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Flow boiling heat transfer of R407C in a microchannels based heat spreader Hugo Leonardo Souza Lara Leão ⇑, Francisco Júlio do Nascimento, Gherhardt Ribatski Department of Mechanical Engineering, Escola de Engenharia de São Carlos (EESC), University of São Paulo (USP), São Carlos, Brazil

a r t i c l e

i n f o

Article history: Received 30 September 2013 Received in revised form 5 February 2014 Accepted 25 March 2014 Available online xxxx Keywords: Flow boiling Temperature ﬂuctuation Microchannels Heat spreader

a b s t r a c t New ﬂow boiling experimental results for R407C in a microchannel based heat spreader are presented. Boiling curves were obtained for heat ﬂuxes up to 310 kW/m2 (based on the footprint area), mass velocities from 400 to 1500 kg/m2s, liquid subcoolings at the test section inlet of 5, 10 and 15 °C and saturation temperatures referred to the pressure at the heat sink inlet of approximately 25 °C. Based on these results, heat sink averaged heat transfer coefﬁcients during convective boiling were estimated. The heat sink evaluated in the present study is comprised of ﬁfty parallel rectangular channels with cross-section dimensions of 100 500 lm, and total length of 15 mm. Average heat transfer coefﬁcients up to 30 kW/ m2 °C were obtained. It was also found that the boiling curve moves to the left hand side with decreasing the mass velocity and liquid subcooling at the heat-sink inlet. Moreover, for a ﬁxed heat-sink averaged vapor quality, the average heat transfer coefﬁcient increases with increasing mass velocity. Under similar experimental conditions, the refrigerant R134a provided higher heat transfer coefﬁcients than R407C. Additionally, during ﬂow boiling of R407C, pressure oscillations with lower amplitude and frequency were observed compared to R134a. No one of the heat transfer predictive methods evaluated in the present study was accurate enough to predict the present R407C database. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction In recent years, ﬂow boiling heat-sinks based on micro-scale channels has been considered by the electronic industry as an alternative to replace air cooling heat spreaders because of its compactness and excellent heat transfer performance. According to Ribatski et al. [1] and Qu and Mudawar [2], the main advantage of heat-sinks based on ﬂow boiling in microchannels compared with the competing cooling technologies is the combination of high surface area in direct contact with the refrigerant and high heat transfer coefﬁcients due the ﬂow boiling mechanism. These characteristics allow reducing the coolant inventory, minimizing the heat exchanger size and providing more uniform temperature distribution along the heat spreader. However, a better understanding of the heat transfer mechanisms associated with the different two-phase ﬂow topologies during convective boiling inside microchannels is still necessary as pointed out by Harirchian and Garimella [3]. Harirchian and Garimella [4] performed a comprehensive investigation on the effects of channel size and mass velocity on the heat ⇑ Corresponding author. Tel.: +55 1633733415. E-mail addresses: [email protected] (Hugo Leonardo Souza Lara Leão), [email protected] (F.J. do Nascimento), [email protected] (G. Ribatski).

transfer coefﬁcient and pressure drop during ﬂow boiling in microchannels-based heat sinks. They have split the heat transfer behaviors into two regions dominated by nucleate boiling and convective effects. In the nucleate boiling region, the heat transfer coefﬁcient and the boiling curve are not affected by the mass velocity. According to them, by increasing heat ﬂux, the heat-sink averaged vapor quality increases, and, then, the parcel of the heat sink length under annular ﬂow conditions also increases. For annular ﬂow, convective effects are dominant and the heat transfer coefﬁcient increases with increasing mass velocity. As already expected, for a ﬁxed heat ﬂux the pressure drop increases with increasing mass velocity and decreasing channel size. According to the comprehensive review of Tibiriçá and Ribatski [5], despite of the large number of studies concerning this topic, distinct pressure drop and heat transfer trends during ﬂow boiling in micro-scale channels are pointed out by independent studies. Additionally, the main heat transfer mechanisms prevailing during ﬂow boiling inside micro-scale channels are still unknown. This statement is corroborated by Agostini and Thome [6] which have found that out of 13 of the most recent studies on convective boiling in heat-sinks containing microchannels, 8 of them have presented drastic differences and contradictory heat transfer trends. According to Kuo and Peles [7], these large discrepancies observed when studies from independent laboratories are compared might

http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014 0894-1777/Ó 2014 Elsevier Inc. All rights reserved.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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Hugo Leonardo Souza Lara Leão et al. / Experimental Thermal and Fluid Science xxx (2014) xxx–xxx

Nomenclature A cp db Dh ef es f fD F G g H h i ilv k L M ONB p pr Q q00 S T T t V W x x X

area (m2) speciﬁc heat (J/Kg K) bubble departure diameter (m) hydraulic diameter (m) multiplicator factor of F (dimensionless) multiplicator factor of S (dimensionless) frequency (Hz) Darcy friction factor (dimensionles) enhancement factor (dimensionless) mass velocity (kg/m2 s) gravity (m/s2) microchannel depth (m) heat transfer coefﬁcient (W/m2 K) enthalpy (kJ/kg) enthalpy of vaporization (kJ/kg) thermal conductivity (W/m K) length (m) molar mass (kg/Mol) Onset of nucleate boiling (°C) absolute pressure (kPa) reduced pressure (dimensionless) dissipated energy (W) heat ﬂux (W/m2) suppression factor (dimensionless) temperature (°C) average temperature (°C) time (s) velocity (m/s) microchannel width (m) vapor quality (dimensionless) average vapor quality (dimensionless) Martilelli parameter (dimensionless)

Greek symbols d liquid ﬁlm thickness (m) Dp differential pressure (kPa) DT temperature difference (°C) DT wall superheating (°C) l dynamic viscosity (Pa s) g mean error (%) m kinematic viscosity (Pa s) q density (kg/m3)

be related to ﬂow oscillations caused by the instabilities during ﬂow boiling inside small diameter channels. Recently, Ribatski [8] has pointed out that the ﬂow pattern dynamics in multichannel conﬁgurations are quite different than in single channels. In case of multichannels, the presence of backﬂows, caused by bubble growing under conﬁned conditions, and the interactions among neighbor channels and the ﬂow-header may drastically affect the two-phase topology and dynamics. By using high resolution IR thermography, Szczukiewicz et al. [9] investigated the effects of unsteady ﬂow and ﬂow mal-distribution on the temperature distribution on the heat sink surface. They also highlighted the need of properly reducing the experimental data in order to perform a correct comparison among different studies. Szczukiewicz et al. [9] found that stable and well distributed ﬂow along the heat sink can be obtained by adding restrictions to the ﬂow at the inlet of each microchannel. Greco [10] investigated the effect of ﬂuid properties on ﬂow boiling by performing experiments for pure and mixed refrigerants in a macro-scale tube (6 mm ID). In his study, experimental results were obtained for pure refrigerants (R22 and R134a), azeotropic

r n

s

surface tension (N/m) data predicted to within ±30% (%) elongated bubble period (s)

Subscripts 0 initial 1/ single-phase ﬂow 2/ two-phase ﬂow C convective D decreasing power eff effective, effectively in contact with ﬂuid electrical electrical power end end env environment ﬂuid ﬂuid ﬁlm ﬁlm fp foot print g gas-phase heated heated I increasing power in heat spreader inlet l liquid-phase max maximum min minimum NB nucleate boiling out heat spreader outlet plenums inlet and outlet plenums sat saturation sub subcooling total total length w wall Dimensionless numbers q00 BO boiling number, BO ¼ Gi (dimensionless) lv 2

Bo

bond number, Bo ¼ Dqh Gr (dimensionless)

Fr

G Froude number, Fr ¼ q gD (dimensionless) h l

Pr

Prandtl number, Pr ¼

Re

Reynolds number, Re ¼ l (dimensionless) 2 h Webber number, We ¼ GrD q (dimensionless)

We

l

2

cp l (dimensionless) k GDh

and quasi-azeotropic (R404A, R410A and R507) and zeotropic (R407C and R417A) mixtures. Greco [10] veriﬁed that the pure refrigerants present higher heat transfer coefﬁcients than the mixtures. The refrigerant R134a provided the highest heat transfer coefﬁcient. The zeotropic mixtures R407C and R417A have presented the lowest heat transfer performance. Studies concerning heat transfer performance of heat sinks based on ﬂow boiling inside multi-microchannels for refrigerant mixtures are still necessary since they are inexistent according to the search in the literature performed in the present work. Based on experimental results for ﬂow boiling of R134a in a microchannel-based heat sink, Do Nascimento et al. [11] have shown that the heat transfer coefﬁcient increases with increasing mass velocity for a ﬁxed heat-sink averaged vapor quality. Similar behaviors were also indicated by Bertsch et al. [12]. Do Nascimento et al. [11] have also observed that the 3-Zone model by Thome et al. [13] provides accurate predictions of their results. In the present paper, new ﬂow boiling results for R407C were obtained, extending the database for R134a obtained by Do Nascimento et al. [11] using the same experimental facility and

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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multi microchannel heat-sink. Despite the fact that the R407C presents a lower heat transfer coefﬁcient when compared with the R134a [10], lower pressure drops are expected for R407C under the same experimental conditions due to the higher working pressure, lower viscosity, density and surface tension presented by this ﬂuid. Moreover, it is well known that the ﬂow oscillations can promote an early dryout and, so, being harmful to the heat spreader performance. In this context, it is also expected that R407C minimizes ﬂow oscillation, ﬂuid mal-distribution and back ﬂow effects promoted by bubble growing under conﬁned conditions. Experimental boiling curves were obtained for heat ﬂuxes up to 310 kW/m2 (based on the footprint area) and saturation temperatures referred to the pressure at the microchannels inlet of approximately 25 °C. Based on the wall temperature measurements, heatsink averaged heat transfer coefﬁcients during convective boiling were calculated. Experimental results displaying temperature ﬂuctuations due to thermal instabilities were also analyzed and a comparison between the two refrigerant ﬂuids is made. In resume, the main goals of the present paper are the following: (i) present new experimental results for the refrigerant R407C obtained during ﬂow boiling inside a multi-microchannel heat sink; (ii) compare these data for heat transfer coefﬁcient and thermal instabilities against previous results for R134a in the same heat sink; and (iii) evaluate the capability of predictive methods available in literature to predict the experimental heat transfer coefﬁcient data obtained in the present study for R407C.

2. Experimental setup The experimental setup is shown schematically in Fig. 1. It comprises a gear micropump to drive the working ﬂuid through the closed loop, a pre-heater to establish the experimental conditions at the test section inlet, a test section containing the heat spreader, a plate-type heat exchanger to condense the vapor created in the heated sections, and a refrigerant tank.

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The microchannel based heat spreader, shown schematically in Fig. 1 is comprised of ﬁfty parallel rectangular microchannels with cross-sectional dimensions of 100 lm in width and of 500 lm in depth, and total length of 15 mm. The ﬁns between consecutive microchannels have thicknesses of 200 lm. The inlet and outlet plenums are rectangular with dimensions of 4 mm wide, 16 mm long and 2 mm deep. The heat sink is made of copper through micromilling process and presents an internal surface roughness of 5 lm. The heat sink within the test section is heated on its bottom surface by an electrical resistance distributed as a serpentine on a footprint area of 15 15 mm2. Needle valves were placed before the pre-heater, V1, and after the heat-sink, V2, to avoid propagation of instabilities through the test circuit. The heat sink is covered with a Pyrex sheet of 15 mm thickness, allowing high-speed ﬂow visualizations. The refrigerant is supplied to the inlet plenum and drained from the outlet plenum of the heat sink by 3.5 mm diameter channels machined through the Pyrex cover. One additional pair of channels machined through the transparent cover and positioned over the inlet and outlet plenums is connected to the absolute and differential pressure transducer taps to measure the pressure at the test section inlet, and the pressure drop along the test section. To distribute the ﬂow among the microchannels homogeneously, the ﬂuid inlet duct machined in the Pyrex sheet is located close to the inlet of the 1st microchannel and the ﬂuid outlet duct is close to the outlet of the 50th microchannel. The wall average heat-sink temperature is estimated from the measurements of 9 thermocouples arranged as a 3 3 matrix and embedded within the bottom wall of the heat sink. For single-phase ﬂow, the average liquid temperature is estimated by averaging the values of the thermocouples at the inlet, Tin, and outlet, Tout, of the heat-sink. When two-phase ﬂow occurs, an energy balance associated with the pressure drop estimative (friction factor estimated by Shah and London [14] correlation for laminar, non-developed ﬂow) are used to calculated the length at which the saturation condition is reached. The average temperature of

Fig. 1. Experimental setup.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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the ﬂuid is then estimated based on the average temperature of the single-phase region (inlet temperature, Tin, and saturation temperature at the end of the single-phase region, Tend,1/) weighted by its length, L1/, and the average temperature of the two-phase region (saturation temperature at the end of the single-phase region, Tend,1/, and the outlet temperature of the heat-sink, Tout) weighted by the two-phase ﬂow length, 1 L1//Ltotal. It should be highlighted that the ﬂuctuations of the single-phase length caused by pressure oscillations were not measured. The heat ﬂux is based on the footprint area (15 15 mm2) considering only the microchannels region and subtracting from the total power input the heat losses to the environment and the heat transferred to the working ﬂuid in the region of the plenums. The average heat transfer coefﬁcient is given as the ratio between the heat ﬂux, based on the footprint area, and the average heat-sink superheating calculated as the difference between the average temperatures of the heat-sink wall and the ﬂuid. Experimental results were obtained for the conditions described in Table 1. The electrical signals of the transducers concerning temperature, pressure, electrical power and mass ﬂow rate measurements were acquired, processed and stored by a National Instruments SCXI-1000 chassis with a SCXI 1102 board plate that communicates with the Labview software. A program in Labview was developed and used to control the facility and record the measurements from the transducers. Additional details of the experimental setup are described by Do Nascimento et al. [11]. 3. Data analysis To estimate the total heat transferred to the ﬂuid in the region comprising the microchannels, Qeff, heat losses to the environment and the heat transferred to the ﬂuid in the inlet and outlet plenums were subtracted from the total electrical power as follows:

Q eff ¼ Q electrical Q env Q plenums

ð1Þ

The power supplied by the DC power source to the electrical resistance, Qelectrical, was estimated from the product between the electrical current and voltage, which values are provided by the power source to the data acquisition system. The heat losses to the environment, Qenv, were evaluated from single-phase experiments and an average value of 16% was found. The heat transferred in the region of the plenums, Qplenums, was estimated based on the superﬁcial area in contact with the ﬂuid, the local temperature of the refrigerant and the heat sink average temperature. For this purpose, the heat transfer correlations of Stephan and Preuber [15] and Warrier et al. [16] were used for single-phase and ﬂow boiling conditions, respectively. The heat transferred in this analysis considers only the copper surfaces, i.e. the Pyrex surface was neglected. To plot the boiling curves, the footprint heat ﬂux is referred to the heated area, Aheated , given by the product between the microchannel length and the total width comprising the 1st and the 50th microchannels (15 15 mm2). To compare heat transfer ﬂow boiling data and predictive methods, the effective heat ﬂux is referred to the effective heat transfer area, Aeff , given by the Table 1 Experimental conditions.

product between the microchannel length and the heated perimeter of each channel. The wall temperature superheating was calculated as follows:

DT ¼ T w T fluid

where T w is the wall heat sink average temperature based on the arithmetic mean value of the temperature measurements by the thermocouples embed within the heat sink wall. The refrigerant average temperature, T fluid is estimated assuming an uniform heat ﬂux along the channels surface and taking into consideration the subcooled region length, the temperature at the end of the singlephase region in case of the occurrence of two-phase ﬂows and the variation of the saturation temperature with the local pressure and the vapor quality as follows:

T fluid ¼

Liquid subcooling at the test section inlet (°C)

Heat ﬂux range (kW/m2)

400 500 600 1000 1500

5 and 10 5 and 10 5 and 10 5, 10 and 15 5, 10 and 15

Up Up Up Up Up

to to to to to

310 310 310 310 310

ðT in þ T end;1/ Þ L1/ ðT end;1/ þ T out Þ L1/ 1 þ 2 2 Ltotal Ltotal

ð3Þ

For single-phase ﬂow experiments along all the channels, the ﬂuid temperature is given as the average temperature between the inlet and outlet temperatures. For two-phase ﬂow, the temperature of the end of the single-phase, Tend,1/, is the boiling temperature at L1/ and the temperature at the exit of the heat sink, Tout, is the local temperature, measured by the thermocouple at the heat sink exit. In order of evaluating the error of approximating the average liquid temperature by Eq. (3) for a zeotropic ﬂuid, the refrigerant temperature proﬁle along the two-phase ﬂow region was estimated and the average temperature of the refrigerant over this region was calculated. To obtain the temperature proﬁle, the two-phase region was discretized and for each element the local pressure and vapor quality were determined based on energy balance over each discrete element and the corresponding pressure drop calculated according to the homogenous model, with the two-phase dynamic viscosity given by Ciccitti et al. [17]. Then, the local refrigerant temperature was estimated based on local vapor quality and pressure. For the worst condition, corresponding to G = 400 kg/m2 s, DTsub = 5 °C e q00 = 300 kW/m2, a difference of only 0.3 °C was found between the average temperature calculated from the refrigerant temperature proﬁle and the average temperature calculated as the arithmetic mean value between the temperature at the beginning and ending of the two-phase region. Based on this result, the procedure adopted in the present study can be considered accurate enough since the difference of 0.3 °C is almost similar to the uncertainty of the average wall temperature estimation. The heat sink averaged heat transfer coefﬁcient based on the footprint area is estimated according to the Newton’s cooling law. The mass velocity, G, is given as the ratio between the mass ﬂow, measured by the Coriolis ﬂow meter, and ﬁfty times the cross sectional area of one single channel (50 100 500 lm2). The average vapor quality over the heat spreader was determined as the arithmetic average value of the thermodynamic vapor qualities at the inlet and outlet plenums as follows:

x¼

xin xout 2

xin ¼

Mass velocity (kg/m2 s)

ð2Þ

ð4Þ

il;in ðpin ; T in Þ iðl;inÞsat ðpin Þ ilv ;in ðT in Þ

xout ¼

Q eff 50GAeff

þ il;in ðpin ; T in Þ il;out ðT out Þ ilv ;out ðT out Þ

ð5Þ

ð6Þ

Temperature measurements were calibrated and the experimental uncertainties associated with the sensors and calculated parameters are listed in Table 2.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

Hugo Leonardo Souza Lara Leão et al. / Experimental Thermal and Fluid Science xxx (2014) xxx–xxx Table 2 Uncertainty of measured and calculated parameters. Parameter

Uncertainty

Parameter

Uncertainty

H W Ltotal T

5 lm 5 lm 5 lm 0.15 °C 0.2 °C

DTsub p Dp G q00

0.3 °C 20 kPa 0.22 kPa 56 kg/m2 s 0.4 kW/m2

Tw

0.4 °C

h

525 W/m2 °C

DT

0.4 °C

T fluid

4. Results and discussion Figs. 2–4 display for mass velocities of 400, 600 and 1000 kg/ m2 s, respectively, and different degrees of subcooling at the inlet plenum, boiling curves obtained under conditions of gradually increasing (I) the heat ﬂux until a peak and, then, decreasing (D) its value. Critical heat ﬂux conditions were avoided in order to keep the test section undamaged. According to these ﬁgures, the boiling curve moves to the left hand side with decreasing the liquid subcooling at the heat-sink inlet. It can be also noted that the boiling curves obtained for different degrees of liquid subcooling tend to merge with increasing wall superheating. This trend is in agreement with the results of Park and Thome [18]. The boiling curve also moves to the left hand side with decreasing the mass velocity. Additionally, the boiling curves exhibit the hysteresis phenomenon corresponding to higher wall superheating for the curve obtained under condition of gradually increasing the heat ﬂux. An excess of superheating for the onset of nucleate boiling can be also noted in Figs. 2–4. In summary, from the analyses of the experimental results for a ﬁxed heat-spreader averaged wall superheating, it was found that the dissipated heat ﬂux increases with decreasing the mass velocity and liquid subcooling. When analyzing Figs. 2–4, it is important highlighting that the boiling process is established only downstream a certain position along the microchannel length, once a certain degree of ﬂuid superheating has been reached. So, the parcel of the area of the heat-sink under boiling conditions increases with increasing heat ﬂux and decreasing mass velocity and liquid subcooling. For the same mass velocity, the ﬂow boiling heat transfer coefﬁcient is signiﬁcantly higher than for single-phase ﬂows. This behavior explains the results displayed in Figs. 2–4, based on the fact that the parcel of the heat sink surface under boiling conditions and,

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so, corresponding to higher local heat transfer coefﬁcients, increases with decreasing liquid subcooling and mass velocity. Figs. 5–7 illustrate the effects of mass velocity and liquid subcooling on the behavior of the heat-sink averaged heat transfer coefﬁcient with increasing the heat-sink averaged vapor quality. According to these ﬁgures, for a ﬁxed average vapor quality, the heat-sink averaged heat transfer coefﬁcient increases with increasing mass velocity and decreasing the liquid subcooling at the microchannels inlet. The effect of the liquid subcooling on the averaged heat transfer coefﬁcient becomes negligible for heat-sink averaged vapor qualities higher than 0.1. Fig. 8 displays a comparison between the heat transfer coefﬁcient data for R134a from Do Nascimento et al. [11] and the results for R407C obtained in the present study. In general, according to this ﬁgure under conditions of heat-sink averaged vapor quality higher than 0.02, the refrigerant R134a provides higher heat transfer coefﬁcients than R407C. Higher ﬂow boiling heat transfer coefﬁcients for R134a than for R407C were also observed by Greco [10] for experiments in a 6 mm I.D. tube. The fact that zeotropic mixtures provide lower heat transfer coefﬁcient than pure refrigerants can be explained based on Thome [19]. According to Thome [19], the low concentration of the most volatile component at the bubble interface due to the evaporation process during bubble growth is responsible for the necessity of additional superheating for further liquid evaporation. In microchannels, the elongation of bubbles during their growth provides a higher interfacial area relative to the channel size when compared with the growing process of bubbles under similar conditions inside macrochannels. This behavior promotes relatively larger diffusional interface for ﬂow boiling inside microchannels compared to conventional channels. Consequently, it is expected that zeotropic mixtures are more detrimental to the heat transfer coefﬁcient for micro-scale channels than for conventional channels. According to the literature for conventional ducts, the ﬂow boiling heat transfer rate is given as the superposition of forced convection and nucleated boiling effects. Nucleate boiling is predominant under low vapor quality conditions while forced convection is the main mechanism under high vapor quality conditions, mainly, for annular ﬂow. Although, due to conﬁnement effects, the boiling process in small-diameter tubes is not the same as in macro-scale channel, an approach based on superposition effects has been applied here to explain the results for micro-scale channels obtained in the present study. In fact, the presence of active nucleation sites and their relative contribution to the overall

Fig. 2. Boiling curves for R407C for saturation temperature of 25 °C and mass velocity of 400 kg/m2 s.

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Fig. 3. Boiling curves for R407C for saturation temperature of 25 °C and mass velocity of 600 kg/m2 s.

Fig. 4. Boiling curves for R407C for saturation temperature of 25 °C and mass velocity of 1000 kg/m2 s.

Fig. 5. Effect of liquid subcooling on the heat spreader averaged heat transfer coefﬁcient for R407C, saturation temperature of 25 °C and mass velocity of 600 kg/m2 s.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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Fig. 6. Effect of liquid subcooling on the heat spreader averaged heat transfer coefﬁcient for R407C, saturation temperature of 25 °C and mass velocity of 1000 kg/m2 s.

Fig. 7. Effect of mass velocity on the heat spreader averaged heat transfer coefﬁcient for R407C, saturation temperature of 25 °C and liquid subcooling at the test section inlet of 5 °C.

Fig. 8. Comparison between the heat spreader averaged heat transfer coefﬁcient of the refrigerants R134a and R407C for mass velocity of 400 kg/m2 s and liquid subcooling at the test section inlet of 5 °C.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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heat transfer rate in micro-scale channels is a controversial topic characterized by severe disagreements among authors. However, it is important highlighting that Tibiriçá and Ribatski [20] have observed bubbles nucleating even under annular ﬂow conditions and high vapor qualities during ﬂow boiling in a 0.4 mm I.D. tube. For a broad discussion on aspects concerning the main heat transfer mechanism actuating during ﬂow boiling in micro-scale channels, the recent review just published by Ribatski [8] is recommended. In this review, Ribatski [8] presents the different views of authors investigating this topic and he concludes that this is still an open issue. In the present study, most of the results were obtained for averaged vapor qualities lower than 0.16 corresponding to maximum outlet vapor qualities of approximately 0.32. Under these conditions, based on two-phase ﬂow visualizations through a high speed camera, annular ﬂows are rare and as abovementioned for comparison purpose, nucleate boiling effects can be considered the driven

heat transfer mechanism. So, the experimental data displayed in Fig. 8 agrees qualitatively with the results given by Cooper’s [21] correlation for pure ﬂuids. For the heat ﬂux range covered in the present study, the pool boiling heat transfer coefﬁcient of R407C varies from 40% to 55% of the value estimated for R134a according to Cooper’s [21] correlation. This behavior is corroborated by the fact that the refrigerant R407C is a zeotropic mixture with a temperature glide of approximately 6 °C what contributes for lower ﬂow boiling heat transfer coefﬁcients. As mentioned by Greco [10], in case of zeotropic mixtures, the nucleate boiling contribution to the global heat transfer coefﬁcients is strongly reduced by diffusional limitation. In Figs. 9 and 10, the two-phase ﬂow data for R407C obtained under condition of gradually decreasing the heat ﬂux are compared against the six ﬂow boiling heat transfer predictive methods presented in Table 3. For comparison purposes and based on the experimental conditions, these methods were

Fig. 9. Comparison between the trends of the experimental results and predictive methods for R407C, mass velocity of 400 kg/m2 s and liquid subcooling at the test section inlet of 5 °C.

Fig. 10. Comparison between the experimental results and the ﬂow boiling predictive methods.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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implemented along the two-phase length over discrete elements considering local vapor quality and ﬂuid properties. Then, the average heat transfer coefﬁcient over the two-phase length was calculated. The predictive method by Bertsch et al. [24], based on Chen’s [26] approach, was included in the present analysis because this correlation was developed considering an extensive database.

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The database consists of 3899 data points from 14 studies in the literature for single and parallel multi-microchannels conﬁgurations covering 12 different wetting and non-wetting ﬂuids, hydraulic diameters ranging from 0.16 mm to 2.92 mm and rectangular channels. According to Bertsch et al. [24] in their predictive method, the effects of heat ﬂux, mass velocity, vapor quality and bubble conﬁnement are accounted.

Table 3 Flow boiling heat transfer predictive methods. Author(s)

Correlations

Liu and Winterton [22]

h2/ = (S hNB)2 + (F hC,1/)2 hC;1u ¼ 0:023 Dkhl Re0:8 Prl0:4 l hNB ¼ 55 p0:12 ð ln pr Þ M 0:5 ðq00 Þ0:67 r h i0:35 ql F ¼ 1 þ x Prl q 1 g 1 S ¼ 1 þ 0:055 F 0:1 Re0:16 l 0:55

If Frl 6 0:05, replace F by eF ¼ Frð0:12FrÞ and S by eS ¼ Warrier et al. [16]

pﬃﬃﬃﬃﬃ Fr

h 2u hC;1u

¼ 1 þ 6 BO1=16 þ fsat BO x0:65 h i 0:086ðGzl Þ1:33 hC;1/ ¼ 4:364 þ Dkhl [15] 0:83 1þ0:1Prl ðRel Dh =LÞ

fsat = 5.3 (1 855 Bo) Thome et al. [13]

t

t

g h2/ ¼ tsl hl þ film s hfilm þ s hv l hfilm ¼ d0 2k þdmin qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ0:84 h i1=8 8 d0 ¼ 0:29 3 V 2/mDh ð0:07 Bo0:41 Þ þ 0:18 Dh h i V 2u ¼ G qx þ ð1xÞ q g

l

00

dðtÞ ¼ d0 qqilv t l tmax;film ¼ qql i00lv ½d0 dmin 00

If tmax,ﬁlm > tg, so dend ¼ d0 qqilv tfilm e tfilm ¼ t g l If tmax,ﬁlm < tg, so dend ¼ dmin e t film ¼ t max;film 7 dmin = 3 10 (m) 1:74 q00 s¼ 0:5 3328ðpr Þ

tl ¼

q

s

x 1þq l ð1xÞ g

tg ¼

s

q ð1xÞ

1þ qg l

Saitoh et al. [23]

x

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Dh Rel or g k 6 2300, so hlorg ¼ 2 0:455 3 Prlorg Dlorg L h 2=3 k 2 ðfD =8ÞðRe1000ÞPr ½1 þ DLh Dlorg and fD ¼ ð1:82 logðReÞ 1:64Þ g > 2300, so hlorg ¼ 1=2 2=3 h

If Rel

or g

If Rel

or

1þ12:7ðfD =8Þ

ðPr

1Þ

h2/ = S hEN + F hC,1/ hC;1/ ¼ 0:023 Dkhl Re0:8 Pr0:4 l l 0:745

00

db hNB ¼ 207 dkl ðqk T Þ b l l h i0:5 db ¼ 0:51 gðq2rq Þ l

S¼

q 0:581

ð qg Þ l

Prl0:533

g

1 1:4 1þ0:4ðRe2/ 104 Þ 1:05

ð1=XÞ F ¼ 1 þ 1þWe 0:4 g

Re2/ = Rel F1.25 Bertsch et al. [24]

h2/ = S hNB + F hC,1/ hC,1/ = hC,l (1 x) + hC,g x h i hC;l ¼ 3:66 þ 0:0668ðDh =LÞRel Prl2=3 Dkhl 1þ0:04½ðDh =LÞRel Prl

0:0668ðDh =LÞReg Prg k hC;g ¼ 3:66 þ Dgh 2=3 1þ0:04½ðDh =LÞReg Prg 0:55

hNB ¼ 55 p0:12 ð ln pr Þ M 0:5 ðq00 Þ0:67 r S=1x F ¼ 1 80 e0:6C 0 ðx2 x6 Þ Tibiriçá [25]

h2/ = S hNB + F hC,1/ hC;1/ ¼ 0:023 Dkhl Re0:8 Pr0:4 l l 00 0:745 q 0:581 kl q db g hNB ¼ 207 d k T q Prl0:533 b l l l h i0:5 db ¼ 0:51 gðq2rq Þ l

S¼

g

1 1:14 1þ0:233ðRe2/ 104 Þ 0:915

F ¼ 1 þ ð1=XÞ 1þWe55 g

Re2/ = Rel F1.25

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

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Table 4 Statistical parameter of the comparison between the R407C database and predictive methods. Correlations

Mean error, g (%)

Data predicted to within ±30%, f (%)

Bertsch et al. [24] Warrier et al. [16] Thome et al. [13] Liu and Winterton [22] Saitoh et al. [23] Tibiriçá [25]

57.75 66.05 26.64 34.93 65.14 68.08

8.47 0 62.71 37.29 12.43 9.04

According to Ribatski [8] based on an analyses of a broad database from the literature, the 3-Zones model by Thome et al. [13] provides the best predictions of ﬂow boiling data in multi-microchannels. The 3-Zones model is a phenomenological model that describes the evaporation of elongated bubbles in microchannels. The heat transfer model consists of quantify the variation of the local heat transfer coefﬁcient during cyclic passage of a liquid slug, an elongated bubble and a vapor slug when intermittent dryout occurs. Dupont et al. [27] based on an extensive database covering single and multiple parallel channel arrangements, tube diameters from 0.77 to 3.1 mm, several ﬂuids and vapor qualities from 0.01 to 0.99 showed that the 3-Zones model provides reasonable predictions of the heat transfer coefﬁcient and captures relatively well the effects of heat ﬂux, mass ﬂux, vapor quality and bubble conﬁnement. As indicated by Qu and Mudawar [2], the predictive method developed by Warrier et al. [16] provides the best predictions of their experimental results in multi-microchannels, so this method was also included in the present analyses. Warrier et al. [16] have investigated the heat transfer performance of a heat sink with ﬁve parallel rectangular microchannels of hydraulic diameter of 0.75 mm under ﬂow boiling condition using FC-84 as working ﬂuids. Based on these results and the correlation proposed by Tran et al. [28], Warrier et al. [16] developed a simple predictive method according to which the ratio between the ﬂow boiling and singlephase heat transfer coefﬁcients is given as a function of the Boiling number and vapor quality. The predictive method of Tibiriçá [25] was included in this analysis due to its extensive database (1920 experimental data) for a single microchannel and three different diameters. Tibiriçá [25]

has modiﬁed the predictive method of Saitoh’s et al. [23] by adopting new empirical parameters based on his own database. Saitoh et al. [23] based on Chen’s [26] method proposed a new correlation taking into account the effect of tube diameter and the onset of dryout. Saitoh et al. [23] have adjusted their method based on experiments of R134a in single tubes for a wide range of tube diameters from 0.51 to 10.92 mm. Because it is commonly found in the literature being compared against macro and micro-scale experimental results, the macroscale correlation proposed by Liu and Winterton [22] has been also included. According to Figs. 9 and 10, no one of the predictive methods evaluated in the present study provides accurate predictions of the R407C ﬂow boiling results. It can be speculated that this result is due to the fact that this refrigerant is a zeotropic mixture and no one of the methods includes experimental data for R407C in its original database. Although not accurate, the methods of Warrier et al. [16] and Thome et al. [13] have captured reasonably well most of heat transfer trends. Table 4 depicts the statistics of the comparisons of experimental and predicted data according to the following two criteria: the fraction of data predicted to within ±30%, f, and the mean absolute error, g. According to this table, the predictive method developed by Thome et al. [13] provided the lowest mean absolute error and predicted 44.3% of data within an error band of ±30%. The fact that the methods of Warrier et al. [16] and Thome et al. [10] are based on experimental results for multi-microchannels heat sinks as abovementioned seems to explain the fact that they have provided the best predictions, capturing the trends of the experimental results. Actually, these predictive methods should account for the effects on the heat transfer coefﬁcient of the interactions among neighbor channels since they are based on experimental data weighted by this effect. Fig. 11 displays the transient signal from the micro-thermocouple located at the test section outlet plenum for R134a and R407C. Fig. 12 presents the Fast Fourier Transform (FFT) of the signals displayed in Fig. 11. According to these ﬁgures, the refrigerant R134a presents oscillations with higher frequency and amplitude than R407C. These oscillations are frequently observed during ﬂow boiling in micro-scale conditions and are related to the thermal instability effects present during the bubble growing process under conﬁned conditions. The lowest frequency of R407C is related to the fact that this refrigerant at a saturation temperature of 25 °C

Fig. 11. Temperature ﬂuctuations at the outlet plenum for mass velocity of 1500 kg/m2 s, liquid subcooling at the test section inlet of 5 °C, heat sink averaged vapor quality of 0.015, and heat ﬂux (footprint) of 272 kW/m2.

Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014

Hugo Leonardo Souza Lara Leão et al. / Experimental Thermal and Fluid Science xxx (2014) xxx–xxx

11

Fig. 12. FFT of the outlet temperature signal for mass velocity of 1500 kg/m2 s, liquid subcooling at the test section inlet of 5 °C, averaged vapor quality of 0.015, and heat ﬂux (footprint) of 272 kW/m2.

presents lower vapor–liquid speciﬁc volume ratio and higher latent heat of vaporization than R134a. Also, to this fact can be included the need of a higher superheating to evaporate the less volatile component of the R407C at the gas–liquid interface. These characteristics are responsible for the lowest bubble growing velocity of R407C.

5. Conclusions New R407C ﬂow boiling heat transfer data in a microchannel based heat sink were obtained. Heat transfer coefﬁcient results up to 30 kW/m2 °C were achieved. By increasing the liquid subcooling at the inlet plenum and the mass velocity, the ﬂow boiling curves move to the right hand side. Therefore, the heat sink performance improves with decreasing mass velocity and the liquid subcooling for the experimental conditions evaluated in the present study. For a ﬁxed average vapor quality, the heat-sink averaged heat transfer coefﬁcient increases with increasing mass velocity. By comparing the present results against the data obtained by Do Nascimento et al. [11] in a previous study for the same heat-sink, it was found that R134a presents a higher heat transfer performance. Under the same experimental condition, the refrigerant R407C provides temperature oscillations with lower frequency and amplitude than R134a. No one of the methods evaluated in the present study provided accurate predictions of the heat transfer coefﬁcient for R407C during ﬂow boiling in a heat-sink based on microscale channels. However, the methods of Warrier et al. [16] and Thome et al. [13] have captured the main trends of the experimental results. Acknowledgements The authors gratefully acknowledge the scholarships to the ﬁrst and second authors given by FAPESP (The State of São Paulo Research Foundation, Brazil) under the contract number 2011/ 13119-0 and by the research program titled NANOBIOTEC of CAPES (Coordination for the Improvement of Higher Level- or EducationPersonnel, Brazil). The ﬁnancial support under contract number 576982/2008-3 given by CNPq (The National Council for Scientiﬁc and Technological Development, Brazil) is also appreciated and recognized.

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Please cite this article in press as: H.L.S.L. Leão et al., Flow boiling heat transfer of R407C in a microchannels based heat spreader, Exp. Therm. Fluid Sci. (2014), http://dx.doi.org/10.1016/j.expthermﬂusci.2014.03.014