weber number based on the hydraulic diameter (–) Lockhart–Martinelli parameter (–) quality (–) molar fraction of the more volatile component in the liquid phase (–)
Ah Bo Cc Ci Dh f G g h hlv L Ma m Pr q00 Re T
vl W WeD X2 x xm
c k
q r Dhsub, Dr DP DTsat
in
contraction or expansion area ratio (–) aspect ratio (–) density (kg/m3) surface tension (N/m) enthalpy change corresponding to the inlet subcooling (kJ/kg) difference in surface tension between fluid at the dew point and bubble point (N/m) pressure drop (kPa) wall superheat (K)
Subscripts a acceleration CHF critical heat flux f frictional h homogeneous in channel inlet l liquid max maximum out channel out sat saturation sp single-phase tot total tp two-phase v vapor w wall
Greek symbols a void fraction (–) b divergence angle of a channel (°)
q00CHF ¼ 0:00216Ghlv We0:078 1 0:44 D
Ma jMamax j
1 ð1Þ
where hlv is the latent heat of the vaporization, WeD = (G2Dh)/(rql) is the Weber number based on the hydraulic diameter of the channel (Dh), and Ma is the Marangoni number, defined by Fujita and Bai [19] as:
Ma ¼
Dr
r
ql v 2l gðql qv Þ
1=2 Pr
ð2Þ
here Dr is the difference in the fluid surface tension between the dew point and the bubble point, r is the surface tension of the fluid, ql is the liquid density, qv is the vapor density, vl is the liquid kinematic viscosity, g is the gravitational acceleration, and Pr is the Prandtl number. Recently, Fu et al. [20], a follow up study of Lin et al. [18], reported the visualization of flow boiling of binary mixtures (methanol–water and ethanol–water mixtures) in a microchannel. Four boiling regimes were reported: bubbly-elongated slug flow, annular flow, liquid film breakup, and dryout. The flow visualization results demonstrated that liquid film breakup persists up to the highest heat flux at molar fractions of 0.3 and 0.1 for the methanol–water and ethanol–water mixtures, respectively. This is because the Marangoni effect is most significant at these particular molar fractions. They also constructed flow pattern maps in the plane of heat flux versus molar fraction of methanol or ethanol. A significant effect of the molar fraction on the evolution of the two-phase flow pattern is observed, especially in the liquid film breakup regime. In addition, generalized flow pattern maps are constructed using coordinates of nondimensional parameter space (boiling number, Weber number, and Marangoni number), wherein relatively distinct boundaries between the flow patterns are identified. Consequently, they further proposed transition criteria
between flow patterns in the form of nondimensional groups as follows:
Bo 1 0:44
Ma ¼ C 1 WeCD2 jMamax j
ð3Þ
where C1 and C2 are flow-pattern-based constants, and Bo = q00 /(Ghlv) is the boiling number. The boundary between liquid film breakup and dryout is consistent with the correlation for the CHF of binary mixtures, i.e., Eq. (1). Fu et al. [21], further complementary to studies of Lin et al. [18] and Fu et al. [20], investigated experimentally the convective boiling heat transfer and the critical heat flux of ethanol–water mixtures in a diverging microchannel. The CHF data in their study show an excellent agreement and demonstrate a consistent trend with an empirical correlation for the CHF prediction, i.e., Eq. (1), proposed by Lin et al. [18]. They also reported that the two-phase heat transfer coefficient is much higher than that of single-phase convection region and is significantly affected by the wall superheat and the molar fraction. The two-phase heat transfer coefficient reaches a maximum in the region of the bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. Furthermore, they proposed a flow-pattern-based empirical correlation for the two-phase heat transfer coefficient (htp) of flow boiling of ethanol–water mixtures as follows:
htp ¼ C 3 Bo0:27 We0:67 1 0:44 D
Ma jMamax j
0:84
hsp
ð4Þ
where C3 is a flow-pattern-based constant and hsp is the singlephase heat transfer coefficient.
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Besides boiling heat transfer, critical heat flux, two-phase flow pattern, flow pattern maps, and transition criteria between flow patterns during flow boiling of mixtures in a microchannel, it is also of critical concern to understand the characteristics of the pressure drop across the microchannel. Recently, the pressure drop during flow boiling of pure component in a microchannel were investigated extensively, such as Hsieh and Lin [22], Harirchian and Garimella [23], Kim and Mudawar [24], Maqbool et al. [25], and Kaew-On et al. [26]. Some pressure drop correlations for microchannel flow boiling have also been proposed in those studies. Comprehensive discussions on prediction of pressure drop of flow boiling in a microchannel are available in [27]. However, few studies focus on pressure drop during flow boiling of mixtures in a mini or micro channel. For example, Táboas et al. [14] investigated the pressure drop of ammonia/water mixtures in a plate heat exchanger. They found that two-phase frictional pressure drop may be estimated by the Chisholm model with modified value of the Chisholm constant of 3. Dawidowicz and Cies´lin´ski [15] presented the two-phase flow pressure drop during flow boiling of pure refrigerants and refrigerant/oil mixtures in a tube with inner diameter of 8.8 mm and porous coating. Influence of oil mass fraction on pressure drop for flow boiling of R107C/oil mixtures was demonstrated. Li et al. [16] reported the pressure drop of flow boiling of HFO1234y and R32 refrigerant mixtures in a tube with inner diameter of 2 mm. They indicated that the two-phase flow pressure drop of the mixtures can be predicted by the Lockhart– Martinelli correlation. Although the two-phase flow pressure drop were reported in [15,16], only two mass fractions of the mixtures were tested. In addition, no correlation involving the concentration effect for two-phase flow pressure drop during flow boiling of mixtures in a microchannel was proposed. In light of the issues mentioned above, the present study, a follow up study of Fu et al. [20,21], presents the pressure drop during flow boiling of ethanol–water mixtures, with a full range of molar fractions, i.e., from 0 (pure water) to 1 (pure ethanol), in a microchannel. The two-phase heat transfer coefficient has close
relationship with the two-phase flow pressure drop, as suggested by the presence of Lockhart–Martinelli parameter (X2), which is resulted from the two-phase flow pressure drop, in many classical correlations for two-phase heat transfer coefficient of convective boiling in a microchannel. Consequently, based on the correlation development of boiling heat transfer coefficient [21], flowpattern-based empirical correlations involving the concentration effect (also Marangoni effect) for the two-phase frictional pressure drop are proposed.
2. Experimental details The experimental setup, shown in Fig. 1, is the same as that employed in Fu et al. [21], consisting of a high-performance liquid chromatography (HPLC) pump (HPG-3200P, Dionex), pressure transducer (model 692, Huba Control UK), flow visualization system, data acquisition system (MX100, YOKOGAWA), test section, and heating module. The HPLC pump provided forced flow of the working fluids in the microchannel with accurate and stable mass flow rates. Moreover, the exhausted fluids from the test section were drained into a container placed on an electronic balance, which provided a calibration of flow rate. The pressure taps were located near the inlet and outlet chambers at the connecting glass tube. The differential pressure transducer used in the present study had a short response time of 0.005 s; the sampling rate for the pressure measurement was set at 100 Hz. Flow visualization was conducted using a high-speed digital camera (MotionPro X4 Plus, IDT) with a microlens (Zoom 125C, OPTEM), 250-W illuminator (FOI-250, TECHNIQUIP), monitor, and personal computer. To capture the rapidly changing flow pattern, the typical frame rate and exposure time were set at 5000 frames/s and 50 ls, respectively. The data acquisition system, connected to the personal computer, recorded signals from five T-type thermocouples and a differential pressure transducer. The present study employed ethanol–water mixtures as the working fluid. Seven molar fractions (xm = 0, 0.1,
Fig. 1. Experimental setup.
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0.2, 0.5, 0.7, 0.89, and 1) of ethanol–water mixtures at a given mass flux of 175 kg/m2 s were tested. Here, molar fractions of 0 and 1 are referred to as pure water and ethanol, respectively. The detailed phase diagram, surface tension, and Marangoni parameter of ethanol–water mixtures as a function of ethanol molar fraction can be retrieved in Fu et al. [21]. Fig. 2 illustrates the test module, including the test section and heating module. Fig. 2(a) shows a single channel with a divergence angle of b, i.e., half of the included angle. Fig. 2(a) also illustrates 24 artificial cavities distributed throughout the bottom wall of the microchannel, with a uniform spacing of 1 mm. These artificial cavities are laser-drilled pits with mouth diameters of about 20 lm. A silicon strip with a dimension of 40 mm 10 mm is used as a test section for a single diverging microchannel, as shown in Fig. 2(b). The length and depth of the channel are 25 mm and 85 lm, respectively. The width of the diverging microchannel varies linearly from 215 lm (Win) to 1085 lm (Wout), resulting in a divergence angle of 1° and a mean hydraulic diameter of 147 lm. The test section were prepared by microfabrication via silicon dry etching on SOI (silicon on insulator) wafer, which may provide uniform channel depth through the etching stop mechanism at the box layer of
335
the SOI wafer, laser direct writing for micromachining of through holes and artificial cavities, and anodic bonding with Pyrex 7740 glass for flow visualization. The detailed processes of microfabrication are given in [28]. Fig. 2(c) illustrates that two thermocouples are placed at the inlet and outlet chambers, and that three thermocouples are embedded 2 mm under the heating surface to measure the wall temperature distribution along the microchannel. The interval between the two neighbouring thermocouples is 5 mm. The experimental results demonstrate that the differences between these three temperatures are within 1.2 K. The wall temperature of the microchannels could be obtained by evaluating the total thermal resistance from the location of the thermocouple to the bottom wall of the microchannel. For energy conservation, the total heat input must be balanced with the heating power applied to the microchannel and with heat losses via different paths, e.g., heat loss from the glass surface due to natural air convection; radiation heat loss; sensible heat loss to the inlet chamber due to axial conduction of the test section; and other unknown heat losses, including sensible and latent heat losses to the exit chamber and possible latent heat loss to the inlet chamber. In general, the heat loss decreases with increasing the
Fig. 2. Schematic of the test module: (a) geometry of the microchannel, (b) top view, and (c) cross-section of the test section (not to scale).
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heating power and/or mass flux [21]. The main heat loss is that to the inlet and outlet chambers owing to axial conduction. The channel wall heat flux can be obtained by dividing the channel power by the total area of the bottom and the two sidewalls. The detailed procedure for the evaluation of various heat losses has been presented in Lee et al. [29]. The measurement uncertainty in the volume flow rate for the microchannels after calibration was estimated at ±3%. The uncertainties in the temperature measurements were ±0.2 K for T-type thermocouples. The uncertainty in the pressure transducer measurements was ±1%. The average overall uncertainty for the wall heat flux under flow boiling was ±4.5%. The uncertainty for the heat flux generally decreases with an increase in the heat flux and/or mass flux. 3. Data reduction As stated in the previous section of the experimental setup, taps of the pressure differential transducer are located near the inlet or outlet chamber and, therefore, the pressure drop measured could be considered as the pressure drop between the inlet and outlet chambers. The total pressure drop (DPtot), which is composed of frictional pressure drop (DPf), acceleration pressure drop (DPa), and pressure drop of the contributions of the inlet contraction (DPin) and outlet expansion (DPout), can be expressed as follows:
DPtot ¼ DPf þ DP a þ DPin þ DPout
ð5Þ
where the pressure drop due to acceleration, inlet contraction, and outlet expansion can be estimated by the following equations [30]:
DP a ¼
" G2 x2
qv a
G2 DPin ¼ 2q l
DPout
þ
G2 ð1 xÞ2 ql ð1 aÞ
"
1 1 Cc
2
#
" G 2 x2
qv a
out
þ
G2 ð1 xÞ2 ql ð1 aÞ
# ð6Þ in
# ql þ ð1 c Þ 1 þ xin 1 2
qv
" # G2 cð1 cÞ ð1 xout Þ2 ql x2out ¼ þ ql 1 aout qv aout
ð7Þ
ð8Þ
Here, Cc is the contraction coefficient, and Cc = 1 is used in the present study, based on the reports in [24,31]; c is the contraction or expansion area ratio; and aout is the void fraction at the channel outlet, which can be determined by the following correlation [32]:
aout ¼
0:03a0:5 h 1 0:97a0:5 h
ð9Þ
where ah is the homogeneous void fraction. xin and xout are qualities at the channel inlet and outlet, respectively. In the present study, xin = 0 because the working fluid at the channel inlet is subcooled liquid, and xout can be determined as follows:
xout ¼
q00 Ah Dhsub;in mhlv h lv
ð10Þ
where Ah is the total heated area of the channel, m is the total mass flow rate, and Dhsub,in is the enthalpy change corresponding to the inlet subcooling.
Fig. 3. Boiling curves for ethanol–water mixtures as a function of ethanol molar fraction at G = 175 kg/m2 s [21].
fraction on boiling curve. For the single-phase convection region, the heat flux increases with a decrease in the molar fraction at a given wall superheat. The heat flux of pure water is always greater than that of pure ethanol. This is primarily due to the differences in the thermophysical properties between water and ethanol. Water has much larger latent heat of evaporation and surface tension than ethanol. After boiling incipience (two-phase flow region), the heat flux increases rapidly with increasing the wall superheat until approaching the CHF condition. The figure indicates the presence of boiling hysteresis for certain mixture with certain molar fractions. The boiling curve for xm = 0.1 appears to have the highest heat flux for DTsat > 10 K. More detailed discussions on the boiling heat transfer and critical heat flux have been reported in Fu et al. [21]. Moreover, pool boiling studies in the literature, e.g., Peyghambarzadeh et al. [33] also demonstrated such heat transfer enhancement at very low concentration of second component. 4.2. Two-phase flow pattern Fig. 4 illustrates typically the total pressure drop as a function of wall heat flux for the mixtures with xm = 0.1. Four typical flow patterns can also be indentified in the figure, namely: (a) bubbly-elongated slug flow, (b) annular flow, (c) liquid film breakup, and (d) dry-out. Under the conditions of relatively low heat flux, bubbles nucleated and grow rapidly becoming an elongated slug bubble, named bubbly-elongated slug flow; for medium to high heat fluxes, the bubbly-elongated slug flow evolves to the annular flow, especially in the region near the exit; further increasing the heat flux, breakup in the liquid film appears and the flow pattern is referred to as liquid film breakup. More detailed discussions on twophase flow patterns, flow pattern maps, and the criteria for transitions between flow patterns have been presented in Fu et al. [20]. Fig. 4 demonstrates that the slope of two-phase flow pressure drop increases with the evolution of flow pattern from bubbly-elongated slug flow to dry-out. The pressure drop increases sharply from the latter stage of liquid film breakup to the occurrence of dry-out.
4. Results and discussion 4.3. Pressure drop 4.1. Boiling curve Fig. 3 illustrates the heat flux (q00 ) as a function of wall superheat (DTsat = Tw Tsat) at different molar fractions of ethanol for G = 175 kg/m2 s [21]. There is a significant effect of the molar
Fig. 5 shows the total pressure drop as a function of wall superheat at different molar fractions during experiments. Similar to boiling curves [21], as one may expect, Fig. 5 clearly demonstrates the significant effects of the molar fraction on the pressure drop. In
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fraction in the channel for both pure water and mixture with xm = 0.1 is higher than the mixture with other concentrations. Fig. 6 further depicts the various components of two-phase flow pressure drop as a function of heat flux for xm = 0.1. The figure demonstrates that frictional pressure drop is most dominant; the acceleration pressure drop contributes about 5–15% of the total pressure drop; and the inlet and outlet pressure losses due to sudden area change are very small. For the present study, the inlet contraction pressure drop is negligible small (<0.2 kPa) and the maximum value of outlet expansion pressure drop is only about 1.5% of the total pressure drop. The much smaller contribution of the acceleration pressure drop than the frictional one demonstrates the merit of diverging cross-sectional design. To improve the representation of the present results and based on the correlation development of boiling heat transfer coefficient [21], i.e., Eq. (4), a flow-pattern-based empirical correlation for the two-phase flow pressure drop during flow boiling of ethanol– water mixtures is established and expressed as follows:
DPf ;tp ¼ C 0 Bo1:58 We0:57 1 0:44 D
0:86 Ma DPf ;sp jMamax j
ð11Þ
the single-phase convection region, the pressure drop decreases with an increase in the wall superheat (also heat flux, as demonstrated earlier in Fig. 4) due to the decrease in the liquid viscosity with temperature (or heat flux). The pressure drop for pure water is the smallest due to the smaller viscosity of pure water than that of ethanol–water mixtures. During flow boiling, the pressure drop increases rapidly with a further increase in the wall superheat. This is because the void fraction generally increases with an increase in the temperature, which results in an increase in both acceleration and frictional pressure drops. In general, Fig. 5 indicates that the two-phase flow pressure drops for pure water and the mixture with xm = 0.1 are greater than that of other mixtures at a given wall superheat. This is because the higher boiling heat flux and so void
where C0 is a flow-pattern-based constant, DPf,tp is the two-phase frictional pressure drop, and DPf,sp is the saturated single-phase frictional pressure drop, which is estimated based on the results of the present experiments, i.e., single-phase frictional pressure drop corresponding to DTsat = 0 K. The proposed correlation is similar to the empirical correlation for boiling heat transfer coefficient, i.e., Eq. (4), with different numerical values of the coefficients and exponents. In particular, the exponent for the boiling number is positive, suggesting the positive correlation of pressure drop with heat flux as one may expect, in the proposed correction, while it is negative for boiling heat transfer coefficient. For the present study, different values of C0 are obtained for different flow patterns: C0 = 56,500 for bubbly-elongated slug flow, C0 = 33,400 for annular flow and liquid film breakup, and C0 = 40,000 for dry-out region. It is interesting to note that the constants for annular flow and liquid film breakup are the same. Indeed, in the proposed flow-pattern-based empirical correlation for the two-phase heat transfer coefficient, the constants (C3) for annular flow and liquid film breakup are also the same. It may be due to the major mechanism of the two-phase flow is liquid film evaporation for these two flow types.
Fig. 5. Pressure drop during flow boiling of ethanol–water mixtures as a function of ethanol molar fraction at G = 175 kg/m2 s.
Fig. 6. The various components of two-phase flow pressure drop as a function of heat flux for xm = 0.1.
Fig. 4. Typical two-phase flow patterns in the coordinates of pressure drop and heat flux. The images of two-phase flow patterns are from Fu et al. [21].
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In case the saturated single-phase frictional pressure drop is unavailable from the experiments, one may use the following conventional equations [34] to estimate it:
DPf ;sp ¼ f
L 1 G2 Dh 2 ql
ð12Þ
and f¼
96 1 1:3553k þ 1:9467k2 1:7012k3 þ 0:9564k4 0:2537k5 Re
ð13Þ
where f is the friction factor, L is the channel length, Re is the Reynolds number, and k is the aspect ratio (depth-to-width ratio) and must be less than 1. If k > 1, the inverse value of k should be employed. For the present study using the diverging microchannel, the mean values of the aspect ratio and the Reynolds number are used. In addition, while using Eqs. (12) and (13) to obtain DPf,sp, the proposed correlation, Eq. (11), should be slightly modified as:
DPf ;tp ¼ C 0 Bo1:56 We0:86 1 0:44 D
Ma jMamax j
0:87
DPf ;sp
ð14Þ
Fig. 7. Comparison of the experimental data and predicted results of Eq. (11).
where C0 = 57,800 for bubbly-elongated slug flow, C0 = 34,300 for annular flow and liquid film breakup, and C0 = 43,100 for dry-out region. Figs. 7 and 8 further compare the predictions of the proposed correlations, i.e., Eqs. (11)–(14), with experimental data, respectively. The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively. More than 90% of the experimental data can be predicted within a ±25% error band. The present correlation predictions show excellent agreement with the experimental data and further confirm that the proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel, and may be applied to predict the two-phase flow pressure drop for other binary mixtures. 4.4. Summary of correlations The correlation for two-phase frictional pressure drop in the present study is based on the nondimensional parameters, such as boiling number, Weber number, and Marangoni number. These nondimensional parameters were also employed in previous studies of Fu et al. for critical heat flux [18], transition criteria between flow patterns [20], and two-phase heat transfer coefficient [21]. To illustrate the similarity and difference between two-phase heat transfer and fluid flow, Table 1 summarizes all these four correlations. It should be mentioned that for employing those proposed correlations more easily, the properties are taken at the condition of the channel outlet during developing the correlations. In
Fig. 8. Comparison of the experimental data and predicted results of Eq. (14).
addition, those correlations can also be used to predict the pure component by straight simplifying the term of (1 0.44Ma/ |Mamax|) to 1 because of Ma = 0 for pure component, as which have been verified by comparison with data of xm = 0 (water) and 1 (ethanol). Comparing the correlations between two-phase heat transfer coefficient and two-phase frictional pressure drop, it is clearly found that the exponents for the Weber number are all negative, while the exponents for the boiling number and
Table 1 Summary of the proposed correlations for flow boiling of ethanol–water mixtures in a microchannel. Correlation (Authors)
Proposed correlation
Value of flow-pattern-based constants (Ci)
Critical heat flux (Lin et al. [18]) Transition criteria between flow patterns (Fu et al. [20])
1 q00CHF ¼ 0:00216Ghlv We0:078 1 0:44 jMaMa D max j Bo 1 0:44 jMaMa ¼ C 1 WeCD2 max j
(N/A)
Two-phase heat transfer coefficient (Fu et al. [21]) Two-phase flow pressure drop (Present study)
0:84 0:67 htp ¼ C 3 Bo0:27 WeD 1 0:44 jMaMa hsp max j (i) based on experimental value of DPf,sp 0:86 DP f ;tp ¼ C 0 Bo1:58 We0:57 1 0:44 jMaMa DP f ;sp D max j (ii) based on theoretical value of DPf,sp 0:87 DP f ;tp ¼ C 0 Bo1:56 We0:86 1 0:44 jMaMa DP f ;sp D max j
C1 = 2.97 104 and C2 = 0.20 (single-phase flow to bubbly-elongated slug flow) C1 = 8.65 104 and C2 = 0.16 (bubbly-elongated slug flow to annular flow) C1 = 1.49 103 and C2 = 0.12 (annular flow to liquid film breakup) C1 = 2.16 103 and C2 = 0.078 (liquid film breakup to dry-out) C3 = 0.668 (bubbly-elongated slug flow) C3 = 0.887 (annular flow) C3 = 0.887 (liquid film breakup) C3 = 0.481 (dry-out) C0 = 56,500 (bubbly-elongated slug flow) C0 = 33,400 (annular flow) C0 = 33,400 (liquid film breakup) C0 = 40,000 (dry-out) C0 = 57,800 (bubbly-elongated slug flow) C0 = 34,300 (annular flow) C0 = 34,300 (liquid film breakup) C0 = 43,100 (dry-out)
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(1 0.44Ma/|Mamax|) are negative for two-phase heat transfer coefficient and positive for two-phase frictional pressure drop. The different trend of heat flux and wall superheat on the twophase frictional pressure drop should be noticed. 5. Summary and conclusions This paper, an extended work of Fu et al. [20,21], investigates the pressure drop during flow boiling of ethanol–water mixtures in a diverging microchannel with artificial cavities. Experimental results show that pressure drops for both single-phase and boiling two-phase flow are significantly influenced by the molar fraction. For single-phase convection regions, the pressure drop decreases with increasing wall superheat (also heat flux) due to the decrease in the liquid viscosity. The pressure drop for water is the smallest due to the smaller viscosity than that of other mixtures. During flow boiling, the pressure drop increases rapidly with a further increase in the wall superheat. Two-phase flow pressure drop for the mixture with xm = 0.1 is the highest generally at a given wall superheat, due to the higher boiling heat flux. Two flow-pattern-based empirical correlations based on experimental or theoretical saturated single-phase frictional pressure drop, respectively, for the two-phase frictional pressure drop during flow boiling of ethanol–water mixtures are proposed and expressed in the form of nondimensional numbers (boiling number, Weber number, and Marangoni number). The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively, and more than 90% of the experimental data can be predicted within a ±25% error band. The proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel, and may be applied to predict the two-phase flow pressure drop for other binary mixtures. Acknowledgements This work was supported by the National Science Council of Taiwan under the contract No. NSC 97-2221-E-007-126-MY3. References [1] T. Inoue, M. Monde, Enhancement of nucleate pool boiling heat transfer in ammonia/water mixtures with a surface-active agent, Int. J. Heat Mass Transfer 55 (2012) 3395–3399. [2] A. Sathyabhama, T.P. Ashok Babu, Experimental investigation in pool boiling heat transfer of ammonia/water mixture and heat transfer correlations, Int. J. Heat Fluid Flow 32 (2011) 719–729. [3] S.M. Peyghambarzadeh, M. Jamialahmadi, S.A. Alavi Fazel, S. Azizi, Saturated nucleate boiling to binary and ternary mixtures on horizontal cylinder, Exp. Therm. Fluid Sci. 33 (2009) 903–911. [4] M.M. Sarafraz, S.M. Peyghambarzadeh, S.A. Alavi Fazel, Enhancement of nucleate pool boiling heat transfer to dilute binary mixtures using endothermic chemical reactions around the smoothed horizontal cylinder, Heat Mass Transfer 48 (2012) 1755–1765. [5] M.M. Sarafraz, S.M. Peyghambarzadeh, Influence of thermodynamic models on the prediction of pool boiling heat transfer coefficient of dilute binary mixtures, Int. Commun. Heat Mass Transfer 39 (2012) 1303–1310. [6] M.M. Sarafraz, S.A. Alavi Fazel, Y. Hasanzadeh, A. Arabshamsabadi, S. Bahram, Development of a new correlation for estimating pool boiling heat transfer coefficient of MEG/DEG/water ternary mixture, Chem. Ind. Chem. Eng. Q. 18 (2012) 11–18. [7] M.M. Sarafraz, Nucleate pool boiling of aqueous solution of citric acid on a smoothed horizontal cylinder, Heat Mass Transfer 48 (2012) 611–619.
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[8] A. Greco, Convective boiling of pure and mixed refrigerants: an experimental study of the major parameters affecting heat transfer, Int. J. Heat Mass Transfer 51 (2008) 896–909. [9] B. Raja, D. Mohan Lal, R. Saravanan, Flow boiling heat transfer coefficient of R134a/R-290/R-600a mixture in smooth horizontal tubes using varied heat flux method, Appl. Therm. Eng. 29 (2009) 1778–1785. [10] B. Raja, D. Mohan Lal, R. Saravanan, Stratified flow boiling heat transfer study of a HFC/HC refrigerant mixture in smooth horizontal tubes, Heat Mass Transfer 46 (2010) 323–331. [11] H.T. Hu, G.L. Ding, W.J. Wei, X.C. Huang, Z. Wang, Heat transfer characteristics of refrigerant–oil mixtures flow boiling in a horizontal C-shape curved smooth tube, Int. J. Refrig. 33 (2010) 932–943. [12] X. Zou, M.Q. Gong, G.F. Chen, Z.H. Sun, Y. Zhang, J.F. Wu, Experimental study on saturated flow boiling heat transfer of R170/R290 mixtures in a horizontal tube, Int. J. Refrig. 33 (2010) 371–380. [13] F. Táboas, M. Vallès, M. Bourouis, A. Coronas, Flow boiling heat transfer of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 33 (2010) 695–705. [14] F. Táboas, M. Vallès, M. Bourouis, A. Coronas, Assessment of boiling heat transfer and pressure drop correlations of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 35 (2012) 633–644. [15] B. Dawidowicz, J.T. Cies´lin´ski, Heat transfer and pressure drop during flow boiling of pure refrigerants and refrigerant/oil mixtures in tube with porous coating, Int. J. Heat Mass Transfer 55 (2012) 2549–2558. [16] M. Li, C. Dang, E. Hihara, Flow boiling heat transfer of HFO1234yf and R32 refrigerant mixtures in a smooth horizontal tube. Part I experimental investigation, Int. J. Heat Mass Transfer 55 (2012) 3437–3446. [17] M.M. Sarafraz, S.M. Peyghambarzadeh, N. Vaeli, Subcooled flow boiling heat transfer of ethanol aqueous solutions in vertical annulus space, Chem. Ind. Chem. Eng. Q. 18 (2012) 315–327. [18] P.H. Lin, B.R. Fu, Chin Pan, Critical heat flux on flow boiling of methanol–water mixtures in a diverging microchannel with artificial cavities, Int. J. Heat Mass Transfer 54 (2011) 3156–3166. [19] Y. Fujita, Q. Bai, Critical heat flux of binary mixtures in pool boiling and its correlation in terms of Marangoni number, Int. J. Refrig. 20 (1997) 616–622. [20] B.R. Fu, P.H. Lin, M.S. Tsou, Chin Pan, Flow pattern maps and transition criteria for flow boiling of binary mixtures in a diverging microchannel, Int. J. Heat Mass Transfer 55 (2012) 1754–1763. [21] B.R. Fu, M.S. Tsou, Chin Pan, Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities, Int. J. Heat Mass Transfer 55 (2012) 1807–1814. [22] S.S. Hsieh, C.Y. Lin, Correlation of critical heat flux and two-phase friction factor for subcooled convective boiling in structured surface microchannels, Int. J. Heat Mass Transfer 55 (2012) 32–42. [23] T. Harirchian, S.V. Garimella, Flow regime-based modeling of heat transfer and pressure drop in microchannel flow boiling, Int. J. Heat Mass Transfer 55 (2012) 1246–1260. [24] S.M. Kim, I. Mudawar, Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks, Int. J. Heat Mass Transfer 55 (2012) 3720–3731. [25] M.H. Maqbool, B. Palm, R. Khodabandeh, Flow boiling of ammonia in vertical small diameter tubes: two phase frictional pressure drop results and assessment of prediction methods, Int. J. Therm. Sci. 54 (2012) 1–12. [26] J. Kaew-On, K. Sakamatapan, S. Wongwises, Flow boiling pressure drop of R134a in the counter flow multiport minichannel heat exchangers, Exp. Therm. Fluid Sci. 36 (2012) 107–117. [27] I. Mudawar, Two-phase microchannel heat sinks: theory, applications, and limitations, J. Electron. Packag. Trans. ASME 133 (2011) 041002. [28] P.C. Lee, Chin Pan, Boiling heat transfer and two-phase flow of water in a single shallow microchannel with a uniform or diverging cross section, J. Micromech. Microeng. 18 (2008) 025005. [29] P.C. Lee, F.G. Tseng, Chin Pan, Bubble dynamics in microchannels. Part I: single microchannel, Int. J. Heat Mass Transfer 47 (2004) 5575–5589. [30] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, 3rd ed., Oxford University Press, New York, NY, 1994. [31] F.F. Abdelall, G. Hahn, S.M. Ghiaasiaan, S.I. Abdel-Khalik, S.S. Jeter, M. Yoda, D.L. Sadowski, Pressure drop caused by abrupt flow area changes in small channels, Exp. Therm. Fluid Sci. 29 (2005) 425–434. [32] A. Kawahara, P.M.Y. Chung, M. Kawaji, Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel, Int. J. Multiphase Flow 28 (2002) 1411–1435. [33] S.M. Peyghambarzadeh, M. Jamialahmadi, S.A. Alavi Fazel, S. Azizi, Experimental and theoretical study of pool boiling heat transfer to amine solutions, Braz. J. Chem. Eng. 26 (2009) 33–43. [34] J.P. Hartnett, M. Kostic, Heat transfer to Newtonian and non-Newtonian fluids in rectangular ducts, Adv. Heat Transfer 19 (1989) 247–356.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Flow-pattern-based correlations for pressure drop during flow boiling of ethanol–water mixtures in a microchannel Ben-Ran Fu a, Meng-Shan Tsou a, Chin Pan a,b,c,⇑ a
Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC c Low Carbon Energy Research Center, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC b
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 1 February 2013 Accepted 3 February 2013 Available online 5 March 2013 Keywords: Flow-pattern-based correlation Pressure drop Flow boiling Mixtures
a b s t r a c t This paper constitutes an experimental investigation into the pressure drop during flow boiling of ethanol–water mixtures in a diverging microchannel with artificial cavities. Similar to boiling curves, the experimental results reveal that the single-phase and boiling two-phase flow pressure drops are significantly influenced by the molar fraction. The single-phase pressure drop for water demonstrates the smallest as the water viscosity is smaller than that of ethanol–water mixtures. During flow boiling, in general, two-phase flow pressure drop at a given wall superheat for the mixture with molar fraction of 0.1 is the highest, due to the higher boiling heat flux resulted from the Marangoni effect. Based on the correlation development of boiling heat transfer coefficient in the previous study, two flow-patternbased empirical correlations for the two-phase frictional pressure drop are proposed in the terms of nondimensional parameters, such as boiling number, Weber number, and Marangoni number. The proposed correlations are similar to the empirical correlation for boiling heat transfer coefficient with different numerical values of the coefficients and exponents. Different values of flow-pattern-based constant are obtained for different flow patterns. The constants for annular flow and liquid film breakup are the same. It may be due to the major mechanism of the two-phase flow is liquid film evaporation for these two flow types. The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively. More than 90% of the experimental data can be predicted within a ±25% error band. Such an excellent agreement confirms that the proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Boiling of multi-component mixture is of importance and interest for many applications such as in chemical engineering, in process industries, and for refrigeration systems. Studies on pool boiling of mixtures are widely available in the literature. For example, some up-to-date studies on pool boiling of mixtures are reported by Inoue and Monde [1], Sathyabhama and Ashok Babu [2], Peyghambarzadeh et al. [3], and Sarafraz and his co-workers [4–7]. In addition, there are also many studies on flow boiling of mixtures, mostly mixed refrigerants, in small channels [8–17]. However, there are few researches on flow boiling of mixtures in a microchannel. The flow boiling characteristics of multi-
⇑ Corresponding author at: Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC. Tel.: +886 3 571 5131x34320; fax: +886 3 572 0724. E-mail addresses: [email protected] (B.-R. Fu), [email protected] (C. Pan). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.02.012
component mixture in a microchannel are more complicated than that of pure component. The concentration of mixtures is expected as one of the most important factors during boiling process. In Lin et al. [18], the convective boiling heat transfer and critical heat flux (CHF) of methanol–water mixtures in a diverging microchannel with artificial cavities was investigated. They found that at the same mass flux, the CHF increases slightly as the molar fraction (xm) ranges from 0 (pure water) to 0.3 (methanol–water mixtures) and then decreases as the molar fraction ranges from 0.3 to 1 (pure methanol). The maximum CHF is reached at a molar fraction of 0.3, especially for the highest mass flux (G) of 175 kg/m2 s, owing to the Marangoni effect. A mechanism of Marangoni effect is due to differences in surface tension and may induce an additional liquid restoring force to the three-phase contact line [19]. The flow pattern of liquid film breakup at the molar fraction of 0.3 persists up to a higher heat flux than that at other molar fractions. The Marangoni effect drives the liquid flow toward the contact line, resulting in a higher heat flux and a higher critical heat flux. An empirical CHF correlation, involving the Marangoni number, for flow boiling of binary mixtures has been proposed as follows [18]:
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Nomenclature total heated area of the channel (m2) boiling number (–) contraction coefficient (–) flow-pattern-based constant in the corresponding equation, i = 0, 1, 2, 3 (–) mean hydraulic diameter (m) friction factor (–) mass flux (kg/m2 s) gravitational acceleration (m/s2) heat transfer coefficient (kW/m2 K) latent heat of vaporization (kJ/kg) channel length (m) Marangoni number (–) total mass flow rate (kg/s) Prandtl number (–) heat flux (kW/m2) Reynolds number (–) temperature (K) liquid kinematic viscosity (m2/s) channel width (m) Weber number based on the hydraulic diameter (–) Lockhart–Martinelli parameter (–) quality (–) molar fraction of the more volatile component in the liquid phase (–)
Ah Bo Cc Ci Dh f G g h hlv L Ma m Pr q00 Re T
vl W WeD X2 x xm
c k
q r Dhsub, Dr DP DTsat
in
contraction or expansion area ratio (–) aspect ratio (–) density (kg/m3) surface tension (N/m) enthalpy change corresponding to the inlet subcooling (kJ/kg) difference in surface tension between fluid at the dew point and bubble point (N/m) pressure drop (kPa) wall superheat (K)
Subscripts a acceleration CHF critical heat flux f frictional h homogeneous in channel inlet l liquid max maximum out channel out sat saturation sp single-phase tot total tp two-phase v vapor w wall
Greek symbols a void fraction (–) b divergence angle of a channel (°)
q00CHF ¼ 0:00216Ghlv We0:078 1 0:44 D
Ma jMamax j
1 ð1Þ
where hlv is the latent heat of the vaporization, WeD = (G2Dh)/(rql) is the Weber number based on the hydraulic diameter of the channel (Dh), and Ma is the Marangoni number, defined by Fujita and Bai [19] as:
Ma ¼
Dr
r
ql v 2l gðql qv Þ
1=2 Pr
ð2Þ
here Dr is the difference in the fluid surface tension between the dew point and the bubble point, r is the surface tension of the fluid, ql is the liquid density, qv is the vapor density, vl is the liquid kinematic viscosity, g is the gravitational acceleration, and Pr is the Prandtl number. Recently, Fu et al. [20], a follow up study of Lin et al. [18], reported the visualization of flow boiling of binary mixtures (methanol–water and ethanol–water mixtures) in a microchannel. Four boiling regimes were reported: bubbly-elongated slug flow, annular flow, liquid film breakup, and dryout. The flow visualization results demonstrated that liquid film breakup persists up to the highest heat flux at molar fractions of 0.3 and 0.1 for the methanol–water and ethanol–water mixtures, respectively. This is because the Marangoni effect is most significant at these particular molar fractions. They also constructed flow pattern maps in the plane of heat flux versus molar fraction of methanol or ethanol. A significant effect of the molar fraction on the evolution of the two-phase flow pattern is observed, especially in the liquid film breakup regime. In addition, generalized flow pattern maps are constructed using coordinates of nondimensional parameter space (boiling number, Weber number, and Marangoni number), wherein relatively distinct boundaries between the flow patterns are identified. Consequently, they further proposed transition criteria
between flow patterns in the form of nondimensional groups as follows:
Bo 1 0:44
Ma ¼ C 1 WeCD2 jMamax j
ð3Þ
where C1 and C2 are flow-pattern-based constants, and Bo = q00 /(Ghlv) is the boiling number. The boundary between liquid film breakup and dryout is consistent with the correlation for the CHF of binary mixtures, i.e., Eq. (1). Fu et al. [21], further complementary to studies of Lin et al. [18] and Fu et al. [20], investigated experimentally the convective boiling heat transfer and the critical heat flux of ethanol–water mixtures in a diverging microchannel. The CHF data in their study show an excellent agreement and demonstrate a consistent trend with an empirical correlation for the CHF prediction, i.e., Eq. (1), proposed by Lin et al. [18]. They also reported that the two-phase heat transfer coefficient is much higher than that of single-phase convection region and is significantly affected by the wall superheat and the molar fraction. The two-phase heat transfer coefficient reaches a maximum in the region of the bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. Furthermore, they proposed a flow-pattern-based empirical correlation for the two-phase heat transfer coefficient (htp) of flow boiling of ethanol–water mixtures as follows:
htp ¼ C 3 Bo0:27 We0:67 1 0:44 D
Ma jMamax j
0:84
hsp
ð4Þ
where C3 is a flow-pattern-based constant and hsp is the singlephase heat transfer coefficient.
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Besides boiling heat transfer, critical heat flux, two-phase flow pattern, flow pattern maps, and transition criteria between flow patterns during flow boiling of mixtures in a microchannel, it is also of critical concern to understand the characteristics of the pressure drop across the microchannel. Recently, the pressure drop during flow boiling of pure component in a microchannel were investigated extensively, such as Hsieh and Lin [22], Harirchian and Garimella [23], Kim and Mudawar [24], Maqbool et al. [25], and Kaew-On et al. [26]. Some pressure drop correlations for microchannel flow boiling have also been proposed in those studies. Comprehensive discussions on prediction of pressure drop of flow boiling in a microchannel are available in [27]. However, few studies focus on pressure drop during flow boiling of mixtures in a mini or micro channel. For example, Táboas et al. [14] investigated the pressure drop of ammonia/water mixtures in a plate heat exchanger. They found that two-phase frictional pressure drop may be estimated by the Chisholm model with modified value of the Chisholm constant of 3. Dawidowicz and Cies´lin´ski [15] presented the two-phase flow pressure drop during flow boiling of pure refrigerants and refrigerant/oil mixtures in a tube with inner diameter of 8.8 mm and porous coating. Influence of oil mass fraction on pressure drop for flow boiling of R107C/oil mixtures was demonstrated. Li et al. [16] reported the pressure drop of flow boiling of HFO1234y and R32 refrigerant mixtures in a tube with inner diameter of 2 mm. They indicated that the two-phase flow pressure drop of the mixtures can be predicted by the Lockhart– Martinelli correlation. Although the two-phase flow pressure drop were reported in [15,16], only two mass fractions of the mixtures were tested. In addition, no correlation involving the concentration effect for two-phase flow pressure drop during flow boiling of mixtures in a microchannel was proposed. In light of the issues mentioned above, the present study, a follow up study of Fu et al. [20,21], presents the pressure drop during flow boiling of ethanol–water mixtures, with a full range of molar fractions, i.e., from 0 (pure water) to 1 (pure ethanol), in a microchannel. The two-phase heat transfer coefficient has close
relationship with the two-phase flow pressure drop, as suggested by the presence of Lockhart–Martinelli parameter (X2), which is resulted from the two-phase flow pressure drop, in many classical correlations for two-phase heat transfer coefficient of convective boiling in a microchannel. Consequently, based on the correlation development of boiling heat transfer coefficient [21], flowpattern-based empirical correlations involving the concentration effect (also Marangoni effect) for the two-phase frictional pressure drop are proposed.
2. Experimental details The experimental setup, shown in Fig. 1, is the same as that employed in Fu et al. [21], consisting of a high-performance liquid chromatography (HPLC) pump (HPG-3200P, Dionex), pressure transducer (model 692, Huba Control UK), flow visualization system, data acquisition system (MX100, YOKOGAWA), test section, and heating module. The HPLC pump provided forced flow of the working fluids in the microchannel with accurate and stable mass flow rates. Moreover, the exhausted fluids from the test section were drained into a container placed on an electronic balance, which provided a calibration of flow rate. The pressure taps were located near the inlet and outlet chambers at the connecting glass tube. The differential pressure transducer used in the present study had a short response time of 0.005 s; the sampling rate for the pressure measurement was set at 100 Hz. Flow visualization was conducted using a high-speed digital camera (MotionPro X4 Plus, IDT) with a microlens (Zoom 125C, OPTEM), 250-W illuminator (FOI-250, TECHNIQUIP), monitor, and personal computer. To capture the rapidly changing flow pattern, the typical frame rate and exposure time were set at 5000 frames/s and 50 ls, respectively. The data acquisition system, connected to the personal computer, recorded signals from five T-type thermocouples and a differential pressure transducer. The present study employed ethanol–water mixtures as the working fluid. Seven molar fractions (xm = 0, 0.1,
Fig. 1. Experimental setup.
B.-R. Fu et al. / International Journal of Heat and Mass Transfer 61 (2013) 332–339
0.2, 0.5, 0.7, 0.89, and 1) of ethanol–water mixtures at a given mass flux of 175 kg/m2 s were tested. Here, molar fractions of 0 and 1 are referred to as pure water and ethanol, respectively. The detailed phase diagram, surface tension, and Marangoni parameter of ethanol–water mixtures as a function of ethanol molar fraction can be retrieved in Fu et al. [21]. Fig. 2 illustrates the test module, including the test section and heating module. Fig. 2(a) shows a single channel with a divergence angle of b, i.e., half of the included angle. Fig. 2(a) also illustrates 24 artificial cavities distributed throughout the bottom wall of the microchannel, with a uniform spacing of 1 mm. These artificial cavities are laser-drilled pits with mouth diameters of about 20 lm. A silicon strip with a dimension of 40 mm 10 mm is used as a test section for a single diverging microchannel, as shown in Fig. 2(b). The length and depth of the channel are 25 mm and 85 lm, respectively. The width of the diverging microchannel varies linearly from 215 lm (Win) to 1085 lm (Wout), resulting in a divergence angle of 1° and a mean hydraulic diameter of 147 lm. The test section were prepared by microfabrication via silicon dry etching on SOI (silicon on insulator) wafer, which may provide uniform channel depth through the etching stop mechanism at the box layer of
335
the SOI wafer, laser direct writing for micromachining of through holes and artificial cavities, and anodic bonding with Pyrex 7740 glass for flow visualization. The detailed processes of microfabrication are given in [28]. Fig. 2(c) illustrates that two thermocouples are placed at the inlet and outlet chambers, and that three thermocouples are embedded 2 mm under the heating surface to measure the wall temperature distribution along the microchannel. The interval between the two neighbouring thermocouples is 5 mm. The experimental results demonstrate that the differences between these three temperatures are within 1.2 K. The wall temperature of the microchannels could be obtained by evaluating the total thermal resistance from the location of the thermocouple to the bottom wall of the microchannel. For energy conservation, the total heat input must be balanced with the heating power applied to the microchannel and with heat losses via different paths, e.g., heat loss from the glass surface due to natural air convection; radiation heat loss; sensible heat loss to the inlet chamber due to axial conduction of the test section; and other unknown heat losses, including sensible and latent heat losses to the exit chamber and possible latent heat loss to the inlet chamber. In general, the heat loss decreases with increasing the
Fig. 2. Schematic of the test module: (a) geometry of the microchannel, (b) top view, and (c) cross-section of the test section (not to scale).
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heating power and/or mass flux [21]. The main heat loss is that to the inlet and outlet chambers owing to axial conduction. The channel wall heat flux can be obtained by dividing the channel power by the total area of the bottom and the two sidewalls. The detailed procedure for the evaluation of various heat losses has been presented in Lee et al. [29]. The measurement uncertainty in the volume flow rate for the microchannels after calibration was estimated at ±3%. The uncertainties in the temperature measurements were ±0.2 K for T-type thermocouples. The uncertainty in the pressure transducer measurements was ±1%. The average overall uncertainty for the wall heat flux under flow boiling was ±4.5%. The uncertainty for the heat flux generally decreases with an increase in the heat flux and/or mass flux. 3. Data reduction As stated in the previous section of the experimental setup, taps of the pressure differential transducer are located near the inlet or outlet chamber and, therefore, the pressure drop measured could be considered as the pressure drop between the inlet and outlet chambers. The total pressure drop (DPtot), which is composed of frictional pressure drop (DPf), acceleration pressure drop (DPa), and pressure drop of the contributions of the inlet contraction (DPin) and outlet expansion (DPout), can be expressed as follows:
DPtot ¼ DPf þ DP a þ DPin þ DPout
ð5Þ
where the pressure drop due to acceleration, inlet contraction, and outlet expansion can be estimated by the following equations [30]:
DP a ¼
" G2 x2
qv a
G2 DPin ¼ 2q l
DPout
þ
G2 ð1 xÞ2 ql ð1 aÞ
"
1 1 Cc
2
#
" G 2 x2
qv a
out
þ
G2 ð1 xÞ2 ql ð1 aÞ
# ð6Þ in
# ql þ ð1 c Þ 1 þ xin 1 2
qv
" # G2 cð1 cÞ ð1 xout Þ2 ql x2out ¼ þ ql 1 aout qv aout
ð7Þ
ð8Þ
Here, Cc is the contraction coefficient, and Cc = 1 is used in the present study, based on the reports in [24,31]; c is the contraction or expansion area ratio; and aout is the void fraction at the channel outlet, which can be determined by the following correlation [32]:
aout ¼
0:03a0:5 h 1 0:97a0:5 h
ð9Þ
where ah is the homogeneous void fraction. xin and xout are qualities at the channel inlet and outlet, respectively. In the present study, xin = 0 because the working fluid at the channel inlet is subcooled liquid, and xout can be determined as follows:
xout ¼
q00 Ah Dhsub;in mhlv h lv
ð10Þ
where Ah is the total heated area of the channel, m is the total mass flow rate, and Dhsub,in is the enthalpy change corresponding to the inlet subcooling.
Fig. 3. Boiling curves for ethanol–water mixtures as a function of ethanol molar fraction at G = 175 kg/m2 s [21].
fraction on boiling curve. For the single-phase convection region, the heat flux increases with a decrease in the molar fraction at a given wall superheat. The heat flux of pure water is always greater than that of pure ethanol. This is primarily due to the differences in the thermophysical properties between water and ethanol. Water has much larger latent heat of evaporation and surface tension than ethanol. After boiling incipience (two-phase flow region), the heat flux increases rapidly with increasing the wall superheat until approaching the CHF condition. The figure indicates the presence of boiling hysteresis for certain mixture with certain molar fractions. The boiling curve for xm = 0.1 appears to have the highest heat flux for DTsat > 10 K. More detailed discussions on the boiling heat transfer and critical heat flux have been reported in Fu et al. [21]. Moreover, pool boiling studies in the literature, e.g., Peyghambarzadeh et al. [33] also demonstrated such heat transfer enhancement at very low concentration of second component. 4.2. Two-phase flow pattern Fig. 4 illustrates typically the total pressure drop as a function of wall heat flux for the mixtures with xm = 0.1. Four typical flow patterns can also be indentified in the figure, namely: (a) bubbly-elongated slug flow, (b) annular flow, (c) liquid film breakup, and (d) dry-out. Under the conditions of relatively low heat flux, bubbles nucleated and grow rapidly becoming an elongated slug bubble, named bubbly-elongated slug flow; for medium to high heat fluxes, the bubbly-elongated slug flow evolves to the annular flow, especially in the region near the exit; further increasing the heat flux, breakup in the liquid film appears and the flow pattern is referred to as liquid film breakup. More detailed discussions on twophase flow patterns, flow pattern maps, and the criteria for transitions between flow patterns have been presented in Fu et al. [20]. Fig. 4 demonstrates that the slope of two-phase flow pressure drop increases with the evolution of flow pattern from bubbly-elongated slug flow to dry-out. The pressure drop increases sharply from the latter stage of liquid film breakup to the occurrence of dry-out.
4. Results and discussion 4.3. Pressure drop 4.1. Boiling curve Fig. 3 illustrates the heat flux (q00 ) as a function of wall superheat (DTsat = Tw Tsat) at different molar fractions of ethanol for G = 175 kg/m2 s [21]. There is a significant effect of the molar
Fig. 5 shows the total pressure drop as a function of wall superheat at different molar fractions during experiments. Similar to boiling curves [21], as one may expect, Fig. 5 clearly demonstrates the significant effects of the molar fraction on the pressure drop. In
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fraction in the channel for both pure water and mixture with xm = 0.1 is higher than the mixture with other concentrations. Fig. 6 further depicts the various components of two-phase flow pressure drop as a function of heat flux for xm = 0.1. The figure demonstrates that frictional pressure drop is most dominant; the acceleration pressure drop contributes about 5–15% of the total pressure drop; and the inlet and outlet pressure losses due to sudden area change are very small. For the present study, the inlet contraction pressure drop is negligible small (<0.2 kPa) and the maximum value of outlet expansion pressure drop is only about 1.5% of the total pressure drop. The much smaller contribution of the acceleration pressure drop than the frictional one demonstrates the merit of diverging cross-sectional design. To improve the representation of the present results and based on the correlation development of boiling heat transfer coefficient [21], i.e., Eq. (4), a flow-pattern-based empirical correlation for the two-phase flow pressure drop during flow boiling of ethanol– water mixtures is established and expressed as follows:
DPf ;tp ¼ C 0 Bo1:58 We0:57 1 0:44 D
0:86 Ma DPf ;sp jMamax j
ð11Þ
the single-phase convection region, the pressure drop decreases with an increase in the wall superheat (also heat flux, as demonstrated earlier in Fig. 4) due to the decrease in the liquid viscosity with temperature (or heat flux). The pressure drop for pure water is the smallest due to the smaller viscosity of pure water than that of ethanol–water mixtures. During flow boiling, the pressure drop increases rapidly with a further increase in the wall superheat. This is because the void fraction generally increases with an increase in the temperature, which results in an increase in both acceleration and frictional pressure drops. In general, Fig. 5 indicates that the two-phase flow pressure drops for pure water and the mixture with xm = 0.1 are greater than that of other mixtures at a given wall superheat. This is because the higher boiling heat flux and so void
where C0 is a flow-pattern-based constant, DPf,tp is the two-phase frictional pressure drop, and DPf,sp is the saturated single-phase frictional pressure drop, which is estimated based on the results of the present experiments, i.e., single-phase frictional pressure drop corresponding to DTsat = 0 K. The proposed correlation is similar to the empirical correlation for boiling heat transfer coefficient, i.e., Eq. (4), with different numerical values of the coefficients and exponents. In particular, the exponent for the boiling number is positive, suggesting the positive correlation of pressure drop with heat flux as one may expect, in the proposed correction, while it is negative for boiling heat transfer coefficient. For the present study, different values of C0 are obtained for different flow patterns: C0 = 56,500 for bubbly-elongated slug flow, C0 = 33,400 for annular flow and liquid film breakup, and C0 = 40,000 for dry-out region. It is interesting to note that the constants for annular flow and liquid film breakup are the same. Indeed, in the proposed flow-pattern-based empirical correlation for the two-phase heat transfer coefficient, the constants (C3) for annular flow and liquid film breakup are also the same. It may be due to the major mechanism of the two-phase flow is liquid film evaporation for these two flow types.
Fig. 5. Pressure drop during flow boiling of ethanol–water mixtures as a function of ethanol molar fraction at G = 175 kg/m2 s.
Fig. 6. The various components of two-phase flow pressure drop as a function of heat flux for xm = 0.1.
Fig. 4. Typical two-phase flow patterns in the coordinates of pressure drop and heat flux. The images of two-phase flow patterns are from Fu et al. [21].
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In case the saturated single-phase frictional pressure drop is unavailable from the experiments, one may use the following conventional equations [34] to estimate it:
DPf ;sp ¼ f
L 1 G2 Dh 2 ql
ð12Þ
and f¼
96 1 1:3553k þ 1:9467k2 1:7012k3 þ 0:9564k4 0:2537k5 Re
ð13Þ
where f is the friction factor, L is the channel length, Re is the Reynolds number, and k is the aspect ratio (depth-to-width ratio) and must be less than 1. If k > 1, the inverse value of k should be employed. For the present study using the diverging microchannel, the mean values of the aspect ratio and the Reynolds number are used. In addition, while using Eqs. (12) and (13) to obtain DPf,sp, the proposed correlation, Eq. (11), should be slightly modified as:
DPf ;tp ¼ C 0 Bo1:56 We0:86 1 0:44 D
Ma jMamax j
0:87
DPf ;sp
ð14Þ
Fig. 7. Comparison of the experimental data and predicted results of Eq. (11).
where C0 = 57,800 for bubbly-elongated slug flow, C0 = 34,300 for annular flow and liquid film breakup, and C0 = 43,100 for dry-out region. Figs. 7 and 8 further compare the predictions of the proposed correlations, i.e., Eqs. (11)–(14), with experimental data, respectively. The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively. More than 90% of the experimental data can be predicted within a ±25% error band. The present correlation predictions show excellent agreement with the experimental data and further confirm that the proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel, and may be applied to predict the two-phase flow pressure drop for other binary mixtures. 4.4. Summary of correlations The correlation for two-phase frictional pressure drop in the present study is based on the nondimensional parameters, such as boiling number, Weber number, and Marangoni number. These nondimensional parameters were also employed in previous studies of Fu et al. for critical heat flux [18], transition criteria between flow patterns [20], and two-phase heat transfer coefficient [21]. To illustrate the similarity and difference between two-phase heat transfer and fluid flow, Table 1 summarizes all these four correlations. It should be mentioned that for employing those proposed correlations more easily, the properties are taken at the condition of the channel outlet during developing the correlations. In
Fig. 8. Comparison of the experimental data and predicted results of Eq. (14).
addition, those correlations can also be used to predict the pure component by straight simplifying the term of (1 0.44Ma/ |Mamax|) to 1 because of Ma = 0 for pure component, as which have been verified by comparison with data of xm = 0 (water) and 1 (ethanol). Comparing the correlations between two-phase heat transfer coefficient and two-phase frictional pressure drop, it is clearly found that the exponents for the Weber number are all negative, while the exponents for the boiling number and
Table 1 Summary of the proposed correlations for flow boiling of ethanol–water mixtures in a microchannel. Correlation (Authors)
Proposed correlation
Value of flow-pattern-based constants (Ci)
Critical heat flux (Lin et al. [18]) Transition criteria between flow patterns (Fu et al. [20])
1 q00CHF ¼ 0:00216Ghlv We0:078 1 0:44 jMaMa D max j Bo 1 0:44 jMaMa ¼ C 1 WeCD2 max j
(N/A)
Two-phase heat transfer coefficient (Fu et al. [21]) Two-phase flow pressure drop (Present study)
0:84 0:67 htp ¼ C 3 Bo0:27 WeD 1 0:44 jMaMa hsp max j (i) based on experimental value of DPf,sp 0:86 DP f ;tp ¼ C 0 Bo1:58 We0:57 1 0:44 jMaMa DP f ;sp D max j (ii) based on theoretical value of DPf,sp 0:87 DP f ;tp ¼ C 0 Bo1:56 We0:86 1 0:44 jMaMa DP f ;sp D max j
C1 = 2.97 104 and C2 = 0.20 (single-phase flow to bubbly-elongated slug flow) C1 = 8.65 104 and C2 = 0.16 (bubbly-elongated slug flow to annular flow) C1 = 1.49 103 and C2 = 0.12 (annular flow to liquid film breakup) C1 = 2.16 103 and C2 = 0.078 (liquid film breakup to dry-out) C3 = 0.668 (bubbly-elongated slug flow) C3 = 0.887 (annular flow) C3 = 0.887 (liquid film breakup) C3 = 0.481 (dry-out) C0 = 56,500 (bubbly-elongated slug flow) C0 = 33,400 (annular flow) C0 = 33,400 (liquid film breakup) C0 = 40,000 (dry-out) C0 = 57,800 (bubbly-elongated slug flow) C0 = 34,300 (annular flow) C0 = 34,300 (liquid film breakup) C0 = 43,100 (dry-out)
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(1 0.44Ma/|Mamax|) are negative for two-phase heat transfer coefficient and positive for two-phase frictional pressure drop. The different trend of heat flux and wall superheat on the twophase frictional pressure drop should be noticed. 5. Summary and conclusions This paper, an extended work of Fu et al. [20,21], investigates the pressure drop during flow boiling of ethanol–water mixtures in a diverging microchannel with artificial cavities. Experimental results show that pressure drops for both single-phase and boiling two-phase flow are significantly influenced by the molar fraction. For single-phase convection regions, the pressure drop decreases with increasing wall superheat (also heat flux) due to the decrease in the liquid viscosity. The pressure drop for water is the smallest due to the smaller viscosity than that of other mixtures. During flow boiling, the pressure drop increases rapidly with a further increase in the wall superheat. Two-phase flow pressure drop for the mixture with xm = 0.1 is the highest generally at a given wall superheat, due to the higher boiling heat flux. Two flow-pattern-based empirical correlations based on experimental or theoretical saturated single-phase frictional pressure drop, respectively, for the two-phase frictional pressure drop during flow boiling of ethanol–water mixtures are proposed and expressed in the form of nondimensional numbers (boiling number, Weber number, and Marangoni number). The overall mean absolute errors of the proposed correlations are 13.7% and 11.6%, respectively, and more than 90% of the experimental data can be predicted within a ±25% error band. The proposed correlations may predict the Marangoni effect on the two-phase flow pressure drop during flow boiling of binary mixtures in a microchannel, and may be applied to predict the two-phase flow pressure drop for other binary mixtures. Acknowledgements This work was supported by the National Science Council of Taiwan under the contract No. NSC 97-2221-E-007-126-MY3. References [1] T. Inoue, M. Monde, Enhancement of nucleate pool boiling heat transfer in ammonia/water mixtures with a surface-active agent, Int. J. Heat Mass Transfer 55 (2012) 3395–3399. [2] A. Sathyabhama, T.P. Ashok Babu, Experimental investigation in pool boiling heat transfer of ammonia/water mixture and heat transfer correlations, Int. J. Heat Fluid Flow 32 (2011) 719–729. [3] S.M. Peyghambarzadeh, M. Jamialahmadi, S.A. Alavi Fazel, S. Azizi, Saturated nucleate boiling to binary and ternary mixtures on horizontal cylinder, Exp. Therm. Fluid Sci. 33 (2009) 903–911. [4] M.M. Sarafraz, S.M. Peyghambarzadeh, S.A. Alavi Fazel, Enhancement of nucleate pool boiling heat transfer to dilute binary mixtures using endothermic chemical reactions around the smoothed horizontal cylinder, Heat Mass Transfer 48 (2012) 1755–1765. [5] M.M. Sarafraz, S.M. Peyghambarzadeh, Influence of thermodynamic models on the prediction of pool boiling heat transfer coefficient of dilute binary mixtures, Int. Commun. Heat Mass Transfer 39 (2012) 1303–1310. [6] M.M. Sarafraz, S.A. Alavi Fazel, Y. Hasanzadeh, A. Arabshamsabadi, S. Bahram, Development of a new correlation for estimating pool boiling heat transfer coefficient of MEG/DEG/water ternary mixture, Chem. Ind. Chem. Eng. Q. 18 (2012) 11–18. [7] M.M. Sarafraz, Nucleate pool boiling of aqueous solution of citric acid on a smoothed horizontal cylinder, Heat Mass Transfer 48 (2012) 611–619.
339
[8] A. Greco, Convective boiling of pure and mixed refrigerants: an experimental study of the major parameters affecting heat transfer, Int. J. Heat Mass Transfer 51 (2008) 896–909. [9] B. Raja, D. Mohan Lal, R. Saravanan, Flow boiling heat transfer coefficient of R134a/R-290/R-600a mixture in smooth horizontal tubes using varied heat flux method, Appl. Therm. Eng. 29 (2009) 1778–1785. [10] B. Raja, D. Mohan Lal, R. Saravanan, Stratified flow boiling heat transfer study of a HFC/HC refrigerant mixture in smooth horizontal tubes, Heat Mass Transfer 46 (2010) 323–331. [11] H.T. Hu, G.L. Ding, W.J. Wei, X.C. Huang, Z. Wang, Heat transfer characteristics of refrigerant–oil mixtures flow boiling in a horizontal C-shape curved smooth tube, Int. J. Refrig. 33 (2010) 932–943. [12] X. Zou, M.Q. Gong, G.F. Chen, Z.H. Sun, Y. Zhang, J.F. Wu, Experimental study on saturated flow boiling heat transfer of R170/R290 mixtures in a horizontal tube, Int. J. Refrig. 33 (2010) 371–380. [13] F. Táboas, M. Vallès, M. Bourouis, A. Coronas, Flow boiling heat transfer of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 33 (2010) 695–705. [14] F. Táboas, M. Vallès, M. Bourouis, A. Coronas, Assessment of boiling heat transfer and pressure drop correlations of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 35 (2012) 633–644. [15] B. Dawidowicz, J.T. Cies´lin´ski, Heat transfer and pressure drop during flow boiling of pure refrigerants and refrigerant/oil mixtures in tube with porous coating, Int. J. Heat Mass Transfer 55 (2012) 2549–2558. [16] M. Li, C. Dang, E. Hihara, Flow boiling heat transfer of HFO1234yf and R32 refrigerant mixtures in a smooth horizontal tube. Part I experimental investigation, Int. J. Heat Mass Transfer 55 (2012) 3437–3446. [17] M.M. Sarafraz, S.M. Peyghambarzadeh, N. Vaeli, Subcooled flow boiling heat transfer of ethanol aqueous solutions in vertical annulus space, Chem. Ind. Chem. Eng. Q. 18 (2012) 315–327. [18] P.H. Lin, B.R. Fu, Chin Pan, Critical heat flux on flow boiling of methanol–water mixtures in a diverging microchannel with artificial cavities, Int. J. Heat Mass Transfer 54 (2011) 3156–3166. [19] Y. Fujita, Q. Bai, Critical heat flux of binary mixtures in pool boiling and its correlation in terms of Marangoni number, Int. J. Refrig. 20 (1997) 616–622. [20] B.R. Fu, P.H. Lin, M.S. Tsou, Chin Pan, Flow pattern maps and transition criteria for flow boiling of binary mixtures in a diverging microchannel, Int. J. Heat Mass Transfer 55 (2012) 1754–1763. [21] B.R. Fu, M.S. Tsou, Chin Pan, Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities, Int. J. Heat Mass Transfer 55 (2012) 1807–1814. [22] S.S. Hsieh, C.Y. Lin, Correlation of critical heat flux and two-phase friction factor for subcooled convective boiling in structured surface microchannels, Int. J. Heat Mass Transfer 55 (2012) 32–42. [23] T. Harirchian, S.V. Garimella, Flow regime-based modeling of heat transfer and pressure drop in microchannel flow boiling, Int. J. Heat Mass Transfer 55 (2012) 1246–1260. [24] S.M. Kim, I. Mudawar, Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks, Int. J. Heat Mass Transfer 55 (2012) 3720–3731. [25] M.H. Maqbool, B. Palm, R. Khodabandeh, Flow boiling of ammonia in vertical small diameter tubes: two phase frictional pressure drop results and assessment of prediction methods, Int. J. Therm. Sci. 54 (2012) 1–12. [26] J. Kaew-On, K. Sakamatapan, S. Wongwises, Flow boiling pressure drop of R134a in the counter flow multiport minichannel heat exchangers, Exp. Therm. Fluid Sci. 36 (2012) 107–117. [27] I. Mudawar, Two-phase microchannel heat sinks: theory, applications, and limitations, J. Electron. Packag. Trans. ASME 133 (2011) 041002. [28] P.C. Lee, Chin Pan, Boiling heat transfer and two-phase flow of water in a single shallow microchannel with a uniform or diverging cross section, J. Micromech. Microeng. 18 (2008) 025005. [29] P.C. Lee, F.G. Tseng, Chin Pan, Bubble dynamics in microchannels. Part I: single microchannel, Int. J. Heat Mass Transfer 47 (2004) 5575–5589. [30] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, 3rd ed., Oxford University Press, New York, NY, 1994. [31] F.F. Abdelall, G. Hahn, S.M. Ghiaasiaan, S.I. Abdel-Khalik, S.S. Jeter, M. Yoda, D.L. Sadowski, Pressure drop caused by abrupt flow area changes in small channels, Exp. Therm. Fluid Sci. 29 (2005) 425–434. [32] A. Kawahara, P.M.Y. Chung, M. Kawaji, Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel, Int. J. Multiphase Flow 28 (2002) 1411–1435. [33] S.M. Peyghambarzadeh, M. Jamialahmadi, S.A. Alavi Fazel, S. Azizi, Experimental and theoretical study of pool boiling heat transfer to amine solutions, Braz. J. Chem. Eng. 26 (2009) 33–43. [34] J.P. Hartnett, M. Kostic, Heat transfer to Newtonian and non-Newtonian fluids in rectangular ducts, Adv. Heat Transfer 19 (1989) 247–356.