heat transfer investigations in micro-channel...

15th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008

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Heat transfer investigations in micro-channel flows

Vânia Silvério*,1, António L.N. Moreira

1, Viriato Semião

1

C. Nunes de Carvalho2, Guilherme Lavareda

2, Pedro Parreira

2 and Ana Amaral

3

1: Department of Mechanical Engineering, Instituto Superior Técnico, Av. Rovisco Pais 1049-001 Lisbon, Portugal

2: DCM/ICEMS, Faculty of Sciences and Technology, New University Lisbon, Qta. Torre, 2829-516 Caparica, Portugal

3: ICEMS, Department of Physics, Instituto Superior Técnico, Av. Rovisco Pais 1049-001 Lisbon, Portugal

*: [email protected]

Abstract Experiments were conducted to investigate transfer of heat and momentum of fluid flowing through horizontal micro-channels with square cross section (Dh= 195 and 522µm) and 100mm length. The flow was set up by a syringe pump in borosilicate glass tubes heated by an electrical conductive transparent film of InOx deposited in the channel outer wall, which allowed establish a constant axially and longitudinally uniform heat flux boundary layer at the same time that it provided optical access to the inner flow. Experimental horizontal single and two-phase flow images are presented. The single-phase liquid flow experiments encompassed measurements of longitudinal distribution of temperature and pressure drop, complemented by velocity measurements of the inner flow with a Microscopic Particle Image Velocimetry (µPIV) system. The discrepancy between the PIV measurements and the predicted 2D velocity distributions (White, 1974) is less than 1% near the center and increases to 12.6% for the measurements closest to the wall for non-heated channels. Integration of the µPIV 2D flow fields to compute the volumetric flow rate where within 4.12% of the volumetric flow rate established by the syringe pump. Results obtained for diabatic flows presented a decrease of the mean velocity gradient near the wall, and an increase at the channel middle plane with the heat flux increase. CFD simulation results fitted well with the relation proposed by Martinelli and Viktorov (2009). The qualitative the two-phase flow results show good agreement with flow patterns well accepted for conventional horizontal circular cross section channels.

1. Introduction

Systems miniaturization in diverse applications, either industrial or laboratorial, raises the need to

better comprehend the scale effects induced on convective heat transfer inside micro-tubes. Several

reviews related to mini-channel and micro-channel heat transfer, pressure drop, critical heat flux,

flow instabilities and flow patterns are available in the literature (Bertsch et al., 2008) and all agree

that there is no uniformity in the experimental data.

Despite the extensive body of literature reported on these effects, experimental results are often

influenced or even masked by several phenomenon, such as viscous dissipation (Morini and Spiga,

2007), axial conduction along the walls (Lelea, 2007), the validity of the slip-flow model (Kudussi

and Çetegen, 2007) caused by molecular interactions at the surface-fluid interface (Meinhart, 2007)

and/or by surface roughness effects (Hrnjak and Tu, 2007, Croce et al., 2007), or experimental

uncertainties associated with channel dimensions (Steinke and Kandlikar, 2006), pumping power

(Husain and Kim, 2008), pressure drop (Ngoma and Erchiqui, 2007), entrance and exit effects

(Gamrat et al., 2005), thermal boundary conditions (Horiuchi and Dutta, 2004) or variation of fluid

properties (Liu et al., 2007). Limited spaces for small probes, small flow rates, heat transfer rates

and temperature differences that are difficult to measure accurately or are masked by the electronic

noise are probably the major foundations of inconsistency. Also the channels manufacture and

sealing introduce dimensional uncertainties and surface roughness (Agarwal 2006).

Many heat transfer design methods exist for fluid vaporization inside macrochannels, but these have

been found to not be suitable to the small dimensions found in microscale. Mechanistic heat transfer

models to describe evaporation and condensation inside micro-channels are scarse and many studies

are adiabatic two-phase flow experiments, i.e. liquid and gas flowing in the same channel without

heating, generated by a gas injector or liquid-vapor mixer. The resulting flow pattern and bubble


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characteristics are probably imposed or influenced by the design of the injector or mixer.

The work reported in the present paper is part of a major experimental study concerned with the

fundamentals on single and two-phase heat transfer inside micron sized tubes. The methodology

combines temperature and pressure drop measurements with high speed visualization and velocity

distributions obtained with a Microscopic Particle Image Velocimeter (µPIV) to quantitatively characterize flow patterns and phenomena associated with single-phase and phase transition inside

micro-channels.

2. Description of the experiments The experimental apparatus is schematically shown in Fig. 1. A syringe pump NE-1000 from New

Era Pump Systems, Inc®, with a Syringe B-D Perfusion 50/60mL (Inner Diameter, ID 27.12mm)

supplies a constant mass flux of liquid (uncertainty, u = ±1%) at room temperature. Instantaneous

temperatures along the channel wall are measured with unsheated fine gage 25µm Outter Diameter,

OD, k-type thermocouples from Omega (u < ± 2%), attached along the channel outer wall with a non-conductive thermal glue (Cooler Master

® PTK-002, thermal conductivity, k > 4.5W.m

-1.K

-1) to

ensure a quick and reliable response and to minimize electrical conductance effects which would

disturb the measurements. Thermocouples are also inserted at the inlet/outlet stagnation chambers.

The ambient temperature is measured with a 1mm OD K-type thermocouple from Omega, placed

near the channel inlet. Pressure losses are measured with two ECO1 pressure transducers from Wika

(pressure, p = 0-4bar, u < ± 0.5%), located at the inlet and outlet stagnation chambers, respectively.

Fig. 1 Schematic of the a) flow delivery system; b) µPIV system and c) high speed visualization system

The micro-channels are made of very smooth borosilicate glass from Vitrocom®, USA, with

rectangular and square cross sections as shown in the sample photo of Fig. 2 obtained with the

Hitachi S_2400 scanning electronic microscope. Though these images are not used to quantify the

amplitude of roughness, EDS (energy dispersive spectroscopy) elemental analysis show that all the

tubes used in the experiments have similar chemical composition (Fig. 3). Multi Image V2.1

software and Matlab® is used to assess the shape of the cross section and to accurately measure the

inner and outer dimensions of the channels (±4.4%).

Fig. 2 SEM image of C_500 (Dh=543µm), S_200 (Dh=196µm) and C_200 (Dh=192µm) cross sections. The tubes are externally coated with a thin transparent film of Indium Oxide (InOx) to provide

a)

b)

c)


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heating by Joule effect at the same time it allows optical access to the inner flow. A similar method

has been employed by Yen et al. (2006) who made use of a tin-doped indium oxide (ITO) and silver

sputtered in pyrex micro-tubes. ITO films exhibit low resistivity and high transmittance in the

visible range of the spectrum, which make them useful as transparent electrodes in of many devices

such as liquid crystal displays (LCDs), plasma displays or solar cells. But their properties have been

extensively reported to be sensitive to the techniques and parameters of deposition, as well as to

post-deposition treatments, e g., Abe and Ishiyama (2006), Yamada et al. (1998). Moreover, Sn

doping in InOx thin films deposited at room temperature deteriorates the properties of the film (e g.,

Dekkers et al., 2006) and the addition of silver gives a large negative temperature coefficient of

resistivity, e g., Subrahmanyam and Barik (2006). Therefore, films would be too thin and difficult to

control during the process of deposition to achieve the required highest temperature.

The suitability of the optical properties of the InOx deposit to obtain fluorescence measurements, as

well of its chemical stability to provide accurate thermal boundary conditions are the main keys for

the evaluation. Most transparent conductors consist of metal oxides that possess both good electrical

conductivity and transparency in the visible and near infrared (IR) regions of the electromagnetic

spectrum. If transparent conductors /semiconductors thin films can be deposited at room

temperature, transparent electronic devices can be laid upon any type of substrates, from glass to

flexible polymers (Liu et al. 2002). In the present work InOx deposition is made by radio frequency

plasma enhanced reactive thermal evaporation (rf-PERTE) at low substrate temperature (<100ºC).

Details of the method and of the resulting relevant film properties are reported by Nunes de

Carvalho et al. (2008). Only a summary is given here to contextualize the accuracy of the thermal

boundary conditions. The source material (indium metal) is evaporated at steady state in the

presence of oxygen, inside a glass chamber in vacuum (∼10-4 mbar) at low substrate temperature; the formation of the metal oxide layer is basically a condensation process of metal oxide vapor at

the outer surface of the tube, which is placed horizontally 10cm apart. Rotation of the micro-tube

guarantees uniformity of the film thickness around the perimeter of the tubes and, therefore, of the

electrical resistance. Even though, the thermocouples connected to the outer surface of the tubes are

randomly lined and, therefore, any potential relation which would arise with the position of the tube

in the evaporation chamber is statistically damped.

a) b) Fig. 3 EDS elemental analysis of a) borosilicate glass channel outer wall b) InOx thin film deposit at the outer wall and

corresponding surface SEM images

SEM investigations of the undoped InOx films deposited on different substrates showed a strong

correlation between the nanoscopic features of the films surface and their macroscopic properties

such as visible optical transmittance and electrical conductivity.

Fig. 4 shows the variation of specular transmittance spectra with substrate for undoped InOx films

deposited by rf-PERTE at room temperature. Transmittance spectra of bare substrates are shown for

comparison. The InOx visible transmittance does not vary significantly as a function of substrates,

showing that transmittance is not strongly related to the film surface morphology variations

observed. In overall, all the undoped InOx films show relatively high values of visible transmittance

(around 81%) and the highest loss of visible transmittance by the substrates is obtained for PET

(Polyethylene terephthalate polymer resin) substrates due to their less smooth surface morphology,


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inducing this characteristic to the InOx films deposited on them. (Parreira et al., 2008)

Fig. 4 Variation of specular transmittance spectra as a

function of substrates (Alkali Free (AF) glass, Fused

Silica (FS) and Polyethylene terephthalate polymer resin

(PET)) for undoped InOx films deposited by rf-PERTE at

room temperature. (Parreira et al., 2008)

Fig. 5 Conductivity vs temperature for undoped InOx

films deposited by rf-PERTE at room temperature on AF

glass and polymer (PET) substrates (Parreira et al., 2008)

Moreover, the thin transparent film shows good chemical stability in the range of temperatures up to

70ºC, therefore indicating that the thermal boundary condition approximates a constant wall heat

flux condition. Fig. 5 shows the electrical conductivity as a function of substrate for undoped InOx

films deposited by rf- PERTE at room temperature on polymer (PET) and AF glass, the two most

representative substrates. The undoped InOx thin film presents a conductor behavior. The deposit on

AF glass show an electrical conductivity of about σ25°C=1100(Ω.cm)-1. Electrical contacts are achieved by means of electrically conductive silver containing acrylic paint,

Elecolit® 340 (sheet resistance < 0.001Ω.cm) and heating is provided by a direct current

(GEN150-5, from TDK-Lambda, u < ±0.14%). Furthermore, temperature measurements made in the absence of inner flow, showed a constant value along the tube wall, which gives a clear

indication that the thermal boundary condition approximates a constant heat flux condition (u <

±0.6%).

The experiments were conducted with distilled water, H2O (IST Inorganic Chemistry Lab),

methoxy-nonafluorobutane, C4F9OCH3 (HFE7100, 99.5%, 3MTM) and methanol, CH3OH (99.8%,

BDH) with thermophysical properties listed in Table 1 at 25ºC.

Table 1. Thermophysical properties of the working fluids

Fluid

H2O (Lemon et al., 2005)

CH3OH (Lide, 2004)

C4F9OCH3 (3M)

ρ [kg.m-3] 1000 788 1488

µ x1004 [kg.m-1s-1] 8.9 5.6 5.7

σ x1003 [kg.s-2] 72.8 22.3 13.6

α x1008 [m2.s-1] 15 10.4 3.9

k x1003 [W.m

-1.K

-1] 607.1 203.3 68.8

cp [J.kg-1.ºC

-1] 4182 2481 1177

Tb [ºC] 100 65 61

hfg [kJ.kg-1] 2260 1158 126

Two-phase flow patterns in the channels were obtained with simultaneous measurements of


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temperature, pressure drop and visualization using a Phantom V4.2 high speed camera from Vision

Research® connected to the acquisition system (Phantom Camera Control Version: 9.0.640.0-C

PhCon:640), which triggerd and controled the camera and stored the captured images (Fig. 1c). For

the experiments, a resolution of 512x32pixel2 (pixel size 22µm) @ 3000fps was employed. All high

speed visualization images were obtained with a Melles Griot microscopic lens with magnification

M=6.3 and numerical aperture NA=0.20. The flow was illuminated with a light source, provided by

a 1250W spotlight, placed in front of the camera, but behind the channel. Moreover, to homogenize

and to reduce the loss of light through scattering a diffusing glass was placed between the light

source and the channel. The incident light deflects at the vapor-liquid interface, resulting in a

darkening at these positions as described by Hsieh et al. (1997).

Temperature and pressure data were acquired by the National Instruments acquisition system at a

frequency of 100Hz. All the results are post processed with a Matlab ® code to determine all the

desired parameters.

The µPIV system (Fig. 1b) uses an inverted Leica DM ILM epi-fluorescent microscope and a

Flowsense®_ 2M CCD (charge coupled device) camera from Dantec Dynamics to record 1µm

average diameter nile red fluorescent tracing particles from Invitrogen® with an image field of

1600x1186 pixel2 (pixel size 7.41µm) at a maximum rate of 15Hz and 8/10-bit intensity resolution.

The particles are illuminated via a dual Nd:YAG laser New Wave_Solo II-15 emitting at λ=532nm with a repetition rate of 15Hz. The time delay between laser pulses is set between 100 and 500µs in which the particles have a maximum displacement of ¼ of the interrogation area length. An

epi-fluorescent prism/filter cube is used to filter wavelengths lower than λ=575nm (particles wavelength emission) to prevent the influence of background noise. The field is magnified with an

air-immersion N PLAN objective lens with magnification M=40 and numerical aperture NA=0.55.

FlowManager® V4.0 from Dantec Dynamics is used in acquisition, calculus and post processing of

the data as well as in the correlation and validation algorithms. Synchronization is assured by

National Instruments hardware. µPIV measurements were performed only in the square section micro-channels to minimize light distortion effects, as pressure and temperature measurements were performed with square and

circular cross section channels.

In pressure and temperature data reduction, the flow is assumed laminar, incompressible, steady and

fully developed (either hydrodynamically and/or thermally), gravity forces are ignored and the

fluids are considered Newtonian. Momentum and heat transfer data are obtained and processed as in

Silvério and Moreira (2008). The Poiseuille number, f.Re, for fully developed laminar flow of an

incompressible fluid through a stationary smooth circular cross section is 64 and is 56.92 for square

cross sections. The Reynolds number µ

ρ hm DueR

..= is defined with the hydraulic diameter Dh

=4ACS/P and the bulk velocity CSm Amu ⋅= ρ& (µ is dynamic viscosity, ρ is the specific weight, m&

is the mass flux and ACS is the channel cross section area. The Darcy friction factor f is then defined

as

2

21 .. m

h

u

D

dz

dpf

ρ−= (1)

To obtain the pressure drop (dp) along the channel longitudinal distance z, pressure measurements

are performed at the inlet and outlet plenums, as shown in Fig. 1a). The entrance and exit effects are

eliminated making use of two channels with different lengths (100mm and 50mm), but with the


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same entrance and exit conditions, as in Celata et al. (2006).

The heat flux transferred to the fluid, q”s, is calculated from the Joule heating, q

”eff, taking into

account the heat losses by convection, q”loss and by radiation, q

”rad from the outer surface of the film

to the environment as found in Silvério and Moreira (2008).

""""

radlosseffs qqqq −−= (2)

The Nusselt number is then calculated from the heat transfer coefficient, h ( )( )mis TTq −≡ /" and the

fluid thermal conductivity, kfl

( ) ( )

zcm

PqTTc

k

qTT

TTTThA

RIq

TT

qh

k

DhNu

p

sinletwm

soutwinw

suroutwairoutwloss

HT

s

minw

s

fl

h

&

"

,

"

,,

44

,,

2"

,

"

+=+=

−−−−=−

=

=

(3)

The pressure and temperature data are both acquired with a PCI-6024E/BNC-2120 data acquisition

system from National Instruments and processed with a Matlab® code to determine all the desired

parameters.

The 2D velocity distributions at any square cross section of inner dimension Λi and coordinate axes

(x,y) with the origin at the center of the duct is given as (White, 1974).

( ) ( )∑∞

=

−

Λ

Λ−−

−Λ

=,...5,3,1

32

1

3

2cos

2cosh

cosh

114

,i

iii

i

i

xi

i

yi

dz

dpyxu

π

π

π

πµ

(4)

Velocity distributions are obtained by scanning the measurement plane across the depth of the tube

and perpendicularly to the side wall. The accuracy of the measurements is evaluated by comparing

the volumetric flow rate yielded by the syringe pump with that obtained from the integration of the

measured velocity distributions, as in Silva et al. (2008).

Measurements with µPIV for imposed heat flux are compared with CFD simulations using Gambit® 2.2.30. A structured mesh with around 4400 hexahedron cells is used in the domain discretization,

imposing control volumes sizes equal to those of the µPIV measurements. The numerical simulations are performed with FLUENT

® 6.2.16. The flow field is modeled as steady and laminar,

and the inlet/outlet boundary conditions are set as mass flow inlet and outflow, respectively. Inlet

conditions take the experimental volumetric flow rate provided by the syringe pump. Impermeable

walls and the no-slip velocity condition at solid boundaries are applied to all the micro-channel

walls. Ambient temperature is considered.

3. Characterization of the Flow Regimes


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Two-phase flow in circular conventional size channels has been considered by numerous

investigators. Studies focus on both horizontal and vertical orientations, as well as inclined

orientations. Flow patterns are identified and the transitions between flow patterns are defined,

primarily from visual observations. As such, the determination is somewhat subjective and the

simultaneous measure of pressure drop and temperature with high speed visualization is necessary

to the characterization of flow pattern transitions and flow pattern maps.

Fig. 6 shows examples of images of flow patterns obtained experimentally for a horizontal circular

cross section channel with Dh=543µm, heated by a uniform low heat flux and fed with methanol just below saturation temperature. Representative of five different flow pattern types are presented

according to generally accepted definitions adapted from Collier and Thome (1994) and described

below.

Bubbly flow occurs when the gas or vapor phase is distributed as discrete bubbles in a continuous

liquid phase. The size of bubbles does not approach the diameter of the channel and bubbles tend to

travel in the upper half of the channel. The intermittent flow that occurs at low gas flow rates and

moderate liquid rate is described as plug flow. In this regime, liquid plugs, free entrained gas

bubbles, are separated by zones of elongated gas bubbles. When the gas velocity is increased in a

plug flow, the liquid slugs become aerated and contain small bubbles (slug flow). The flow is more

chaotic compared with plug flow and the interface between gas and liquid is not as clearly defined.

For wavy flow, as the gas velocity is increased, waves are formed on the liquid-gas interface, and

tend to travel in the direction of the flow. This flow pattern corresponds to stratified wavy flow.

When higher gas flow rates cause the liquid to form a film on the tube wall (the film at the bottom

of the tube may be thicker than the film at the top) it is named annular flow.

Single-phase liquid flow Bubbly flow

Plug flow Slug flow

Wavy flow Annular flow

Single-phase vapor flow

Fig.6 Schematic of flow patterns encountered in conventional horizontal two-phase flow during evaporation (Collier

and Thome, 1994) and experimental flow patterns in internal horizontal micro-channel flow heated by a uniform heat

flux. Methanol, Channel C_500 (Dh = 543µm), 17µL.s-1 ≤ Q ≤ 170µL.s-1, Tm,inlet = 28ºC, 6kW.m

-2 ≤ q

”s ≤ 22 kW.m

-2.

The optical method for two-phase flow characterization in micro-channels is being applied to

determine the frequency of bubbles, the coalescence rate of these bubbles and their lengths as well

as their mean two-phase vapor velocity. Qualitative and quantitative measurements will then


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contribute to a better understanding of single and two-phase flow inside micro-channels.

In the present paper, only single-phase liquid flow is addressed.

4. Objectives The main goal of the analysis is to assess the suitability of the experimental methodology to identify

and characterize the interfacial effects of fluid flow inside micron sized channels. The experiments

consider the use of borosilicate micro-channels of square cross section with hydraulic diameters of

195µm (S_200) and 522µm (S_500), coated with a transparent metallic film to provide a constant wall heat flux at the same time it provides optical access for the use of visualization and laser

diffraction techniques. Velocity measurements are reported for inlet volumetric flow rates of 31, 230

and 306µL.s-1 and heat fluxes from about 3 to 20kW.m-2. Averaged velocity distributions are

calculated from the µPIV data. Particular attention is paid here to the construction of a dedicated experimental facility which allows

the use of optical diagnostic and flow visualization techniques, namely µPIV, which provides a valuable asset to assess the flow behavior, as it allows resolving the whole field (Wereley and

Meinhart, 2005) by scanning the measurement plane across the channel depth, (Santiago et al.

1998).

5. Results and Discussion The application of analytical correlations usually well established for the single-phase liquid friction

factor and the Nusselt number at the “macroscale” (represented with a dashed line in Fig. 7 and 8)

show significant deviations to low Reynolds numbers in microscale flows.

Fig. 7 depicts the friction coefficient, f, for water as a function of the Reynolds number calculated

with viscosity at room temperature for square cross section, for five different hydraulic diameters

ranging from 50µm to 522µm. The results show that scale effects are significant in smaller Dh

channels, where friction in the water flows clearly deviates from the classical laminar theory for Re

< 100.

H2O Square

0.01

0.10

1.00

10.00

100.00

1 10 100 1000 10000

Re

fDarcy

f = 56.92/Re

S_500

S_300

S_200

S_100

S_050

Fig. 7 Friction factor variation for distilled water in square

cross section channels. 50µm ≤ Dh ≤522µm. ---- f.Re=constant

Fig. 8 Variation of the Nusselt number with the

Reynolds number in fully developed flows. Channel

S_300; q”eff ≈ 5000Wm-2; - water; - HFE7100; -

methanol

In Fig. 8, the average Nu is plotted against the Reynolds number for three fluids, water, methanol

and HFE7100. The straight lines represent the Nu analytical value of 3.61 predicted by the laminar

theory. The variations from “macroscale” are evident for all the fluids (water, methanol and

HFE7100) for lower Reynolds numbers.

These deviations are attributed to the lowering of the interfacial activity associated to the

0

2

4

6

8

0 50 1000 1500 2000

Re

Nu

H2O, 5069W.m-2

HFE7100, 4461W.m-2

CH3OH, 5075W.m-2

Nu = 3.61


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hydrophobic character of the channel internal wall induced by air pockets entrapped within the

walls asperities (Silvério et al., 2009), as observed by Moreira et al. (2007) and by Bonaccurso et al.

(2002) in the flow of water in micro-tubes of glass.

5.1. Velocity measurements Velocity measurements have been performed in water and methanol flows established in square

cross section channels. Measurements are obtained far from the distance required for the flow to

attain 99% of the fully developed centerline velocity, as given by 0.056Re.Dh, (Spurk and Aksel,

2008), such that the flow is surely fully developed. This is confirmed by comparing the mean

velocity profiles taken at downstream locations (Fig. 9). The flow is not expected to vary in the

streamwise direction across the length of the PIV image, unless there are spatial variations caused

by surface roughness effects. The velocity fields are measured at several horizontal planes over the

channel height (y direction).

The data plotted in Figures 9, 10 and 11 are obtained with a time delay of 20µs between image pairs. Regarding the optimization of the signal-to-noise ratio, a time delay between laser pulses ranging

from 100 to 300µs and a repetition rate of 15Hz are used to have a maximum particles displacement of approximately ¼ of the interrogation area extent. The PIV interrogation regions used here each

contain an average of five particles (8.28µL particles to 1mL of deionized water corresponding to a concentration of 2.31x10

8particles.mL

-1). This concentration of seed particles is small enough that

any two-phase effects are considered negligible, and the working fluid can be considered a

single-phase fluid.

Fig. 9 Velocity vector field at five different downstream

locations.

Fig. 10 Velocity vector field inside the S_200

micro-channel for Re=10 at the horizontal plane height

y=40µm overlapping the micro-channel image. Axial distance, z0=28.21mm

The time average correlation algorithm is applied over 100 correlation maps (Meinhart et al., 2000).

The lens used in the experiments has M=40 and NA=0.55, which corresponds to a

depth-of-correlation value of 6.5µm (Silva et al., 2008b). In other words, particles up to ±3.25µm in front or behind the object plane may be enough in focus to be included in the measured velocity.

Fig. 10 shows the velocity vector field in the S_200 square cross-section borosilicate glass

micro-channel with an InOx thin film deposited on the channel outer wall, acquired at ambient

temperature. The mass flow inlet value was set to a value of 1.91x10-6kg.s

-1 that corresponds to the

volumetric flow rate of 115µL.min-1. The measurement volume is located 156µm from the bottom wall (40µm from the horizontal midplane). The Reynolds number of these flows based on hydraulic diameter and area-averaged velocity is 10.


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The interrogation regions for the measurements shown in Fig. 11 were 64 by 64 pixels with a 50%

overlap in both the horizontal and vertical directions. Hence, a distance between individual vectors

of 5.92 x 5.92µm2 was attained and measurements were found to be within 5.92µm of each wall.

The consistency of vectors along the streamwise direction shows the fully developed flow.

Fig. 11 Comparison between the measured velocity

profile for S_200 micro-channel for Re=10 at the

horizontal plane height y=40µm (), and the analytical solution from equation 4 ().

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580µm

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

µm

Image size: 1600×1186 (0,0), 8-bits (frame 1)

Burs t#; rec#: 1; 1 (1), Date: 02-05-2008, Time: 10:58:17:000

Analog inputs : 0.000; 0.000; 0.000; 0.0000 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580µm

0

20

40

60

80

100

120

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160

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µm

Image size: 1600×1186 (0,0), 8-bits (frame 1)

Burs t#; rec#: 1; 1 (1), Date: 02-05-2008, Time: 12:00:11:000

Analog inputs: 0.000; 0.000; 0.000; 0.000

Fig. 12 Example of a clean channel wall (left) and a

contaminated wall with particle agglomerates (right).

The discrepancy between the PIV measurements and the velocities predicted by equation (4) is less

than 1% near the center and increases to 12.6% for the measurements closest to the wall. The

under-prediction of velocity for distances from ¼ of the channel to the wall is probably due to

near-wall measurement effects. The hydrodynamic interactions between the particle and the wall

and background reflections from the wall overshadow particle images (Fig. 12). In addition to the

challenges of understanding and predicting the flow behavior, understanding and predicting the

response of the particles adds considerable complexity.

Although the InOx thin film has an average visible transmittance of approximately 81%, it does not

contribute in a significant manner to the overall error registered near the wall. The major

contributors are the shape of the channel and particle agglomerates. The square channel has rounded

exterior corners (Fig. 2) that can induce distortion near the walls (Jenkins and White, 1981) while

particles agglomerates forming close to the walls will contribute for the error in measurements due

to their higher intensity emission. Techniques to improve PIV image interrogation near stationary

interfaces are discussed by Theunissen et al. (2008).

A similar experimental methodology was employed to obtain the velocity profiles for the methanol

flow in the S_300 channel. The profiles are plotted in Fig. 13 for two different Reynolds numbers.

Fig. 13 Velocity profiles obtained for methanol flow in S_300 at Re=10 and Re=14.


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For comprehensiveness, it was also matched up the volumetric flow rate yielded by the integration

of the µPIV 2D flow fields (Fig. 14b) against that derived for the syringe pump used in the experiments. In this case, the volumetric flow rate predicted using the velocity profile

measurements were within 4.12% of the volumetric flow rate established by the syringe pump. It is

to note that the uncertainty associated with the volumetric flow rate imposed by the syringe pump is

of the order of 1.00%.

Based on the analytical results from equation (4), the ratio maximum velocity at the channel

midplane umax to mean velocity um for the square channels is found to be 2.57.

a) b)-100

-500

50100

0

100

200

0

50

100

x [µµµµm]y [µµµµm]

u [mm/s]

Fig. 14 Integration of 2D velocity profiles for water flow in S_200, Re=10 a) attained from the analytical solution from eq.

4 and b) measured with µPIV.

Experiments performed for constant heat fluxes q”s ≤ 20kW.m

-2, for the same mass flow inlet at two

different horizontal planes are to be seen in Fig. 15. CFD computation results are also shown. The

local velocity values in the streamwise direction are normalized by the average velocity value at the

cross section under study, whereas the x-distance is normalized by the channel width, ΛI.

a)

0

0.5

1

1.5

2

2.5

-2 -1 0 1 2

x-distance/(Λ i /2)

u/u

m

CFDqëff ~0W.m-2qëff ~5900 W.m-2qëff ~8800W.m-2qëff ~13700 W.m-2qëff ~19700W.m-2

b)

0

0.5

1

1.5

2

2.5

-2 -1 0 1 2

x-distance/(Λ i /2)

u/u

m

CFD

qëff ~0W.m-2

qëff ~2600W.m-2

qëff ~5900W.m-2

qëff ~8000 W.m-2

Fig. 15 Velocity profiles obtained for water flow in S_500 at different heat fluxes for a) y=119µm and b) y=0µm; Q=306µL.min-1

The numerical results fit well with the relation proposed by Martinelli and Viktorov (2009). They

state that for fully-laminar flow, the ratio between the maximum velocity at the midplane and the

mean velocity (um) is 2.09.

6. Summary Results were collected for both water and methanol, for several mass fluxes at ambient temperature

and with imposed heat flux. In general, the experiments performed up to now evidence that the use

of a InOx thin film deposited on the channel outer wall is of major relevance for the application of

the µPIV technique allowing to generate a constant heat wall heat flux with deviation smaller than


-12-

0,6% at the same time that it allows keeping high levels of transmittance (≈81%). Deviations of the velocity measurements are estimated to be smaller than 1% at the channel

midplane, increasing to about 13% near the walls for non heated S_200. By integrating µPIV 2D flow velocity fieds, showed results were within 4.12% of the volumetric flow rate established by the

syringe pump.

Velocity distributions are further analyzed based on computational predictions performed with

Fluent® for the heated flow and the experimental data is found to be in fairly good agreement with

calculated values. The results show a decrease of the mean velocity gradient at the tube wall with

the heat flux, in detriment of an increase at the middle plane. Overall, the combination of simultaneous measurements of temperature, pressure and the flow velocity profiles in well defined homogeneous transparent channel walls with or without heat transfer is a major asset to assist in the comprehension of fluid flow behavior in microscale flows.

General qualitative agreement was found between experimental two-phase flow patterns

encountered in horizontal circular cross section micro-channels and larger circular channels. In

addition to the usual inertia, viscous and pressure forces present in single-phase flow, two-phase

flows are also affected by interfacial tension forces, the wetting characteristics of the liquid on the

tube wall, and the exchange of momentum between the liquid and the vapor phases in the flow. Quantitative agreement is to be evaluated and two-phase flow patterns, pattern transitions and pattern maps are potentially developed using the experimental facility described above.

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