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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Heat transfer during convective boiling inside microchannels Fabio Toshio Kanizawa ⇑, Cristiano Bigonha Tibiriçá, Gherhardt Ribatski 1 Heat Transfer Research Group, São Carlos School of Engineering, University of São Paulo, Brazil

a r t i c l e

i n f o

Article history: Received 4 August 2015 Received in revised form 26 September 2015 Accepted 29 September 2015

Keywords: Heat transfer coefficient Convective flow boiling Two-phase flow Micro-scale channels

a b s t r a c t This paper presents experimental results for the heat transfer coefficient during flow boiling of refrigerants R134a, R245fa and R600a inside small diameter tubes plus a new heat transfer predictive method. The experimental database comprises 2047 data points covering tube internal diameter ranging from 0.38 to 2.6 mm, mass velocities from 49 to 2200 kg/m2s, and heat fluxes up to 185 kW/m2. The data are parametrically analyzed and the effects of the experimental parameters (mass velocity, tube diameter, heat flux, refrigerant type and saturation temperature) on the heat transfer coefficient and dryout vapor quality are identified. In general, the heat transfer coefficient increases with increasing mass velocity, heat flux and saturation temperature, and decreasing the tube diameter. Moreover, the dryout vapor quality decreases with increasing mass velocity and vapor specific volume. The method proposed in the present study predicted 97% of the experimental results within an error margin of ±30% and with a mean absolute error of 11%. The new method provided better predictions of its database than seven of the most quoted predictive methods available in the literature, and was also accurate to predict independent databases. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Ribatski et al. [1] and Tibiriçá and Ribatski [2] presented extensive reviews on flow boiling in micro-scale channels, covering upto-date experimental studies about the subject. Ribatski et al. [1] gathered more than 2100 experimental results for the heat transfer coefficient (HTC) during convective boiling from literature, and compared this broad database with four predictive methods available by that time. They indicated that, even for similar experimental conditions, significant discrepancies are observed among results from different laboratories. Ribatski et al. [1] attributed these differences to superficial characteristics of the channels, thermal instabilities [3], or even experimental carelessness. Since then, a great number of studies focused on this subject have been carried out, and better agreement among experimental results can be verified, as pointed out by Tibiriçá and Ribatski [2]. The reduction of differences among experimental results can be attributed to the adoption of more precise equipment and experimental techniques. It must be highlighted that instrumenting a micro-scale test section is quite challenging, because the measurement probes, e.g. thermocouples junctions, can present almost the same size of ⇑ Corresponding author. E-mail addresses: [email protected] (F.T. Kanizawa), [email protected] (C. B. Tibiriçá), [email protected] (G. Ribatski). 1 Mechanical Engineering Department, Av. Trabalhador São Carlense, 400, Parque Arnold Schmidt, São Carlos 13566-590, São Paulo, Brazil. Tel.: +55 (16) 3373 9415. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.09.083 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

the channel being evaluated. Additionally, since the study presented by Ribatski et al. [1], predictive methods appropriated for micro-scale flow phenomena have been developed for estimative of flow pattern, void fraction, pressure drop, critical heat flux and heat transfer coefficient. As pointed out recently by Tibiriçá and Ribatski [2], there is still no consensus about the definition of the threshold dimension to identify the size of the channel that characterizes micro-scale conditions. A number of criteria to determine the transition between micro and macro-scale were proposed, usually based on manufacturing technique, heat exchanger applications and bubble confinement number. In this context, Mehendale et al. [4] characterized the transition between conventional and micro-channels based on its application, and Kandlikar and Grande [5] considered manufacturing techniques employed for heat exchanger construction. Based on bubble confinement aspects, Triplett et al. [6] proposed a transition criteria similar to the one presented by Kew and Cornell [7], which takes into account surface tension and buoyancy effects. More recently, additional criteria were proposed, e.g. Ong and Thome [8] and Tibiriçá and Ribatski [2,9], also based on bubble confinement. The characterization of the transition between micro and macro-scale condition is out of the scope of the present paper, and Tibiriçá and Ribatski [2,9] are indicated as supplementary material concerning this subject. In the present study, based on the work of Kandlikar and Grande [5], tubes with internal diameter smaller than 3.0 mm are considered as micro-scale channels.

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567

Nomenclature A Bd Bo cp d EP F Fr g G h i k L _ m p Pr Re S T u v We X

cross sectional area bond number boiling number specific heat at constant pressure internal diameter electrical power enhancement factor for convective parcel Froude number gravitational acceleration mass flux heat transfer coefficient specific enthalpy linear thermal conductivity length mass flow rate pressure Prandtl number Reynolds number suppression factor for nucleate boiling parcel temperature in situ velocity specific volume Weber number Lockhart and Martinelli parameter

During the design stage of heat spreaders, accurate predictive methods are needed for the estimative of pressure drop, heat transfer coefficient and critical heat flux, to define channels dimensions and operational conditions of these devices. However, Tibiriçá and Ribatski [9] indicate that predictive methods to estimate these design parameters for a broad range of experimental conditions are still needed. In this context, the present study aims to contribute to the knowledge concerning convective flow boiling inside micro-scale channels. Unpublished experimental results for heat transfer coefficient during R134a and R245fa two-phase flow boiling in 0.38 mm ID tube are presented, and compared with experimental results for R134a, R245fa and R600a two-phase flow boiling in ID tubes ranging from 1.00 to 2.60 mm. A parametric analysis is presented, with the aim of identifying the relevance of distinct experimental parameters. Based on this broad database, a new heat transfer predictive method is proposed. 2. Experimental apparatus and procedure Heat Transfer Research Group, at the University of São Paulo, built the experimental facility used in the present study. Except for the preheater and test section that were modified in order of obtaining data for the 0.38 mm ID tube, the apparatus also is the same used by Tibiriçá and Ribatski [10]. The experimental setup comprises an ethylene-glycol and a refrigerant circuit, schematically illustrated in Fig. 1. The refrigerant circuit comprises a micro-pump to propel the working fluid through the circuit, a preheater to establish the experimental conditions at the inlet of the test section, a test section, a visualization section, a condenser and a refrigerant reservoir. The ethylene-glycol/water circuit (not shown in Fig. 1) is used to condense and subcool the working fluid, as well to control the pressure of the test circuit, and operates with a 60% solution as intermediary fluid. In the refrigerant circuit, starting from subcooler 1, the working fluid flows through the filter and the liquid visor to the gear

x z

a ci

Dp

e l q qratio U

u

r

vapor quality axial distance void fraction parcel of data correctly predicted within ±i% pressure difference mean absolute deviation dynamic viscosity density two-phase density ratio heat flux mean relative error surface tension

Subscripts c convective parcel crit critical heat flux condition di dryout inception l relative to liquid phase lv liquid vapor latent nb nucleate boiling parcel r reduced property sat saturation condition v relative to vapor phase w wall

micro-pump (self lubricating without oil). Downstream the pump, a Coriolis mass flowmeter (Micro Motion CMF025 M) and the subcooler 2 were installed, to determine mass flow rate and to ensure subcooled state for the fluid at the preheater inlet, respectively. Then, the fluid is directed to the preheater PH, test and visualization sections. The system also counts with two needle valves, to impose additional restriction to the flow in order to avoid instabilities [3]. Just upstream the pre-heater, the enthalpy of the liquid is estimated based on its temperature T1 and pressure p1, determined through a thermocouple in contact with the working fluid and an absolute pressure transducer, respectively. All temperature measurements in the system are performed by K type thermocouples, using a National Instruments acquisition card. The temperature measurement channels were previously calibrated, adopting procedure presented by Abernethy and Thompson [11], from which an uncertainty of ±0.15 °C was obtained. The absolute pressure p1 is determined through Endress–Hauser PMP131 transducers, and because saturation pressures of R245fa and R134a are different by an order of magnitude, distinct absolute pressure transducers are used for each fluid, with measurement ranges up to 400 and 1200 kPa, respectively. The total pressure drop Dp is measured with a differential pressure transducer Endress–Hauser PMD75, with measurement range up to 300 kPa and 0.075% uncertainty of the set span. Test section outlet temperature is determined through a thermocouple T2 installed in contact with the fluid, and the pressure p2 is given by the inlet pressure p1 minus Dp. Flow videos were recorded at the visualization section using a highspeed camera Optronis CAMRECORD 600. For flow pattern results and their discussions see Tibiriçá and Ribatski [12]. The mass flow rate is adjusted with the help of a frequency inverter, which controls the pump rotation velocity. The heat flux at the preheater and test sections are imposed through Joule effect by applying electrical current directly to the tube walls. The electrical power to the heated sections is supplied by two DC power sources (Lambda Genesys 750W, 20V-40A), controlled by the data

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Refrigerant reservoir Ethylene glycol / water solution

Ethylene glycol / water solution

Condenser

Visualization section

Test section

Power supply

p Preheater section

Power supply

p1 T1 Needle valve 1

Ethylene glycol / water solution

p2 T2

Needle valve 2 Subcooler 1

High speed camera

In the case of the results for flow boiling in a 0.38 mm ID tube, the test section comprises only one measuring section with one thermocouple installed. Data for the 0.38 mm ID tube were obtained for R245fa and R134a, for G ranging from 280 to 2200 kg/m2s, U from 15 to 185 kW/m2, and Tsat from 30 to 58 °C. In the foregoing analysis, experimental results previously obtained and presented by Tibiriçá and Ribatski [2,10,13] and Copetti et al. [14] are used to evaluated experimental trends, and were all performed in experimental facilities with similar layout of the one depicted in Fig. 1. Table 1 summarizes the experimental conditions, and Table 2 presents fluids thermophysical properties. It should be mentioned that even though parcel of experiments presented by Tibiriçá and Ribatski [2,10,13] were performed in distinct laboratories, hence using different experimental facilities, the experimental results from both laboratories agreed with each other, as pointed out by Tibiriçá et al. [15]. Experimental results for R600a were only obtained by Copetti et al. [14].

Filter

3. Data regression

Liquid visor

For all experiments, mass flux G is given as the ratio between _ and cross sectional area A. The heat flux U is mass flow rate m given as the ratio of electrical power EP divided by the heated area, as follows:

Micropump

U¼

Subcooler 2 Ethylene glycol / water solution

Coriolis mass flowmeter

Fig. 1. Schematics of experimental bench.

acquisition and control system. The preheater aims to adjust fluid thermodynamic state at test section inlet. The circuit pressure, hence saturation temperature, is adjusted with the help of a refrigerant reservoir, which counts with a serpentine circulating an ethylene-glycol/water solution in its interior. The temperature of this solution is controlled by a PID system, using a condenser unit, evaporator and electrical resistances. The test and preheater sections are made of commercial stainless steel tubes, with similar characteristics, and are thermally insulated using subsequent layers of ceramic and elastomeric foams. The visualization section consists of a fused silica tube with internal diameter close to the test section ID. All sections are assembled using PVDF intermediary connections. Test section wall temperature measurements are performed using K type thermocouples, which present thermal junctions of reduced diameter (0.125 mm for 0.38 mm ID tube, and 0.250 mm for 1.1 and 2.32 mm ID tube). The thermal junctions were painted with electrical insulating glaze, positioned externally to sections wall and tightly fixed with polyamide adhesive tapes. In order to increase the contact pressure between the junction and the tube wall, elastomeric sealing rings (o-rings) were positioned over the set. To perform the experiments, initially the fluid temperature in the reservoir is adjusted through the auxiliary ethylene-glycol/ water circuit, and then the micropump is activated with the mass flow adjusted by a closed loop control system. Subsequently heat fluxes are imposed in the preheater and test sections. After the achievement of steady state condition, the datalog was started and experimental results were recorded for at least one minute. Steady state condition is considered to be attained when no temperature variations higher than thermocouple uncertainties are observed during two minutes.

EP

pdL

ð1Þ

where L corresponds to the tube length between electrodes. Copetti et al. [14] took into account heat dissipation to the environment, based on efficiency factors. Tibiriçá and Ribatski [13] evaluated the heat loss for the environment, and concluded that this parcel corresponds to less than 1% of the local heat flux for d = 2.32 mm and U higher than 10 kW/m2, therefore it can be considered as negligible. Similar analysis is adopted for the preheater section. The vapor quality x is determined locally, based on energy balance as follows:

_ þ iPH;in Þ il ðzÞ=ilv ðzÞ x ¼ ½ððEPPH þ U p d zÞ=m

ð2Þ

where EPPH is the electrical power supplied to preheater section, z is the distance from the upstream electrode of the test section to the section for which the vapor quality is evaluated. The term iPH,in is the preheater inlet enthalpy, evaluated based on p1 and T1, and il and ilv are the local liquid and vaporization enthalpy estimated based on the local saturation pressure psat. Local fluid saturation temperature Tsat is estimated based on saturation pressure psat considering the following approach: the single-phase length, defined as the length from PH inlet to the point of saturated liquid, is estimated considering the non-heated and heated regions along preheater; then single-phase pressure drop is estimated considering Petukhov [16] method for turbulent flow (Re > 2300) and 64/Re for laminar flow; therefore it is possible to determine the pressure at the end of single-phase length p1/; the local pressure along the test section is estimated considering constant pressure drop gradient along the two-phase length, hence psat is given by a linear interpolation in z from the end of singlephase length to the test section outlet, p1/ and p2. The internal surface temperature Tw is estimated based on the thermocouples installed on the external surface based on the heat diffusion equation and considering one-dimensional conduction. It is also assumed that the system is externally insulated, and heat is uniformly generated within the tube wall. Therefore, the local heat transfer coefficient h is determined based on Newton’s cooling law, Tsat, Tw and U as follows:

h¼

U T w T sat

ð3Þ

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F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583 Table 1 Summary of experimental conditions. R134a d [mm] (Roughness [lm])

U [kW/m2]

G [kg/m2s] Tsat [°C] x [–] h [kW/m2K] a b

R245fa a

b

R600a a

0.38 (1.3 ), 1.00 (0.595 ), 1.10 (0.53a), 2.20 (0.827b), 2.32 (0.33a) 5–185 49–2200 21.5–42.5 0.05–0.93 1.8–34.0

b

a

0.38 (1.3 ), 1.00 (0.595 ), 1.10 (0.53 ), 2.20 (0.827b), 2.32 (0.33a) 10–163 99–1400 25.5–58.3 0.054–0.90 2.3–21.0

2.60 (2.05a) 46, 67, 100 240, 400 22 0.01–0.69 1.8–24.5

Ra. RMS.

Uncertainties of derived parameters are evaluated based on transducers and measurement devices employed for the experiments, and are equal to 1.2 and 2.0% for U and G, and lower than 30 and 5% for h and x, respectively. For sections layout that counts with more than one thermocouple per measurement section, the local heat transfer coefficient is considered as the weighted mean along the local test section perimeter. The boiling number Bo and the two-phase density ratio qratio are parameters frequently considered in the literature for the analyses of the heat transfer coefficient and are defined as follow:

Bo ¼ U=ilv G

ð4Þ

qratio ¼ ql =qv

ð5Þ

where q is the density and the subscripts l and v refers to the liquid and vapor phases, respectively. To validate the experimental apparatus and data regression procedure, single-phase flow experiments were performed and the obtained results were compared with well-known predictive methods for heat transfer coefficient. As presented by Tibiriçá and Ribatski [10], experimental results for heat transfer coefficient during developed single-phase flow presents satisfactory agreement with Gnielinski [17] predictions. Two-phase flow experiments were performed for adiabatic conditions in the test section to confirm absence of geometric irregularities along the tube, which can affect h and pressure drop Dp measurements. For these experiments, thermocouples installed along the test section length indicate almost constant pressure drop gradient. Therefore, it can be concluded that the tubes used as test sections do not present, or present negligible, variations of geometry along their length and connections. 4. Experimental results 4.1. Database description The database described in this section includes unpublished results for 0.38 mm ID tube, and recent results published by Tibiriçá and Ribatski [2,10,13] and Copetti et al. [14]. The database comprises more than 2000 data points and covers the experimental conditions described in Table 1.

Fig. 2 presents the distribution of the experimental results according to the distinct experimental parameters. As can be observed from Fig. 2a, approximately 80% of the database comprises results for tubes with internal diameters of 2.20 and 2.32 mm, and similar parcel corresponds to data for R134a (Fig. 2b). Experimental results for R245fa and R600a correspond to approximately 20 and 3% of the database, respectively. According to Fig. 2c, the majority of the data for R134a concerns saturation temperatures close to 20 and 30 °C while for the refrigerant R245fa only data for saturation temperatures higher than 30 °C are available. This temperature saturation range correspond to two-phase density ratios from 21 to 154, as shown in Fig. 2j. Fig. 2d illustrates that the experimental database comprises results covering a broad range of reduced pressure, varying from 0.04 to 0.28. Experimental results for R245fa correspond to the lowest reduced pressures in the database and, consequently, the highest density ratios, as can be noted in Fig. 2j On the other hand, experimental results for R134a correspond to the highest pr values thus to the lowest reduced density ratios. Results for R600a were obtained only for Tsat of 22 °C, which correspond to qratio of 66. According to Fig. 2e, the database comprises experimental results for mass velocities ranging from 45 to 920 kg/m2s, with significant parcel of data for G between 180 and 620 kg/m2s. Flow conditions for mass velocities higher or lower than this range are inappropriate for heat spreaders because they may imply on high pressure drop and reduced critical heat flux, respectively. Fig. 2f reveals that approximately 50% of the database corresponds to results for heat fluxes lower than 16 kW/m2, which correspond to typical operational conditions of compact heat exchangers. About 37% of the database corresponds to results for heat fluxes between 16 and 60 kW/ m2, and less than 3% for conditions of U higher than 60 kW/m2. This heat flux range correspond to boiling numbers between 5 105 and 1.3 103. According to Fig. 2i, experimental results for R134a and R245fa comprise mostly conditions for Bo lower than 0.7 103. On the other hand, the results for R600a correspond to Bo between 0.3 103 and 1.3 103, with more than 40% of the experimental results for boiling number between 0.56 103 and 0.70 103. Fig. 2g shows that the majority of the experimental results correspond to vapor qualities from 0.1 to 0.7. Data for vapor qualities higher than 0.7 may corresponds to post-dryout conditions and, so, in order of keeping the test section undamaged, the present database includes data only up to the dryout vapor quality.

Table 2 Fluids thermophysical properties. Fluid

Tsat [°C]

psat [kPa]

qv [kg/m3]

ql [kg/m3]

mv [m3/kg]

kl [W/m.K]

ll [kg/m.s]

R134a

21.5 42.5 25.5 58.5 22.0

599 1087 151 442 321

29.1 53.8 8.7 24.6 8.4

1219.8 1136.0 1337.2 1241.4 553.7

0.034349 0.018591 0.115267 0.040712 0.119347

0.0849 0.0744 0.0810 0.0713 0.0900

0.000203 0.000156 0.000403 0.000259 0.000155

R245fa R600a

570

F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583 100

100

a

80

Parcel of data [%]

Parcel of data [%]

80

b

60

40

20

60

40

20

0

1.00, 1.10

0.38

2.20, 2.32

0

2.60

R134a

R245fa

R600a

Fluid

d [mm] 50 100

d

c R134a

40 R134a

R245fa

Parcel of data [%]

Parcel of data [%]

80

R600a 60

40

30

20

R134a

R245fa R134a

10

R600a R245fa

20

R134a

0. 2

0. 2

40

00

.2 8

.2 4

.2 0 0. 1

20 0. 1

0. 0

60

.1 6

.1 2

40-42

80

30 - 32

Tsat [°C]

0. 0

21 - 23

40

0

.0 8

0

p r [-] 25

25

e

35

g

>1 00

80 -1 00

4. 55. 5 9. 510 .5

Φ [kW/m²]

G [kg/m²s] 20

60 -8 0

0

50 -6 0

0

>9 20

5

95 -1 05 18 022 0 28 032 0 38 042 0 48 052 0 58 062 0 68 072 0 88 092 0

5

43 -4 8

10

33 -3 7

10

15

24 -2 6

15

14 -1 6

Parcel of data [%]

20

45 -5 5

Parcel of data [%]

20

f

h

30

Parcel of data [%]

Parcel of data [%]

15

10

5

25 20 15 10 5

x [-]

>1 4

12 -1 4

10 -1 2

810

68

46

24

02

0. 91. 0

0. 80. 9

0. 70. 8

0. 60. 7

0. 50. 6

0. 40. 5

0. 30. 4

0. 20. 3

0

0. 10. 2

0. 00. 1

0

h [kW/m²K]

Fig. 2. Experimental results distribution according to distinct parameters.

According to Fig. 2h most of the heat transfer coefficient results are between 4 and 6 kW/m2K. Values lower than 6 kW/m2K are typical of fin-and-tube evaporators, operating with halocarbon refrigerants under conditions of low mass velocities and heat fluxes. Approximately 12% of the database corresponds to heat

transfer coefficients higher than 10 kW/m2K. Such values are required in heat spreaders of electronics, and correspond to conditions of high G, and U and for the fluid R600a. High heat transfer coefficients correspond also to flow boiling in the 0.38 mm ID tube and for vapor qualities close to the dryout.

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F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583

100

i

j

R134a

R134a

R245fa

80

R600a

Parcel of data [%]

30

20

10

R600a 60

40

20

0

60 -1 0 14

0

-1

40

20

ρratio = (ρl / ρg ) [-]

Bo x 10³ [-]

12

10

0

-1

-1 00

0

0

-8

80

20

60

-4

0

.4 0 -1

1. 2

6

2 1. 1

8

-1

-1

.2 6

.1 2

.9 8

0. 8

0. 9

4

-0

-0

.8 4

.7 0 0 0. 7

0. 5

6

-0

.5 6

.4 2 -0

-0 2 0. 4

8

4 0. 1

0. 2

-0

-0

.2 8

.1 4

0

0 0. 0

R245fa

-6

Parcel of data [%]

40

40

50

Fig. 2 (continued)

a

25

b

Φ [kW/m²] / Bo x10³ 47 / 0.59

20

10 Region with relevant effects of Φ 8

100 / 1.25

15

h [kW/m²C]

h [kW/m²K]

67 / 0.84

10

5

0.2

0.4

R245fa, G = 300 kg/m²s, Tsat ≈ 41 °C, d = 2.32 mm 0.6

0.8

1.0

d

16

h [kW/m²C]

R134a, G = 400 kg/m²s, Tsat ≈ 22 °C, d = 2.32 mm

8

h [kW/m²K]

9

6

0 0.0

Φ [kW/m²] / Bo x10³ 5 /0.07 35/0.48 15/0.21 45/0.62 25/0.35 55/0.76 0.2

0.4

0.2

0.4

0.6

0.8

1.0

x [-]

12

3

4

0 0.0

x [-]

c

Φ [kW/m²] / Bo x10³ 15/0.28 45/0.83 25/0.46 55/1.02 35/0.65

2

R600a, G = 240 kg/m²s, Tsat ≈ 22 °C, d = 2.6 mm

0 0.0

6

0.6

0.8

Φ [kW/m²]/Bo x10³ G = 600 kg/m²s 35 / 0.36 12 45 / 0.46 55 / 0.56

4

1.0

R134a, Tsat ≈ 41 °C, d = 2.32 mm

G = 200 kg/m²s 5 / 0.15 15 / 0.46 25 / 0.77

0 0.0

0.2

0.4

0.6

0.8

1.0

x [-]

x [-] Fig. 3. Evaluation of influence of U on h.

4.2. Analyzes of the experimental data Fig. 3 illustrates the effect of the heat flux on the trends of the heat transfer coefficient with varying the vapor quality. Fig. 3c, for R134a, reveals that the heat transfer coefficient increases with increasing heat flux and also the boiling number. For low heat fluxes, the heat transfer coefficient increases with increasing vapor quality while for the highest heat flux the effect of x on the heat transfer coefficient becomes almost negligible. According to Fig. 3b for R245fa, the heat transfer coefficient increases with increasing heat flux only for vapor qualities lower than 0.4 and heat fluxes higher than 45 kW/m2 (Bo higher than 0.83103). At vapor qualities higher than 0.4, the curves displaying h versus x

converges to a single curve according to which the heat transfer coefficient increases with increasing vapor quality. An analysis of R134a data also reveals that the influence of heat flux is more pronounced under conditions of reduced mass velocity. According to Fig. 3d, under a condition of d = 2.32 mm, Tsat = 41 °C and G equal to 200 kg/m2s, a heat flux variation of 20 kW/m2 (from 5 to 25 kW/m2) corresponds to an increment of h of approximately 4 kW/m2K, while for G equal to 600 kg/m2s a similar heat flux variation causes a increment on the heat transfer coefficient of only 1.5 kW/m2K. The different behaviors of R134a and R245fa are explained based on the relative influence of nucleate boiling and convective effects on the heat transfer coefficient. The vapor specific volume

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of R245fa is about twice higher than of R134a, as can be observed from Fig. 2j. Thus, convective effects and nucleate boiling suppression are enhanced due to the higher two-phase flow velocity of the refrigerant R245fa. Moreover, as can be observed from Fig. 2d the pr values for R134a data are higher than for R245fa data, implying on higher nucleate boiling effects for the first one. The results for R600a were obtained under conditions of higher heat fluxes (from 47 to 100 kW/m2) than for R134a and R245fa, consequently, under higher influence of nucleate boiling effects. Fig. 2i corroborates this predominance, which indicates boiling number values for R600a higher than for R134a and R245fa in general. In this context and according to Fig. 2j, it must be mentioned that even though the density ratio for R600a is higher than that for R134a, the influence of the heat flux overcomes the higher gas velocity of R600a, prevailing the nucleate boiling effects over convective effects on the heat transfer coefficient during flow boiling of the hydrocarbon. As a result, the data for R600a (not shown), for a condition prior the onset of dryout, display that the heat transfer coefficient increases with increasing heat flux. For vapor qualities higher than approximately 0.5, the heat transfer coefficient for this refrigerant decreases abruptly due to onset of dryout. In fact, the vapor specific volume of R600a is approximately four times higher than the value of R134a (Fig. 2j), enhancing droplet detachment from the liquid film by dragging effects, and, consequently, favoring the surface dryout at lower vapor qualities. Fig. 4 illustrates the influence of mass velocity on h. According to Fig 4a and b, the heat transfer coefficient presents two distinct tendencies with increasing vapor quality: (i) h is almost independent of x, and (ii) for vapor qualities higher than a certain value, the heat transfer coefficient increases linearly with increasing x. The threshold vapor quality, characterizing the change of trends, moves to lower vapor qualities as the mass velocity increases, and the boiling number decreases. Based on these behaviors, it can be concluded that the mass velocity effect on the heat transfer coefficient is negligible for vapor qualities lower than the threshold value and that the heat transfer coefficient increases with increasing mass velocity for vapor qualities higher than the threshold vapor quality. As observed for R600a, according to the results for R245fa in a 0.38 mm ID displayed in Fig. 4d, the heat transfer coefficient increases with vapor quality until a peak is achieved, and after this value, additional increments of x imply on the reduction of h due to dryout effects. On contrary to observed for R600a, for R245fa and the tube diameter of 0.38 mm, the vapor quality value corresponding to the heat transfer coefficient peak is independent of G and U. Fig. 4c depicts the variation of h with x for R600a and heat fluxes of 47 and 100 kW/m2. In this figure, for the lowest values of G and U, the heat transfer coefficient is almost independent of x until achieving dryout conditions. However, for the other conditions displayed in Fig. 4c, h increases with x until a peak, and then decreases with additional increments of x. Contrasting behaviors are observed in Fig. 4c for the lowest mass velocity between the data for U = 47 kW/m2 and U = 100 kW/m2. In the case of U = 100 kW/m2, the heat transfer coefficient increases with increasing x until its value achieves a maximum, then, a drastic reduction of h is observed with further increase of the vapor quality. On the other hand, for U = 47 kW/m2, the heat transfer coefficient is almost constant with varying the vapor quality from zero until a threshold vapor quality that characterizes a drastic reduction of the heat transfer coefficient with additional increment of the vapor quality. It must be highlighted from Fig. 4c that the heat transfer coefficient gain with increasing G from 240 to 440 kg/m2s is less pronounced for the highest U, even though the variation of boiling number is approximately 84% for both heat fluxes. This behavior also suggests a counterbalance between nucleate boiling and convective effects; thus, it is not possible to infer a threshold

boiling number characterizing the predominance of either nucleate boiling or convective effects on the heat transfer process. Therefore, additional experimental parameters must be taken into account to characterize this threshold viz. density ratio, phases proportion and the mass velocity. Moreover, it must be emphasized that independently of G and U the heat transfer coefficient values tends to a unique curve, characterized by a drastic decrease of h with increasing x. Fig. 5 illustrates the effect of Tsat on the heat transfer coefficient for flow boiling of R134a in a 2.32 mm ID tube. According to this figure, the effect of Tsat on h is almost negligible for U = 5 kW/m2, and the heat transfer coefficient increases with increasing x independent of the saturation temperature. Such a behavior indicates that, under low heat flux conditions, convective evaporation is the main heat transfer mechanism. On the other hand, for heat fluxes higher than 5 kW/m2, the heat transfer coefficient is independent of x for almost the entire range of vapor quality and increases with increasing the saturation temperature. The progressive predominance of nucleate boiling effects over convective evaporation with increasing heat flux seems responsible for such behaviors. This phenomenon is related to the fact that the number of active sites increases with increasing U and Tsat with both enhancing nucleate boiling effects. On the other hand, the temperature gradient of the fluid close to the wall increases with increasing mass velocity and vapor quality, suppressing nucleate boiling and enhancing convective effects. Fig. 6 illustrates the effect of the tube diameter on the heat transfer coefficient for convective boiling of R134a and R245fa. This figure depicts higher heat transfer coefficients prior the dryout for the 0.38 mm ID tube while almost similar results are observed for 1.00 and 2.32 mm ID tubes. According to Fig. 6c, it seems that decreasing the tube diameter induces an earlier dryout. For small diameter channels, it is important highlighting that the progressive reduction of h with increasing x after the dryout is not as abrupt as for conventional channels. It can be speculated that this difference is due to the following mechanisms: (i) entrained liquid in the vapor core and its deposition along the heated surface; and (ii) intermittent liquid pumping from upstream of the dryout region due to the bubble growth under confined conditions. Both mechanisms promote intermittent rewetting of the channel wall inducing a more gradual reduction of time-averaged heat transfer coefficient. Fig. 7 illustrates the influence of the working fluid on the heat transfer coefficient. According to Fig. 7a, prior to the dryout, the heat transfer coefficient increases with increasing the vapor quality for R600a, while remains almost constant for R134a. From these behaviors, it can be inferred that convective effects are prominent for R600a while nucleate boiling effects are dominant for R134a. Such hypothesis are corroborated by the following aspects: (i) The pool boiling heat transfer coefficient given by the method of Gorenflo et al. [18] reveals a heat transfer coefficient for R134a two times higher than the value predicted for R600a; (ii) The specific volume of the vapor phase of R600a is almost four times higher than for R134a, as can be observed from Fig. 2j. This fact implies an in situ vapor velocity of approximately 4 times higher for R600a than for R134a for the same mass velocity and vapor quality; (iii) The refrigerant R134a presents a higher liquid viscosity than R600a, implying a thicker liquid film during annular flow, and consequently, higher liquid film thermal resistance; (iv) The liquid thermal conductivity is higher for R600a than for R134a, implying lower liquid film thermal resistance for the first one; (v) The boiling number for these experimental conditions for R134a is almost twice that for R600a. On the other hand, these characteristics favor an earlier dryout for R600a than for R134a as shown in Fig. 7a.

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a

8

b

R134a, Φ = 15 kW/m², Tsat ≈ 22 °C, d = 2.32 mm

R134a, Φ = 35 kW/m², Tsat ≈ 31 °C, d = 1.00 mm 12

h [kW/m²K]

6

h [kW/m²K]

16

4

G [kg/m²s] / Bo x10³

2

0 0.0

0.2

0.4

100/0.83

400/0.21

200/0.42

600/0.14

0.6

0.8

8

G [kg/m²s] / Bo x10³ 300/0.68 600/0.34 400/0.51 900/0.23 500/0.41

4

0 0.0

1.0

0.2

0.4

x [-] 25

20

h [kW/m²K]

d

R600a, Tsat ≈ 22 °C, d = 2.6 mm G [kg/m²s] / Bo x10³

15

Φ = 47 kW/m² 240 / 0.59 440 / 0.32

10

4

0.4

0.6

0.8

R245fa, d = 0.38 mm Tsat ≈ 36 ± 2 °C

G [kg/m²s] 300 500 400 600

8

240 / 1.25 440 / 0.68 0.2

1.0

12

5 Φ = 100 kW/m²

0 0.0

0.8

20

16

h [kW/m²K]

c

0.6

x [-]

Φ [kW/m²] 15 35

0 0.0

1.0

55 75 0.2

95 115 0.4

x [-]

0.6

0.8

1.0

x [-] Fig. 4. Evaluation of influence of G on h.

8 Φ = 15 kW/m² T sat [°C] / Bo x10³

h [kW/m²K]

6

b

R134a, G = 200 kg/m²s, d = 2.32 mm

≈ 22 / 0.42 ≈ 31 / 0.44 ≈ 41 / 0.46

4 Φ = 5 kW/m² T sat [°C] / Bo x10³ ≈ 22 / 0.14 ≈ 31 / 0.15 ≈ 41 / 0.15

2

0 0.0

0.2

12

9

h [kW/m²K]

a

0.4

0.6

0.8

T sat [°C] / Bo x10³ Φ = 55 kW/m² ≈ 22 / 0.61 ≈ 31 / 0.64 ≈ 41 / 0.68

6

3

R134a, G = 500 kg/m²s, d = 2.32 mm 1.0

0 0.0

0.2

0.4

0.6

Φ = 5 kW/m² ≈ 22 / 0.05 ≈ 31 / 0.06 ≈ 41 / 0.06 0.8

1.0

x [-]

x [-] Fig. 5. Evaluation of influence of Tsat on h.

Similar conclusions can be obtained by extending the same analysis to the comparison between the data of R134a and R245fa displayed in Fig. 7b. According to the predictive method of Gorenflo et al. [18], the heat transfer coefficient of R134a is almost three times higher than the one of R245fa. The vapor specific volume of R245fa is more than twice the one of R134a. These aspects indicate the predominance of convective effects for R245fa, inferred in Fig. 7b by the increment of h with x, and the predominance of nucleate boiling effects for R134a characterized in the same figure by a heat transfer coefficient independent of vapor quality for U = 25 kW/m2 and d = 2.32 mm. From an analysis of the experimental results of R245fa and R134a for the 0.38 mm ID tube displayed in Fig. 7c, it can be con-

cluded that the refrigerant R245fa presents higher heat transfer coefficients than R134a, under pre-dryout conditions. However, an earlier onset of dryout, characterized by a decrease of h with increasing x, is observed for R245fa compared to R134a. For this last refrigerant, the onset of dryout is not observed even for heat fluxes as high as 95 kW/m2. Based on the trends of the experimental results and on the classification proposed by Tibiriçá and Ribatski [2], Fig. 8 displays the heat transfer behaviors identified in the present study for flow boiling inside small diameter channels. In general, under conditions characterized by the predominance of convective effects, h increases with increasing x until achieving dryout conditions. For vapor qualities higher than the dryout value, further increments

574

h [kW/m²K]

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5. Comparison of experimental data and predictive methods

20

R134a, G = 300 kg/m²s, 16 T ≈ 32 °C sat

Table 3 describes the database used by the original authors for the development of their predictive methods considered in the present analysis. From this table, it can be observed that except for Liu and Winterton [19] and Kandlikar and Balasubramanian [20], all predictive methods were developed based on experimental results that comprise ID tubes smaller than 3 mm. Due to the fact that the test sections are made of stainless steel, the parameter that depends on the surface material and fluid properties proposed by Kandlikar and Balasubramanian [20], FFI, is equal to the unity as recommended by the original authors. The methods proposed by Warrier et al. [21] and Lee and Mudawar [22] were developed based on experimental results for multi

Φ = 55 kW/m² Φ = 35 kW/m²

12 Φ = 15 kW/m²

8

d [mm] 0.38 1.00 2.32

4

0 0.0

0.2

0.4

0.6

0.8

1.0

x [-]

16

h [kW/m²K]

a

20

R134a, G = 500 kg/m²s, Tsat ≈ 32 °C

13.5

Φ = 75 kW/m²

12

8

Φ = 55 kW/m²

4

Φ = 15 kW/m²

0 0.0

0.2

0.4

0.6

0.8

b

12

Φ = 15 kW/m²

Φ = 55 kW/m²

0.2

0.4

0.6

0.8

1.0

16

12

Dec rement due to wall dryout

h [kW/m²K]

h [kW/m²K]

16

R134a, Φ = 45 kW/m², G = 400 kg/m²s, d = 2.32 mm, Bo=0.62x10-3

x [-]

1.0

20

R245fa, G = 300 kg/m²s, Tsat ≈ 32 °C

R600a, Φ = 47 kW/m², G = 440 kg/m²s, d = 2.60 mm, Bo=0.32x10-3

0.0 0.0

x [-]

c

9.0

4.5

d [mm] 0.38 1.00 2.32

Φ = 35 kW/m²

18.0

T sat ≈ 22 °C

Φ = 95 kW/m²

h [kW/m²K]

b

8

Φ = 15 kW/m² d = 1.00 mm R134a, Bo=0.44x10-3 R245fa, Bo=0.40x10-3 Φ = 25 kW/m² d = 2.32 mm R134a, Bo=0.73x10-3 R245fa, Bo=0.67x10-3

8

4 Φ = 35 kW/m²

0 0.0

0.2

0.4

4

d [mm] 0.38 1.00 2.32 0.6

0.8

G = 200 kg/m²s, Tsat ≈ 31 °C 0 0.0

1.0

x [-]

0.4

0.6

0.8

1.0

x [-]

c 20

Fig. 6. Evaluation of influence of d on h.

16

h [kW/m²K]

of x implies on the reduction of the heat transfer coefficient. Moreover, the vapor quality corresponding to the onset of dryout xdi decreases with increasing G. On the other hand, when nucleate boiling is the main heat transfer mechanism, h increases with increasing U and Tsat independently of G and x. The effect of saturation temperature on h is negligible under conditions of predominance of convective evaporation. In general, prior the dryout the heat transfer coefficient increases with decreasing the tube diameter from 1.00 to 0.38 mm. The effect of tube diameter on h becomes negligible for tube diameters higher than 1.00 mm. On the other hand, xdi increases with increasing the tube diameter.

0.2

R134a G = 300 kg/m²s G = 600 kg/m²s

R245fa G = 300 kg/m²s G = 600 kg/m²s

12

8

Φ [kW/m²]

4

15 35

d = 0.38 mm, Tsat ≈ 36 ± 2 °C 0 0.0

0.2

0.4

0.6

55 75 0.8

x [-] Fig. 7. Evaluation of working fluid influences on h.

95 115 1.0

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F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583

h

with G , and xdi with G .

, and h with present “V” format with x .

h with Tsat for reduced x, and does not depends on Tsat for high x.

h

with d until dryout.

Fig. 8. Verified trends for experimental results.

Table 3 Experimental conditions of database used for predictive methods development. Author

Fluid

U [kW/m2]

G [kg/m2s]

Dir.

pr [–]

Geo.

d [mm]/w h [mm2]

Liu and Winterton [19]

H2O, R11, R12, R113, R114, ethylene-glycol R12, R113 –

0.352620

12.48179.3

l?

0.00230.895

O

2.9532

3.6129 0.032280

44832 138179

? "?

0.045; 0.12; 0.20 –

O‘ O

2.46, 2.92, 4.06 1.70 432

FC-84 R11, R12, R113, R123, R134a, R141b, CO2 H2O, R11, R12, R113

089 2178

5571600 50564

? l?

– 0.0320.778

‘ O‘

0.7a 1.1, 3.1, 1.47 3.28, 0.73 0.72

2.952511

23.42939

l?

0.00460.211

O‘

R134a, H2O R134a R134a R11, R12, R123, R134a, R141b, R22, R404a, R407c, R410a, CO2, H2O R134a R134a, R245fa R245fa, R236fa, R1234ze(E) R134a

1591300 539 0200 5109

127654 150742 20.381 441500

? ? ? "?

0.00530.162 0.08620.1204 0.09850.1845 0.00450.6103

‘ O ‘ O‘

1.45, 6.0, 1.70 4.06, 0.4 20, 1.0 20, 2 20 0.231 0.713 0.5110.92 0.762 1.905 0.216.5, 0.3 12.7, 0.214 0.214, 1.47 3.28, 1.2 1.79, 1.2 1.57

0350 5200 8.3400

3001500 501500 3111290

? ? ?

0.1210.286 0.05030.257 0.049580.3249

O O O‘

Tran et al. [44] Kandlikar and Balasubramanian [20]b Warrier et al. [21] Thome et al. [26] Zhang et al. [34] Lee e Mudawar [22] Saitoh et al. [24] Bertsch et al. [36] Sun and Mishima [37]

Basu et al. [54] Tibiriçá [33] Costa-Patry et al. [31] a b c

c

0.5, 0.96, 1.60 1.00, 1.10, 2.20, 2.32 1.03, 2.20, 3.04, 0.085 0.560, 0.163 1.560

Only hydraulic diameter was informed. Experimental database presented by Kandlikar [55]. Used Cioncolini e Thome [32] method for annular flow, and adjusted Thome et al. [26] method for elongated bubble flow pattern.

rectangular channels. Therefore, it is expected that these methods provide unsatisfactory predictions of the database, because flow boiling in multichannel layout is subjected to plenums effects, as well as flow maldistribution among the channels. In this context, Do Nascimento et al. [23] present an extensive discussion concerning the differences between results for single- and multi-channels test sections. In the present analysis, the method of Saitoh et al. [24] was implemented as performed by the original author i.e. considering only turbulent regime for the liquid phase in the evaluation of the Martinelli parameter and the single-phase heat transfer coefficient. Analysis considering laminar flow were also performed, however worst predictions were obtained. Due to the fact that Warrier et al. [21] did not mention the method considered by them for the estimative of the single-phase heat transfer coefficient, in the present study their method was implemented assuming a constant Nusselt number equal to 4.36 for Re < 1000 and the Gnielinski [17] correlation for Re > 2300. For Reynolds numbers within the range from 1000 to 2300, it is adopted a linear interpolation between the heat transfer coefficients for Reynolds numbers equal to 1000 and 2300 weighted according to the Reynolds number. Except for the minimum film thickness assumed as the surface roughness, the empirical constants presented by Dupont et al. [25] were considered for the implementation of the three-zone model proposed by Thome et al. [26]. The surface roughness was also

adopted by Thome and coworkers in their most recent studies, e.g. Ong and Thome [27,8], Agostini et al. [28–30] and CostaParty et al. [31]. The remaining predictive methods were implemented in the present analysis as they were proposed in their original publications. The method proposed by Costa-Party et al. [31] consists of a combination of Cioncolini and Thome [32] method for annular flow and Thome et al. [26] method for elongated bubble flow, with the transition between these flow patterns given according to Ong and Thome [27]. The method of Cioncolini and Thome [32] was developed specifically for annular flow, and, so, give the same predictions of the method of Costa-Party et al. [31] for this flow pattern. Therefore, the method of Cioncolini and Thome [32] was not included in the analysis. The method of Thome et al. [26] is included in the present analysis, because although the method was developed for elongated bubble flow, the authors considered results for annular flow in the database used for the adjustment of the empirical constants of the method. The method of Kandlikar and Balasubramanian [20] was implemented as recommended by the original authors, adopting the term FFI equal to the unity. Nonetheless, it is possible to evaluate the value of FFI based on the experimental results, which resulted in average values of 1.10, 1.03 and 1.49 for R134a, R245fa and R600a, respectively, with standard deviations of 0.33, 0.20 and 0.62. Based on these results, it can be concluded that adopting FFI = 1 is not reasonable only for the R600a.

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Table 4 Statistical parameters resulting from the comparison. Author

c30 [%]

c20 [%]

u [%]

e [%]

Liu and Winterton [19] Tran et al. [44] Warrier et al. [21] Kandlikar and Balasubramanian [20] Thome et al. [26] Zhang et al. [34] Lee and Mudawar [22] Saitoh et al. [24] Bertsch et al. [36] Sun and Mishima [37] Basu et al. [54] Tibiriçá [33] Costa-Patry et al. [31]

86 59 11 50 47 83 1 94 51 76 43 95 68

66 48 6 31 28 65 1 81 19 62 28 89 54

3 26 55 33 7 6 77 11 31 7 34 2 14

17 28 58 34 32 18 77 14 32 21 40 11 24

Table 4 presents the statistical parameter obtained from the comparison between the predictions and the experimental results. The results of comparisons are given in terms of the parcel of experimental results predicted within error bands of ±30 and 20%, c30 and c20, respectively, and the mean relative deviation u and the absolute mean relative deviation e, defined as follows:

/¼

N 1X hexp;i hest;i N i¼1 hexp;i

ð6Þ

e¼

N 1X hexp;i hest;i N i¼1 hexp;i

ð7Þ

As can be observed from Table 4, the methods proposed by Tibiriçá [33], Saitoh et al. [24], Liu and Winterton [19] and Zhang et al. [34] presents satisfactory predictions of database, predicting more than 80% of the experimental results within an error band of ±30%. In fact, the method proposed by Tibiriçá [33] was developed based on a significant parcel of the present database, except for the experimental results of 0.38 and 2.60 mm ID tubes. Saitoh et al. [24] developed their method based on experimental results for R134a, and as presented in the previous section, this fluid corresponds to approximately 80% of the present database. These coincidences of database characteristics favor good agreement between the predictions and the experimental database. The methods of Liu and Winterton [19] and Zhang et al. [34] do not comprises results for R134a, R245fa and R600a in their adjustment, even though these methods showed good agreement with experimental results. Moreover, the method of Liu and Winterton was developed based on experimental data for channels with internal diameter higher than 2.95 mm, so, out of the range of the present database. It should be highlighted that the methods of Tibiriçá [33], Saitoh et al. [24], Liu and Winterton [19] and Zhang et al. [34] were developed based on the approach proposed by Chen [35], which consists of the superposition of convective and nucleate boiling effects including convective enhancement and nucleate boiling suppression factors. This fact corroborate the conclusions pointed out from the data analyses presented in the previous item, according to which heat transfer behaviors seems characterized by the superposition of nucleate boiling and convective effects. The methods proposed by Warrier et al. [21], Thome et al. [26], Lee and Mudawar [22], Bertsch et al. [36], Sun and Mishima [37] and Costa-Party et al. [31] predicted less than 80% of the experimental results within an error band of ±30%. Contributes for such results, the fact that in the development of these methods data for multichannel configurations with rectangular cross sections were considered. It is expected that the boiling process under these conditions is different from for a single circular channel. In fact, the corners of the rectangular geometry results in a non-uniform film

thickness along the channel perimeter as observed for small diameter circular channels. Bubble nucleation is favored at the channel corners. Moreover, due to the different manufacturing process, different surface finishing are expected between rectangular multichannel configurations and circular single channels. As pointed out by Do Nascimento et al. [23], flow boiling in multichannels configurations is susceptible to reverse flow due to bubble growth under confined conditions, to interactions among neighbor channels due to conduction through the fins separating them, and to the influence of inlet and outlet plenums on the refrigerant maldistribution. Frequently, individual restrictions at the inlet of each channel are used for damping thermal instabilities effects and for minimizing maldistribution. However, this procedure causes additional uncertainties on the characterization of the thermodynamic state of the fluid downstream the restriction and, consequently, on the estimative of the heat transfer coefficient. For single channels, the flow restriction is implemented through a needle valve located upstream the channel inlet and the thermodynamic state of the fluid is evaluated based on its temperature and pressure measured downstream the singularity. It is expected that methods for prediction of the heat transfer coefficient are not only accurate in terms of average statistical parameters, but also capture the main trends of the experimental results. In this context, Fig. 9 presents the parcel of experimental results predicted with an error band of ±30% according to different operational ranges for the four best predictive methods according to Table 4. From Fig. 9a–c, it can be observed that the data for R600a are poorly predicted by the methods. On the other hand, Saitoh et al. [24] and Tibiriçá [33] methods predicted almost 100 and 90% of the results for R134a and R245fa, respectively, within an error band of ±30%. None of the methods was able of predicting satisfactorily experimental results for d = 2.60 mm, performed only for R600a, while they predicted satisfactorily results for d smaller than 2.3 mm. It should be highlighted the fact that Saitoh et al. [24] method correctly predicted diameter influence, since it predicts more than 80% of results for d = 0.38 mm within an error band of ±30%. This can be justified based on the database used by the authors to develop their method, which comprises experimental results for circular tubes with ID ranging from 0.51 to 10.92 mm, while the remaining methods considered only results for diameters higher than 1.00 mm. It should be highlighted the fact described in the previous section, according to which the influence of diameter on the HTC becomes more pronounced for conditions of d smaller than 1 mm. According to Fig. 9d, the methods of Saitoh et al. [24] and Tibiriçá [33] provides values of c30 higher than 80%, independent of the range of mass velocity. Fig. 9e shows that none of the methods is able to satisfactorily predict the experimental results for x higher than 0.8, while Saitoh et al. [24] and Tibiriçá [33] predicted more than 90% of the data within an error band of ±30% for x lower than 0.8. Liu and Winterton [19] method also predicted reasonably well experimental results for x ranging from 0.2 to 0.8. The fact that the heat transfer coefficient increases with x until achieving a maximum value and then decreases with further increase of the vapor quality due to dryout effects is only predicted by the methods of Saitoh et al. [24] and Tibiriçá [33]. This fact justify the reason for the methods of Liu and Winterton [19] and Zhang et al. [34] providing much worst predictions of the experimental results for x higher than 0.8. In this context, it is important to highlight that the correct estimative of the vapor quality corresponding to the onset of dryout, xdi, greatly affects the estimative of the heat transfer coefficient for post-dryout conditions. Fig. 9f reveals that none of the methods provides satisfactory predictions of the experimental results for U higher than 80 kW/ m2. Despite of the fact that the database considered by Saitoh

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F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583

a

b 100

100

Liu and Winterton [23]

R134a

R134a

Zhang et al. [37]

γ30 [%]

Tibiriçá [15]

γ30 [%]

R134a

80

Saitoh et al. [28] 80

R134a R245fa

60

60 R600a R245fa 40

40

20 20

.2 8 24 -0

20 -0

.2 4 0.

0.

0.

0.

16 -0

.1 6 12 -0

.1 2 0.

08 -0

.0 8

R600a

04 -0

R245fa

0.

R134a

.2 0

0 0

p r [-]

c

d 100

100

80

γ30 [%]

γ 30 [%]

80

60

40

60

40

R600a

20 20

48 068 0

>6 80 >8 0

d [mm]

48 -8 0

2.60

28 048 0

2.32

10 528 0

1.00

45 -

0.38

10 5

0 0

G [kg/m²s]

80

60

60

40

40

4. 510 .5

0.

0.

0.

0.

0.

81. 0

0 60. 8

0 40. 6

20

20. 4

20

26 -4 8

γ 30 [%]

80

x [-]

g

100

10 .5 -2 6

f

00. 2

γ30 [%]

e

100

Φ [kW/m²]

100

γ30 [%]

80

60

40

20

h [kW/m²K]

>1 2

912

69

36

03

0

Fig. 9. Analysis of predictive methods for distinct experimental ranges.

et al. [24] comprises results for U up to 39 kW/m2, while the other methods comprise results for U up to at least 200 kW/m2, the method of Saitoh et al. provides better predictions of the data

obtained under conditions of high heat fluxes. Moreover, although the method of Saitoh et al. [24] is based on experimental results for G lower than 150 kg/m2s, this method provides satisfactory

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predictions of the results for mass velocities higher than this value. These evidences suggest that the nucleate boiling suppression and convective enhancement factors were well defined by the authors, and that the adoption of the Stephan and Abdelsalam [38] correlation for the estimative of nucleate boiling parcel is appropriate. Finally, according to Fig. 9g, the methods poorly predicted the experimental results for h higher than 12 kW/m2K, which correspond to experimental results for R600a, x higher than 0.8 and high heat fluxes.

6. New predictive method for the heat transfer coefficient during flow boiling inside small diameter channels None of the methods for the estimative of the heat transfer coefficient evaluated in the previous item was able of providing accurate predictions of the results for conditions of h values higher than 12 kW/m2K. In the present study, such high heat transfer coefficients correspond to conditions of high heat flux and vapor quality, consisting of the data for the tube with d = 0.38 mm and for the refrigerant R600a. Moreover, the evaluated methods also failed in order to predict dryout conditions. This is not surprising because most of them neglects the surface dryout. In this item, a new predictive method is proposed based on the approach presented by Saitoh et al. [24]. This approach was considered as initial step for the development of the new method due to the following aspects: (i) based on the analysis of the experimental results and the comparison of these data with the methods from literature, it was found that the approach of Saitoh et al. [24] seems to capture the effects of the superposition of nucleate boiling and convective effects on the heat transfer coefficient; (ii) the approach of Saitoh et al. [24] considers the effects of dryout inception on the heat transfer coefficient. The new method considers the following heat transfer mechanisms according to the vapor quality range: (i) convective boiling, comprising vapor qualities from the onset of nucleate boiling until the dryout inception; (ii) dryout region, covering vapor qualities from the dryout inception to its completion, corresponding to x = 1; (iii) forced convection for gas single-phase flow, corresponding to x values higher than the dryout completion vapor quality.

6.1. Convective boiling The method of Saitoh et al. [24] is based on the superposition of nucleate boiling hnb and convective hc heat transfer coefficients as follows:

h ¼ Fhc þ Shnb

ð8Þ

where F is the enhancement factor of convective effects and S is the factor relative to the suppression of nucleate boiling due to the twophase flow acceleration as result of the evaporation process. In the present study, asymptotic exponents different than 1 in Eq. (8), as suggested by Kutateladze [39] were evaluated, nonetheless, worst predictions of the experimental data were obtained According to Saitoh et al. [24], the nucleate boiling effects are estimated by the correlation of Stephan and Abdelsalam [38] for pool boiling of halocarbon refrigerants, given as follows:

hnb ¼ 207

0:745 0:581 kl Ud qv ll ql cpl 0:533 d kl T sat ql ql kl

ð9Þ

In the new method, besides Eq. (9) for halocarbon refrigerants, the correlation for hydrocarbons proposed by Stephan and Abdelsalam [38] was considered for R600a. This correlation is given by the following equation:

hnb ¼ 0:0546 " #0:670 2 !0:248 kl qv 0:5 Udb ql qv 4:33 2 ql c pl ilv db db ql kl T sat ql kl ð10Þ where k is thermal conductivity, U is the heat flux, Tsat is the saturation temperature (in Kelvin), q is fluid density, l is dynamic viscosity, cp is the specific heat at constant pressure, and ilv is the vaporization enthalpy. The sub-indexes l and v refer to liquid and gas phases, respectively. Stephan and Abdelsalam [38] recommend the adoption of the bubble equilibrium break-off diameter in an infinite quiescent medium as the characteristic length db.

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ db ¼ 0:51 2r=½gðql qg Þ

ð11Þ

where r is the surface tension. In the development of the new method, the pool boiling correlations of Ribatski and Saíz-Jabardo [40], Cooper [41] and Gorenflo et al. [18] were also evaluated providing worst predictions of the experimental database. The heat transfer coefficient related to convective effects hc is estimated assuming only the liquid phase flowing in the tube as turbulent flow given by the correlation of Dittus and Boelter [42] according to the following equation:

hc ¼ 0:023

kl 0:8 1=3 Re Prl d l

ð12Þ

where d is the tube diameter, Rel is the liquid Reynolds number and Prl is the liquid Prandtl number. The liquid Reynolds number is given as follows:

Rel ¼

Gð1 xÞd

ll

ð13Þ

Empirical constants for the new method were also obtained considering both the correlation of Gnielinski [17] for transitional and turbulent Reynolds numbers and a liquid Nusselt number of 4.36 for laminar liquid flows. However, these approaches provided worst predictions of the experimental data compared to Dittus and Boelter [42]. For annular flow that is the dominant flow pattern in small diameter channels, drag effects of the vapor on the liquid film induces waves on the film surface and, consequently, the detachment of liquid droplets, decreasing the film thickness. For flow boiling in micro-scale channels compared to conventional channels, liquid droplet detachment is enhanced due to the higher velocity gradients close to the wall for the same two-phase superficial velocity. The enhancement of film waviness and droplet detachment causes the reduction of the thermal resistance of the liquid film. Recently, Tibiriçá and Ribatski [12] published images illustrating the interfacial waves under conditions of high vapor qualities (close to dryout) for a tube with internal diameter of 400 lm. Based on numerical simulations for annular flow, during condensation inside small diameter channels, Da Riva et al. [43] pointed out that the effect of increasing mass velocity on the heat transfer coefficient is only captured when turbulent effects within the liquid film are taken into account, even for liquid Reynolds numbers down to 600. These facts imply that characterizing the liquid film as laminar considering a superficial analysis taken into account only the liquid Reynolds number based on the tube diameter is not correct. Moreover, estimative of hc based on the correlation of Dittus and Boelter [42] combined with an appropriate formulation for the convective enhancement factor is able of capturing the effects of waviness and turbulence within the film on the heat transfer coefficient, giving suitable representations of the convective contribution to the heat transfer process.

F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583

The formulation of the convective enhancement factor as proposed by Saitoh et al. [24] was modified in the present study through the inclusion of a multiplicative constant cF,1 as follows:

F ¼1þ

cF;1 X cF;2 1 þ WecuF;3 v

ð14Þ

The Weber number in Eq. (14), based on the gas in situ velocity, and the gas velocity uv are given respectively as follows:

qud Weuv ¼ v v 2

uv ¼

Gx

ð16Þ

qv a

In the new method, the void fraction a in Eq. (16) is evaluated according to Kanizawa and Ribatski [44] method, developed based on the principle of minimization of kinetic energy. This method takes into account the cross-sectional velocities distribution of both phases and is based on more than 2300 experimental data points covering tubes with internal diameters from 0.50 to 89 mm and mass velocities from 37 to 4500 kg/m2s. This method predicted more than 92% of the data for horizontal flows within an error band of ±10%. According to this method, the void fraction is given as follows:

"

a ¼ 1 þ 1:021 Fr0:092 m

ll lv

0:368

qv ql

1=3 2=3 #1 1x x

ð17Þ

where the Froude number Frm relative to the two-phase mixture is given as follows:

Fr m ¼

G2

ð18Þ

ðql qv Þ2 gd

In Eq. (14), the Lockhart–Martinelli parameter X is estimated assuming turbulent flow for the liquid phase as recommended by Da Riva et al. [43]. Therefore, X is given as follows:

8 0:9 qv 0:5 ll 0:1 > < X tt ¼ 1x for Rev > 1000 x ql lv X¼ 0:5 > ll 0:1 : X ¼ 1 Re0:4 1x 0:9 qv for Rev 6 1000 tl v 18:7 x q l l

ð19Þ

v

In the new method, the nucleate boiling suppression factor S is given as follows: c

S¼

cS;1 Bd S;2 1 þ cS;3 ðRe2p;mod =10000ÞcS;4

ð20Þ

Differently than Liu and Winterton [19] and Saitoh et al. [24], in the new method, the factor S includes the Bond number Bd to capture effects of confined bubble growth on the suppression of nucleate boiling. In fact, during convective boiling in micro-scale channels, the bubble size increases with a square root time dependence after its detachment, achieving almost immediately the size of tube diameter, as pointed out by Tibiriçá and Ribatski [12]. Therefore, the predominance of convective effects is induced at lower vapor qualities with decreasing tube diameter due to an earlier transition to elongated bubbles flow pattern. The two-phase modified Reynolds number Re2p,mod and the Bond number in Eq. (20) are given respectively as follows:

Re2p;mod ¼ Rel0 F 1:25 ðql qv Þd g

ð21Þ

2

Bd ¼

r

The constants and exponents cF,i and cS,i were obtained through regression analyses of the entire database described in the item 4, using the fitting function with robust method for least absolute residual (LAR) from Matlab [45]. The nucleate boiling suppression and convective enhancement factors with the calculated coefficients and exponents are given as follows:

F ¼1þ

ð15Þ

r

ð22Þ

where Rel0 is the Reynolds number evaluated assuming the mixture flowing as liquid, F is the intensification factor given by Eq. (14), g is the gravitational acceleration and r is the surface tension.

579

S¼

2:50X 1:32

ð23Þ

1 þ We0:24 uv 1:06Bd

8:103

1 þ 0:12ðRe2p;mod =10000Þ0:86

ð24Þ

Thus, the heat transfer coefficient for convective boiling conditions is given by Eq. (8) assuming the enhancement and suppression factors given by Eqs. (23) and (24), respectively, and the heat transfer coefficients corresponding to nucleate boiling and convective effects given by Eqs. (9)–(11). 6.2. Dryout inception The establishment of dryout conditions depends on two-phase flow characteristics, working fluid, heat flux, test section geometry (including channel diameter, wall material and surface roughness) and also from the characteristics and operational conditions of the experimental loop responsible for supplying the refrigerant to the test section. As pointed out by Tibiriçá et al. [3], all these parameters affects the occurrence in the test section of flow instabilities which are intrinsically related to the dryout appearance. In the present study, the vapor quality for dryout inception xdi is considered as equal to the critical vapor quality xcrit, which is determined assuming the critical heat flux (CHF) as the imposed heat flux U. This approach is adopted based on the fact that predictive methods for critical heat flux have been proven accurate over broad databases. On the other hand, experimental data for dryout inception in small diameter tubes are quite rare and, so, it is not surprising the absence of consensus in the literature about the mechanism leading its occurrence. It should be emphasized that this approach overestimate the dryout inception vapor quality, because the CHF is expected to occur closer to the dryout completion vapor quality. Based on this approach, assuming xdi as equal to the critical vapor quality, xdi is obtained from the simultaneous solution of a CHF predictive method from the open literature, e.g. Zhang et al. [46], Katto and Ohno [47], Ong and Thome [8], Wojtan et al. [48] or Tibiriçá et al. [15] and an equation consisting of an energy balance over a heated length. In this procedure, Tsat, G, D, xi (inlet vapor quality) and U (the applied heat flux) are the known parameters. Solving a CHF predictive method with the known conditions and equaling the CHF = U, the critical heated length, Lcrit, consisting the tube length necessary for achieving the dryout inception is obtained. Next, solving the energy balance equation with the know conditions plus Lcrit, the dryout inception vapor quality, xdi, is determined. Fig. 10 and Table 5 presents comparisons of estimative of xdi based on CHF methods from literature and experimental data gathered in the open literature from the studies of Saitoh et al. [49], Tibiriçá and Ribatski [10] and Ali and Palm [50]. In general, the method of Zhang et al. [46] provides the best predictions of the experimental results, predicting 45% of the entire database within an error margin of ±30%. The method of Ong and Thome [8] predicted 100% of the data of Ali and Palm [50] for dryout completion within an error margin of ±30%. However, Ong and Thome [8] predicted 4% of the xdi data of the same authors within the same error margin. The method of Zhang et al. [46] is less accurate for the data

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1.6

hv 0 ¼ 0:023

kv 0:8 1=3 Rev 0 Prv d

ð25Þ

where Rev0 is the Reynolds number for the mixture flowing as gas and Prv is the vapor Prandtl number as follows:

1.2

xdi predicted [-]

6.4. Method implementation The method for estimative of the heat transfer coefficient during flow boiling inside small diameter tube is implemented as following:

0.8

First, xdi is calculated based on the procedure described in the Section 6.2; Then: o for x < xdi the heat transfer coefficient is given by the procedure described in Section 6.1 through the solution of Eqs. (8)–(24); o for xdi 6 x 6 1 the heat transfer coefficient is given as a linear interpolation weighted by x of the heat transfer coefficient for x = xdi based on Eqs. (8)–(24) for convective boiling and the heat transfer coefficient for the mixture flowing as gas given by Eq. (23), as follows:

Ong and Thome [8] Tibiriçá et al. [15] Zhang et al. [46] Katto and Ohno [47] Wojtan et al. [48]

0.4

0.0 0.0

0.4

0.8

1.2

1.6

x di experimental [-]

Fig. 10. Comparison between experimental and predicted values for xdi from Saitoh et al. [49], Tibiriçá and Ribatski [10] and Ali and Palm [50].

h ¼ hEq:ð8Þ ðxdi Þ

of Ali and Palm [50], which were obtained under conditions of subcooled R134a at the test section inlet. The experimental results of Saitoh et al. [49] and Tibiriçá and Ribatski [10] were obtained for saturated conditions at the test section inlet, therefore, under conditions similar to those of the experimental results evaluated in the present study. According to the experimental results presented by Saitoh et al. [49], the dryout completion occurs for gas single-phase flow. The experimental results presented by Tibiriçá and Ribatski [10] do not comprise dryout completion. In order of keeping the test section undamaged, dryout completion conditions were avoided by them during their experiments using electrical heating. Based on the above analyses, the method of Zhang et al. [46] is suggested for prediction of xdi according to the procedure proposed in the present study. However, additional experimental studies focusing on the characterization of the vapor qualities at dryout inception and completion are recommended in order of developing more accurate heat transfer predictive methods.

1x x xdi þ hv 0 1 xdi 1 xdi

ð26Þ

6.5. Evaluation of the proposed methodology The method proposed in the present study predicts more than 97 and 88% of the experimental data within an error band of ±30 and ±20%, respectively, and provides an e value of only 11%. Such a performance correspond to better predictions than those provided by the methods from literature evaluated in the present study. According to Fig. 11 displaying hpredicted vs. hexperimental, most of the data are predicted within ±20%. The proposed method presents good agreement with the experimental results, except with parcel of the experimental results for R600a, similar to the methods available in the open literature. As shown in Fig. 12, the method proposed in this study captures reasonably well the effects of mass velocity, heat flux, vapor quality and tube diameter for the refrigerants R134a and R245fa. Moreover, for these fluids, the method also predicts satisfactorily the dryout inception, and the increment of heat transfer coefficient with increasing x and G for conditions close to the dryout. Unfortunately, the method fails to predict the heat transfer coefficient of the refrigerant R600a for intermediary and high vapor qualities due to the much earlier dryout inception observed for this fluid (not shown in Fig. 12).

6.3. Gas single-phase flow For x 1, corresponding to single-phase vapor flow, the correlation of Dittus and Boelter [42] is recommended for the estimative of the heat transfer coefficient, given as follows: Table 5 Statistical analysis of the comparison between experimental and predicted xdi values. Database

Entire database

Parameter

a

Saitoh et al. [49] Tibiriçá and Ribatski [10] Ali and Palm [50] – Inception Ali and Palm [50] – Completion a

Results for inception.

c30 [%] e [%] c30 [%] e [%] c30 [%] e [%] c30 [%] e [%] c30 [%] e [%]

Method Katto and Ohno [47]

Ong and Thome [8]

Tibiriçá [33]

Wojtan et al. [48]

Zhang et al. [46]

36 61 60 47 78 43 4 77 0 66

2 124 0 125 0 149 4 114 100 18

36 66 60 51 78 51 4 82 0 72

40 92 60 78 56 97 22 99 0 80

45 46 60 40 89 35 17 55 0 92

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F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583 Table 6 Independent experimental conditions of databases for h from the literature.

105

R134a

Working fluid

+20%

R245fa

Li et al. [51] R1234yf, R32 2.0 100–400 Choi et al. [52] R1234yf, R290 1.5, 3.0 150–435 Consolini and R134a, R236fa 0.51, 0.79 300–1400 Thome [53]

R600a

hpredicted [W/m²K]

G [kg/m2s] U [kW/m2] Tsat [°C]

d [mm]

-20%

15 0–11 24–33

Table 7 Comparison between independent databases and predictive methods.

104

Database

Condition

Parameter

Proposed method

Entire database

e [%] c30 [%]

17 89

R1234yf R32

c30 [%] c30 [%]

89 90

Entire database

e [%] c30 [%]

97 57

R290 R1234yf

c30 [%] c30 [%]

32 81

d = 1.5 mm d = 3.0 mm

c30 [%] c30 [%]

18 35

Entire database

e [%] c30 [%]

16 93

R134a R236fa

c30 [%] c30 [%]

96 88

d = 0.51 mm d = 0.79 mm

c30 [%] c30 [%]

95 86

Li et al. [51]

Choi et al. [52]

3

10 103

104

105

hexperimental [W/m²K] Fig. 11. Comparison between predicted and experimental results for heat transfer coefficient.

In order to check the accuracy of the proposed method to predict independent databases, experimental results gathered in the open literature from Li et al. [51], Choi et al. [52] and Consolini and Thome [53] were compared with the predictions given by the new method. Table 6 present a brief description of these databases and Table 7 gives the statistical parameters resulting from the comparisons between experimental and predicted values. Fig. 13 displays a comparison between the independent database gathered in the literature and the corresponding prediction provided by the new method. As shown in Fig. 13 and Table 7, the new method satisfactorily predicts the experimental results of Li et al. [51], Choi et al. [52] and Consolini and Thome [53] for R1234yf, R32, R134a and R236fa. However, unsatisfactory predictions are observed for the results of Choi et al. [52] for the hydrocarbon R290 (C3H8), similar to verified for the results for hydrocarbon R600a discussed in this study. The reduced pressure for the experimental conditions for R290 presented by Choi et al. [52] is approximately 0.15, which is closer to the conditions for R600a performed by Copetti et al. [14] and depicted in Fig. 2. Nonetheless, the heat flux is considerably lower, ranging from 5 to 15 kW/m2, thus it can be

Consolini and Thome [53]

argued that the discrepancy between the predicted and experimental values are mainly related to the fluid characteristics of hydrocarbons and to the reduced pr of the experimental databases. In the case of R600a results (characteristic of high U) the method usually under predicts the experimental results, while for R290 (characteristic of reduced and intermediate U) the method over predicts the results. Hence, for hydrocarbons the effect of the heat flux on the HTC is not properly captured by the proposed method. This fact can be attributed to the imprecise prediction of the boiling parcel of the heat transfer coefficient. Nonetheless, these experimental results were also compared with the predictive methods of Saitoh et al. [24] and Liu and Winterton [19], which presented reasonable estimative of the database of this study. The method proposed in this study presented better predictions than the methods from the literature, except for the results for R290 of Choi et al. [52], which 59% of the data was correctly predicted within ±30% margin error by Saitoh et al. [24] method. 14000

20000

R245fa

R134a, d = 1.00 mm, T sat = 31 °C

12000

15000

10000

h [W/m²K]

h [W/m²K]

4–24 5–24 12–200

10000

6000 4000

5000 G = 200 kg/m²s, Φ = 15 kW/m² G = 300 kg/m²s, Φ = 15 kW/m² G = 900 kg/m²s, Φ = 55 kW/m²

0 0.0

8000

d = 1.00 mm, G = 200 kg/m²s, Φ = 15 kW/m², Tsat = 31 °C d = 2.32 mm, G = 300 kg/m²s, Φ = 10 kW/m², Tsat = 31 °C d = 2.32 mm, G = 300 kg/m²s, Φ = 15 kW/m², Tsat = 42 °C

0.2

0.4

x [-]

0.6

0.8

2000

1.0

0 0.0

0.2

0.4

x [-]

Fig. 12. Comparison between experimental and estimated heat transfer coefficient.

0.6

0.8

1.0

582

F.T. Kanizawa et al. / International Journal of Heat and Mass Transfer 93 (2016) 566–583

method considers the occurrence of surface dryout. The dryout inception is estimated based on Zhang et al. [46] predictive method for CHF, and assumes xdi as xcrit for the CHF equal to the imposed heat flux. The new method predicted 97% of the experimental database used on its development within an error margin of ±30%; The proposed method also provided satisfactory predictions of independent experimental results presented by Li et al. [51], Choi et al. [52] and Consolini and Thome [53] for R134a, R1234yf, R236fa and R32;

105

+30%

hpredicted [W/m²K]

-30% 104

Acknowledgements

10

3

The authors gratefully acknowledge the Grants given by FAPESP (São Paulo Research Foundation) under Contract Numbers 2010/20670-2, 2014/06902-9, 2015/00854-5, 2011/01372-3 and 2011/50176-2, respectively. The third author also acknowledge the Grant number 303852/2013-5 given by CNPq (National Counsel of Technological and Scientific Development of Brazil).

Li et al. [51] Choi et al. [52] Consolini and Thome [53] 2

10 102

103

104

105

hexperimental [W/m²K] Fig. 13. Comparison between independent experimental and predicted results.

7. Conclusions This study presents new experimental results for the HTC during flow boiling of R134a and R245fa in a 0.38 mm ID tube. These data are compared with previous experimental results for R134a, R245fa and R600a for flow boiling in tubes with diameter ranging from 1.00 to 2.60 mm. From a detailed analysis of the overall database the following conclusions can be drawn: A broad experimental database for heat transfer coefficient during two-phase flow boiling in micro-scale channels is presented, comprising 2047 experimental results for halogenated and hydrocarbon fluids, heat flux ranging from 5 to 185 kW/m2, mass velocities from 49 to 2200 kg/m2s, saturation temperature from 22 to 58 °C, tube internal diameters from 0.38 to 2.6 mm and heat transfer coefficients up to 34 kW/m2K; A parametric analysis of the results was presented with the aim of characterizing the influence of each experimental parameter on the trends of the heat transfer coefficient. From this analysis, conditions corresponding to flow boiling dominated by convective and nucleate boiling effects were identified; As expected, under conditions dominated by convective effects the heat transfer coefficient increases with vapor quality, until surface dryout is achieved and subsequent increments of vapor quality result in a drastic decrease of the heat transfer coefficient. For these conditions and before the dryout occurrence, diameter reduction implies the increment of the heat transfer coefficient. On the other hand, the vapor quality corresponding to the dryout inception decreases with decreasing of tube diameter and saturation temperature, and increasing the mass velocity. Moreover, refrigerants with lower vapor specific volume provide an earlier onset of dryout; For flow conditions dominated by nucleate boiling effects, heat transfer coefficient increases with increasing heat flux and saturation temperature. Moreover, under these conditions the mass flux and vapor quality affects the heat transfer coefficient only marginally; A new predictive method for the heat transfer coefficient during flow boiling inside small diameter tubes was proposed based on the approaches of Chen [35] and Saitoh et al. [24]. The new

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. ijheatmasstransfer.2015.09.083. References [1] G. Ribatski, L. Wojtan, J.R. Thome, An analysis of experimental data and prediction methods for two-phase frictional pressure drop and flow boiling heat transfer in micro-scale channels, Exp. Thermal Fluid Sci. 31 (1) (2006) 1– 19, http://dx.doi.org/10.1016/j.expthermflusci.2006.01.006. [2] C.B. Tibiriçá, G. Ribatski, Flow boiling in micro-scale channels–Synthesized literature review, Int. J. Refrig. 36 (2) (2013) 301–324, http://dx.doi.org/ 10.1016/j.ijrefrig.2012.11.019. [3] C.B. Tibiriçá, L.E. Czelusniak, G. Ribatski, Critical heat flux in a 0.38 mm microchannel and actions for suppression of flow boiling instabilities, Exp. Thermal Fluid Sci. 67 (2015) 48–56, http://dx.doi.org/10.1016/j. expthermflusci.2015.02.020. [4] S.S. Mehendale, A.M. Jacobi, R.K. Shah, Fluid flow and heat transfer at microand meso-scales with application to heat exchanger design, Appl. Mech. Rev. 53 (7) (2000) 175–193, http://dx.doi.org/10.1115/1.3097347. [5] S.G. Kandlikar, W.J. Grande, Evolution of microchannel flow passages – thermohydraulic performance and fabrication technology, Heat Transfer Eng. 24 (1) (2003) 3–17, http://dx.doi.org/10.1080/01457630304040. [6] K.A. Triplett, S.M. Ghiaasiaan, S.I. Abdel-Khalik, D.L. Sadowski, Gas–liquid two-phase flow in microchannels Part I: two-phase flow patterns, Int. J. Multiph. Flow 25 (3) (1999) 377–394, http://dx.doi.org/10.1016/S0301-9322 (98)00054-8. [7] P.A. Kew, K. Cornwell, Correlations for the prediction of boiling heat transfer in small-diameter channels, Appl. Therm. Eng. 17 (8) (1997) 705–715, http://dx. doi.org/10.1016/S1359-4311(96)00071-3. [8] C.L. Ong, J.R. Thome, Macro-to-microchannel transition in two-phase flow: Part 2–flow boiling heat transfer and critical heat flux, Exp. Thermal Fluid Sci. 35 (6) (2011) 873–886, http://dx.doi.org/10.1016/j.expthermflusci.2010. 12.003. [9] C.B. Tibiriçá, G. Ribatski, Flow boiling phenomenological differences between micro-and macro-scale channels, in: Heat Transfer Eng. 36 (11) (2014) 937– 947, http://dx.doi.org/10.1080/01457632.2015.972726 (Special Issue: selected papers presented at ENCIT 2012). [10] C.B. Tibiriçá, G. Ribatski, Flow boiling heat transfer of R134a and R245fa in a 2.3 mm tube, Int. J. Heat Mass Transfer 53 (11) (2010) 2459–2468, http://dx. doi.org/10.1016/j.ijheatmasstransfer.2010.01.038. [11] R.B. Abernethy, J.W. Thompson, Measurement Uncertainty Handbook: A Reprint of NTIS AEDC-TR-73-5 Handbook-uncertainty in Gas Turbine Measurements. ISA, 1980. [12] C.B. Tibiriçá, G. Ribatski, Flow patterns and bubble departure fundamental characteristics during flow boiling in microscale channels, Exp. Thermal Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermflusci.2014.02.017. [13] C.B. Tibiriçá, G. Ribatski, Two-phase frictional pressure drop and flow boiling heat transfer for R245fa in a 2.32-mm tube, Heat Transfer Eng. 32 (13–14) (2011) 1139–1149, http://dx.doi.org/10.1080/01457632.2011.562725. [14] J.B. Copetti, M.H. Macagnan, F. Zinani, Experimental study on R-600a boiling in 2.6 mm tube, Int. J. Refrig. 36 (2) (2013) 325–334, http://dx.doi.org/10.1016/j. ijrefrig.2012.09.007. [15] C.B. Tibiriçá, G. Ribatski, J.R. Thome, Saturated flow boiling heat transfer and critical heat flux in small horizontal flattened tubes, Int. J. Heat Mass Transfer

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[16]

[17] [18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

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