Film condensation of steam flowing on a hydrophobic surface

International Journal of Heat and Mass Transfer 107 (2017) 307–318

Contents lists available at ScienceDirect

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

Film condensation of steam flowing on a hydrophobic surface D. Del Col a,⇑, R. Parin a, A. Bisetto b, S. Bortolin a, A. Martucci a a b

Dipartimento di Ingegneria Industriale, Università degli Studi di Padova, Via Venezia 1, 35131 Padova, Italy Riello S.p.A., Via Mussa 20, 35017 Piombino Dese (PD), Italy

a r t i c l e

i n f o

Article history: Received 29 December 2015 Received in revised form 27 October 2016 Accepted 27 October 2016

Keywords: Flow condensation Hydrophobic surface Steam Hydrophilic surface Aluminum substrate

a b s t r a c t Nano-engineered surfaces have recently been studied as a promising solution for several heat transfer applications. In particular, the modification of surface wetting properties for condensation heat transfer is an extremely interesting field of research. In the present work, an aluminum substrate has been modified to obtain a hydrophobic surface and the influence of the wetting properties during condensation of pure steam on a vertical surface is investigated. Condensation tests, at heat flux between 250 and 500 kW m
2 and vapor velocity between 2.2 m s
1 and 6.4 m s
1, have been performed on multiple samples, both hydrophilic (advancing contact angle <90°) and hydrophobic samples, with advancing contact angle 140°. The condensation mode during the present test runs is purely filmwise, even on the hydrophobic surfaces, due to the complete flooding of the surface. The results of filmwise condensation on the hydrophobic surfaces display higher heat transfer coefficients compared to the untreated hydrophilic plate. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Owing to their water repellency properties, hydrophobic and superhydrophobic surfaces have been studied as a promising solution to several challenges, such as drag reduction, anti-icing and enhancement of two-phase heat transfer performance [1–3]. These surfaces are also widely studied to promote dropwise condensation and thus enhance condensation heat transfer. In fact, condensation is present in many industrial processes, such as power industry. With the motivation for improved energy efficiency and miniaturization of heat exchangers, an extensive research has been undertaken in the area of enhanced condensation heat transfer from the report by Schmidt et al. [4] where the dropwise condensation was studied for the first time and this research nowadays is powered by the new potential of surfaces with modified wettability. However film condensation, not dropwise, is the most common condensation mode in condensers for industry application and thus it is of great importance to understand how hydrophobicity may affect heat transfer during filmwise condensation. Surface wettability is defined using the contact angles of a water drop sitting over it. For a static drop, equilibrium contact angle is taken into account, while, for moving drops, the advancing and receding contact angles are taken as the reference. The differ⇑ Corresponding author. E-mail address: [email protected] (D. Del Col). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.092 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

ence among advancing and receding angles gives the contact angle hysteresis. Surfaces presenting contact angles lower than 90° are called hydrophilic, while those having h > 90° are named hydrophobic. Moreover, if the surface presents extremely high contact angles, i.e. greater than 150°, and extremely low contact angle hysteresis, i.e. lower than 10°, it is named superhydrophobic. Hydrophobic surfaces are produced by lowering surface free energy of the substrate, for example by coating with a thin layer of a material having low surface energy, such as organic substances, polymers, and noble metals [5–9]. The use of organic substances as low-surface energy promoters requires strong, long-term adhesion forces between the coating and the metal substrate. Usually, the thicker is the coating, the better its resistance to corrosion/erosion. However, due to very low thermal conductivity, thick organic coatings add a heat transfer resistance that may deteriorate the condensation performance. Moreover, the coating material, if inadvertently removed from the condenser surface, may contaminate the system. The correlation between surface wetting properties and condensation heat transfer enhancement is still not well established. As an example, Xuehu et al. [10] reported heat transfer measurements on a superhydrophobic nanostructured copper sample and compared them to those obtained on a mirror polished hydrophobic specimen. They found that the nanostructured substrate does not improve the condensation heat transfer performance as expected from the higher contact angle, but better results were achieved with the hydrophobic substrate. Flow condensation tests

308

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

Nomenclature (dp/dz)F A c Dh g G h Hlv HTC L _ m p Q q S T T0 T00 uA uB uC uM uTOT z z1 z2

frictional pressure gradient, Pa m
1 heat transfer area, m2 specific heat capacity, J kg
1 K
1 hydraulic diameter, m gravitational acceleration, m s
2 specific mass flow rate, kg m
2 s
1 specific enthalpy, J kg
1 latent heat of vaporization, J kg
1 heat transfer coefficient, W m
2 K
1 length, m mass flow rate, kg s
1 pressure, Pa heat flow rate, W heat flux, W m
2 cross section area, m2 temperature, K specimen temperature at z1, K specimen temperature at z2, K type-A uncertainty, % type-B uncertainty, % combined uncertainty, % expanded uncertainty, % global uncertainty, % orthogonal axis of the sample, m position (1.5 mm) along z, m position (3.25 mm) along z, m

Greek symbols b slip length, m C condensate mass flow rate per unit width, kg m
1 s
1

of saturated vapor on superhydrophobic nanotextured copper surfaces presented by Torresin et al. [11] show that condensing drops form and penetrate into the surface texture, with a reduction of their mobility. However, the authors found that the vapor shearinduced roll-off of droplets compensates for the reduced drops mobility and enhances the overall thermal transport with respect to non-treated copper surfaces. Works cited above refer to dropwise condensation mode and from its discovery several authors [12–14] managed to promote it over hydrophobic or superhydrophobic surfaces. Instead, very limited studies have addressed the phenomenon of film condensation over a hydrophobic surface, which is the actual subject of the present investigation. 1.1. Literature review Some works in the literature studied vapor condensation inside micro and minichannel with different surface wettability. In Fang et al. [15] flow condensation inside hydrophilic, hydrophobic and semi-hydrophobic microchannel is presented. The authors show some images of the condensation flow patterns, where the wall is wetted by drops or liquid film depending on the surface wettability and on the position along the microchannel. In Ref. [8] vapor condensation is studied in minichannels. Hence, the heat transfer coefficient does not depend on vapor quality, in fact for each mass flow rate, the heat transfer coefficients at low vapor quality (x = 0.2) and at high vapor quality (x = 0.9) are comparable. It is interesting to notice that at very low vapor quality, high HTCs are measured on hydrophobic surfaces during vapor condensation; this may occur in filmwise mode although this is not clearly stated in the paper.

d Dh DT DTml h k

l q si

liquid film thickness, m contact angle hysteresis, ° temperature difference, K mean logarithmic temperature difference, K contact angle, ° thermal conductivity, W m
1 K
1 dynamic viscosity, Pa s density, kg m
3 interfacial shear stress, Pa

Subscripts adv advancing BC boiling chamber CALC calculated cool cooling side EXP experimental HPHIL hydrophilic HY hydrophobic IN inlet l liquid m mean Nu Nusselt component OUT outlet rec receding SAT saturation SS shear stress component V vapor WALL surface

Some papers in the literature investigate the effect of the hydrophobicity during single phase flow and heat transfer [1,16,17]. In these works the heat transfer coefficients measured over hydrophilic and hydrophobic surfaces were compared, showing a relationship between the surface wetting properties and the heat transfer and flow parameters. Two main results have been achieved over the hydrophobic surfaces: a drag reduction and a heat transfer decrease. For example in Ref. [16] the hydrophilic microchannel consistently shows a higher heat transfer coefficient than that of the hydrophobic microchannel although this increase is only about 8%; in Ref. [17] the heat transfer coefficients of superhydrophobic tubes display a small decrease as compared to untreated tubes, depending on the tube diameter. In the same work [17], the drag reduction ranged from 8.3% to 17.8% when moving from untreated to superhydrophobic tubes. The explanation of these results has been attributed to the existence of a slip velocity at the wall, which was, moreover, measured during those experimental tests. The most validated theory about the slip boundary explains that air cavities can be entrapped in between the surface roughness and, since the dynamic viscosity of air is remarkably smaller than that of liquid, large velocity gradients near the hydrophobic wall are achieved and, thus, the frictional flow resistance is reduced [1,18,19]. Normally, studies on film condensation heat transfer essentially comply with no-slip boundary conditions at the solid surface. In fact, for macroscopic flows of simple fluids, the slip length is usually so small (b is equal to few nanometers) that it can be neglected, and the no-slip boundary condition can be used without loss of accuracy [20]. However, some literature shows the existence of a slip velocity when a liquid flows on hydrophobic or superhydrophobic treated surfaces [1,16–19,21–24]. Recent exper-

309

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

imental and computation work indicates that slip boundary increases with an increase of Reynolds number and a reduction of the viscous sub-layer thickness, but a more detailed understanding of the physical nature of this scaling has yet to be presented [1,19,23]. Pati et al. [25] theoretically studied how the slip velocity can influence the condensation heat exchange over vertical surfaces. The authors studied the relationship between slippage phenomenon and two-phase heat transfer performance by introducing a nonzero slip length, defined as the distance behind the solid interface at which the liquid velocity extrapolates to zero, into the classical condensation theory. In [25] the authors demonstrated that when promoting a slip length b – 0 the condensate film thickness over the surface reduces, in comparison to classical theory (b = 0), the more the higher is the slip length. This is because an increase of b is associated with an augmentation of the slip velocity at the surface, resulting in a thinner condensate layer. The reduction of the liquid film thickness is associated with a reduced thermal resistance of the condensate layer, thus it leads to an enhancement of the two-phase heat transfer coefficient. Similar results are shown in Ref. [26], where variation of the velocity along the liquid layer, of the condensate film thickness and of the condensation mass flow rate per unit width are reported for different slip lengths. The authors showed that a non-zero slip length reflects on a non-zero slip velocity at the solid-liquid interface, leading to reduced condensate film thickness and enhanced condensation mass flow rate per unit width. However, to the best of the present authors’ knowledge, no experimental analysis about film condensation over hydrophobic surfaces has been presented in the literature and the effect of hydrophobicity on the liquid film and the heat transfer coefficient has never been experimentally investigated. The present paper presents an investigation of vapor condensation on hydrophobic aluminum substrates being aluminum a material of great interest for many industrial fields, especially in the heat transfer area. First, a technique for achieving hydrophobic properties over aluminum substrates is introduced, and surface properties characterization, by means of contact angles analysis, Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM), is presented. Then, the experimental investigation of film condensation over hydrophobic surfaces is addressed. Heat transfer data are presented and compared against values obtained during condensation over standard hydrophilic aluminum substrates. 2. Surface wetting properties modification The effect of the wetting properties of the metallic surface on the heat transfer coefficient during pure steam condensation has been investigated by modifying the wettability of the aluminum substrates through a proper chemical process, in order to obtain hydrophobic characteristics. In this Section, the method used to impart low wetting properties and the surface characterization are presented.

2.1. Methods A high purity (AW 1050, minimum Al quantity 99.50%) aluminum smooth plate was used for specimen fabrication. Hexane (anhydrous, P99%) and 1H,1H,2H,2H-Perfluorooctyltriethoxysi lane (98%) (FOTS) were purchased from Sigma Aldrich. Five samples have been prepared for the condensation tests. Their main characteristics are summarized in Table 1. Two tested surfaces were hydrophilic, while three samples were hydrophobic. The HPHIL #1 sample has not undergone any treatment: it was tested in the apparatus as it was provided. For the HPHIL #2 surface, the as-received aluminum substrate has been sanded using emery paper #1200 and then washed in distilled water. The three hydrophobic surfaces (HY #1, HY #2 and HY #3) have all been obtained with the same procedure: the samples were sanded using emery paper #1200 and then were immersed for 15 min into Isopropanol (IPA), continuously stirring the solution through a sonication probe, and dried into a nitrogen stream, for cleaning purposes. Then a low surface tension coating was deposited on the clean substrate. The process consisted in spin-coating a Hexane–FOTS mixture (5% by volume) onto the sample at 800 rpm for 30 s. After spin coating, the sample was baked at 150 °C for 30 min for final solvent evaporation and film stabilization. 2.2. Characterization The morphology of the surface has been investigated by Scanning Electron Microscopy (SEM). In Fig. 1 it is possible to see the morphology of the aluminum substrate before and after the deposition of the hydrophobic coating. The deposited coating is homogenous without any crack. A film thickness of 100 nm has been measured by a profilometer on a scratch made just after the film deposition. Surface wetting properties and morphological characteristics were analyzed by means of contact angles analysis. Contact angles are measured using the standard sessile drop method, recording a water drop (backlight illuminated by a LED light) expanding and contracting quasi-statically over the horizontally oriented surface of interest. Advancing (hadv) and receding (hrec) contact angles are evaluated by post-processing the videos and fitting with a circle the drop profile near the contact point. Contact angle hysteresis (Dh) is calculated as the difference between hadv and hrec. The values of the contact angles reported in this paper are the average between at least five measurements taken at different positions over the surface; in addition the standard deviation is reported together with the corresponding mean value. Fig. 2 shows the advancing and receding contact angles measured over the untreated and the hydrophobic substrates. Prior to any treatment, the as-received aluminum sample presents an advancing contact angle equal to 84.8° ± 4.4°, a receding contact angle equal to 17.4° ± 4.6° and a contact angle hysteresis equal to 67.3° ± 4°. After the use of emery paper, the advancing and the receding contact angle decreases and they are hadv ¼ 31:6  4:4 and hrec ¼ 6:4  1:2. These surfaces, according to the usual classification, can be named as hydrophilic and they

Table 1 Advancing and receding contact angles and contact angle hysteresis of the tested aluminum surfaces. Mean value

HPHIL #1 HPHIL #2 HY #1 HY #2 HY #3

Standard deviation

hadv [°]

hrec [°]

Dh [°]

hadv [°]

hrec [°]

Dh [°]

84.8 31.6 143.5 127.0 133.1

17.4 6.4 43 24.8 37.9

67.3 25.2 100.5 102.2 95.2

±4.4 ±4.4 ±2.6 ±4.0 ±4.2

±4.6 ±1.2 ±4.8 ±4.4 ±3.9

±4 ±4.6 ±3.4 ±6.9 ±5.7

310

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

AFM analysis has also been done over a 2  2 cm sample obtained with the same treatment of the HY #1, HY #2 and HY #3 in order to measure the surface roughness; an image of AFM on the hydrophobic surface is shown in Fig. 3. The analysis has been done on areas with dimensions of 50  50 lm, where a mean surface roughness was measured equal to 507 nm, with a minimum value of 187 nm and a maximum value of 917 nm. The surface roughness measured with the AFM may provide an explanation of the high advancing contact angle measured over the hydrophobic substrates.

(a)

2 m

3. Experimental setup 3.1. Two-phase flow loop

(b)

2 m Fig. 1. SEM images of: a) flat polished aluminum and b) hydrophobic surface.

are listed as HPHIL #1 and HPHIL #2 in Table 1. After the treatment, the functionalized hydrophobic sample is characterized by a mean advancing contact angle equal to 135°, a mean receding contact angle equal to 35° and a mean Dh = 99°. Such surfaces are usually considered as hydrophobic and they are listed as HY #1, HY #2 and HY #3 in Table 1.

Advancing Contact Angle

Receding Contact Angle

HYDROPHOBIC

UNTREATED

Sample

A schematic diagram of the new two-phase flow loop for condensation measurements is shown in Fig. 4. The system consists of four main components: the boiling chamber, the test section, the cooling water loop and the postcondenser. Steam is generated in a cylindrical stainless steel boiling chamber which is connected to the test section by a stainless steel vapor line. The water vaporization is promoted inside the chamber by means of four electrical heaters with a total power of 4 kW. The electrical power supplied to the heaters is measured using a power analyzer NORMA 4000. The pipe connections between the boiler and the test section are thermally insulated and heated by means of a resistance wire installed around the pipe, to avoid formation of condensate before the entrance of the test section (wall temperature is checked through a T-type thermocouple). The steam enters the test section in saturated conditions with vapor quality equal to one. In the test section, steam is partially condensed over the test aluminum surface and the latent heat is removed by the cold water coming from a thermostatic bath. The coolant inlet temperature is measured by a T-type thermocouple, while the coolant temperature difference between the inlet and the outlet is measured by means of a three-junction copperconstantan thermopile. The coolant mass flow rate is measured

Fig. 2. Examples of advancing and receding contact angles for the hydrophilic and the hydrophobic specimens.

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

3.7 μm

0 0

50 μm Fig. 3. AFM image of a hydrophobic sample (scan area 50 x 50 lm).

311

by means of a Coriolis effect mass flow meter. The vapor pressure and temperature are gauged at the inlet of the measuring section by means of a differential pressure transducer (coupled with an absolute one for ambient pressure evaluation) and a T-type thermocouple, respectively. Downstream the test section, the twophase mixture passes through a secondary water condenser where the condensation is completed and the liquid subcooled. The subcooled liquid returns to the boiler driven by the difference between liquid and vapor density and it closes the loop. The cooling water temperature is measured at the inlet and the outlet of the postcondenser by means of T-type thermocouples while its mass flow rate is measured using a magnetic flow meter. To regulate the system pressure, a hydraulic accumulator is installed in the liquid line downstream the post-condenser. A needle valve, placed before the boiling chamber, is used to regulate the liquid flow in the main loop and it allows to achieve stable conditions during the tests. In between the hydraulic accumulator and the needle valve, a mechanical filter and a liquid indicator are installed. Before entering the boiling chamber the temperature of the subcooled liquid is measured by means of a T-type thermocouple. All the components of the test rig, with the exception of the test section, are made of stainless steel in order to avoid contami-

Fig. 4. Schematic of the experimental thermosyphon loop for condensation tests. P = Pressure transducer, T = Thermocouple, dT = Thermopile, CFM = Coriolis mass Flow Meter, MFM = Magnetic mass Flow Meter, MF = Mechanical Filter.

312

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

nation of the fluid. The boiling chamber and the stainless steel lines are thermally insulated to prevent heat losses to the ambient. Since even a few concentration of non-condensable gases (NCG) in the vapor could lead to a huge decrease in the thermal performance of the condensation process, several actions have been undertaken to avoid it. First of all, the test rig is always operated in overpressure to prevent air infiltration inside the test loop. Furthermore, before each test run, the whole system is vacuumed; then the test rig is charged with deionized (DI) water coming from the supplying tank and pumped inside the test rig by a centrifugal pump. When the pressure inside the setup becomes higher than the ambient pressure, some water is released from the top valve while the refill pump is continuing to run, in order to get rid of the non-condensable gases still present inside the setup. After one minute of free water discharging, the top valve and the filling line are closed. Subsequently the boiler is started: when the water reaches the saturation temperature and boils for several minutes, the vapor is released from the top of the system and from a discharge valve located in the upper part of the post-condenser. This procedure is repeated several times in order to get rid of the gases dissolved in the water. In all these operations, particular care is observed to keep always the test rig pressurized. The hydraulic accumulator is used to maintain the system in overpressure overnight, thereby avoiding the need for DI water refilling every day.

at 1.5 mm and two at 3.25 mm depth below the front surface of the sample. The sample is vertically mounted and is located in between the two main parts of the test section: one contains the steam channel (in contact with the frontal face of the specimen) and the other contains the cooling channel (in contact with the back face of the specimen). The cooling path consists of a 20 mm  5 mm rectangular PEEK channel and it is used to remove the heat from the condensation process. The cooling water flows in countercurrent to the steam direction inside the test section. In between the vapor block and the cooling system block, two frames are located for thermocouples and gaskets positioning.

3.2. Test section

q¼

The test section (Fig. 5) is designed for the measurement of the heat transfer coefficient over a metallic surface and for the simultaneous visualization of the condensation process. It consists of several pieces realized both in PEEK and glass. A rectangular channel 160 mm long (cross section 30 mm  5 mm) was grooved into a PEEK block and the vapor, coming from the boiling chamber, flows inside it. The PEEK channel is fitted with a rectangular aluminum plate (vertically oriented), over which condensation occurs. One side of the channel is covered by a double glass (with an air chamber for thermal insulation) to allow the visualization of the process. In addition, the frontal glass is heated up by means of an electrical heater to avoid vapor condensation over it. The other side of the channel, opposite to the glass, is machined for accommodating the metallic substrate. The metallic specimen has 10 mm thickness and the condensation surface is 50 mm high and 20 mm wide. The specimen is fitted with four T-type thermocouples located at the inlet and at the outlet of the condensing surface, inside four 0.7 mm holes, two located

where A is the heat transfer area of the specimen (50  20 mm). Since the wall temperatures are measured with the thermocouples placed in the aluminum (1.5 mm and 3.25 mm deep), the surface temperatures can be obtained from the measured values with the hypothesis of one-dimensional temperature distribution, since the PEEK thermal conductivity is much lower in comparison to the aluminum sample. At the inlet and outlet of the aluminum sample the two surface temperatures are calculated as:

(b)

VAPOR OUTLET

WATER INLET

ð1Þ

where ccool is the specific heat capacity of the coolant evaluated at the mean temperature between the inlet and the outlet. Hence, the condensation heat flux q is given by

Q cool A

ð2Þ

T WALL;IN ¼ T 0IN þ ðT 0IN
T 00IN Þ

z1 z2
z1

T WALL;OUT ¼ T 0OUT þ ðT 0OUT
T 00OUT Þ

ð3Þ

z1 z2
z1

ð4Þ

where T0 are the inlet and outlet temperatures measured in the aluminum sample at z1 = 1.5 mm and T00 are the inlet and outlet temperatures measured in the aluminum sample at z2 = 3.25 mm from the condensing surface.

(c)

T''IN

T''OUT

T'IN

WATER

WATER OUTLET

_ cool ccool DT cool Q cool ¼ m

METALLIC SAMPLE

GLASS

(a)

_ cool is directly measured, as Since the coolant mass flow rate m well as the inlet coolant temperature TIN-cool and the coolant temperature difference DTcool, the heat flow rate extracted from the condensing vapor can be obtained as

VAPOR

VAPOR INLET

3.3. Data reduction

T'OUT

Fig. 5. Test section: a) Sketch of the assembled component. b) View of a cross section. c) Metallic specimen.

313

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

Finally, the condensation heat transfer coefficient is evaluated as:

q DT ml

ð5Þ

where DTml is the mean logarithmic temperature difference between the surface and the steam. The steam saturation temperature is obtained from the pressure measurement at the inlet of the test section. _ steam is obtained from Eq. (6), where The steam mass flow rate m QBC is the heat flow rate given to the boiling chamber (measured from the electrical power supplied to the heaters), besides hV and hIN,BC are the enthalpy values of the saturated steam and of the subcooled liquid at the entrance of the boiling chamber, respectively.

_ steam ¼ m

Q BC hv
hIN;BC

ð6Þ

All the thermodynamic and transport properties of the steam are evaluated by means of NIST Refprop Version 9.1 [27] from temperature and pressure measurements. Once the mass flow rate is known, the mass velocity of the vapor flowing inside the test section can be calculated as

Gsteam ¼

_ steam m S

ð7Þ

where S is the cross section area of the channel. By acting on the power supplied to the boiling chamber, it is possible to regulate the mass flow rate of the steam inside the system and to perform tests at varying mass velocity. 3.4. Uncertainty analysis The experimental uncertainties are calculated following the general rules reported in ISO Guide to the Expression of Uncertainty in Measurement [28]. For each parameter, the combined uncertainty uc is calculated considering ‘‘Type A” and ‘‘Type B” components. Type A uncertainty is equal to the standard deviation of the measured value while Type B uncertainty is related to the instrument properties. Table 2 reports Type B uncertainty of the most relevant measured parameters. The uncertainty of the thermocouples position is assumed to be negligible. The global uncertainty of the measured data xi is evaluated as

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uTOT ðxi Þ ¼ u2A ðxi Þ þ u2B ðxi Þ

4. Experimental analysis 4.1. Results over untreated hydrophilic surface: validation of experimental procedure vs. literature The condensation heat transfer was first studied on an aluminum hydrophilic surface (HPHIL #1) presenting advancing and receding contact angles equal to hadv ¼ 84:8  4:4 , and hrec = 17.4° ± 4.6°, respectively. Tests were performed at G = 1.5 kg m
2 s
1, TSAT = 107 °C and _ cool = 0.11 kg s
1, while the coolant inlet temperature was varied, m leading to changes in the temperature difference between saturation and wall. Fig. 6 reports the experimental values of the HTC (Section 3.3) measured on the untreated hydrophilic surface. As expected for film condensation, the mean heat transfer coefficient decreases when the mean logarithmic temperature difference increases. These measurements have also been compared with correlations available in the literature for filmwise condensation to verify the present experimental technique. When applying a model for condensation driven only by gravity, one would expect to underestimate the experimental data because the effect of velocity would be neglected. Therefore a more complete model, which combines gravity and shear stress components, has been adopted [29]. The global heat transfer coefficient can be then calculated by Eq. (10):

HTC CALC ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi HTC 2Nu þ HTC 2ss

ð10Þ

where "



HTC Nu ¼ 1:15 0:026

Hlv ll kl ðT SAT
T wall Þ

#

0:5

"

þ 0:79 0:943

ql ðql
qv ÞgHlv k3l ll ðT SAT
T wall ÞL

#0:25

ð11Þ

20

ð8Þ

where uA(xi) and uB(xi) are respectively the Type A and Type B uncertainties of the i-th parameter xi. The combined standard uncertainty of the derived data y ¼ f ðx1 ; x2 ;    ; xn Þ is evaluated as

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n  2 uX df uC ðyÞ ¼ t u2TOT ðxi Þ dxi i¼1

ð9Þ

The expanded uncertainty uM(xi) is finally obtained by multiplying uC(xi) by a coverage factor k ¼ 2. In this analysis the uncertainties of the thermodynamic properties evaluated using NIST Refprop Version 9.1 [27] are neglected.

15

HTC [kW m-2 K-1]

HTC ¼

The results of the uncertainty analysis lead to a mean expanded uncertainty of the logarithmic temperature difference between the steam and the wall equal to ±1.6%, a mean expanded uncertainty of the heat flux removed in the measuring section equal to ±7.8% and a mean expanded uncertainty of the heat transfer coefficient equal to ±11.1%.

10

Experimental HTC Serie3 Calc. HTC (gravity + SS)

5

UNTREATED (HYDROPHILIC)

Serie2 Calc. HTC (gravity) 0

Table 2 Type B uncertainty of the measured parameters. Temperature Cooling water flow rate Differential pressure Absolute pressure Electrical power

±0.05 K   _ ±0.15% ± 0:1 _  100 % of the flow rate m m ±0.04% ±0.1% ±0.1%

0

5

10

15

20

25

30

35

ΔTml [°C] Fig. 6. Calculated and experimental heat transfer coefficient versus mean logarithmic temperature difference between saturated vapor and wall during condensation on the untreated hydrophilic sample (HPHIL #1) at G = 1.5 kg m
2 s
1. The values ‘‘Calc. HTC (gravity)” are obtained by means of Eq. (11). The values ‘‘Calc. HTC (gravity + SS)” are determined using Eq. (10).

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

Eq. (11) is referred to the gravity controlled condensation heat transfer coefficient: it includes the Nusselt equation [30] together with terms which account for wave formation and inertia effects. Since waves formation was observed on the condensate film during the experiments, the heat transfer enhancement has to be taken into account introducing the correction factor 1.15 [31]. The inertia effects, which are neglected in the Nusselt’s theory, are included by the terms in between the square brackets, as suggested in Ref. [32]. The variation of the physical properties of the condensate with temperature must also be considered and this is done here by calculating all the physical properties of the condensate at the mean temperature:

T m ¼ 0:75 T WALL þ 0:25 T SAT

deviation between experiments and calculations is equal to 4.5%, far below the experimental uncertainty.

4.2. Investigation over hydrophobic surfaces Condensation tests over the hydrophobic aluminum specimens (HY #1) are hereinafter presented and compared against the values obtained during condensation over the untreated hydrophilic sample (HPHIL #1). Condensation heat transfer measurements were performed at about 106 °C saturation temperature, which corresponds to a saturation pressure pSAT  1.25 bar. Experimental tests were performed by varying the inlet temperature and the mass flow rate of the cooling water, resulting in variable mean logarithmic temperature difference between the steam and the wall and thus variable heat flux. Tests were performed varying the vapor mass velocity by acting on the power of the boiling chamber. During tests, the heat flux was varied between 250 and 500 kW m
2 and the steam velocity was varied between 2.2 and 6.4 m s
1. Thanks to visualization, it was possible to verify that filmwise condensation occurred in all the tests, without presence of drops. Fig. 7a reports an image of the steam condensing on the surface taken with the high speed video camera Photron FASTCAM Mini UX100 high speed camera (CMOS sensor with Bayer color filter array) at 1280 by 606 pixel resolution and 2000 frames per second. As it can be seen in Fig. 7a, there is no presence of drops on the condensing surface and the condensation mode is completely filmwise; no solid-liquid-vapor contact line can be detected. Other images like the one in Fig. 7a have been taken during the tests, and they all confirm that, at present operating conditions, filmwise condensation always occurred. The reason why dropwise condensation is not observed at these operating conditions must be related to the flooding mechanism over the surface. When a hydrophobic-rough surface is subject to a sufficiently high condensation heat flux, thus high temperature difference between the wall and the saturated vapor, the surface may be in a ‘‘flooded” state and single droplets could not be observed. As outlined in [35], hydrophobic and rough surfaces may be optimal to promote dropwise condensation at low heat flux while at higher heat flux smooth condensing surfaces with low contact angle hysteresis have a better performance, avoiding the flooding mechanism which would occur on a superhydrophobic surface. Enright et al. [13,36] noted that 80 kW m
2 is a limiting heat flux value in the case of superhydrophobic surfaces. It is interesting to note that this

ð12Þ

while the latent heat Hlv and the density of the saturated steam qv are calculated at TSAT [33]. The second term under the square root in Eq. (10) is due to the vapor velocity and it is expressed as follows

sffiffiffiffiffiffiffiffiffiffiffiffiffi k2l si ql HTC ss ¼ 2 Cl l l

ð13Þ

The shear stress correlation used in the present work (Eq. (13)) is the one proposed in [33] for the shear-controlled condensation process with laminar flow in the condensate film (the maximum Reynolds number of the condensate film is about 130 for the present data). As reported in Ref. [30], the condensate mass flow rate per unit width in Eq. (13) can be evaluated from the liquid film thickness as

C¼

ql ðql
qv Þgd3 3ll

ð14Þ

and the shear stress at the liquid-vapor interface can be obtained from the frictional pressure gradient:

si ¼


  Dh dp 4 dz F

ð15Þ

The model by Friedel [34] has been used in the present work to compute the frictional pressure gradient in Eq. (15). The calculated values of the heat transfer coefficients are presented in Fig. 6. As expected, if the vapor velocity is neglected (HTC calculated using Eq. (11)), the calculated HTCs underpredict the experimental values, whereas when using Eq. (10) the mean

(a)

(b)

160

35

HTC

140 120

T’IN

Temperature [°C]

100

30 25

T’’IN

20

80 15

60 T’OUT

40 20

T’’OUT

10 5

Tin,ref

0

HTC [kW m-2 K-1]

314

0

0

2000

Time [s]

4000

6000

Fig. 7. a) Image of the filmwise condensation process over the sample HY #1. b) Wall temperatures measured by thermocouples within the specimen ðT 0IN ; T 00IN ; T 0OUT ; T 00OUT Þ plotted versus time (T0 and T00 are measured at 1.5 mm and 3.25 mm depth, respectively) during condensation over the HY #1 sample. The inlet water temperature (Tin,ref) and the measured heat transfer coefficient (HTC) are also reported. Data refer to G = 5.1 kg m
2 s
1.

315

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

limiting value is considerably lower than the experimental heat flux in the present tests, being the minimum value around 250 kW m
2. Therefore, the roughness of the present hydrophobic surfaces, as measured by means of AFM, and the heat flux exchanged during the tests suggest that the hydrophobic surfaces must be in a flooded state, yielding a filmwise condensation mode. The occurrence of a film condensation process can be also checked by looking at the four temperatures measured by thermocouples within the specimen wall (T 0IN ; T 00IN ; T 0OUT ; T 00OUT , Section 3.3) which are plotted vs. time in Fig. 7b. The inlet water temperature (Tin,ref) and the measured HTC are also plotted in the same graph, which refers to a test run at vapor mass flux equal to 5.1 kg m
1 s
1. A confirmation of the film condensation is provided by the comparison between the wall temperatures at the inlet and the wall temperatures at the outlet: during filmwise condensation, one can expect lower wall temperatures at the outlet as compared to the inlet, because of the liquid film thickness, while, under dropwise condensation, typically no difference between inlet and outlet is expected. Instead, Fig. 7b displays a clear difference between T0 IN and T0 OUT and between T00 IN and T00 OUT. When the inlet water temperature Tin,ref decreases, the global temperature difference between steam and cooling water increases and the wall temperatures at inlet and outlet diverge

600

more, meaning that the thermal resistance between saturated vapor and aluminum surface grows along the flow of the steam, i.e. a condensate film is present and its thickness increases between inlet and outlet when increasing the difference between saturation and surface temperature. The heat flux and heat transfer coefficient values measured during filmwise condensation over the hydrophobic treated aluminum substrate are reported in Fig. 8, at three values of mass velocity (1.5–3.1–5.1 kg m
2s
1). Trends are those expected during filmwise condensation. Heat flux increases both when increasing steam mass velocity and saturation-to-wall temperature difference. Instead, the condensation heat transfer coefficient increases with Gsteam, but it tends to decrease almost linearly when increasing DTml, with higher slope at higher steam velocity. Fig. 9 shows a comparison between heat transfer coefficients measured on the untreated and the hydrophobic surfaces, for different saturation-to-wall temperature difference and steam mass velocity. The Figure shows that heat transfer coefficients on the hydrophobic surface are higher by 10–45% than those on the untreated surface, for the present conditions. Two aspects can be seen: – the ratio HTC HY =HTC HPHIL increases with the increase of Gsteam at a fixed DT ml . The increase of the vapor mass flow rate entails the increase of the condensate velocity;

30 25

400

HTC [kW m-2 K-1]

q [kW m-2]

500

300 200

-2 -1

G=1.5 kg m s

G=3.1 kg m-2 s-1

100

5

10

15

20

25

10 -2 -1

5

G=5.1 kg m s 0 0

15

G=1.5 kg m s

HYDROPHOBIC

-2 -1

20

0

30

0

ΔTml [K]

-2 -1

G=5.1 kg m s

HY

HY

HY

HPHIL

HPHIL

HPHIL

10

20 ΔTml [K]

(a)

30

40

(a)

35

1.5

30

1.4

25

HTCHY / HTCHPHIL [/]

HTC [kW m-2 K-1]

-2 -1

G=3.1 kg m s

20 15 -2 -1

G=1.5 kg m s

10

G=3.1 kg m-2 s-1 5

G=5.1 kg m-2 s-1

HYDROPHOBIC

5

10

15

20

25

1.2 -2s-1 s-1 1.5 kg GG==1.5 kgmm-2 -2s-1 s-1 GG==3.1 kgmm-2 3.1 kg -2s-1 5.1 kg GG==5.1 kgmm-2 s-1

1.1 1

0 0

1.3

30

ΔTml [K]

(b) Fig. 8. Heat flux (a) and heat transfer coefficient (b) versus mean logarithmic temperature difference between saturated steam and surface during condensation over the hydrophobic sample (HY #1). Data refer to different steam mass velocities G (1.5–3.1–5.1 kg m
2 s
1).

0

10

20

30

ΔTml [K]

(b) Fig. 9. Comparison between the heat transfer coefficient on the hydrophobic (HY #1) and on the untreated (HPHIL #1) sample (a), and ratio between the two values (b), as a function of wall subcooling degree, for different steam mass velocities G [kg m
2 s
1].

316

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

– the ratio HTC HY =HTC HPHIL decreases with the increase of DT ml at a fixed Gsteam. The increase of the mean logarithmic temperature difference between the steam and the surface leads to the augmentation of the condensate film thickness. 4.3. Repeatability and discussion of results To the best of the present authors’ knowledge, the results shown in Fig. 9 are the first ones of this kind, i.e. the heat transfer enhancement due to the surface hydrophobicity during filmwise condensation has never been experimentally proved in the literature before. Several tests have been made to verify those results and check the reliability of the present data. As previously reported, beside HPHIL #1 and HY #1, more samples have been prepared with the aim of collecting more data points during condensation over hydrophilic and hydrophobic surfaces. The test samples and their values of contact angle measurements are listed in Table 1. The experimental tests have been carried out keeping the same vapor mass flow rate, saturation temperature and cooling water mass flow rate as adopted in the tests of Fig. 9, while the inlet cooling water temperature is varied to vary the mean logarithmic temperature difference between steam and wall. In Fig. 10 the main results are summarized, in particular the HTCs measured on the hydrophilic samples (HPHIL #1 and HPHIL #2) and on the hydrophobic ones (HY #1, HY #2 and HY #3) are displayed. Tests on both hydrophilic and hydrophobic surfaces present a good repeatability, meaning that the phenomenon has always the same behavior independently from the specimen and it is related to the surface wettability. All the results plotted in Fig. 10 are obtained on new samples to avoid the effect of surface degradation. In fact, it was seen that the degradation of the hydrophobic layer can severely affect the present results. In particular, after testing the surface for a certain period, which can vary from one hour to two hours, all the hydrophobic samples (HY #1, HY #2 and HY #3) displayed lower heat transfer coefficients, in agreement with those measured on the hydrophilic samples. The contact angles were then checked after tests, finding hadv ¼ 39:6  12:6 and hrec  0 and thus proving the surface degradation from the initial hydrophobic characteristics.

In the light of these results, the enhancement of condensation heat transfer over hydrophobic surfaces cannot be explained with dropwise condensation on some part of the heat transfer area because discrete droplets were not observed neither a solidliquid-vapor contact line was observed. No physical explanation of the present results can be proved at the moment. Nevertheless, since our surfaces are completely flooded, some discussion can be done by looking at previous experiments during liquid flow on hydrophobic surfaces. As reported in Section 1.1, the drag reduction of liquid flow over hydrophobic surfaces could be explained by supposing a slip velocity at the wall. In the present tests, the presence of a slip mechanism cannot be demonstrated, however it may be interesting to notice that the assumption of a slip velocity of the condensate layer at the wall implies some heat transfer enhancement. The ratio of HTCHY to HTCHPHIL reflects how the hydrophobicity affects the condensation performance as compared to an untreated (hydrophilic) specimen. The present results suggest that the measured heat transfer enhancement must be related to two main parameters: vapor velocity and heat flux. As shown in Fig. 9, the ratio of heat transfer coefficient (HTCHY/HTCHPHIL) at constant DTml increases with the steam velocity, which means that for the same temperature difference between saturation and wall the relative performance of the hydrophobic surface is better at higher steam velocity. Limiting this discussion at qualitative level, it can be said that a higher heat transfer coefficient must be due to a lower film thickness. Studies in the literature [19] suggest that when a slip velocity occurs, it is proportional to the fluid velocity which means that by increasing the liquid-vapor interfacial velocity we get a higher slip velocity and thus a lower liquid film thickness. The results in Fig. 9 also show that the ratio of heat transfer coefficient (HTCHY/HTCHPHIL) decreases when the saturation-to-wall temperature difference increases, i.e. when the film thickness increases. This suggests that, if a slip mechanism occurs, its effect diminishes when the film is thicker. Interesting to say, as pointed out in Section 1.1, these two effects of steam velocity and heat flux on the heat transfer enhancement are in agreement with the literature on slippery mechanism [1,17,19]. In the present study no measurement of the condensate film velocity is performed. However, a qualitative analysis compared with the literature shows that assuming a slip velocity at the wall goes in the direction of explaining the measured heat transfer enhancement.

40

4.4. Comparison with condensation model

HYDROPHOBIC SAMPLES

35

HTCEXP [kW m-2 K-1]

30 25 20

HPHIL #1 HPHIL #2

15

HY1 10

HY2

HYDROPHILIC SAMPLES

HY3

5 0 0

5

10

15

20

25

ΔTml [°C] Fig. 10. Heat transfer coefficient versus temperature difference between the saturated steam and the surface during condensation over hydrophilic (HPHIL #1 and HPHIL #2) and hydrophobic (HY #1, HY #2 and HY #3) samples. Data refer to G = 5.1 kg m
2 s
1.

The present experimental data are compared against a model available in the open literature for filmwise condensation. In the present data, both the gravitational effect and the shear stress effect affect the condensation process, thus both need to be accounted for in the calculations. The calculations start from the classical theories of gravity [30] and shear controlled condensation heat transfer [33]. Thus, the model applied here is the one already mentioned in Section 4.1 (Eq. (10)). The results of this comparison are reported in Fig. 11, both for the hydrophilic surface (HPHIL #1 in Fig. 11a) and the hydrophobic sample (HY #1 in Fig 11b). The deviation between the calculated and the experimental values increases when increasing the steam mass flow rate: this is typical in the case of shear driven condensation process, because of the higher uncertainty in the estimation of the shear stress effect on the heat transfer. However, the model clearly underestimates the experimental data measured on the hydrophobic surface (Fig. 11b), by 20 to 30%, while the agreement is within 10% for the heat transfer coefficients measured over the untreated hydrophilic sample (Fig. 11a). Therefore, the classic filmwise condensation theory is not able to describe the present phenomenon.

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

20 -2 -1

G=1.5 kg m s

+10%

-2 -1

Serie3 kg m s G=3.1

HTCCALC [kW m -2 K-1]

-10%

-2 -1

15

Serie9 G=5.1 kg m s

10

5

HYDROPHILIC 0 0

5

10 HTCEXP [kW m -2 K-1]

15

20

(a) 30 -2 -1

+10%

G=1.5 kg m s 25

-2 -1 -2 -1

HTCCALC [kW m -2 K-1]

3. During steam condensation over the hydrophobic treated substrates, enhanced heat transfer has been measured although condensation always occurred in filmwise mode caused by the flooding of the surfaces, due to the high heat flux and the surface roughness. 4. The heat transfer enhancement with respect to the hydrophilic samples increases when increasing vapor mass velocity and reduces when increasing saturation-to-wall temperature difference. In the tested conditions, the heat transfer coefficient is higher by 10–45% on the hydrophobic surface as compared to the hydrophilic sample. 5. Several samples, both hydrophilic and hydrophobic, have been tested and the repeatability of the present results was confirmed. On the hydrophobic samples, after a certain period, a change in the surface wettability was found, with decrease of the heat transfer coefficients to the values of the hydrophilic surface. Contact angle measurements have been done after tests on the hydrophobic surfaces, demonstrating the degradation of the fluorosilane layer. 6. The condensation heat transfer enhancement cannot be explained using the classical model of filmwise condensation. Besides, no droplets were observed on the surface neither a solid-liquid-vapor contact line was observed. 7. Available literature on liquid flow over hydrophobic surfaces suggests an explanation of the present results by assuming some slip of the condensate at the wall. This assumption is not experimentally proved in the present study but it goes in the direction of explaining the measured heat transfer enhancement because it implies a thinner condensate film.

-10%

Serie3 G=3.1 kg m s

Serie9 G=5.1 kg m s

20

317

Acknowledgments The European Space Agency is greatly acknowledged for supporting this work through the MAP Condensation program.

15

References

10

5

HYDROPHOBIC 0 0

5

10 15 20 HTCEXP [kW m -2 K-1]

25

30

(b) Fig. 11. Comparison between the experimental data acquired during condensation over the hydrophilic (HPHIL #1) sample (a) and over the hydrophobic (HY #1) sample (b). The values are calculated with the filmwise condensation model (Eq. (10)).

5. Conclusions 1. In this paper, a method to impart hydrophobic properties over aluminum substrates is presented. This consists in forming onto the metal a low surface energy film, by spin coating a fluorosilane-Hexane solution over it. 2. Tests of pure steam flow condensation over hydrophobic treated surfaces ðhadv ffi 140 Þ are performed at heat flux between 250 and 500 kW m
2 and steam velocity between 2.2 and 6.4 m s
1. The present results are compared with those found when testing hydrophilic untreated specimens ðhadv < 90 Þ.

[1] J.P. Rothstein, Slip on superhydrophobic surfaces, Annu. Rev. Fluid Mech. 42 (2010) 89–109. [2] C. Antonini, M. Innocenti, T. Horn, M. Marengo, A. Amirfazli, Understanding the effect of superhydrophobic coatings on energy reduction in anti-icing systems, Cold Reg. Sci. Technol. 67 (2011) 58–67. [3] A.R. Betz, J. Jenkins, C.J. Kim, D. Attinger, Boiling heat transfer on superhydrophilic, superhydrophobic, and superbiphilic surfaces, Int. J. Heat Mass Transfer 57 (2013) 733–741. [4] E. Schmidt, W. Schurig, W. Sellschopp, Versuche über die kondensation von wasserdampf in film- und tropfenform, Forsch. Ingenieurwes. 12 (1930) 53– 63. [5] S. Vemuri, K.J. Kim, An experimental and theoretical study on the concept of dropwise condensation, Int. J. Heat Mass Transfer 49 (2006) 649–657. [6] S. Vemuri, K.J. Kim, B.D. Wood, S. Govindaraju, T.W. Bell, Long term testing for dropwise condensation using self-assembled monolayer coatings of noctadecyl mercaptan, Appl. Therm. Eng. 26 (2006) 421–429. [7] R. Jafari, M. Farzaneh, Fabrication of superhydrophobic nanostructured surface on aluminum alloy, Appl. Phys. A Mater. Sci. Process. 102 (2011) 195–199. [8] M.M. Derby, A. Chatterjee, Y. Peles, M.K. Jensen, Flow condensation heat transfer enhancement in a mini-channel with hydrophobic and hydrophilic patterns, Int. J. Heat Mass Transfer 68 (2014) 151–160. [9] R.A. Erb, Dropwise condensation on gold – improving heat transfer in steam condensers, Gold Bull. 6 (1973) 2–6. [10] L. Zhong, M. Xuehu, W. Sifang, W. Mingzhe, L. Xiaonan, Effects of surface free energy and nanostructures on dropwise condensation, Chem. Eng. J. 156 (2010) 546–552. [11] D. Torresin, M.K. Tiwari, D. Del Col, D. Poulikakos, Flow condensation on copper-based nanotextured superhydrophobic surfaces, Langmuir 29 (2013) 840–848. [12] J.W. Rose, Dropwise condensation theory and experiment: a review, Proc. Inst. Mech. Eng. Part A J. Power Energy 216 (2002) 115–128. [13] R. Enright, N. Miljkovic, J.L. Alvarado, K. Kim, J.W. Rose, Dropwise condensation on micro- and nanostructured surfaces, Nanoscale Microscale Thermophys. Eng. 18 (2014) 223–250. [14] N. Miljkovic, E.N. Wang, Condensation heat transfer on superhydrophobic surfaces, MRS Bull. 38 (2013) 397–406.

318

D. Del Col et al. / International Journal of Heat and Mass Transfer 107 (2017) 307–318

[15] C. Fang, J.E. Steinbrenner, F.M. Wang, K.E. Goodson, Impact of wall hydrophobicity on condensation flow and heat transfer in silicon microchannels, J. Micromechan. Microeng. 20 (2010) 45018. [16] S.S. Hsieh, C.Y. Lin, Convective heat transfer in liquid microchannels with hydrophobic and hydrophilic surfaces, Int. J. Heat Mass Transfer 52 (2009) 260–270. [17] F.Y. Lv, P. Zhang, Drag reduction and heat transfer characteristics of water flow through the tubes with superhydrophobic surfaces, Energy Convers. Manage. 113 (2016) 165–176. [18] D.C. Tretheway, C.D. Meinhart, A generating mechanism for apparent fluid slip in hydrophobic microchannels, SOCAR Proc. 2010 (2010) 60–68. [19] S. Granick, Y. Zhu, H. Lee, Slippery questions about complex fluids flowing past solids, Nat. Mater. 2 (2003) 221–227. [20] G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge Univ. Press, 1985. [21] D.C. Tretheway, C.D. Meinhart, Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids 14 (2002) 8–12. [22] R.S. Voronov, D.V. Papavassiliou, L.L. Lee, Slip length and contact angle over hydrophobic surfaces, Chem. Phys. Lett. 441 (2007) 273–276. [23] C.H. Choi, K.J.A. Westin, K.S. Breuer, Apparent slip flows in hydrophilic and hydrophobic microchannels, Phys. Fluids 15 (2003) 2897–2902. [24] B. Bhushan, Y. Wang, A. Maali, Boundary slip study on hydrophilic, hydrophobic, and superhydrophobic surfaces with dynamic atomic force microscopy, Langmuir 25 (2009) 8117–8121. [25] S. Pati, S.K. Som, S. Chakraborty, Slip-driven alteration in film condensation over vertical surfaces, Int. Commun. Heat Mass Transfer 46 (2013) 37–41.

[26] J.A. Al-Jarrah, A.F. Khadrawi, M. A. AL-Nimr, Film condensation on a vertical microchannel, Int. Commun. Heat Mass Transfer 35 (2008) 1172–1176. [27] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1., 2013. [28] ISO Guide to the Expression of Uncertainty in Measurement, 1995. [29] A. Bisetto, S. Bortolin, D. Del Col, Experimental analysis of steam condensation over conventional and superhydrophilic vertical surfaces, Exp. Therm. Fluid Sci. 68 (2015) 216–227. [30] W. Nusselt, Die Oberflächenkondensation des Wasserdampfes, Zeitschrift VDI. 60 (27) (1916), 541–546 and 569–575. [31] H.D. Baehr, K. Stephan, Waerme- und Stoffuebertragung, Springer-Verlag, 2004. [32] C.A. Depew, R.L. Reisbig, Vapor condensation on a horizontal tube using teflon to promote dropwise condensation, I&EC Process Des. Dev. 3 (1964) 365–369. [33] G.F. Hewitt, G.L. Shires, T.R. Bott, Process Heat Transfer, 1994. [34] L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow, in: Eur. Two-Phase Flow Gr. Meet. Ispra, 1979. [35] N. Miljkovic, R. Enright, Y. Nam, K. Lopez, N. Dou, J. Sack, E.N. Wang, Jumpingdroplet-enhanced condensation on scalable superhydrophobic nanostructured surfaces, Nano Lett. 13 (2013) 179–187. [36] R. Enright, N. Miljkovic, A. Al-Obeidi, C.V. Thompson, E.N. Wang, Condensation on superhydrophobic surfaces: the role of local energy barriers and structure length scale, Langmuir 28 (2012) 14424–14432.