Heat transfer engineering an international journal, tập 32, số 7 8, 2011

In nucleate boiling, the heat transfer coefficient is affected by the heat flux inputted into the system but it is independent of the fluid flow rate and vapor quality.. Therefore, the s

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York, USA

It gives us great pleasure to present this special issue

high-lighting some of the papers presented at the ASME Seventh

In-ternational Conference on Nanochannels, Microchannels, and

Minichannels, held at the Pohang University of Science and

Technology (POSTECH), in Pohang, South Korea, June 22–24,

2009 The conference was held under the sponsorship of ASME

and was co-hosted by Dr Moo-Hwan Kim, professor and

direc-tor of the Two Phase Flow Laboradirec-tory at POSTECH On behalf

of the conference organizing committee and the participants, we

would like to thank him and his team of students and staff for

putting together a world-class event

Pohang, home of the Pohang Steel Corporation, is a

prosper-ous port city on the eastern side of Korea As one of Korea’s top

universities dedicated to science and engineering, POSTECH

of-fers 4-year programs in 10 departments and POSTECH’s

Grad-uate School offers programs in 14 departments The excellence

of the university extends far beyond the campus, as POSTECH

has international cooperative agreements in place with 68

sis-ter universities We had more than 150 papers presented over 3

days in 24 sessions The conference theme of interdisciplinary

research was once again showcased with researchers working

in diverse areas such as traditional heat and mass transfer,

lab-on-chips, sensors, biomedical applications, micromixers, fuel

Address correspondence to Professor Satish G Kandlikar, Mechanical

En-gineering Department, Rochester Institute of Technology, James E Gleason

Building, 76 Lomb Memorial Drive, Rochester, NY 14623-5603, USA E-mail:

sgkeme@rit.edu

cells, and microdevices, to name just a few Selected papers

in the field of heat transfer and fluid flow are included in thisspecial volume

There are 19 papers included in this special volume.The topics covered include review of cooling technology us-ing microchannels, single-phase flow in microchannels withporous/fibrous structures, boiling and bubble dynamics, T-junction micromixers for two-phase flow, capillary filling, wet-ting in microgrooves with liquid metals, gas flow in roughnanochannels, effect of ultrasound on subcooled flow boiling,explosive boiling, flow patterns, and falling film flow on peri-odic structures These topics indicate that the microchannels arenow being used in many diverse applications

The conference organizers are thankful to all authors forparticipating enthusiastically in this conference series Spe-cial thanks are due to the authors of the papers in this spe-cial issue The authors have worked diligently in meetingthe review schedule and responding to the reviewers’ com-ments The reviewers have played a great role in improv-ing the quality of the papers The help provided by EnricaManos in the Mechanical Engineering Department at RochesterInstitute of Technology with this special issue is gratefullyacknowledged

We thank Professor Afshin Ghajar for his dedication to thisfield and his willingness to publish this special issue highlightingthe current research going on worldwide He has been a majorsupporter of this conference series, and I am indebted to him forthis collaborative effort

525

Satish G Kandlikar is the Gleason Professor of

Me-chanical Engineering at Rochester Institute of nology (RIT) He received his Ph.D degree from the Indian Institute of Technology in Bombay in 1975 and was a faculty member there before coming to RIT in 1980 His current work focuses on heat transfer and fluid flow phenomena in microchannels and minichannels He is involved in advanced single- phase and two-phase heat exchangers incorporating

Tech-smooth, rough, and enhanced microchannels He has published more than 180 journal and conference papers He is a fellow of the ASME, associate editor

of a number of journals including ASME Journal of Heat Transfer, and utive editor of Heat Exchanger Design Handbook published by Begell House and Heat in History Editor for Heat Transfer Engineering He has received

exec-RIT’s Eisenhart Outstanding Teaching Award in 1997 and Trustees ing Scholarship Award in 2006 Currently he is working on a Department

Outstand-of Energy-sponsored project on fuel cell water management under freezing conditions.

heat transfer engineering vol 32 nos 7–8 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.506390

A Review of Cooling in Microchannels

JAMI F TULLIUS, ROBERT VAJTAI, and YILDIZ BAYAZITOGLU

Department of Mechanical Engineering and Material Science, Rice University, Houston, Texas, USA

Advancements in electronic performance result in a decrease in device size and increase in power density Because of these

advancements, current cooling mechanisms for electronic devices are beginning to be ineffective Within the localized hot

spots, the materials of the components are reaching temperature values that can lead to improper functioning of the device.

Many techniques have been successful in the past, such as heat sinks, cavities or grooves, micro pin-fins, etc., but still do not

provide adequate cooling necessary to maintain temperature values low enough for the electronic components to operate.

Microchannels, with their large heat transfer surface to volume ratio, cooled with either gas or liquid coolant, have shown

some potential By modifying the walls of the microchannel with fins, pins, or grooves, the cooling performance can be

improved A possible fin material used to increase the surface area of a microchannel is carbon nanotubes, which possess

excellent thermal and mechanical properties Numerical and computational methods needed to analyze flow at the micro- and

nano-scale are also introduced The numerical methods such as lattice Boltzmann, molecular dynamics, and computational

fluid dynamics may lessen the cost and time that often accompany experimentation.

INTRODUCTION

Electrical gadgets are continuously advancing in society by

creating larger computing power in more reduced physical

di-mensions than ever before The heat produced per unit area

has increased, because of the reduction of the size of these

electronic devices With the increase in power and heat,

over-heating of these electrical components has caused concern [1]

The overall well-being of the component, as well as its proper

functioning, is being threatened by the elevated temperatures

Semiconductor components must maintain a relatively low

con-stant surface temperature Therefore, the development of

elec-tronic technology is limited by the efficient cooling methods

necessary to maintain the operation of the mechanisms Many

techniques have been studied, such as thermal interface

materi-als, heat spreaders and heat sinks, and microchannels A method

of appropriate cooling is necessary to allow for more

advance-ment in the years to come while maintaining proper functioning

This paper provides a brief overview on the thermal cooling of

microchannels

Microchannels have been proven effective in cooling small

surfaces of electrical components such as microchips These

This work was partially supported by LANCER directed research funds

from Lockheed Martin POTT0715421 and Alliances for Graduate Education

and the Professoriate (AGEP) program through the NSF grant HRD-0450363.

Address correspondence to Professor Yildiz Bayazitoglu, Department of

Mechanical Engineering and Material Science, Rice University, 6100 Main,

Houston, TX 77005-1827, USA E-mail: bayaz@ruf.rice.edu

channels act as heat exchangers or heat sinks, which can ciently cool the microchip The high temperatures can be dissi-pated through the modified surfaces of the microchannel withnatural or forced convection of the fluid flowing within the chan-nel [2–6] Microchannels contain a much higher heat transfersurface area to fluid volume ratio, which allows the convection

effi-to be enhanced when compared effi-to the macro-scale systems Asthe hydraulic diameter decreases in a microchannel, the heattransfer coefficient increases, providing an excellent coolingmechanism However, these small channels experience a veryhigh pressure drop A basic microchannel with a smooth wallsurface has demonstrated to cool a heat flux of approximately

790 W/cm2at a temperature of 71◦C, while the pressure dropwas roughly 214 kPa In altering the channel surface with smallcavities or fins, the performance of the channel can improvewith a slight increase in pressure drop [7, 8]

The most commonly used fluids in microchannels are air,water, and refrigerants; however, there are limitations to theirheat transferring capabilities due to their transport properties.Air has been a preferred fluid used in microchannels to coolelectronic components However, with heat fluxes going beyond

100 W/cm2, air cooling methods have become inadequate formost applications Liquids have a much higher convection heattransfer coefficient providing a better performance in cooling [7,9] Fluids with higher convection heat transfer coefficients andhigher specific heats are more effective in reducing heat fromthe surface The increase of the heat transfer coefficient or thesurface area of the finned structures can help reduce convection527

Figure 1 Thermal properties of different fluids of convection flow Adapted from [11], [12], and [13].

resistances [10] In Figure 1, a qualitative comparison of

differ-ent heat transfer coefficidiffer-ents is presdiffer-ented [11–13] Two-phase

systems have an advantage over one-phase systems, because of

the latent heat during the phase change process [1]

Nanofluids consist of small nanosized particles usually no

bigger than 100 nm in size in a base fluid such as water, ethylene

glycol, engine oil, or refrigerant In recent studies, nanofluids

have emerged, having unique properties that consist of a very

high thermal conductivity and maintaining stability Metallic

materials that have been used for these nanoparticles are

ox-ide ceramics (Al2O3, CuO), nitride ceramics (AlN, SiN),

car-bide ceramics (SiC, TiC), metals (Cu, Au, Ag), semiconductors

(SiC, TiC2), carbon nanotubes, and some composite materials

(Al70Cu30) The most common materials used are the oxide

ce-ramics These nanofluids increase the thermal conductivity and

will in turn increase the heat transfer performance Although

adding nanoparticles to a base fluid can influence the cooling

process positively, there are still challenges These fluids leave

sedimentation of particles, fouling, high pressure drop, and

ero-sion, and may even clog the channel over time [14–19]

This paper reviews the effects of a microchannel with

vari-ous fluids as it flows in both one and two phases Many methods

have been proven to be efficient by thermally enhancing the

channel Some methods include treating the surface with

cav-ities, fins, micro pin-fins, and increasing the roughness on the

surface Carbon nanotubes (CNT) are considered to improve the

heat dissipation in a microchannel with their excellent thermal

and mechanical properties A section describing the

mechani-cal behaviors of CNT will also be discussed At the nanosmechani-cale,

Navier–Stokes equations (NS) are proven to be inaccurate

be-cause the assumptions made at the continuum level are no longer

valid A review of the mathematical methods needed to calculate

micro- and nano-scale problems is discussed

an adiabatic outer wall With lower slip velocity, the exchange

of momentum at the liquid/solid interface is also lowered, viding a decrease of the friction factor and an increase of theKnudsen number (Kn) Because of the thermal resistance atthe interface, the Nusselt number (Nu) in the smooth channeldecreases [20] Nonino et al [21] investigated a developinglaminar flow in a microchannel with different cross sectionsand uniform wall heat flux Channel cross-sectional shapes of

pro-a rectpro-angle, trpro-apezoidpro-al, pro-and hexpro-agonpro-al were expro-amined for thisstudy Nonino et al discovered that viscous dissipation close

to the entrance and the temperature dependent viscosity shouldnot be ignored The Nu is greatly affected by the viscosity Theshape of the channel can influence how well the channels per-formance can be; however, it does not have much influence onthe effect of pressure drop, which is mainly influenced by thetemperature-dependent viscosity The channel shape can influ-ence the cooling performance of the microchannel

heat transfer engineering vol 32 nos 7–8 2011

Surface roughness is also a major factor in optimizing the

thermal performance Microchannels can have smooth surface

walls or can contain small structures meant to disturb the fluid

as it flows Shokouhmand et al [22] studied the surface

rough-ness effects of a fully developed, laminar, rough rectangular

microchannel analytically using the Gaussian technique The

aspect ratio was varied from 0 to 1 and the relative roughness

from 0 to 0.15 For roughness values less than 0.01, there was

little effect on the friction factor; however, for roughness

val-ues between 0.01 and 1 with an aspect ratio of 1, there was an

increase of 11.3%, with an aspect ratio 0.5 there was a 5.5%

increase of the friction factor, and for an aspect ratio of 0.1 there

was a 1.7% increase For the convective heat transfer coefficient,

there is a parabolic profile with the values of the lower aspect

ratio close to 0 and the higher aspect ratio near 1 being high

and the values with the aspect ratio of 0.5 reaching a minimum

Decreasing the relative roughness of the channel, the heat

trans-fer coefficient also decreases slightly For a relative roughness

of 0.01, the aspect ratio has little effect As the relative

rough-ness value increases, so does the friction factor, while Nu is not

dependent on the roughness scale With an increase in surface

roughness the convection heat transfer coefficient will increase

slightly [22]

A method used to impact the cooling performance is

ap-plying small grooves to the surface Lee and Teo [8], Solovitz

[23], and Baghernezhad and Abouali [9] all adjusted the wall

surface of a microchannel with grooves These openings can

induce more disturbances in the flow, providing a more

effec-tive cooling mechanism When applying gaps in the surface, the

pressure drop was maintained—that is, it did not increase from a

smooth microchannel—and the heat transfer performance was

increased by roughly 12% The spacing and the size of the

grooves are still being tested to obtain the maximum efficiency

of the channel [8] Solovitz [23] modeled a two-dimensional

(2D) simulation with a small dimple-like groove imbedded in

the channel surface When varying the dimensions of the cavity

and the Reynolds number, there was a 70% increase in the heat

transfer performance with only a 30% increase in pressure drop

when compared to a smooth base model using a depth/diameter

ratio of 0.4 and a Reynolds number of 1000 The depth of the

cavity was proportional to the cooling performance of the

chan-nel Baghernezhad and Abouali [9] compared the shapes of the

grooves used to disrupt the flow A rectangular groove and an

arc-shaped groove were compared, and it was found that both

shapes can improve the cooling performance but the arc-shaped

one is more effective This is probably due to the

aerodynam-ics of the flow past the gap From these studies, grooves can

increase performance while maintaining pressure drop

Micro pin–fins, micro-studs, pillars, and square pin–fins are

all synthetically engineered structures, usually made of

sili-con but also of other thermally sili-conducting materials, which

have shown significant improvements in removing heat These

structures protrude out of the surface, increase the wall surface

area, and interrupt the steady flow of the fluid They can take

different shapes and sizes and be placed in different patterns

Figure 2 Different shapes used for fins on the surface of the microchannel.

to improve the thermal heat transfer performance Vanapalli

et al [24] investigated the pillar “fin” shape, which containsthe lowest friction factor with nitrogen gas flowing through themicrochannel These pillars are used to increase the contact be-tween the surface and the fluid with minimal thermal resistance.The geometries tested were circles, squares, rhombus, ellipti-cal, eye-shaped, and sine-shaped cross sections in staggeredarrangements across the surface Pillars with the sine-shapedcross sections, when compared to all of the other geometries,have the lowest friction factor A three-dimensional (3D) rep-resentation of similar shapes that Vanapalli et al [24] used isshown in Figure 2 Shapes of the fins can affect the motion offlow When the pillars are aerodynamic in shape, there is lessseparation of the fluid from the solid body, creating less thermalresistance at the interface

Lee et al [25] implemented oblique fins into a microchannel

to understand the effects of the local and overall heat fer performance and pressure drop By introducing the obliquesilicon fins to replace the conventional microchannel heat sinkwith continuous fins, the thermal boundary layer developmentalong the channel surface is disrupted and a secondary flow ofthe fluid is created The opening between the fins disrupts themomentum and the trailing edge of the thermal boundary layer

trans-of each oblique fin This causes the leading edge to redevelop,allowing the flow to remain in the developing state This in turnenhances the heat transfer performance Also the secondary flowcan produce mixing of the flow as the fluid flows through thefin opening, improving the performance The heat transfer co-efficient of the channel with the oblique fins was enhanced by80% when compared to the conventional channel Within thisinvestigation, Lee et al [25] studied the pressure drop effects

of the oblique finned channel and a conventional channel imal differences were obtained With the oblique fins, and theworking conditions already described, there was a significantheat transfer performance enhancement with little effects onpressure drop

Min-A key factor that can influence the performance of heattransfer is the thermal conductivity of the fins, pins, and mi-cro pin–fins used on the surface of the microchannel With amaterial that has a higher thermal conductivity, the thermalresistance is decreased and the temperature decreases Zhong

et al [2] investigated the effects of varying the properties of anheat transfer engineering vol 32 nos 7–8 2011

array of microstructures placed along the bottom surface of the

channel When the thermal conductivity of the microstructures

was varied, the temperature decreased and the pressure drop

remained fairly constant With a material with a higher thermal

conductivity, the resistance at the interface decreases and the

convection heat transfer performance is increased

Pasupuleti and Kandlikar [1] have applied many of these

factors—fluid properties, material properties, fin shape, etc.—to

their investigation where they studied the effects of refrigerant

R-123 as the working fluid in a single-chip module setup A

single-chip module is essentially a heat sink on a silicon

mi-crochip The silicon wall is coated with mini ellipse-shaped fins

to increase the surface area In contrast to water, this refrigerant

is considered a safe working fluid for electronic devices that do

not require corrosion inhibiters or biocide The results of

refrig-erant R-123 were compared to those of water and it was found

that they had similar results [1]

Countless modifications to the surfaces of microchannels

have been extensively studied and tested to improve the

perfor-mance of the cooling devices Surface roughness, grooves, and

microfins are among the few alterations made to the

microchan-nels in order to remove temperature from the surface using a

single-phase laminar flow Despite these encouraging effects,

microchannels with single-phase fluids are still not enough to

keep up with the innovations of the electronic industry

TWO-PHASE FLOW

Phase change of a fluid can cause a substantial amount of

heat to be absorbed When a liquid turns into a gas or a gas

into a liquid, the temperature reaches a constant temperature

until the percentage composition of the fluid is either solely

liquid or solely vapor The evaporation of fluid can result in

the absorption of heat during the phase change between liquid

and vapor More evaporation of the fluid flowing though the

microchannel can result in a higher heat flux [26] The fluid

surrounding the component reaches a temperature that exceeds

the fluid saturation temperature, and vapor bubbles originate in

the small cavities or pores on the surface

There are two types of boiling occurrences: pool boiling and

flow boiling Pool boiling is the thermal cooling of a surface

with a stagnant fluid that can effectively remove heat Flow

boiling refers to boiling where the liquid has a high-velocity

flow field Both techniques are limited in the nucleate boiling

regime by the critical heat flux (CHF), which is the maximum

point of operation for engineering system To influence the flow

boiling and pool boiling process, one should consider reducing

the boiling incipience temperature and increasing the CHF in

efforts to improve the boiling process [12]

Pool Boiling

Pool boiling is the boiling of an inert liquid At low heat

flux levels, natural convection is dominant, but at high heat flux

levels, nucleate superheating begins to occur Nucleate ing is the means by which vapor bubbles form and escape theheated surface A larger bubble size on a nucleation site for

boil-a given boil-amount of time results in boil-a more effective thermboil-alperformance More liquid is being evaporated as the bubblesize increases [27, 28] When boiling is initiated, the growth

of the bubble from one cavity extends to other nucleation sites,causing those to initiate The boiling spreads rapidly over thesurface, increasing the convective heat transfer coefficient anddecreasing the surface temperature [29] Using liquids withlow boiling points, phase change from a liquid to a gas occursmore quickly, more heat can be removed, and the pressure dropdecreases

Nucleate boiling initiates when the temperatures of the fluidsare few degrees higher than the saturation temperature, wheresmall surface defects appear As the microchip is heated, theboiling incipience appears but only with a few vapor bubbles.Bubbles are generated between the gaps of the fins or surfacecavities With the evaporation of the surrounding liquid, the bub-ble grows in between the fins that are confining it As the vaporgrows, the thin film surrounding the bubble evaporates with ahigh heat transfer coefficient value With its increasing size, thebubble forces itself to the top of the fin surface Liquid fromunder the rapidly growing bubble attracts the remaining liquidsurrounding the fins This process enhances the microconvec-tion of the liquid along the walls of the fins With this suctionreaction, there is an increase in evaporation, which effectivelyenhances effective heat transfer With increasing heat flux, there

is an increase in nucleation sites When there are more ation sites, a domino effect is triggered, creating more vaporbubbles [27, 28]

nucle-When compared to a smooth surface, the optimal effect ofthe phase change phenomena ideally produced by microstruc-tures or microcavities in the surface is to have a lower boilingincipience, decrease the surface temperature, increase the CHF,and increase the evaporation to obtain more nucleation bubbles[28, 30] Many factors must be considered when attempting tooptimize the performance of the cooling method Surface rough-ness, orientation of the microchip relative to the flowing fluid,and geometry or configuration of the fin arrays can all alter theeffect of cooling A higher thermal conductivity, an enlargement

of the interface surface area, and optimization of fin placement,geometry, and dimensions are needed to improve the efficiencyand performance of microstructures [2]

The orientation of the channel can influence the thermalperformance A comparison of a vertically and a horizontallymounted chip was observed for a smooth surface and a finnedsurface using FC-72 The surface orientation of the chip in-creases the heat transfer performance in the nucleate boilingregime as the angle increases toward a vertical position for asmooth surface It is believed that gravity assists the increase

in performance as the chip is mounted in a relatively verticaldirection For a treated surface, however, the orientation of thechip has little or no effect on the heat transfer performance[27, 29]

heat transfer engineering vol 32 nos 7–8 2011

Surface roughness can also influence the thermal

perfor-mance for a pool boiling process Testing of surfaces with

differ-ent degrees of roughness using FC-72 was performed by Honda

and Wei [31] A high surface roughness lowered the boiling

incipience, increases the CHF, and increases nucleate boiling

Shokouhmand et al [22] studied numerically the effects of

sur-face roughness in microchannels on convective heat transfer in

fully developed, laminar flow With increasing relative

rough-ness, the friction factor increases, the Nu remains unchanged,

and the convective heat transfer coefficient slightly increases

The use of small cavities is one of the techniques that increase

the heat transfer area In this process, an array of holes with

precise dimensions is drilled into the silicon surface; in effect,

these holes act as nucleation cavities and enhance nucleate

boil-ing An investigation of the thermal performance on artificial

micro cavity surfaces was conducted by Yu et al [12] using a

dielectric fluid, FC-72 as the working fluid The 16× 16, 25 ×

25, and 33× 33 arrays of microcavities were tested varying the

heat flux, diameter, and depth When increasing the diameter of

the cavity at moderate and high heat fluxes, an earlier decay and

low peak value of the heat transfer coefficient were experienced

Varying the cavity depth too much can lead to the overall heat

transfer coefficient’s rapid decline Also, because of the larger

flow resistance created by the deeper cavities, the rewetting of

the surface diminishes The test section with a 33× 33 array

of cavities results in an increase of the CHF by a factor of 2.5

when compared to that of the plain silicon surface with a heat

flux value of 30 W/cm2

Micro pin-fins, micro-studs, pin-fins, and square pin-fins are

manually manufactured structures, usually silicon, proven to

significantly enhance nucleate boiling Wei et al [27]

sub-merged two different pin-fin geometries in FC-72 to monitor

the pool boiling performance These fin types, each in its

dif-ferent topology and shape, improve thermal convection when

they are submerged in the liquid These cooling mechanisms,

because of the increase of chip surface area, allows for a higher

heat flux to be used These microchannel modifications have

proven to be effective in decreasing the boiling incipience and

surface temperature and improving the CHF

The use of nanofluids as the working fluid supplements heat

transfer performance with its higher thermal conductivity than

a pure fluid–air, water, or fluorochemicals [32] Nanofluids

are colloidal nanoscale metallic or nonmetallic particles in a

base fluid [32–37] By adding nanoparticles to the volume of

fluid, thermal conductivity can be increased by about 40% [38]

Kedzierski [39] investigated the effect that CuO nanoparticle

concentration had on a roughened horizontal flat surface A 2%

and a 4% volume concentration of CuO in R-134a were

com-pared in this study On average the mixtures with a 4% CuO

volume concentration had a 140% larger value for boiling heat

flux than the mixture with only 2% volume [39] CHF is

en-hanced up to 45% with a 1% volume concentration of alumina

nanofluid at a mass flux of 2500 kg/m2[33] Wright et al [40]

studied the effects of the percentage of metal particles in the

nanofluid using CNT to increase the thermal conductivity of the

fluids If the concentration of the metal particles is too low, thereare no significant improvements At 1% volume concentration ofCNT, there was about a 10–20% increase in the thermal conduc-tivity The higher concentration of these metal particles insidethe fluids increases the viscosity, making it more difficult for thefluid to flow through microstructures [40, 41] An explanationfor the amount of metallic nanoparticles is that the orientationand alignment of the CNT are random in the fluid and the CNTneed physical contact with each other in order to increase thethermal conductivity With a low concentration, there is minimalcontact as there are fewer metallic particles [40] Gold nanopar-ticles have also been placed in refrigerant R-141b to increase theCHF Boiling coefficients of the fluid increase with an increasedconcentration of nanoparticles For only a 1% volume concen-tration of nanosized Au particles in refrigerant R-141b, the heattransfer coefficient doubled when compared to the fluid withoutnanoparticles Nanosized Au particles can significantly increasepool boiling heat transfer when placed in refrigerant R-141b, butthe surface roughness and the particle size aged after one test,decreasing the effects [42] Using nanofluids will improve theheat transfer due to the nanoparticle interaction with the surfaceroughness when compared to those without nanoparticles

In general, the wettability of the surface can play a criticalrole in improving the heat transfer performance Truong et al.[30] used nanofluids to investigate how the surface wettabil-ity affects the CHF and the heat transfer coefficient Minimumwettability contact angle will maximize the CHF To achieve ahigh heat transfer coefficient, the optimal surface is one with lowwettability containing many nucleation sites Surfaces should behydrophilic, having an intrinsic contact angle no higher than 90◦.Too much surface roughness can cause a higher contact angle,leading to a smaller CHF and a hydrophobic surface Nanoparti-cles suspended in fluids will not directly affect the heat transfercoefficient through the contact angle; rather, the nanoparticlescan create many microcavities and therefore nucleation sites.The heat transfer coefficient strongly depends on the number ofactive nucleation sites available for vaporization [30]

Many modifications to microchannel surfaces have beentested in enhancing the cooling performance For pool boil-ing, increasing surface roughness and adding small cavities orfins to the channel walls can lower the boiling incipience, in-crease the CHF, and increase the nucleate boiling of the system

To further enhance the thermal performance, nanofluids with

an optimal amount of volume concentration of particles can

be used Because of the continuous advancements in electroniccomponents, further enhancements of the microstructure mate-rials, configurations, geometry, etc still need to be investigated

Flow Boiling

Flow boiling has the capability of increasing the thermal formance of the microchannel; it can provide a much higher heattransfer coefficient than both the single-phase flow and the poolboiling Flow boiling is a two-phase process that convectivelyremoves heat as a fluid that is flowing with some given velocity.heat transfer engineering vol 32 nos 7–8 2011

per-Figure 3 Flow patterns in flow boiling.

To understand the flow boiling process, it is essential to

un-derstand how it relates to the macro-scale assumptions Among

many of the previous works done regarding flow boiling, there

is a controversy about the dominant mechanism driving the heat

transfer at the micro-scale Is it the conventional nucleate boiling

that is dominant in the macro-scale, or is it the forced

convec-tion of the vapor bubble that transfers the most heat? In nucleate

boiling, the heat transfer coefficient is affected by the heat flux

inputted into the system but it is independent of the fluid flow

rate and vapor quality On the other hand, convective boiling is

driven by the fluid’s flow rate and the vapor quality and is not a

function of the inputted heat flux [43] Thome et al [44] believe

flow boiling has the most heat transfer from convection At the

macro-scale, experimental studies have concluded that nucleate

boiling is the dominant factor in removing heat with little effect

of the convective flow; however, at the micro-scale, the heat

transfer is mainly affected by a thin liquid film that surrounds

the elongated vapor bubbles, not nucleate boiling [45] Because

of this, using macro-scale assumptions in microchannels is not

realistic when predicting the flow boiling coefficients

The principal flow regimes in flow boiling are bubbly,

elon-gated bubble (slug), churn, annular, mist, and flows with partial

dry-out Figure 3 displays a schematic of the main flow

pat-terns that may be experienced with a constant heat flux Flow

patterns in a small channel can vary slightly, depending on the

orientation of the channel because of the effects of gravity For

a horizontal channel, when the fluid reaches temperatures just

above the saturation temperature, small bubbles begin to

nu-cleate This is known as the bubbly regime As vapor bubbles

increases, a flow pattern develops that entraps the vapor

bub-bles in the main flowing liquid, known as plug flow With more

heat, the bubbles grow to be within a few micrometers of the

channel’s hydraulic diameter The bubble is now confined by

the microchannel and it can no longer grow in diameter, but

elongates, growing in length This is now the elongated bubble

regime or the slug regime This pattern is the dominant regime

for flow boiling where the most heat is transferred convectively

Separating the growing elongated bubbles is a section of fluidalso known as liquid slug There is a small thin film of liquid sur-rounding the vapor bubble separating it from the microchannelwall If the liquid film enclosing the elongated bubble reaches

a minimum thickness, the region is considered dried out, alsoknown as the vapor slug As the length of the vapor continues togrow, it swallows up the liquid slug until the elongated bubbleemerges to the next cycle or the next patch of vapor This isshown in Figure 4 When the dominant flow is vapor and has asmall film of liquid surrounding the bubble, this is known as theannular regime This flow pattern may have small droplets ofliquid dispersed throughout the vapor core The vertical channel

is very similar as it experiences the slug, churn, annular, andmist pattern It initiates with the bubbly flow and quickly thevapor pockets grow to a slug regime The vapor bubble con-tinues to grow into churn, then annular, and then mist fashion.Because of the influence of gravity, the horizontal flow pat-terns are more likely to have intermittent drying and rewetting

of the upper surfaces of the tube for slug and annular patterns[44, 46, 47]

Figure 4 shows a model used to describe the elongated ble flow regime in the flow boiling process At a fixed referenceframe, a liquid slug of some length will pass, followed by anelongated bubble, and if the thin film dries out before it reachesthe next liquid slug, there will pass a vapor slug This cycle re-peats itself until the vapor is continuous throughout the channel[44, 46]

bub-To better understand the flow boiling profiles, Thome et al.[44] developed a three-zone model in an effort to qualitativelyand quantitatively describe the heat transfer effects due to flowboiling in microchannels This model describes the evaporation

of the elongated bubble as it flows through a microchannel andpredicts the local heat transfer coefficient in the liquid slug,evaporating elongated bubble, and a vapor slug or the dry-out re-gion The three-zone model takes into account the frequency ofthe vapor bubbles with respect to time, the minimum liquid filmthickness as dry-out occurs, and the liquid film thickness When

Figure 4 Model used to describe the flow boiling process.

heat transfer engineering vol 32 nos 7–8 2011

compared to the liquid slug region, the heat transfer coefficient

in the thin film evaporation region (elongated bubble) is several

times higher The values for the vapor slug region, annular, are

almost negligible as the heat transfer coefficient of air is much

lower

Like in single-phase flow and pool boiling, adding

mi-crostructures to the surfaces of microchannels can enhance the

cooling performance Chien et al [48] added square pin-fins of

dimension 400µm × 400 µm × 400 µm (width × thickness ×

height) to a rectangular 20 mm× 25 mm Cu plate and

investi-gated the heat transfer effects when varying the heat flux and the

flow rate For both a smooth and pin-finned surface, water and

FC-72 were used as the working fluids in the microchannel For

water, the performance is influenced by the flow rate for heat flux

lower than 60 W/cm2 At low flow rates, the heat transfer

coeffi-cients increase with increasing heat flux However, at high flow

rates, the heat flux is almost negligible with minimal effect to the

heat transfer coefficient For lower heat fluxes the performance

is driven by the nucleate boiling, and for higher flow rates, the

forced convection is dominant However, when using FC-72 as

the working fluid, the most influential parameter is the heat flux

When varying the flow rate, the heat transfer coefficient curves

were similar, implying that the boiling heat transfer is the more

dominant effect, rather than the forced convection With the

saturation temperature in FC-72 (56◦C) being much lower than

that of water (100◦C), one should expect to see the nucleation

start sooner More vapor bubbles are observed with Fluorinert

For low heat fluxes, the heat transfer coefficient increases as the

flow rate decreases, but for lower flow rates, partial dry-out was

observed during the experiments, which drastically degrades the

performance The pin-finned surface increases the heat transfer

coefficient by about 30% and contains a greater CHF for a fixed

flow rate when compared to the smoothed surface The

convec-tive heat transfer was greater at low flow rates (80–160 mL/min)

and heat fluxes (18–35 W/cm2) for FC-72 than for water Water,

however, had a superior performance compared with FC-72 for

higher flow rates [48] Chien et al [49] in another investigation

compared the effect of FC-72 cooling fluid flow boiling through

two different square pin-fin geometries A comparison was

con-ducted of square pin-fins with geometries of 400µm × 400 µm

× 400 µm and 200 µm × 200 µm × 200 µm with various flow

rates (80–960 mL/min) and heat fluxes (18–50 W/cm2) Similar

to the previous investigation, the heat flux is the driving force

influencing the heat transfer coefficient, as opposed to the flow

rate, because of the dominant nucleate boiling effect With the

square pin-fins, the partial dry-out only occurred at the lowest

flow rate (80 mL/min), unlike with the smoothed surface,

be-cause the gaps of the fins prevent the drying out by the liquid

it retains on the surface Therefore, the structured surface had a

significantly higher heat transfer performance because the

sur-face was kept from drying out for lower flow rates and high

heat fluxes At high flow rates, both geometries contain

simi-lar results, but at the lowest flow rate tested (80 mL/min), the

geometry with the smaller square pin-fins had a 5–10% higher

heat transfer coefficient For both pin-finned surfaces, there is

a 10–20% increase in the heat transfer coefficient when pared to the smooth surface as the flow rates were between 320and 960 mL/min [49] Similar results were found in the studyconducted by Lie et al [50]

com-Cetegen et al [51] used refrigerant R-245fa and passed itthrough a force-fed evaporation element and a microgroovedsurface using three mass flow rates From the results, for allmass flow rates, there was no variance in the trend below aheat flux of 320 W/cm2 For lower heat fluxes in this experi-ment, the heat transfer coefficient was due to the variance ofthe heat flux Therefore, it can be concluded that the dominantheat transfer mechanism was nucleate boiling with negligibleconvective boiling At a heat flux of 320 W/cm2 there was ahuge temperature jump and a drop in heat transfer coefficientwhere it is believed to have reached the CHF Grooved surfaces,like finned surfaces, can also influence the thermal performance

of flow boiling process

For space applications, the effects of gravity on flow boilingthrough microchannels can be very useful Kandlikar andBalasubramanian [52] varied the orientation of a six-parallel-microchannel system with flow boiling of water in threedifferent directions: horizontal, vertical with an upward flow,and vertical with a downward flow, all while maintaining theheat and mass flux conditions For all directions, the flowregimes encountered were bubbly flow, thin film nucleation,plug flow, churn flow, and annular flow The flow patterns seem

to be similar for all orientations of the channel, except theshapes of the vapor bubbles in the vertical down flow orientationare more bullet-shaped, while there was an elongated circularshape for the horizontal orientation A flow reversal effect wasalso encountered for all orientations, but was more noticeable

in the vertical downward flow case Similar results of theheat transfer performance for the vertical up flow and thehorizontal flow case were better than that of the vertical downflow case due to this higher flow reversal encountered Luciani

et al [53] compared the effects of microgravity to terrestrialgravity in a single vertical microchannel using a transparent,nonflammable and nonexplosive fluid with a low boilingtemperature A microchannel was placed in an Airbus A300Zero G, flying in a parabolic fashion, starting from terrestrialgravity and peaking at microgravity At microgravity, vaporpatterns lead to larger bubble sizes than in terrestrial gravity.Churn and slug flow patterns were dominant, while in terrestrialgravity, for the same conditions, bubbly flow and some slugflow patterns were visible The heat transfer coefficient inmicrogravity was much higher Because of the larger vaporbubbles and the higher heat transfer coefficient, Luciani et al.[53] concluded his heat transfer performance was driven by theconvective flow and not nucleate boiling Gravity has little effect

on the heat transfer performance at a terrestrial level, whichseems to be influenced by nucleate boiling At microgravitylevels, the forced convection of the fluid guides the heat transferperformance

As stated earlier, nanofluids can effectively enhance the mal performance of microchannels Peng et al [54] investigatedheat transfer engineering vol 32 nos 7–8 2011

ther-the effects of a refrigerant-based nanofluid, CuO/R-113, as ther-the

working fluid in a flow boiling process for a rectangular, smooth

tube This nanofluid was analyzed by varying the mass flux (100

kg/m2-s, 150 kg/m2-s, 200kg/m2-s), the heat flux (3.08 kW/m2,

4.62 kW/m2, 6.16 kW/m2), and the volume concentration of the

nanoparticles in the base fluid (0%, 0.1%, 0.2%, 0.5%) The

re-sults conclude that the heat transfer coefficient increases as the

vapor quality of the fluid increases When comparing the heat

transfer coefficients with respect to mass flux, for a 0.5% volume

concentration, there is a 29.7%, 22.7%, and 25.6% enhancement

of heat transfer coefficient with mass fluxes of 100 kg/m2-s, 150

kg/m2-s, and 200 kg/m2-s, respectively, when compared to the

base fluid with 0% concentration The thermal performance of

the channel will increase due to the enhancement of the heat

transfer coefficient provided by nanofluids

Flow boiling in microchannels can improve the thermal

per-formance Based on these papers, flow boiling is made up of

nucleate boiling and forced convection The dominant form of

heat transfer in flow boiling varies depending on the heat flux

for nucleate boiling and the mass flow rate for forced convection

dominance Flow boiling is influenced by microstructures, fluid

flow rates (in some cases), heat flux variance (in some cases),

gravity, etc

CARBON NANOTUBE STRUCTURES ACTING AS

MICROFINS

Carbon nanotubes (CNT) may become a novel material that

can considerably improve microchannel cooling performance

The unique molecular structure of CNT results in excellent

physical and mechanical properties such as great mechanical

strength, great flexibility, and low weight Their mechanical

and chemical stability provides resistance against damage from

external physical and chemical factors applied by their

envi-ronment [4, 55–57] The main sp2 hybridized bonds of CNT,

similar to the in-plane ones in graphite, place them among the

strongest materials known today CNT have a Young’s modulus

as high as 1000 GPa, which is approximately 5 times higher than

steel, and a tensile strength of about 63 GPa, which is almost

50 times higher than steel [4, 58–61] These cylindrical tubes

remain stable up to very high temperatures, similar to graphite,

with values approximately 4000 K [62]

There are two types of CNT: single-walled carbon

nan-otubes (SWNT) and multiwalled carbon nannan-otubes (MWNT)

An SWNT is a cylindrical graphene shell with diameters ranging

from 0.45 to 2.5 nm; it can be considered as a giant molecule

An MWNT consists of several concentric cylindrical shells with

the outer diameters ranging from 2.5 to 60 nm and inner

diame-ters between 1.5 to 40 nm MWNT can be considered materials

similar to graphite The distance between the concentric shells

of a MWNT is approximately 3.4 Å [58, 60]

CNT are single sheets of graphite, named graphene, made up

of a honeycomb-shaped lattice representing an atomic layer of

the crystalline material, rolled up to make tubes with diameters

of 0.45 to about 100 nm The circumference of a CNT is equal

to the length of the chiral vector describing its symmetry andunit cell; the chiral vector is created from the unit vector as

Ch= na1+ ma2 The integers n and m specify the chiral vectorand therefore the chirality or helicity and the atomic structure ofthe tube Specific chiralities are zigzag and armchair structures.The classification of nanotubes can also be given by the chiralangle (θ) at which the graphite sheet is rolled to create thatcylindrical shape When the chiral angle and m in the chiralvector are zero it is known as zigzag Armchair is a nanotubewith the chiral angle equaling 30◦and n= m in the chiral vector[60, 63]

For an ideal individual SWNT, the thermal conductivity hasbeen reported to be higher than diamond, roughly 6000 W/m-K

As a comparison, graphite has a thermal conductivity of about

2000 W/m-K and diamond between 2000 and 2500 W/m-K [60].However, measurements on larger number of nanotubes resulted

in thermal conductivity values as low as about 250 W/m-K forSWNT samples and 20 W/m-K for MWNT samples [40, 57, 64].Thermal conductivity is determined by many factors: e.g., for

an ideal SWNT, its (m,n) chiral vector and its length Moleculardynamics (MD) studies, explained later in this paper, have beenconducted investigating the thermal conductivity of CNT asthey vary in length and chirality of SWNT with a finite length.Higher thermal conductivity has been obtained for SWNT withlower diameter (chirality (5,5)) The length and the thermalconductivity of a SWNT are proportional to each other, while thethermal conductivity does not depend linearly on the diameter[65–68]

CNT can be grown directly onto silicon substrate by cal Vapor Deposition (CVD) CVD is a low cost process and canproduce CNT in many fashions, in either bulk quantities or pre-defined micropatterns In most of the CVD processes, substratesare heated in a furnace while a hydrocarbon gas is flowingthrough the reactor A catalyst—iron, nickel, or cobalt—is de-posited on the substrate [69] or fed into the reactor together withthe hydrocarbon source [70] In the first, more widely used, case,CNT grow in the location of the catalyst and form 3D structureserected above the 2D mold defined from the catalyst materials.Similar patterning is possible in the floating catalyst method asthe CVD growth is template dependent [71–76] In this CVDmethod, ferrocene (Fe(C5H5)2) is dissolved in xylene (C8H10),

Chemi-at concentrChemi-ations of ∼0.01 g/mL, preheated at about 150◦C,

co-evaporated, and fed into the reaction zone After passing thedesired reaction time, estimated by the desired nanotube length,the carbon source and catalyst valves are closed and the tube iscooled down in an argon atmosphere Growth of several tens ofmicrometers thick, uniform, vertically aligned multiwalled nan-otube films (with a narrow diameter distribution of 20–30 nm)can be produced on silica substrates with a growth rate of∼10µm/min Using silicon/silica patterned substrates, the deposition

of nanotubes is extremely selective as nanotube structures growaligned with respect to each other and normal to the substrate, onthe oxide only (but not on Si nor on the native oxide layer of Si).This selectivity is retained down to the small lithographicallyheat transfer engineering vol 32 nos 7–8 2011

Figure 5 Carbon nanotube pillar (fin) structures defined by (a and b) selective CVD (reprinted with permission [74], copyright [2003] IEEE), (c) laser ablation technique (reprinted with permission from [5], copyright 2007, AIP), and (d) solvent treatment [78].

patterned micro-size dimensions of SiO2 on the SiO2/Si

sub-strate, and below that limit the cooperative growth phenomenon

is weakened and the order of the structure is diminished This

simple characteristic of the substrate provides an opportunity

to build ordered nanotube fin structures by designing the SiO2

patterns in terms of dimension, thickness, shape (cross section),

and uniformity High aspect structures also show deviation

from the exact perpendicular growth

Another way of pattern generation is processing the

uni-formly grown CNT layers by laser ablation [5, 77] or solvent

treatment [78, 79] During laser treatment, the pattern of the

structure is given by a computer controlled laser beam and a

wide variety of patterns can be generated The solvent treatment

method can be used to create predefined structures or random

cell structures of CNT In both structures the nanotubes are

pulled together by capillary forces and kept together due to the

van der Waals interactions [78, 79] The solvent-treated

struc-tures have higher CNT population in the pillar and wall This

higher density of the nanotubes is advantageous for reaching

better mechanical properties and higher thermal conductivity

and heat capacity values Figure 5 shows images of CNT fin

structures grown using CVD, laser ablation processes and

sol-vent treatment

Mo et al [64] compared a smooth microchannel to a channel

with carbon nanofins The nanotube fins lowered the

temper-ature by 6◦C The flow rate of the coolant in the CNT coated

channel was decreased by 12% and the heat input increased to

23%, yet the nanotubes still maintained a lower temperature

This more efficient method decreased the temperature without

a significant drop in pressure Zhong et al [2], using

compu-tational fluid dynamics (CFD), also explained further in this

paper, examined the effects of CNT microstructures as they

were coated on the surface of the microchannel walls

Fig-ure 6 shows a schematic of the structural composition of CNT

Figure 6 Microstructure makeup when microchannel is coated with CNT.

microstructures consisting of fins organized into arrays Themicrostructures are roughly about 1 mm × 1 mm × 100 µm(length × width × height) placed on the surface of the mi-crochannel If you magnify the scale further, the microstructure

is made up of hundreds of microfins across that surface area.These are the clusters of CNT forced together mainly by the vander Waals interaction Each microfin is made up of hundreds ofCNT

The effects of CNT clustered together to form tures are still under investigation Microstructure can be mod-eled as a macro-scale continuum; however, as the scales de-crease, alternative methods must be introduced into the problem.CNT are an excellent conducting material that has been tested

microstruc-in the use of microstruc-increasmicrostruc-ing the performance of the microchannelheat sink They are simple to fabricate with the CVD processand they contain excellent physical and mechanical propertiesamong the top known today

NUMERICAL AND COMPUTATIONAL ANALYSIS

OF MICROCHANNELS

Experimentation with microchannels can be very costly inboth time and money The experimental setup has to be nearlyperfect to get the desired effect and satisfy boundary condi-tions In testing more than one experiment with varying param-eters, the setup alone can take weeks Numerical and compu-tational analysis can cut costs and time while investigating thethermal performance The analysis can help predict reasonabletesting parameters for the experimentation of microchannels.The lattice Boltzmann method (LBM) can numerically calcu-late the interaction of small particles and fluid flow To sim-ulate particles at the atomic level, computer software such as

MD is used CFD is computer software that simulates the fluid

as a continuum using NS These numerical and computationalmethods can shorten the design cycle and lessen experimentalcosts

In microchannels, the heat and fluid flow are very ferent from those in macrochannels Because of the highsurface–volume ratio the surface defects affect the domain insmall devices The macroscopic no-slip boundary conditionsare not valid at this micro- and nano-scale under some circum-stances [80] The classification of the fluid regime is measuredheat transfer engineering vol 32 nos 7–8 2011

dif-Figure 7 Flow characteristics based on the Knudsen number.

by the Kn, which is defined by Kn= λ/H, where λ is the mean

free path and H is the characteristic length of the channel in

which the fluid flows The Kn characterizes the different flow

regimes for which certain numerical equations can be used when

calculating the flow patterns This is shown in Figure 7

If Kn≤ 10−3the flow is assumed to be a continuum and the

NS with the no-slip boundary conditions can be utilized For

the flow regime where Kn> 10, the flow is known as a free

molecular flow Free molecular flow is where the molecules are

larger than the size of the chamber or the object being tested,

known as a vacuum A rarefied gas is neither a continuum nor a

free molecular flow but its Kn is between the ranges Between

the continuum flow and the free molecular flow regimes, there

are slip flow and transition flow characteristics When the flow

regime is 10−3< Kn ≤ 10−1, the NS with the slip boundary

conditions can be used to assure accuracy When the rarefaction

factor becomes greater than 10−1the macroscopic method based

on the NS will no longer suffice and a more accurate method

must be used When the rarefaction factor is for 10−1< Kn ≤ 10,

particle-based methods should be used LBM, MD, and direct

simulation Monte Carlo (DSMC) are such methods that can

suf-ficiently calculate the fluid flow regimes as the scales are reduced

[20, 81– 83] Therefore, with the flow regime characteristics,

mi-crochannels with characteristic dimensions between 1µm and 1

mm can be modeled using the NS equation as the fluid will

fol-low macroscopic behavior Channels with dimensions less than

1 µm will follow microscopic flow and NS can no longer be

used [24, 83–87] Harley et al [88], Araki et al [89], and Arkilic

et al [90, 91] all investigated the flow continuum in

microchan-nels, concluding that the conventional equations were no longer

adequate in predicting the flow patterns Harley et al [88]

in-vestigated gas flow through a channel with varying depths of

0.5–20µm and a width of 100 µm using nitrogen, helium, and

argon gas The results were compared to the macroscopic

cal-culations and they did not correlate Araki et al [89] studied

the frictional characteristics of nitrogen and helium and found

that the frictional resistance of the gaseous flow is smaller in

microchannels than that of a traditional channel Arkilic et al

[90, 91] investigated the deviation of the transport of gas in

microchannels versus the continuum

LBM can accurately simulate fluid flowing through a crochannel [84, 92–96] This simplified method of the kineticequations is derived from the Boltzmann equations Unlike othermathematical methods such as MD and DSMC, LBM does notdepend on distribution of the number of molecules; rather, itconcentrates on the distribution function dependence of the ve-locity coordinates This method focuses on the local velocityaverages at distinct locations [81, 84, 86, 94, 97] As shown inFigure 7, these equations are suitable for all flow regimes LBM

mi-is considered to be computationally stable, accurate, efficient,and easy to use This method is capable of solving complexgeometries and of effortlessly implementing the boundary con-ditions, and is less difficult to compute, while avoiding the need

to follow every particle in the system like MD, and DSMC [84,

94, 97] Darbandi and Setayeshgar [81] use the LBM to gate a fluid flowing past a confined cylinder in a microchannelwith slip flow regime A result justification through a compar-ison and an examination of the continuum and noncontinuumflow past a confined cylinder in a microchannel was conducted.The results suggested that the Kn increases when the cylinderwas placed in the flow path, decreasing the hydraulic diameter

investi-MD is a particle-based computer simulation program thatcan compute the thermal transport of properties in nanostruc-tures at the atomic scale using classical and quantum physics.This method makes it possible to attain the thermal resistancesfor a solid/solid, solid/liquid, and liquid/liquid interface MD ismade up of two processes: equilibrium and nonequilibrium MD.The equilibrium MD is calculated based on the Green–Kubo re-lations, and nonequilibrium MD is calculated using the Fourierlaws [24] Shibahara et al [98] examined the thermal resis-tance effects of a liquid/solid interface using MD simulations.The resistance was calculated by the heat flux and the tempera-ture jump at the interface, and it was found that by increasing thedensity of the fluid, the thermal resistance decreases betweenthe thermal transport of the solid and liquid MD can evaluatethe data necessary to predict the interaction of the fluid flowingthrough CNT as well as the thermal conductivity through eachgraphite tube as it varies with length and chirality This methodcan isolate and solve one CNT to understand the performanceand the heat effects as it stands by itself Recognizing the heatheat transfer engineering vol 32 nos 7–8 2011

effects through the lone nanotube can be useful when

calculat-ing the effects of many nanotubes close together Hu et al [99]

implemented distinct boundary conditions to simulate one CNT

in the midst of a square array of CNT It was discovered that

the CNT should contain a small gap big enough for a fluid to

flow through the tube separation This will maximize the heat

transfer due the increase of surface area Kharazmi and Kamali

[100] investigated the effects of surface roughness or deviations

along the surface of a fluid in a nanochannel using MD

simula-tions The wall–fluid interaction and the surface irregularity are

factors important to the disturbance of the flow The cavitations

and wall microstructures can vary the local density pattern yet

still maintain an overall average [100] MD can simulate the

in-teraction at the solid–fluid interface accurately in the molecular

scale and also save time and money

The CFD method, calculated through a commercial software

package, is used to approximate the fluid mechanics and heat

transfer characteristics of microchannels CFD can be used in

parallel to experimental setups in an effort to predict the flow and

heat effects of the given surface modifications and the specified

parameters and boundary conditions of a microchannel CFD is

based on the NS equations derived from Newton’s second law

of motion NS is a set of equations that describe the fluid flow

behavior in a continuum CFD simulations have been used to

study the many different aspects of microchannels Zhong et al

[2] modeled a 2D simulation of a microchannel with arrays of

microstructures on the bottom surface A study of the effects

of varying the geometry of the microstructures was completed,

varying the fluid speed and changing the thermal conductivity

of the fin material as they influence the thermal performance

When the results were compared to the mathematical

calcula-tions of the conservation of energy equacalcula-tions, they were almost

identical to the CFD simulation results [2] Srivastava et al

[101] used the CFD software package Fluent to understand the

effect of roughness on fluid flow characteristics Three

rectan-gular channels were simulated: two with different geometries of

roughness, compared to a smooth microchannel [101]

CONCLUSIONS

This paper has reviewed different techniques used in efforts

to modify microchannels in both single- and two-phase

lami-nar flow Some surface modifications discussed include adding

micro-fins, adding grooves, increasing surface roughness, etc

Many of these modifications have been successful in

increas-ing the thermal performance; however, with advancements in

technology, heat transfer in microchannels still needs to be

fur-ther enhanced CNT built onto the surface of microchannels can

improve thermal performance, because of impressive material

and mechanical properties Different configurations and

geome-tries of CNT microstructures in mini-/microchannels need to be

further numerically and experimentally evaluated to maximize

cooling of the electronic components Mathematical analysis of

microchannels can be done through LBM at both the

micro-and nano-scale, whereas at the atomic scale one can use MDand CFD for the continuum regime Each of the mathematicalprocesses can accurately approximate the thermal performance

of the channel for their specified Kn A cooling mechanismneeds to be designed or modified to efficiently cool electroniccomponents and keep them from malfunctioning in order forelectronic innovation to continue [102]

NOMENCLATURE

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CNT carbon nanotubesCVD chemical vapor depositionDSMC direct simulation monte carlo

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Jami F Tullius is a graduate student pursuing a

doc-torate degree in mechanical engineering at Rice versity, Houston, TX She received her bachelor’s de- gree in mechanical engineering from the University

Uni-of Texas at El Paso, El Paso, TX, in 2008 She was one of the recipients of a Graduate Education and the Professoriate (AGEP) program scholarship through

an NSF grant Currently she is an HENACC Scholar, GEM Fellow, and recipient of a NASA–Harriett G Jenkins Pre-Doctoral Fellowship.

Robert Vajtai is a faculty fellow of the Department

of Mechanical Engineering and Materials Science at Rice University, Houston, TX He received his mas- ter’s, doctoral, and Ph.D degrees at University of Szeged, Szeged, Hungary He has more than 100 publications in international scientific journals and these papers received more than 2500 citations He

is editor of Nanopages and Fluctuations and Noise Letters and an editor for the Springer Handbook of Nanomaterials He leads and takes part in projects

for applications of nanomaterials in thermal managements.

Yildiz Bayazitoglu joined Rice University, Houston,

TX, in 1977, and since 1996 has been H S Cameron Chair Professor of Mechanical Engineering in the Department of Mechanical Engineering and Materi- als Science She received her M.S and Ph.D degrees from University of Michigan, Ann Arbor Her current research interests include containerless processing of materials, solution to electromagnetic radiation equa- tion, molecular dynamics studies for nano heat trans- fer, microchannel fluid and heat transfer, and bio heat

transfer She is the editor in chief (Americas) of the International Journal of Thermal Sciences (IJTS), which is published by Elsevier She received several

awards due to her achievements in teaching, mentoring, and research She is a fellow of ASME and AAAS.

heat transfer engineering vol 32 nos 7–8 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.506397

Experiment Investigation of R134a

Flow Boiling Process in Microchannel With Cavitation Structure

HONG ZHANG CAO, HONG BO XU, NAN LIANG, and CHANG QING TIAN

Institute of Engineering Thermal-Physics, Chinese Academy of Sciences, Beijing, China

One cavitation structure in which the channel cross section expanded suddenly was introduced in single straight microchannel.

The experiment was carried out with R-134a as the fluid medium, which was driven by a gear pump The flow pattern was

observed by a charged coupled device (CCD) camera and microscope The average boiling heat transfer coefficient was

estimated with the calculation method proposed in this paper The experimental results show that the boiling began at the

cavitation structure, and stable flow boiling was maintained When heat power rose, the boiling became strong; then the

pressure drop in the micro-channel increased and heat transfer was enhanced The liquid percentage in two-phase flow

increased and the length of boiling area became small when the liquid subcooling degree rose with the fixed heat power.

INTRODUCTION

Many experimental results for flow boiling in unchanged

cross section microchannel or channels have presented unsteady

different patterns of alternating flow [1–8] Especially in slug

flow, the fast growth of a bubble could induce local dryout in a

channel In several investigations [9–13], a restrictive inlet (e.g.,

inlet orifice) where cavitation was caused by static pressure

decrease and velocity increase with sudden reduction in the

flow area was used in microchannel or channels to suppress

flow boiling oscillations Following the results of macro-scale

cavitation showing that cavitation in a submersed jet could reach

onset in the low-pressure kernel of a vortex and the cavitation

bubble collapsing could induce a microjet [14, 15], we supposed

that this phenomenon could occur in a microchannel and the

microjet could break the growing bubbles surrounding it So for

this paper, one cavitation structure in which the channel cross

section expanded suddenly was introduced in a single straight

microchannel and the experiment was carried out with R-134a

This study was supported by Natural Science Foundation of China (grant

50676099).

Address correspondence to Dr Hong zhang Cao, Institute of Engineering

Thermal-Physics, Chinese Academy of Sciences, 100190 bei si huan xi lu 11,

Beijing, China E-mail: caohongzhang@iet.cn

EXPERIMENTAL FACILITY

The experimental apparatus is shown in Figure 1 A gearpump was used to force the liquid through the test sectionwith a constant flow rate measured by a flow meter (K-F massflow meter, accuracy±0.1%) The work fluid through the con-denser was cooled by cooling water whose temperature could beadjusted

The test section is shown in Figure 2 The microchannel wasfluted with an electric line cutting technique in a 2-mm-thick,25-mm-wide, 76-mm-long copper plate, which connected to aninlet tank and outlet tank made from Teflon The channel depthwas 0.5 mm and the width changed from 3 mm (46 mm long)

to 0.5 mm (10 mm long), then to 1 mm (20 mm long) A glassplate was put above the copper plate for visual observation Forestimating the pressure drop of fluid, the whole channel wasdivided into seven parts; part 1 is the channel entrance, part 2

is the 3-mm-wide and 46-mm-long channel, part 3 is the den reduction between part 2 and 4, part 4 is the 0.5-mm-wideand 10-mm-long channel, part 5 is the sudden expansion be-tween part 4 and 6, part 6 is the 1-mm-wide and 20-mm-longchannel, and part 7 is the channel exit The cavitation struc-ture is where the channel cross section expands suddenly, i.e.,part 5 A film heater (15 mm wide, 20 mm long, 27
) shown

sud-by the dashed shape in Figure 2 was set on the copper plate backside and covered by an insulated layer Heat power was sup-plied by direct current, and voltage was measured by voltmeter542

Figure 1 Schematic of experimental apparatus 1—pump, 2—flow-meter,

3—inlet-tank, 4—outlet-tank, 5—text-section, 6—CCD & microscope,

7—condenser

(accuracy:±1%) The channel entrance and exit pressures (Pin,

Pout) were measured by pressure sensors (pressure resistance,

accuracy:±0.5%) in the inlet tank and outlet tank, respectively

Thermocouples (T type, accuracy:±0.1◦C) were used to

mea-sure fluid temperatures in the inlet tank and outlet tank (Tin,

Tout), as well as the wall temperatures (T1, T2, T3, T4, T5, T 6)

at different locations along the microchannel, shown in Figure

2 A CCD camera (Panasonic WV-CP240EXCH) and a

micro-scope located above the test section were used to observe flow

patterns The fluid was driven by a gear pump, and the flow rate

was changed according to the test requirement

CALCULATION OF AVERAGE BOILING HEAT

TRANSFER COEFFICIENT

The average boiling heat transfer coefficient is defined by

hboil= Qhboil/Aboil(Tavewall− Tavesat) (1)

where Tavewallis the average wall temperature of channel, Tavesat

is the average saturation temperature of work fluid, Aboil is the

heat transfer area of boiling part in channel, and Qhboil is the

heat transfer in the boiling part The summation of Qhboil and

Qhliquid, the heat transfer in the single-phase liquid flow part, is

the heat power supplied by the film heater to the test section

1

G Film heater

Cavitation structure, 1st OLNB 2nd OLNB

Figure 2 Test section.

Figure 3 Single-phase liquid flow: (a) flow pattern; (b) pressure drop vs fluid mass flux; (c) friction factor vs fluid mass flux The bottom of channel was not smooth Wales [bright lines showed in part (a)] at bottom of channel were caused by manufacturing effect.

Tavewall, Tavesat, and Qhliquidare defined by:

Tavewall≈ (T i)/n, n = 6, i = 1, , 6 (2)

Tavesat≈ (TOLNBsat+ Tout)/2 (3)

Qhliquid= Cp × G × (TOLNBsat− Tin) (4)where TOLNBsat is the fluid temperature, which is the satura-

tion temperature corresponding to the pressure (POLNB) at theoriginating location of nuclear boiling (OLNB) observed by the

CCD camera and microscope, Cpis liquid specific heat, and G

is fluid mass flux The pressure (POLNB) would be calculated proximately from the experimental results of single-phase liquidflow

ap-In the experiments for single-phase liquid flow, the pressuredifference between the channel entrance and exit is equal to theheat transfer engineering vol 32 nos 7–8 2011

Figure 4 Flow pattern while pump power frequency is 30 Hz: (a) heat power

8 W and mass flux 4.48 kg/h; (b) heat power 15 W and mass flux 4.06 kg/h; (c)

heat power 23W and mass flux 3.82 kg/h.

sum of pressure drops at seven parts (Figure 2), written as

and where ρ is liquid density of refrigerant, ui is refrigerant

velocity, Li is channel length, Di is hydraulic diameter, here

Figure 5 Flow pattern while pump power frequency is 40 Hz: (a) heat power

8 W and mass flux 6.2 kg/h; (b) heat power 15 W and mass flux 5.85 kg/h; (c) heat power 23 W and mass flux 5.33 kg/h.

D2 = 0.86 mm, D4 = 0.5 mm, and D6 = 0.67 mm, fi is thesingle-phase friction factor, andξiis the local loss coefficient.For the channel in this paper, the cross section of part 2 ismuch more than for part 4 or part 6 Therefore, the pressure loss

of part 2 (P2) could be neglected compared to the total pressuredrop The test data for single-phase liquid flow presented inTable 1 showed the values of Reynolds numbers (Re) in part

4 and part 6 are larger than the critical Re in macro-scale(2000–2300) That meant the test single-phase liquid flow was

turbulence So here take f2 = f4 = f6 = f , approximately.

Similarly, the local loss coefficientξiwas valued according tomacro-scale investigating results Hereξ1= 0.5, ξ3= 0.43, ξ5=0.25, andξ7= 1 Through measuring of mass flux and pressuredrop for the single liquid phase flow, the average single-phase

friction factor (f ) could be calculated This result could be used

to approximately calculate the pressure (POLNB) in the flow ing experiment with visual observation

boil-Although there is error for the calculation method of theaverage boiling heat transfer coefficient used in this paper, it isapplicable to find out the variation of pressure loss and boilingheat transfer in a microchannel with the cavitation structure.heat transfer engineering vol 32 nos 7–8 2011

Table 1 Test data of single phase liquid flow (dynamic viscosity, µ = 0.202 × 10 −3Pa-s, 25◦C)

Pin (kPa) Pout (kPa) G (kg/h) Tin ( ◦C) ρ (kg/m 3 ) u2/u4/u6 (m/s) Re 2 /Re 4 /Re 6 PinPout (kPa) f

RESULTS AND DISCUSSION

The test data for single-phase liquid flow are presented in

Table 1 The pressure difference between the channel entrance

and exit increases when mass flux rises On the contrary, the

average single-phase friction factor, f , decreases, as shown in

Figure 3 The single-phase liquid flow pattern is shown in the

same figure

During the experiment of flow boiling in a microchannel,

the power frequency of the gear pump was set at 30 Hz, 40

Hz, and 50 Hz At each rotation speed, the heat power was

increased at three levels, 8 W, 15 W, and 23 W The region

surrounding the cavitation structure (part 5 in Figure 2) was

observed and flow pattern was recorded by the CCD camera and

the microscope A comparison of flow patterns with different

heat power at each pump rotation speed is shown in Figures

4–6

The experimental results show that the boiling originated

in the cavitation structure where the vortex cavity was in the

reentrant region, and boiling became strong with the increase

of heat power Meanwhile the OLNB changed against the flow

direction from part 5 to part 3 in course of the heat power

increasing The OLNB was in part 3 for two reasons First,

in part 3 the cross section became small, which induced the

liquid velocity to increase and the pressure to decrease Second,

with the heat power increasing, the heat flow along the copper

plate induced the wall and liquid temperature to increase in

part 3 This means that part 3 is the second cavitation structure

In this experiment, the OLNB was appointed according to theflow pattern in Figures 4–6 Corresponding to Figure 4c andFigure 5c, the OLNB was in part 3, and in the others it was

in part 5 Otherwise, the liquid proportion in two-phase flowbecame large when the refrigerant mass flux increased In thechannel center, liquid flow could be observed clearly in Figures4–6

Figure 7 shows the influence of refrigerant subcooling degree

on the refrigerant quality and boiling length The liquid age in two-phase flow increased and the length of boiling areabecame small when mass flux rose with the fixed heat power

percent-in the experiment The mass flux rispercent-ing percent-induced the pressureincrease in the entrance, corresponding to the liquid subcoolingdegree of increase Thus, boiling was weakened by liquid sub-cooling degree For cavitation, it depended on liquid velocityand temperature

Figure 8 shows the variation of refrigerant pressures andtemperatures with time, and wall temperature distribution alongthe channel at differing heat power and mass flux The transientchanges of pressures and wall temperatures demonstrate thatflow boiling in the microchannel is stable because there are norelatively observable oscillations The irregular oscillation oftemperature in the outlet tank was caused by the alternate touch

of the liquid droplet and vapor to the thermocouple, due to thespray effect of the microchannel exit in the outlet tank Thewall temperatures increased and then decreased along the flow

Table 2 Calculation of average boiling heat transfer coefficient (C p = 1.42 kJ/kg-K; ρ = 1210 kg/m 3 )

Pout(MPa)/Tout ( ◦C) 0.588/21 0.584/20.8 0.577/20.1 0.564/19.6 0.551/18.8 0.541/18.4 0.531/17.9 0.529/17.6 0.526/17.4

POLNB(MPa)/TOLNBsat

Figure 6 Flow pattern while pump power frequency is 50 Hz: (a) heat power

is 8 W and mass flux 7.79 kg/h; (b) heat power 15 W and mass flux 7.55 kg/h;

(c) heat power 23 W and mass flux 7.3 kg/h.

direction because the subcooling liquid refrigerant absorbed

heat into the saturation liquid first, and then the saturation

temperature went down with the decrease of refrigerant pressure

in the microchannel

Aboil, Tavesat, and Qhliquidcould be approximately determined

with the OLNB, as defined, and the average boiling heat

trans-fer coefficient (hboil) could be calculated with the equations

given earlier Here the liquid specific heat and the liquid

den-sity were maintained constant because the inlet temperatures

were approximately equal The calculation results are showed in

Table 2

Figure 9 presents the changes of pressure drop, average

boil-ing heat transfer coefficient, and average wall superheatboil-ing with

the heat power, respectively Figure 9a shows that the pressure

Figure 7 Flow pattern: boiling area became short when mass flux rose from 1.562 kg/h (a) to1.983 kg/h (b),then to 2.043 kg/h (c), with fixed heat power

23 W.

drop increased when heat power or mass flux rose In Figure

9, b and c, the average boiling heat transfer coefficient andaverage wall superheat rise with the increase of heat powerwhen the pump power frequency is 30 Hz or 50 Hz But thecurves are different when rotation rate is 40 Hz It could beexplained from Table 2 that the OLNB was in the same part

of the channel when the pump power frequency was 30 Hz or

50 Hz but the OLNB changed with the heat power when thepump power frequency was 40 Hz Thus, the experimental re-sults shown in Figure 9 present the average boiling heat transfercoefficient and average wall superheat decrease with the massflux increasing at the same heat power, which means boilingheat transfer in the microchannel was abated by the mass fluxincreasing

heat transfer engineering vol 32 nos 7–8 2011

Figure 8 (a) pressure in inlet-tank and outlet-tank; (b) temperature in inlet-tank and outlet-tank; (c) wall temperature; (d) wall temperature distribution along the channel.

heat transfer engineering vol 32 nos 7–8 2011

Figure 8 (Continued)

heat transfer engineering vol 32 nos 7–8 2011

Figure 8 (Continued)

heat transfer engineering vol 32 nos 7–8 2011

Figure 8 (Continued)

heat transfer engineering vol 32 nos 7–8 2011

Figure 8 (Continued)

Figure 9 Parameter variation along with heat power: (a) pressure drop; (b), hboil ; (c) average wall superheat degree.

CONCLUSION

An experiment was carried out with R-134a to investigate

the flow boiling in the microchannel with a cavitation

struc-ture where the channel cross section expanded suddenly Flow

patterns were observed by CCD camera and microscope The

average boiling heat transfer coefficient was estimated with the

calculation method proposed in this paper The experimental

re-sults show that the boiling originated at the cavitation structure

where the vortex cavity was in the reentrant region and stable

flow boiling was maintained When heat power rose, the

boil-ing became strong then the pressure drop in the microchannel

increase and the boiling heat transfer was augmented The uid percentage in two-phase flow increased and the length ofboiling area became small when the liquid subcooling degreeincreasing was induced by mass flux rising with the fixed heatpower

liq-NOMENCLATURE

Aboil heat transfer area of boiling part in channel, mm2

Cp liquid specific heat, kJ/kg-K

Di i= 2, 4, 6, hydraulic diameter, mmheat transfer engineering vol 32 nos 7–8 2011

f i i= 2, 4, 6, average single phase friction factor

G fluid mass flux, kg/h

hboil average boiling heat transfer coefficient, kW/m2-K

Li i= 2, 4, 6, channel length, mm

OLNB originating location of nuclear boiling

Pin pressure at channel entrance, Pa

Pout pressure at channel exit, Pa

POLNB pressure at originating location of nuclear boiling, Pa

Qhboil heat transfer in the boiling part, W

Qhliquid heat transfer in the single-phase liquid flow part, W

Tin temperature at channel entrance,◦C

Tout temperature at channel exit,◦C

Ti i = 1, 2, ., 6, wall temperatures at different locations

along the microchannel,◦C

TOLNBsat saturation temperature corresponding to the pressure

(POLNB) at originating location of nuclear boiling,◦C

Tavewall average wall temperature of channel,◦C

Tavesat average saturation temperature of refrigerant,◦C

ui i= 2, 4, 6, refrigerant velocity, m/s

x distance along the channel, mm

Greek Symbols

P i i = 1, 2, , 7, pressure drop, Pa

ρ liquid density of refrigerant, kg/m3

ξi i= 1, 3, 5, 7, local loss coefficient

REFERENCES

Hetsroni, G , Mosyak, A., Segal, Z., Pogrebnyak, E., Two-Phase

Flow Patterns in Parallel Micro-Channels, International

Jour-nal of Multiphase Flow, vol 29, pp 341–360, 2003.

Hetsroni, G., Gurevich, M., Mosyak, A., Pogrebnyak, E.,

Rozenblit, R., Yarin, L P., Boiling in Capillary Tubes,

Inter-national Journal of Multiphase Flow, vol 29, pp 1551–1563,

2003

Yu, M H., Lin, T K., Tseng, C C., Heat Transfer and Flow

Pattern During Two-Phase Flow Boiling of R-134a in

Hori-zontal Smooth and Microfin Tubes, International Journal of

Refrigeration, vol 25, pp 789–798, 2002.

Serizawa, A., Feng, Z., Kawara, Z., Two-Phase Flow in

Micro-Channels, Experimental Thermal and Fluid Science, vol 26,

pp 703–714, 2002

Zhang, L., Ko, J M., Jiang, L., Measurements and Modeling

of Two-Phase Flow in Micro-Channels With Nearly

Con-stant Heat Flux Boundary Conditions, Journal of

Micro-electromechanical Systems, vol 11, no 1, pp 12–19,

2002

Brutin, D., Topin, F., Tadrist, L., Experimental Study of

Un-steady Convective Boiling in Heated Mini Channels,

Inter-national Journal of Heat and Mass Transfer, vol 46, pp.

2957–2965, 2003

Wu, H Y., Chen, P., Liquid/Two-Phase/Vapor Alternating Flow

During Boiling in Micro-Channels at High Heat Flux, national Communications in Heat and Mass Transfer, vol.

Inter-30, no 3, pp 295–302, 2003

Qu, W., Mudawar, I., Measurement and Prediction of Pressure

Drop in Two-Phase Micro-Channel Heat Sinks, International Journal of Heat and Mass Transfer, vol 46, pp 2737–2753,

2003

Bergles, A E., Lienhard, V., Kendell, G E., Griffith, P., Boiling

and Evaporation in Small Diameter Channels, Heat Transfer Engineering, vol 24, pp 18–40, 2003.

Bergles, A E., Kandlikar, S G., On the Nature of Critical Heat

Flux in Micro-Channels, Journal of Heat Transfer, vol 127,

pp 101–107, 2005

Mishra, C., Peles, Y., Cavitation in Flow Through a

Micro-Orifice Inside a Silicon Microchannel, Physics of Fluids, vol.

17, no 1, pp 1–15, 2005

Kosar, A., Kuo, C J., Peles, Y., Suppression of Boiling FlowOscillations in Parallel Microchannels by Inlet Restrictors,

Journal of Heat Transfer, vol 128, pp 251–260, 2006.

Schneider, B., Kosar, A., Peles, Y., Hydrodynamic Cavitationand Boiling in Refrigerant (R-123) Flow Inside Microchan-

nels, International Journal of Heat and Mass Transfer, vol.

50, pp 2838–2854, 2007

Knapp, R T., Daily, J W., Hammitt, F G., Cavitation,

McGraw-Hill, New York, 1970

Brujan, E A., Keen, G S., Vogel, A., Blake, J R., The FinalStage of the Collapse of a Cavitation Bubble Close to a Rigid

Boundary, American Institute of Physics, vol.14, pp 85–92,

2002

Hong Zhang Cao is an assistant professor at

Insti-tute of Engineering Thermal Physics (IET), Chinese Academy of Sciences (CAS) Prior to joining IET, he worked at Technical Institute of Physics and Chem- istry, CAS, as a postdoctoral research associate He received his Ph.D from IET, CAS, Beijing, in 2006 His research interests include porous heat and mass transfer, micro-scale flow and heat transfer, and ad- vanced electronic cooling technology He is currently working on cavitation and boiling coupled phenom- ena in microchannels and advanced heat managing technology.

Hong Bo Xu is an assistant researcher in Technical

Institute of Physics and Chemistry, Chinese Academy

of Sciences He received a doctoral degree in eration and cryogenic engineering from Technical In- stitute of Physics and Chemistry, Graduate University

refrig-of Chinese Academy refrig-of Sciences, Beijing, China, in

2009 His research interests focus on microchannel heat transfer, especially on microchannel cooling for high heat flux dissipation He has co-authored 10 pa- pers in archival journals and conference proceedings, and has two Chinese patents.

heat transfer engineering vol 32 nos 7–8 2011

Nan Liang is a Ph.D student at the Technical

Insti-tute of Physics and Chemistry, Graduate University

of Chinese Academy of Sciences He worked on the

simulation of a refrigeration system and on two-phase

flow heat and mass transfer, especially focused on the

instability of evaporation His doctoral research is on

the instability of refrigeration system.

Chang Qing Tian is a professor at the Technical

In-stitute of Physics and Chemistry, Chinese Academy

of Sciences He received a doctoral degree in ing, ventilation, and air conditioning from Tsinghua University, Beijing, China, in 2003, and worked post- doctorally in the Department of Thermal Engineer- ing, Tsinghua University, from 2003 to 2005 His research interests include microchannel heat trans- fer, heat pumps, automobile air conditioning, and new technology for the built environment He has co-authored four books and more than 80 papers.

heat-heat transfer engineering vol 32 nos 7–8 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.506399

A Numerical Analysis of the Fiber

Web Effects on the Pressure Drop, Particles Collection, and Heat

Transfer in a Microchannel

ALIREZA DASTAN and OMID ABOUALI

School of Mechanical Engineering, Shiraz University, Shiraz, Iran

In this paper, pressure drop, heat transfer characteristics, and particle deposition in a microchannel with a fiber web at the

inlet are investigated numerically The fiber web was made up of fibers several hundred micrometers in length caught at the

entrance of the channels Governing equations for the flow field are solved by an Eulerian approach, while the equations of

particle motion in the flow are solved by a Lagrangian approach Assuming the symmetry in the domain, one channel and

the corresponding inlet and outlet plenums are selected as the computational domain Several fiber webs with various fiber

numbers, orientations, and dimensions are modeled The increase in the pressure drop and the decrease of heat transfer due

to the fiber web are computed and discussed A correlation is developed for pressure drop as a function of the fiber web

blockage ratio, microchannel geometry, and flow characteristics The deposition of the microparticles with various diameters

on the fiber webs is investigated, as well Deposition of the particles on the fiber web is because of two different mechanisms,

inertial impaction and interception The numerical results indicate that the fiber webs have no considerable effect on the

heat transfer characteristic of the channel under constant pumping power.

INTRODUCTION

The microchannel heat sink cooling concept was first

in-troduced by Tuckerman and Pease in the early 1980s [1] The

microchannel heat sink is usually made up of a

high-thermal-conductivity solid such as silicon or copper with the

microchan-nels fabricated into its surface by either precision machining or

microfabrication technology These microchannels have

char-acteristic dimensions ranging from 10 to 1000µm, and serve as

flow passages for the cooling liquid Microchannel heat sinks

combine the attributes of a very high surface area to volume

ratio, large convective heat transfer coefficient, small mass and

volume, and small coolant inventory [2]

The term “fouling” was originally used in the oil industry

and became widely used in the literature to describe any

unde-sirable deposition causing an increase in the thermal resistance

of a heat exchanger [3] Perry [4] classified the fouling process

Address correspondence to Dr Omid Abouali, School of

Mechani-cal Engineering, Shiraz University, Mollasadra Street, Shiraz, Iran E-mail:

abouali@shirazu.ac.ir

in seven groups, which are particulate fouling, crystallization orscale formation, chemical reaction, corrosion, biological, solid-ification, and mixed fouling

Benzinger et al [5] studied the fouling in a microchannelwith very small hydraulic diameter of 178µm They focused

on the crystallization type of the fouling Among the previousresearchers, Yiantsios and Karabelas [6–8] and Niida et al [9]studied on the particle deposition in a microchannel Yiantsiosand Karabelas studied about fouling in a single channel with 952

µm hydraulic diameter and Niida et al used a microchannel with

727µm hydraulic diameter

Perry and Kandlikar [10] investigated the fouling in a icon microchannel with hydraulic diameter of 225µm Theyinvestigated the particle fouling of 4-µm silica and 1.25-µmalumina particles dispersed in water They observed no parti-cle deposition within the channels because of high shear stress

sil-in flow at the channel compared to usual channels They pressed that there is a secondary effect in particulate foulingwhen fibrous elements exist They observed fibrous materialswith several hundred micrometers length caught at the channelentrance The additional fibers get caught in this “fiber web.”The fiber web causes increasing in pressure drop and particle554

ex-deposition because it acts as a fiber filter The fibrous material

of about 20µm diameter was found to be from the citric acid

buffer solutions used for preparation of the microfluids

To properly compare different microchannel heat exchanger

geometries, a parameter including both dissipated heat flux and

the pressure drop should be defined A novel parameter called

the pumping power flux has been developed by Steinke and

Kandlikar [11] This new parameter is defined as follows:

P= m
P˙

The pumping power can be manipulated to a flux term by

dividing to free flow area of the flow

P= m˙
P

ρAfree

(2)where the single channel wet area can be considered as the free

flow area

The heat flux and pumping power flux can be related in a

simple manner by defining the coefficient of performance (COP)

In this work, the COP concept is used to investigate the

heat transfer characteristic of the microchannel affected by the

entrance fiber webs

Several fiber webs with various numbers of fibers and

differ-ent oridiffer-entations and dimensions are modeled at the differ-entrance of

a channel with hydraulic diameter of 225µm This specific size

of the microchannel was selected for a qualitative comparison

with the work of Perry and Kandlikar [10] The effects of fiber

webs on the pressure drop, heat transfer, and particles deposition

in three different flow rates are studied numerically

MODEL DESCRIPTION

A microchannel heat sink was selected for numerical study

in this work in which 26 channels were fixed in the given

width Both inlet and outlet plenums have 2.5 mm length and

300µm depth A schematic view of the microchannel and

in-let plenum is shown in Figure 1 The cross section of each

channel has 205µm width and 249 µm depth The channel

length is 10 mm Each separating fin between the channels

has 97µm width Assuming the symmetry in the domain, a

channel with half of each side wall and corresponding inlet

and outlet plenums are selected as a computational domain

The side walls of the plenums are considered as symmetric

walls

To study the effects of different orientations, lengths, widths,

or the number of fibers, some fiber webs are modeled in the

entrance of the channel A schematic of the front view for the

fiber webs at the channel inlet is illustrated in Figure 2 Four

Figure 1 Schematic of the microchannel and inlet plenum.

different fiber web types with one, two, four, or six fibers areconsidered All fiber webs have fibers with square cross sectionexcept one case having six cylindrical fibers According to theobservations of Perry and Kandlikar [10], the caught fibers had

a diameter around 20 µm and several hundred micrometerslength In present numerical model, fibers with 13.3, 20, 25, or

30µm width are studied Fibers are aligned horizontally in theweb with one or two fibers In the webs with four or six fibers,half of the fibers are aligned horizontally and the remainderaligned vertically (Figure 2) Figure 3 shows the front, side, andtrimetric views of a fiber web with six rectangular fibers caught

at the channel entrance

There are two exceptions in the orientation of the fibers

In the first one, fibers are rotated 45◦ and 135◦ relative tohorizontal axis For the other one, the length and orientation

of the fibers are chosen randomly The latter are explainedlater

According to the earlier explanation, the detailed geometry

of the fiber web can be described with five parameters, includingthe geometric center position of each fiber (x,y), the length andthe width (diameter) of the fibers (l,w), and the angle of the fibers

Figure 2 Schematic for the front view of the channel with some modeled fiber webs: (A) fiber web with one fiber (fiber web #1); (B) fiber web with two fibers (fiber web #2); (C) fiber web with four fibers (fiber webs #3 or #4); (D) fiber web with six fibers (fiber webs #5, #6, #7, or #8); (E) fiber web with six inclined fibers (fiber web #9); (F) fiber web with six random distributed fibers (fiber web

#10).

heat transfer engineering vol 32 nos 7–8 2011

Figure 3 (A) The front view of the channel with six fibers; (B) side view; (C) trimetric view Point O is the origin of the coordinate system used to describe the fiber location and orientation in the Table 1.

relative to the x axis in counterclockwise direction (θ) The top

left corner of the computational domain at the channel entrance

(point O in Figure 3) is considered the origin of the coordinate

system, with the z axis along the channel length The position of

geometric center of the fibers in the z direction can be determined

based on the fiber width because they are placed either at half

or one and half times the fiber width (diameter) from channel

entrance The geometric details of the all investigated fiber webs

in the present study are given in Table 1 based on the

already-mentioned parameters It should be noted again that each side of

the channel walls in the computational domain has a 48.5-µm

width (half of the fin width in the physical domain) The plenums

have a 300-µm depth and 2.5-mm length The channel length

is 10 mm with a cross section of 205× 249 µm In the heat

transfer study, a solid substrate of 51µm height is considered

at the bottom of the channel

NUMERICAL METHOD

Some simplifications are assumed before solving the ing equations Steady incompressible flow with constant fluidproperties was considered The flow in all of the cases is lam-inar The only body force is gravitational force, which acts inthe direction of the channel depth Based on these assumptions,the fluid governing equations are continuity, momentum, andenergy equations as follow:

Table 1 Geometric details of the all studied fiber webs

∗Fiber web #6 has cylindrical fibers and w is the diameter of the fibers.

The mass flow rate boundary condition is used at the inlet

plenum and the flow at the outlet plenum is assumed to be

fully developed Two side planes of the plenums (Figure 3) and

the outer fin planes of the channel were set to be symmetric

A no-slip boundary condition is considered for all solid walls

including channel and plenum walls and fiber surfaces In the

heat transfer study, all the walls except the bottom wall of the

channel substrate are considered adiabatic (fiber walls are also

set adiabatic) A constant heat flux boundary condition is set for

the bottom wall of the solid substrate

A multizones grid technique was used in this research and

the whole computational domain was divided into five various

zones (Figure 4) The first and second zones are at the inlet

plenum before the fiber web region and both have 1 mm length

The third zone with a length of 1 mm is around the fiber web,

where the first half is in the plenum and the other half is placed

in the channel The fourth zone is in the channel after the fiberweb region and has a length of 1 mm The fifth zone covers theremainder of the channel (8.5 mm length) and the whole out-let plenum (2.5 mm length) The structured grid is distributeduniformly in the first, second, fourth, and fifth zones in all di-rections The grid resolution in these zones is the same in all 10studied fiber webs (Table 1)

The cells of the third zone are concentrated around thefiber web, where the size ratio of neighbor cells does not ex-ceed 1.1 A combination of the structured and unstructuredcomputational grid is used for the third zone based on thefiber web type The whole domain cells numbers are in therange of 300,000 to 780,000, corresponding to inlet fiber webtype

heat transfer engineering vol 32 nos 7–8 2011

Figure 4 Different zones location used in the grid generation process.

For the grid study purpose, a solution-adaptive grid

refine-ment was performed using the curvature approach [12] The

velocity gradient value is calculated for the whole domain and

10% of the maximum gradient value is selected as a refinement

threshold Cells with gradient values more than the threshold

are refined No noticeable change in numerical results (less than

1.5%) was observed using a finer grid, so the initial

computa-tional grid for each case was selected

The governing equations (4, 5, and 6) and corresponding

boundary conditions are solved by an Eulerian approach The

solution is based on finite volume method by employing a

SIM-PLE algorithm The convective terms are discritized by an

up-wind scheme and viscous term by central differencing

After solving the equations of the flow field, the equations of

solid particles motion are solved by a Lagrangian approach To

predict the path of the microparticle, the force balance equation

for the particle is integrated The force balance equation is as

is the particle Reynolds number based on the relative velocity

of the fluid and particle and CDis the drag coefficient [13]

to shear The used lift force is from Li and Ahmadi [14] and is

a generalized form of that provided by Saffman [15]:

−

→

Flift= 2Kρdij

√ν

ρpdp(d1kdk1)1(−

→u − −→up) (12)where K= 2.594 and dijis the deformation tensor [14]

Figure 5 Velocity vector field in the channel with fiber web #3 for the total flow rate of 67 mL/min: (a) on the middle vertical plane of the channel; (b) on the middle horizontal plane of the channel.

One of the important forces in motion of particle in the liquids

is the virtual mass force that is required to accelerate the fluidsurrounding the particle

differen-Figure 6 Path lines in the fiber web region for four different fiber webs: (a) fiber web #3, (b) fiber web #5, (c) fiber web #6, and (d) fiber web #10.

heat, and thermal conductivity of the water at this temperature

areρ = 997.6 kg/m3,µ = 9.3958 × 10−4kg/m·s, Cp = 4181

J/kg-K, and k= 0.607 W/m-K, respectively The channel walls

and the substrate are made from copper having a density of 8978

kg/m3, specific heat of 381 J/kg-K, and conductivity of 387.6

W/m-K Silica spherical particles with a density ofρp= 2400

kg/m3were used in the particle deposition investigation

RESULTS AND DISCUSSION

Unfortunately, no available experimental data exist for

com-parison of the present numerical results for the microchannel

with fiber webs caught at the channel entrance Some

qual-itative comparison will be done with the work of Perry and

Kandalikar [10] But it should be emphasized that our

numer-ical model was validated before for simple microchannels and

also a grooved microchannel in reference [16] The flow field

is solved for three different total flow rates of 35, 51, and 67mL/min These amounts of flow rates are divided into 26 singlechannels The average velocities in the channel are 0.44, 0.64,and 0.84 m/s and the Reynolds number based on the channelhydraulic diameter is 105, 153, and 201, respectively, for theseflow rates

In Figure 5, the velocity vectors at the entrance of the channelwith fiber web #3 for total flow rate of 67 mL/min is shown Inthe figure, the recirculation zones behind each fiber can be seeneasily and the velocity increases to 1.73 m/s due to the decrease

of the effective area in the inlet cross section

To study the interaction between fluid and the fiber web,Figure 6 is presented The figure shows some path lines in thefiber web region for microchannel with fiber webs #3, #5, #6,and #10 The shown path lines for each part of the figure are thesame and the effects of the different fiber webs on the suddendeviations of the path lines are clear

In the following subsections the results for pressure drop,particles deposition, and heat transfer are presented

heat transfer engineering vol 32 nos 7–8 2011

Figure 7 Pressure drop at various total flow rates for a clean microchannel

and two microchannels with fiber webs #3 and #5.

Pressure Drop

One of the major concerns in the microchannels is the high

flow pressure drop in the channel Pressure drop in a clean

microchannel is due to viscous friction across the channel and

both plenums as well as the pressure losses corresponding to

the contraction and expansion at the channel inlet and outlet [2]

In the case of a fiber web at the channel entrance, the pressure

losses due to interaction of the flow with the fiber web are added

to these losses

Figure 7 shows the pressure drop at different flow rates for a

clean microchannel with no fiber compared with the cases with

two fiber webs, #3 and #5 As was expected, the total pressure

drop increases with increase in the flow rate In addition, the

fiber web causes more pressure drop in the system, and a higher

number of fibers leads to a higher pressure drop The figure

shows that the webs with four and six fibers at the entrance of

the channel increase the pressure drop 10 and 20%, respectively,

compared with that in a clean microchannel The results of this

study (not shown in Figure 7) show that a fiber web with less

than four fibers has no considerable effect on the pressure drop

It should be noted, as Perry and Kandlikar [10] mentioned,

that the fiber web grows thicker and deeper over time and

Figure 8 Pressure drop for three different fiber diameters and the same number

(six) of the fibers (fiber web #5, #7, and #8).

Figure 9 The area (hachured surfaces) used to calculate the blockage ratio for

a caught fiber web at the entrance of the channel The overlapped parts of the fibers in each fiber rows are considered only once.

causes more pressure drop in the channel To investigate theeffect of fiber size, three webs with various widths of 13.3,

20, and 25µm (fiber webs #8, #5, and #7) are numerically vestigated Figure 8 shows that with 88% increase in the fiberwidth, the pressure drop increases 15.3% for the maximumflow rate case It should be emphasized that this increase is notlinear

in-The results of this study show that the pressure drop can becomputed as a function of the fiber web cross section area at thechannel entrance without mentioning the number of fibers andtheir orientation A nondimensional parameter named blockageratio (β) was introduced The blockage ratio is defined as theratio of the projected area of the fiber web on the channel inlet

to the channel cross section area In Figure 9, the hatched area

of the fiber web is the area used to calculate the blockage ratio.The second column of Table 1 also shows the blockage ratios ofeach fiber webs

Some numerical models reported in Table 1 (fiber webs #4and #8) were designed to have fiber webs with various fibernumbers or widths but with the same blockage ratio of fiberwebs #3 and #5 The results show that the pressure drop is afunction of the blockage ratio, not the fibers number or widths

Figure 10 Pressure drop for various blockage ratios and flow rates and parison with Eq (15).

com-heat transfer engineering vol 32 nos 7–8 2011

To study the effect of the fiber geometry, a fiber web with six

cylindrical fibers of 20µm diameter (fiber web #6) was modeled

that has an equal blockage ratio to that for the fiber web #5

Cylindrical fibers cause a little less pressure drop than fibers

with rectangular cross section because the surface curvature of

the cylindrical fibers causes less deviation in the flow path lines

Moreover, the low pressure wake formed behind the fibers is

smaller for the cylindrical fibers But rectangular fibers have

only 3.5% more pressure drop in the maximum flow rate in

comparison to cylindrical fibers So the real shape of the fiber

cross section does not have much effect on the pressure drop in

the range of the cases considered in this study

Considering all other cases shown in Figure 10 shows that the

blockage ratio can be considered the only important geometrical

characteristics of fiber web Clean channel pressure drop (
Po)

and Reynolds number are also considered to include the effect

of the microchannel geometry as well as flow rate Using all thenumerical results shown in Figure 10, except the results of fiberweb #10, a nondimensional correlation was developed for thepressure drop in the channel with a fiber web at the entrance,

as a function of blockage ratio, Reynolds number (based onhydraulic diameter), and the pressure loss in the correspondingclean channel, which is as follows:

the correlation and numerical results is 1.8%, which shows good

agreement Fiber web #9, which has inclined fibers, also follows

the trend of the preceding correlation as shown in the Figure 10

forβ = 0.425

The authors were encouraged to investigate whether the fibers

symmetric orientation and lengths have any effect on the

pres-sure drop Therefore, a random fiber web was considered To

generate a random fiber web, a set of 1000 fibers with

ran-dom position (x,y), ranran-dom length (l), and ranran-dom orientation

(θ) was produced The geometric centers of the fibers were

forced to be on the channel cross section Six fibers were

se-lected randomly from this set The sese-lected fibers were

de-termined if they had at least two supports This random web

is mentioned as fiber web #10 in Table 1 The results of the

pressure drop for this random fiber web with blockage ratio

of 0.396 are shown in Figure 10, which confirms the

accu-racy of the correlation 15 even for the random distribution

of the fibers The results of Figure 10 show that the pressure

drop is independent of the fibers’ orientation and length and

the only effective parameters on the pressure drop in a

mi-crochannel with entrance fiber web are blockage ratio as well as

Reynolds number and the pressure drop in corresponding clean

geometry

Particle Deposition

Another subject studied in this research is the particle

de-position in the fiber web and the microchannel For this aim,

silica spherical microparticles with diameters of 2, 4, 6, and 8

µm are considered The result of the particle deposition study

showed that across the channel length no noticeable

deposi-tion of the particles occurs This is due to the relatively high

shear stress of the flow near the microchannel’s walls The

av-erage shear stresses on the center line at the bottom wall of

the microchannel are 16.6, 24.2, and 31.9 Pa for total flow

rates of 35, 51, and 67 mL/min, respectively It should be

noted these values for the shear stress are relatively high pared to those for the channels and ducts with conventionalsizes

com-In order to study particle deposition on the fiber web, 900 ferent locations distributed uniformly in the inlet of the plenumare considered Particles are injected to the flow from thesepoints separately The trajectory and the deposition location ofparticles are computed The results show that the particle moves

dif-on the path line passing through the injectidif-on point of the cle until it reaches the fiber web region In this region, where theflow path lines directions change sharply, most of the particlesadapt themselves to the path lines and leave the region But afew particles deposit on the fiber web because of the interception

parti-or inertial impaction effect The number of deposited particlesincreases for higher particle diameters, fluid flow rate, and thenumber of fibers in the fiber web As mentioned, no particlesdeposit through the channel and most of the deposited particlestrap on the fiber web The maximum deposition ratio corre-sponds to the highest studied flow rate and particle diameter (8µm) in the case of fiber web #5, which is about 7% of injectedparticles For the cylindrical fibers, particle deposition is lowercompared with rectangular fibers (fiber web #6) In this case themaximum deposition ratio is about 3.3% of injected particles.Figure 11 shows the injection and deposition locations for thecenters of the 8-µm particles in total flow rate of 67 mL/min forfiber webs #3, #5, #6, and #10 in the streamwise cross sections.This figure shows that there is a high resemblance between theinjection and deposition locations of the particles Analysis ofthe data for the collected particles showed that the particlesdeposit by two main mechanisms: interception and inertial im-paction Inertial impaction is a direct function of Stokes number

of the particle [13]

Stk=ρpdp u◦

18µdf

(16)where uoand dfare face velocity and fiber diameter, respectively

By increasing the velocity of the flow and the particle diameter,

Figure 12 The center trajectory of a deposited particle and the path line passes through the injection point: (A) particle diameter of 2 µm (Stk = 0.05); (B) particle diameter of 8 µm (Stk = 0.91).

heat transfer engineering vol 32 nos 7–8 2011

the deposition with inertial impaction increases Also, it was

observed that interception is another important mechanism of

deposition

Particles with higher Stokes number due to their inertia

can-not adjust quickly to the abruptly changing streamlines near the

fibers and cross those streamlines to hit the fibers This

phe-nomenon is illustrated in Figure 12 In Figure 12, one deposited

particle trajectory and the path line passing through the

injec-tion locainjec-tion of the particle are shown in a side view for two

different particle diameters of 2 and 8µm It is obvious that

the smaller particle does not leave the corresponding path line

and deposition occurs due to interception The Stokes number

for this particle using the flow velocity around the fiber web

is equal to 0.05 The figure also shows that for higher particle

diameter and Stokes number, the particle can leave the path line

and the deposition is affected by inertial impaction The Stokes

number for this 8-µm particle and this special flow rate is equal

to 0.91 A Stokes number near unity shows that the inertia effect

is enough to overcome the drag force and the particle can depart

from the corresponding streamline

Heat Transfer

To study the effect of the fiber webs at the channel entrance

on the heat transfer characteristics, various cases of the fiber

webs, #2, #3, #5, and #10, were considered The solid part of

the channel substrate is added to the computational domain for

each case to get correct heat transfer results Performance of the

channel was studied using the coefficient of performance (COP)

defined in Eq (3) The comparison was made between a clean

microchannel and various fiber webs at the inlet of channel in

the same pumping power To reach the same pumping power of a

clean microchannel, various inlet mass flow rates were tried for

the cases including the fiber webs For the heat transfer

investi-gation, the maximum substrate temperature of the channel is set

Figure 13 Dissipated heat flux from the microchannel for various total

pump-ing powers for a clean microchannel and microchannels with various fiber webs

at maximum substrate temperature of 80 ◦C.

Figure 14 Coefficient of performance (COP) for various total pumping powers for a clean microchannel and microchannels with various fiber webs at maximum substrate temperature of 80 ◦C.

to be 80◦C Thus, the energy equation is also solved by tryingvarious heat fluxes on the solid substrate to reach the maximumlimit of the temperature Figure 13 shows the dissipated heat fluxfor channels with various fiber webs and different total pumpingpowers As expected, by increasing the pumping power and flowrate, the dissipated heat will be increased On the other hand,fiber webs decrease the dissipated heat flux The fibers at theinlet of the channel cause an increase in the pressure drop, so theflow rate must be decreased for constant pumping power For

a lower flow rate, the capacity of heat dissipation from the crochannel decreases Thus, the heat flux at constant pumpingpower and maximum substrate temperature would be a function

mi-of the blockage ratio By increasing the blockage ratio, the heatflux decreases The maximum decrease of the heat flux in thisstudy happens for the case of fiber web #5 with pumping power

of 1.54e-3W

Figure 14 compares the COP of the clean microchannel andthe microchannels with the mentioned fiber webs consideredfor heat transfer study As shown, under constant pumpingpower as the fiber web blockage ratio increases, the COP of themicrochannel decreases The fiber webs have small effect onthe heat transfer characteristic of the microchannel The max-imum decrease of the COP of 3.4% happens in the smallestpumping power case for the fiber web #5 It should be notedthat by increase of the pumping power, the COP decreasesconsiderably

CONCLUSIONS

In this research a numerical study was presented for theeffect of a fiber web on the pressure drop, the collection ofmicroparticles, and heat transfer in a microchannel Ten variousfiber webs were considered in the investigation

The present study showed that fiber webs have a considerableeffect on the pressure drop in the microchannel A correlationheat transfer engineering vol 32 nos 7–8 2011