Heat transfer engineering an international journal, tập 31, số 2, 2010

Since the electric field is applied to the test section by a DC high voltage power supply, the electrode attached to a modified automotive spark plug serves as the charged electrode and

e d i t o r i a l

Selected Papers on Improving Heat

Transfer via Electrohydrodynamic

Technique

MAJID MOLKI

Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

Heat transfer processes may be substantially improved with

the aid of electrohydrodynamic (EHD) technique The

improve-ment may be in the form of enhanced convective heat transfer

coefficient, better mass removal in condensers, or it may lead to

a special cooling arrangement such as spot cooling of

electron-ics components The improvement may also be achieved when

the technique is used to control and change the thermal capacity

of a heat exchange device via a variable convective coefficient

Regardless of the specifics of the application, EHD introduces

a novel approach in thermal engineering

This special issue is devoted to thermal-fluid processes that

may benefit from electrohydrodynamics There are six articles

in this issue The cover photo is an application in which the

condensate drainage in evaporators is improved by the

elec-trowetting technique High voltage is applied to electrodes, and

the resulting electrostatic forces reduce the contact angle of the

condensate, leading to better condensate drainage

Electrowet-ting technique is discussed in the article by Kim and Kaviany,

which explains how it facilitates a more efficient removal of

condensate in heat exchangers

The EHD technique has been shown to improve the

two-phase heat transfer The article by Laohalertdecha et al

ad-dresses the use of EHD in enhancing evaporation of refrigerant

R-134a inside smooth and micro-fin tubes Despite the beneficial

effects of EHD on evaporation, there is a pressure drop penalty

associated with this technique Using the enhancement factor, it

Address correspondence to Professor Majid Molki, Department of

Me-chanical and Industrial Engineering, Southern Illinois University Edwardsville,

Edwardsville, Illinois 62026-1805, USA E-mail: mmolki@siue.edu

is shown in the article that, for the range of parameters of thisinvestigation, the heat transfer enhancement is sufficiently large

to compensate for the pressure drop penalty

Another application of EHD is in the design of micropumpsfor pumping liquid nitrogen In the article by Foroughi et al.,two designs of a micropump are presented which differ in theshape of their emitters The pump is intended to circulate nitro-gen for the cryogenic spot cooling of electronics components.With this technique, a cooling strategy may be devised to ap-ply more cooling to locations which are likely to develop hotspots

The EHD technique is especially effective at low velocities,such as flows driven by the buoyancy force In the article byKasayapanand, the technique is applied to natural convection

in a finned channel where the flow and heat transfer are nificantly influenced at lower values of Rayleigh number Theeffects of electrode arrangement and number of electrodes onflow and heat transfer are discussed, and an optimum inclinationangle for the channel is recommended

sig-In the article by Kamkari and Alemrajabi we also see anexample of the EHD application for convective mass transfer Inthis case, high voltage is applied to a wire electrode positionedabove water surface to ionize the air and to generate coronawind, which leads to a higher rate of evaporation from water.The enhancement of water evaporation relies on disturbing thesaturated air layer over the water surface At higher air velocities,the layer is already disturbed and the enhancement effect of EHDdiminishes Therefore, as is the case in buoyancy-driven flows,this technique seems to be more effective in enhancement ofmass transfer at lower air velocities

99

Another aspect of the EHD technique is that, under certain

operating conditions, the flow becomes unstable and oscillates,

because the electric bodyforce and inertia compete with each

other to control the flow In the article by Lai and Tay, the

EHD technique is applied to gas flow in a parallel-plate channel

to investigate the oscillatory motions generated by EHD It is

shown that heat transfer is improved under these conditions

Moreover, heat transfer may be further improved if the primary

flow is excited at a frequency similar to those generated by the

EHD technique

The articles presented in this issue are by no means

exhaus-tive; they are intended to represent a limited set of examples

from a diverse list of possible applications in thermal

engineer-ing I hope you find the topics fascinating and helpful to yourown research and engineering practice

Majid Molki is professor of mechanical

engineer-ing at Southern Illinois University Edwardsville He received his Ph.D from University of Minnesota in

1982 With many years of teaching and research rience in thermal sciences, his research interests are electrohydrodynamic enhancement of heat transfer, electronics cooling, and flow boiling of refrigerants.

expe-He has published extensively in technical journals and conference proceedings He is the Associate Edi-

tor of Heat Transfer Engineering, member of ASME,

member of the American Physical Society, and member of Alpha Chi Chapter

of Pi Tau Sigma honor society.

heat transfer engineering vol 31 no 2 2010

Electrowetting Purged Surface

Condensate in Evaporators

JEDO KIM and MASSOUD KAVIANY

Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

Condensate electrowetting purge in evaporators (heat exchangers) based on the force balance at the three-phase contact

line (TCL) is used in a prototype heat exchanger The electrowetting is described based on overcoming the static three-phase

contact line friction and detailed droplet physics is presented Series of experiments was performed under various conditions

and it was found that electrowetting combined with hydrophobic coating improves the drainage rate by as much as factor of

three Observations show that fins subjected to electrowetting are cleared of liquid droplets, in contrast to the fins which are

not Based on the proposed physics and experimental data, optimized electrode designs for future reference are proposed.

INTRODUCTION

Dropwise condensation occurs when moist air flows in

re-frigeration or air-conditioning evaporators, and can block the air

passage and degrade the performance, thus requiring periodic

water surface droplet or frost purging (Emery and Siegel [1], Na

and Webb [2], and Ren et al [3]) Surface modifications have

been devised to reduce the critical angle at which a given volume

surface droplet begins to slide under gravity These include the

recent study by Adamson [4], who achieved a 50% reduction

in the volume needed for the onset of droplet sliding, using a

micro-grooved (directional) aluminum surface However, these

passive surface modification techniques are not suitable for

ver-satile operating conditions and active control of the condensate

We examine theoretical and experimental aspects of purging

surface droplets by electrowetting, a phenomenon based on the

interaction of the electrostatic, gravity and surface forces In

analyzing the electrowetting process a detailed description of

the dynamics at the three-phase contact line (TCL) is required

However, the classical hydrodynamics cannot fully describe the

motion of the TCL Several strategies have been introduced to

resolve the problem (deGennes [5], Oron [6], and Pismen [7])

These approaches have been used exclusively for dynamic

anal-ysis by estimating the friction force as a product of the friction

We are thankful for useful discussions with Hailing Wu, Michael

Heiden-reich and Steve Wayne of Advanced Heat Transfer LLC, and Jeffrey Bainter of

Circle Prosco, Inc.

Address correspondence to Professor Massoud Kaviany, Department of

Me-chanical Engineering, University of Michigan, Ann Arbor, Michigan

48109-2125 E-mail: kaviany@umich.edu

coefficient and the velocity of the contact line Little is knownabout the static contact line friction just prior to initiation ofTCL motion Nevertheless, since liquid droplets, unlike solidobjects, undergo significant topological changes in response toexternal forces, it is possible to estimate the force necessary toinitiate motion of TCL by examining the topological observ-ables (local radius meniscus curvature, local contact angle, etc.)

at the critical inclination angle The dynamics of the static forcebalance at the TCL have been investigated and the three regimes(gravity dominated, intermediate and surface force dominated)have been identified as shown in Figure 1 (Kim and Kaviany[8]) It was found that the critical inclination angle at an ap-plied potential follows the constant Bo line which suggests thatthe electrostatic force reduces the contribution of the surfaceforces Here, we review the physics behind condensate purgeusing electrowetting Using this physical understanding, elec-trowetting technique is applied to enhance the drainage rate of

a prototype heat exchanger Furthermore, ideal implementationconcepts are presented for future reference

THEORETICAL ANALYSIS Fundamentals of Surface Forces

Liquids form a spherical cap with a well-defined equilibriumcontact angle θc,o or spread across the surface as a thin filmwhen condensed or injected onto a solid surface The preciseequilibrium that determines the topology of a droplet is the bal-ance between the liquid–gas σlg, solid–liquid σsl, and gas–solid101

Figure 1 The critical inclination angle with respect to droplet volume for

three regimes (gravity dominated, intermediate and surface force dominated).

The theoretical curve fit of the experimental results are presented along with

data from [4].

σgsinterfacial tensions This balance of forces is represented by

the free energy at the contact line

F if =
A iσi − λV (1)where λ is the Lagrangian multiplier for the constant volume

constraint, A is area, V is the liquid volume and λ is equal to

the capillary pressure
p across the liquid-gas interface

Mini-mization of the free energy leads the following two conditions

which govern the topology (meniscus) of droplet (Adamson [4]

and Israelachvili [9]) The first is the meniscus Laplace equation

which states that
p is constant over the entire interface

p= σlg

1

r1 + 1

r2



(2)

where r1 and r2 are the two principal radii of curvature of

the meniscus The Laplace equation shows that for

homoge-neous substrates, liquid droplets adopt a spherical cap shape

in mechanical equilibrium The other is the contact line Young

equation

cos θc,o= σsg− σsl

σlg

(3)This relates the interfacial tension to the apparent contact an-

gle θc,o Figure 2a shows the contact angle and the surface

ten-sion in equilibrium for liquid droplet on a horizontal surface For

the relevant scale, often, it is possible to adopt a one-dimensional

model of the contact line, where the three interfacial tensions are

pulling on TCL For a liquid on an inclined surface, the ratio of

the surface forces to gravity is represented by the Bond number

(Bo = ρgD2sin ϕ/σ lg), where ρ is the density of the liquid,

Figure 2 Balance of forces at the TCL for (a) ϕ = 0 ◦and (b) ϕ > 0◦.

g is the gravitational constant and D is the droplet diameter.

We consider moderate Bond numbers (Bo= 0.8–2.5), so thedroplet motion is moderately influenced by gravity For a plateinclination angle ϕ, the mass center of the droplet shifts towards

the advancing side, giving rise to the local capillary pressure
p

at the liquid–gas interface The opposite phenomenon exits onthe receding side TCL of the advancing side is pinned due tothe contact line friction and is not allowed to advance until acritical inclination angle is reached Then at the advancing side,according to Eq (2), reduction in the radius of curvature occursand causes the contact angle to increase At the receding side,

reduction of the local capillary
p requires a larger radius of

curvature and this results in a smaller contact angle This ference between the advancing and receding contact angles isreferred to as the contact angle hysteresis and is shown in Figure2b As seen in the figure, the force balance at the TCL is mod-ified due to the presence of contact line friction From the point

dif-of surface tension equilibrium at the TCL, the contact angle

hys-teresis can be modeled as the addition of friction, f s (per unitlength), to the σslat the advancing side and subtraction of fric-

tion, f s , at the receding side The radial component of f svariesalong the azimuthal angle ζ, thus, the contact angle varies from

θc,a,maxto θc,othen to θc,r,min The contact angle hysteresis and

the retention force (the sum of f s over the entire contact line)can be related using following equation for circular droplets,

F s = kσ lg R(cos θc,r − cos θc,a) (4)

where k is a constant, R is the length scale representing the

size of the meniscus, and θc,r and θc,a are the receding and

advancing contact angles Here k depends on the topology of the

droplet and is found empirically using the measured recedingheat transfer engineering vol 31 no 2 2010

inclination angle can be found Elsherbini and Jacobi [10, 11]

have performed a comprehensive empirical analysis of droplets

on aluminum substrates, with commercially available coatings

They propose an empirical relation between the Bond number

and the ratio of the receding and advancing contact angles, i.e.,

θc,a

θc,r

This relationship is used to estimate the retention force over

the entire range of Bond numbers

Electrowetting

Extensive electrowetting studies have been done with spatial

dimensions where gravity effects are negligible (Bond

num-ber tending to zero) in the areas such as microfluidics or

mi-croelectronics (Berge and Peseux [12], Srinivasan et al [13],

and Yun et al [14]) Figure 3 renders the contact angles

af-fected by electrowetting To relate the applied voltage to the

change in the effective surface tension, the

thermodynamic-electrochemical, energy minimization, and electromechanical

approach have been used (Berge [15], Jones [16], and Jones

[17] All of these approaches converge to a single well-accepted

electrowetting relation which is presented subsequently Here

the electromechanical approach is reviewed which was first

in-troduced by Jones [16] and starts from the Korteweg-Helmholtz

body force density (Landau and Lifschitz [18])

where E is the electric field vector, ρ f is the fluid charge

den-sity, ρ and ε are the mass density and the dielectric constant of

the liquid The last term in Eq (6) describes the electrostriction

and can be neglected If we assume that the liquid is perfectly

conductive, integrating Eq (6) over the entire volume is

equiva-lent to integrating the Maxwell stress tensor over the liquid-gas

interface

F e =



Figure 3 Rendering of electrowetting of the surface droplet on a dielectric

coated substrate The net charge distribution is also shown.

where δik is the Kronecker delta and n is the normal direction.

The tangential component of the electric field at the surfacevanishes and the normal component is related to the local surfacecharge density through ρs = εo ε E • n Now noting that every

term except the component directed along the outward surfacenormal vanishes, Eq (7) becomes

1

The field and charge distribution are found by solving theelectrical Laplace equation for the electrostatic potential withthe appropriate boundary conditions Both the field and chargedistributions diverge upon approaching the contact line [19].Therefore, the Maxwell stress is maximum at the contact lineand exponentially decays with distance from the contact line

After integration using
ϕ = − E • n ds, where
ϕ is the

voltage drop across the interface, the horizontal component ofthe Maxwell stress is

electrode underneath the dielectric layer Ideally, as the potential

is increased, the electrowetted contact angle approaches zero.However, it is found that the contact angle saturates at a value

θc,sat varying between 30◦ and 80◦, depending on the system(Moon et al [20] and Peykov et al [21]) This contact anglesaturation can be explained as an electron-discharge mechanism,together with the vertical component of the electrostatic forceacting on the contact line (Kang [22])

heat transfer engineering vol 31 no 2 2010

Physics of Droplet Purge Initiation

Physics of the electrowetting assisted purge of droplets can be

analyzed using a simple force balance at TCL At TCL, a force

of per unit length is applied in the radial direction as predicted

by Eq (10) As a result, the x component of the electrowetting

force will vary as the cosine of the azimuthal angle ζ In contrast,

the contact line friction is constant along TCL in the x direction,

since it is assumed that the friction is a reaction force existing

only in the x direction and that droplet weight is uniformly

distributed at liquid–solid interface Note that the integral of the

contact line friction at the critical inclination angle is equal to

the retention force, which is given by Eq (4) By curve fitting the

data points under no electrowetting conditions, the magnitude of

kfrom the experiment was found to be 1.845 Then according to

the classical droplet mechanics and by using the retention force

data, the sum of the forces at the critical inclination angle can

We have assumed that the applied forces are concentrated at

TCL, as graphically represented in Figure 4 From the figure we

see that the contact line of the advancing side will start to slip

when the electrowetting overcomes the local static contact line

friction value at the location of θc,a,max As f ebecomes larger

with increase in potential, the portion of the contact line which

Figure 4 Graphical representation of balance between the retention and

elec-trowetting forces, at the advancing TCL.

begins to slip increases Also, as the contact line begins to slip,

it causes an instantaneous reduction in the advancing contactangle When the advancing contact angle is reduced, according

to Eq (12), the retention force is reduced which results in ering of the critical inclination angle (for given liquid volume).When a sufficient portion of the contact line friction is removed,the bulk liquid motion is initiated In sum, the sequence ofliquid motion under electrowetting can be described as first,

low-at the onset of motion, the droplet is charged and experienceselectrowetting which overcomes the static TCL friction Whenthe sum of the gravity and electrowetting force is larger thanthe static friction over the entire contact line of the droplet, thebulk condensate motion is initiated As the droplet advances,the electrostatic energy is dissipated and dewetting becomesapparent When the droplet recovers its original topology, it ex-periences a rise in electrostatic energy due to its proximity tothe over-hanging electrode and this sequence is repeated Usingthe preceding droplet physics, prediction of the electrowettingreduction of the critical inclination angle is possible by using

a simple force balance at the TCL The observation indicatesminimum or no advancing of receding contact line until the ad-vancing contact line has well advanced, thus, it is reasonable toassume that the dominant criteria for the initiation of the dropletmotion is the force balance at the advancing contact line (Kim[8]) As long as the droplet is not separated, this treatment ofthe force on the contact line is valid The retention force can beestimated using Eq (4) with the empirical contact angle relation(5) The electrowetting force can be calculated by integrating

the x component acting on TCL over the azimuthal angle for

the advancing portion of the droplet Then by solving for theinclination angle which the gravity balances, the resultant ofthe retention force and the electrowetting force, it is possible

to obtain a theoretical prediction of the variation of the criticalinclination angle with the applied potential This angle is found

by solving the following equation

φ= sin−1

⎛

⎝

π 2

EXPERIMENTAL ANALYSIS Implementation of Electrowetting in Heat Exchangers

The theoretical analyses in the preceding sections have cated that by using electrowetting droplet motion initiation atheat transfer engineering vol 31 no 2 2010

indi-prediction to practical application, a series of experiments were

designed and performed Figure 5 presents a detailed picture

of an electrowetting assisted droplet purge in prototype heat

ex-changers manufactured by AHT (Advanced Heat Transfer) The

heat exchangers were coated with a dielectric layer (polymer

based electric insulation coating ε= 2.4 and θc,o= 70◦) with

200 µm in thickness A second polymer-based P4 (ε= 3.0 and

θc,o= 110◦) hydrophobic coating (Circle Prosco, Bloomington,

IN, USA) with 300 µm in thickness was coated on top of the first

layer Subsequently, horizontal and vertical copper electrodes

where installed between the fins of the heat exchangers via

ex-Figure 5 Image of initiation of droplet purge using electrowetting using

ver-tical electrodes, for different elapsed times The environmental conditions are

THX = 0.2 ◦C, relative humidity= 80% and exposed time duration of 60 mins.

The location of the droplet is indicated using arrows Note the contrast between

fins with and without electrowetting.

condition for 60 min The heat exchanger surface temperature

T H X was measured to be 0.2◦C When condensation began toform, electric potential of 600 V was applied The experimentwas photographed using a DSLR camera with a 1:1 macrolens.The figure shows that there exists clear contrast between thefins which have been subjected to electrowetting forces andthe ones which were not The droplets which were formed un-der heat exchanger operations have either been purged or onthe verge of purge for the fins which have electrodes, whereassignificant droplet retention is observed on the fins which donot have electrodes Figure 6 shows the drainage rate (mass ofwater drained per unit time) normalized with respect to base(no coat) heat exchanger of different passive and active surfacetreatments The data show approximately 150% improvement

in drainage rate compared to heat exchanger with no coat Also,for manual target excitation (where electrodes were manuallybrought in proximity to the droplets), there was approximately290% increase in the drainage rate showing significantly im-proved drainage potential when optimization is achieved Inlight of previously shown potential-improvement of drainagerate in heat exchangers, we present a ideal conceptual design inwhich the electrowetting assisted drainage can be implemented

in a full scale heat exchanger Figure 7 shows one of the timized implementations of electrowetting technique in heatexchangers The heat exchanger is coated with a hydrophobicdielectric coating and the electrodes are suspended between thefins via external frame The electrodes are vertically oriented

op-to minimize the blockage of liquid droplets Although there

Figure 6 Drainage rate for prototype heat exchangers with different passive and active droplet-retention prevention methods The drainage rates have been normalized with respect to base (no coat) heat exchanger.

heat transfer engineering vol 31 no 2 2010

Figure 7 Conceptual rendering of one of the optimized electrode designs

which utilizes electrowetting as an active means of purging of droplets.

still exist many challenges in electric isolation and current lack

of high performance coating, in the future, we expect that these

kinds of electrowetting assisted drainage in heat exchangers will

significantly reduce the water retention rate thereby improving

the heat exchanger performance by many folds

CONCLUSION

Electrowetting purged surface condensate in evaporators has

been investigated using physics of the force balance at the

three-phase contact line Using a prototype heat exchanger, the theory

was applied to investigate the improvement of drainage

un-der electrowetting conditions Significant improvements—up to

290% increase in the drainage rate—were observed paving the

way to a full scale implementation of physics using

elecrowet-ting as the means of condensate purge Based on the theoretical

insight and the preliminary experimental investigation, we

pro-pose an electrode-heat exchanger design which will enhance thecurrent performance of the evaporator By using the new elec-trowetting implemented heat exchanger design and overcomingthe following challenges: need for enhanced electrical insula-tion, high performance dielectric coating and polished find tip,

it is expected that the evaporator performance will increase bymany folds

ρf liquid charge density, C/m3

ρs surface charge density, C/m3

σij i − j interfacial tension, N/m

Subscripts

c,a advancing contact angle

c,e electrowetted contact angle

c,o equilibrium contact angle

c,r receding contact angle

[1] Emery, A F., and Siegel, B L., Experimental Measurements of

the Effects of Frost Formation on Heat Exchanger Performance,

In Proceedings of AIAA/ASME Thermophysics and Heat Transfer

Conference, Heat and Mass Transfer in Frost and Ice packed Beds

and Environmental Discharges, pp 1–7, 1990.

[2] Na, B., and Webb, R L., New Model for Frost Growth Rate,

International Journal of Heat Mass Transfer, vol 47, no 5, pp.

925–936, 2004

[3] Ren, H., Fair, R B., Pollack, M G., and Shaughnessy, E J.,

Dynamics of Electro-Wetting Droplet Transport, Sensors and

[6] Oron, A., Long-Scale Evolution of Thin Liquid Films, Reviews of

Modern Physics, vol 69, pp 931–980, 1997.

[7] Pismen, L M., Mesoscopic Hydrodynamics of Contact Line

Mo-tion, Colloids and Surfaces A, vol 206, pp 11–30, 2002.

[8] Kim, J., and Kaviany, M., Purging of Dropwise Condensate by

Electrowetting, Journal of Applied Physics vol 101, pp 103520–

103527, 2007

[9] Israelachvili, J N., Intermolecular and Surface Forces, 1st edition,

Academic, San Diego, California, 1985

[10] Elsherbini, A I., and Jacobi, A M., Liquid Drops on Vertical and

Inclined Surfaces I An Experimental Study of Drop Geometry,

Journal of Colloid and Interface Science, vol 273, pp 556–565,

2004

[11] Elsherbini, A I., and Jacobi, A M., Liquid Drops on Vertical and

Inclined Surfaces ii A Method for Approximating Drop Shapes,

Journal of Colloid and Interface Sci., vol 273, pp 566–575, 2004.

[12] Berge, B., and Peseux, J., Variable Focal Lens Controlled by an

External Voltage: An Application of Electrowetting, The

Euro-pean Physical Journal E, vol 3, pp 159–163, 2000.

[13] Srinivasan, V., Pamula, V K., and Fair, R B., An Integrated Digital

Microfluidic Lab-on-a-Chip for Clinical Diagnostics on Human

Physiological Fluids, Lab on a Chip, vol 4, pp 310–315, 2004.

[14] Yun, K S., Bu, I J., Bu, J U., Kim, C J., and Yoon, E., A

Surface-Tension Driven Micropump for Voltage and

Low-Power Operations, Journal of Microelectromechanical Systems,

vol 11, pp 454–461, 2002

1993

[16] Jones, T B., On the Relationship of Dielectrophoresis and

Elec-trowetting, Langmuir, vol 18, pp 4437–4443, 2002.

[17] Jones, T B., An Electromechanical Interpretation of

Electrowet-ting, Journal of Micromechanics and Microengineering, vol 15,

pp 1184–1187, 2005

[18] Landau, L D., and Lifschitz, E M., Electrodynamics of

Continu-ous Media, Pergamon, Oxford, UK, 1960.

[19] Vallet, M., Vallade, M., and Berge, B., Limiting Phenomena for

the Spreading of Water on Polymer Films by Electrowetting, The

European Physical Journal B, vol 11, pp 583–591, 1999.

[20] Moon, H., Cho, S K., Garrell, R L., and Kim, C J., Low Voltage

Electrowetting-on-Dielectric, Journal of Applied Physics, vol 92,

pp 4080–4087, 2002

[21] Peykov, V., Quinn, A., and Ralston, J., Electrowetting: A Model

for Contact-Angle Saturation, Colloid and Polymer Science, vol.

278, pp 789–793, 2000

[22] Kang, K H., How Electrostatic Fields Change Contact

An-gle in Electrowetting, Langmuir, vol 18, pp 10318–10322,

2002

Jedo Kim is a Ph.D student at the Heat Transfer

Physics lab, Department of Mechanical ing, University of Michigan, Ann Arbor He received his M.S from University of Michigan and his B.S from University of Toronto (2004) Currently, he is working in atomic-level heat regeneration using anti- Stokes luminescence.

Engineer-Massoud Kaviany is Professor of Mechanical

Engi-neering and Applied Physics at University of gan, since 1986 His Ph.D is from University of California-Berkeley His education-research field is heat transfer physics.

Michi-heat transfer engineering vol 31 no 2 2010

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903285369

The Effect of the

Electrohydrodynamic on the

Two-Phase Flow Pressure Drop

of R-134a during Evaporation inside Horizontal Smooth and Micro-Fin

Tubes

SURIYAN LAOHALERTDECHA,1JATUPORN KAEW-ON,1,2

and SOMCHAI WONGWISES2

1Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE), Department of Mechanical

Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

2Department of Physics, Faculty of Science, Thaksin University, Papayom, Phattalung, Thailand

This article concerns the pressure drop caused by using the electrohydrodynamic (EHD) technique during evaporation of

pure R-134a inside smooth and micro-fin tubes The test section is a counter-flow concentric tube-in-tube heat exchanger

where R-134a flows inside the inner tube and hot water flows in the annulus A smooth tube and micro-fin tube having an

inner diameter of 8.12 mm and 8.92 mm, respectively, are used as an inner tube The length of the inner tube is 2.50 m The

outer tube is a smooth copper tube having an inner diameter of 21.2 mm The electrode, which is a cylindrical stainless steel

wire having diameter of 1.47 mm, is placed in the center of the inner tube The electrical field is established by connecting

a DC high voltage power supply of 2.5 kV to the electrode while the inner tube is grounded Experiments are conducted

at saturation temperatures of 10–20◦C, mass fluxes of 200–600 kg/m 2 s, and heat fluxes of 10–20 kW/m 2 The experimental

results indicate that the application of EHD introduces a small pressure drop penalty New correlations for the pressure drop

are proposed for practical applications.

INTRODUCTION

Normally, heat transfer enhancement techniques can be

di-vided into two groups: namely passive techniques and active

techniques The passive techniques require special surface

ge-ometries, such as rough surface or extended surface The active

techniques require external forces, such as fluid vibration,

sur-face vibration, and an electrical field An electrohydrodynamic

(EHD) technique is one of the types of active techniques, which

The present study was supported financially by the Joint Graduate School

of Energy and Environment (JGSEE) and the Thailand Research Fund (TRF)

whose guidance and assistance are gratefully acknowledged.

Address correspondence to Professor Somchai Wongwises, King Mongkut’s

University of Technology Thonburi, 126 Pracha-utid Road, Bangmod,

Toongkru, Bangkok 10140, Thailand E-mail: somchai.won@kmutt.ac.th

can be achieved by the interaction between the electrical fieldand the flow of dielectric fluid medium This interaction createsadditional fluid motion which leads to a higher heat transfercoefficient The electrical body force density acting on the fluidelement of dielectric fluid in the presence of an electrical fieldcan be expressed as:

of inhomogeneous or spatial change in the permittivity of thedielectric fluid due to non-uniform electrical fields, temperature108

Source Refrigerant Test section Electrode geometry condition the test section Singh et al [1] R-123 Smooth stainless steel tube Cylindrical stainless steel

electrode having diameter of 3 mm

T sat = 27.52 ◦C Hot water

G = 50–400 kg/m 2 s Inlet quality = 0–0.5 Singh et al [2] R-134a Smooth stainless steel tube Cylindrical stainless steel

electrode having diameter of 3 mm

T sat = 20.15 ◦C Hot water

G = 50–400 kg/m 2 s Inlet quality = 0–0.5 Salehi et al [3] R-404A Micro-fin copper tube Cylindrical stainless steel

wire having diameter of 0.46 mm

T sat = 20.15 ◦C Electric heater

Length = 304.8 mm Helical electrode G = 50–200 kg/m 2 s

ID = 8.92 mm, OD = 9.84 mm

Average quality = 0–0.8 Salehi et al [4] R-134a 1 Smooth copper tube Cylindrical rod Re =500, 1000 Electric heater

2 Corrugated copper tube with helical angle of 18 with height of ridge of 0.25 mm

Bryan and Seyed-Yagoobi [5] R-134a Smooth copper tube Cylindrical brass rod

electrode having diameter of 1.6 mm

T sat = 4.9–25.1 ◦C Hot water

Length = 100, 200, 300,

500 mm (connecting in series)

Inlet quality = 0–0.8

Cotton et al [6] R-134a Smooth stainless steel tube Cylindrical stainless steel

electrode having diameter of 3.175 mm

T sat = 24 ◦C Hot water

Inlet quality = 0–0.6

gradients, and phase differences The third term is caused by

inhomogeneous electrical field strength and the variation in

di-electric constant with temperature and density

Heat transfer enhancement during evaporation using EHD

has been published in the literature Some of the works were

performed by Singh et al ([1, 2]), Salehi et al [3, 4], Bryan and

Seyed-Yagoobi [5] and Cotton et al [6] as shown in Table 1

It can be noted that the mass fluxes of the reported test tubes

are almost all below 300 kg/s.m2 As a consequence, the

ob-jective of this study is to study the pressure drop penalty from

the use of electrohydrodynamic technique during evaporation of

R-134a flowing in a horizontal smooth tube and micro-fin tube

at high mass flux conditions

EXPERIMENTAL APPARATUS

The experimental apparatus can be divided into two parts: the

refrigeration test unit and the direct current (DC) high voltage

power supply unit A schematic diagram of the test apparatus is

shown in Figure 1 This experimental apparatus was designed tomeasure the heat transfer coefficient and pressure drop of pureR-134a over the length of the test tube

The test loop consists of a test section, refrigerant loop, ing water flow loops, sub-cooling loop, and the relevant instru-mentation For the refrigerant circulation loop, liquid refrigerant

heat-is pumped by a magnetic gear pump which heat-is regulated by aninverter The refrigerant flows in series through a filter/dryer, asight glass tube, and enters the test section The inlet quality be-fore entering the test section is controlled by the pre-heater Thepre-heater is a spiral counter flow heat exchanger that suppliesenergy to control inlet quality of the refrigerant The refriger-ant leaving the test section is then condensed and sub-cooled

by the chilling loop that removes heat load receiving from thepre-heater and, returns from the two-phase refrigerant to a sub-cooled state and later collects in a receiver and eventually returns

to the refrigerant pump to complete the cycle

The test section as shown in Figure 2 is a horizontalcounter-flow double tube heat exchanger The length of theheat exchanger is 2.5 m Refrigerant temperature and the tubeheat transfer engineering vol 31 no 2 2010

Figure 1 Schematic diagram of experimental apparatus.

Figure 2 Schematic diagram of test section.heat transfer engineering vol 31 no 2 2010

wall temperatures in the test section are measured by T-type

thermocouples A total of eighteen thermocouples are soldered

at the top, bottom and side at six points along the tube All

the temperature measuring devices are well calibrated in a

controlled temperature bath using standard precision mercury

glass thermometers The uncertainty of the temperature

mea-surements after considering the data acquisition system is ±

0.1◦C All static pressure taps are mounted in the tube wall The

refrigerant flow meter is a variable area type The flow meter is

specially calibrated in the range of 0–8.3× 10−3m3/min for

R-134a by the manufacturer The differential pressure transducer

and pressure gauges are calibrated against a primary standard,

the dead weight tester A stainless steel cylindrical electrode,

1.47 mm in diameter, is used in all experiments The cylindrical

electrode is supported in the center of the test section by

electri-cally insulating spacers (Teflon type material) at intervals of 250

mm The electrode is attached to the spacers by using a special

epoxy-resin Since the electric field is applied to the test section

by a DC high voltage power supply, the electrode attached to a

modified automotive spark plug serves as the charged electrode

and the heat transfer surface as the receiving electrode

The dimensions of the smooth and micro-fin tubes are shown

in Table 2 The cross-section of micro-fin tube is shown in

Figure 3 The cross-section of micro-fin tube.

Mass flow rate of refrigerant, ˙m ref ±2% Full scale

Heat transfer rate at test section, ˙Q T S ±11% Heat transfer rate at pre-heater, ˙Q ph ±8%

Figure 3 The inlet water temperature is controlled by a mostat A differential pressure transducer and thermocouplesare installed at the test section to measure the pressure dropand temperature across the test section respectively The lengthbetween the pressure taps is 3 m

ther-It is necessary to realize that the maximum voltage beforestarting the electrical breakdown in the test section must beknown and should not be exceeded during any steady-statecondition Before the two-phase experiment was performed,the heat balance between refrigerant-side and water-side of thesingle-phase experiment was conducted The uncertainties ofthe heat balance were within 8% and 5% for the pre-heater andthe test section, respectively The uncertainties of the measuredquantities and calculated parameters are shown in Table 3

DATA REDUCTION

The data reduction of the measured results can be rized as follows:

summa-The inlet vapor quality of the test section (xT S,in)

x T S,in= i T S,in − i f @T T S,in

where i f is the enthalpy of the saturated liquid based on the

temperature of the test section inlet, i f gis the enthalpy of

vapor-ization based on the temperature of the test section inlet, i T S,in

is the refrigerant enthalpy at the test section inlet and is givenby:

be-˙

Q ph = ˙m w,ph c p,w (T w,in − T w,out)ph (4)where ˙m w,ph is the mass flow rate of water entering the pre-heater

The outlet vapor quality of the test section (xT S,out)

x T S,out = i TS,out − i f @T TS,out

i f g @T TS,out

(5)heat transfer engineering vol 31 no 2 2010

where i T S,outis the refrigerant enthalpy at the test section outlet,

i fis the enthalpy of the saturated liquid based on the temperature

of the test section outlet, and i f gis the enthalpy of vaporization

As a consequence, the outlet enthalpy of the refrigerant flow is

A inside (T avg,wall − T avg,sat) (8)

where h avg is the average heat transfer coefficient, ˙Q T S is the

heat transfer rate in the test section, T avg,wall is the average

temperature of the wall, T avg,sat is the average temperature of

the refrigerant at the test section inlet, and outlet

T avg,sat= T in,sat + T out,sat

A insideis the inside surface area of the test section:

A inside = πD f L (10)

where D f is the inside diameter of the test tube L is the length

of the test tube The inside diameter of the micro-fin tube is

defined as the outer diameter of the micro-fin tube minus twice

the minimum wall thickness

RESULTS AND DISCUSSION

In general, the EHD technique can provide enhancement of

heat transfer However, the heat transfer enhancement should be

considered together with pressure drop penalty In the present

study, the effects of electrode, supporter, mass fluxes, saturation

temperatures, heat fluxes, and applied voltage of 2.5 kV on

the pressure drop during evaporation of R-134a inside smooth

and micro-fin tubes are experimentally investigated The test

conditions were selected to cover as much as possible of the

range of inlet quality The pressure drop is the sum of a frictional

pressure drop and a momentum pressure drop The pressure drop

per unit length is obtained by dividing the measured pressure

drop by the length between pressure taps In our apparatus, the

length between pressure taps is 3 m, while the length of the heat

exchanger is 2.5 m

There are two phenomena that are usually encountered

in-side EHD-enhanced smooth and micro-fin tubes [7] The first is

the liquid-extraction phenomenon When a coaxial cylindrical

electrode is used with a smooth tube, the highest electrical field

is at the electrode surface due to its small radius of curvature

Figure 4 Liquid-extraction phenomenon [7].

since the liquid surface extends into the gas toward the electrode

as shown in Figure 4 The second is the electro-convection nomenon When a coaxial cylindrical electrode is used with amicro-fin tube, the highest electrical field is at the tip of the findue to its small radius of curvature (sharp) since the liquid inter-face is pulled toward the tip of the fin, as shown in Figure 5 Bothliquid-extraction and electro-convection phenomena generate asecondary fluid motion inside the tube leading to increase inheat transfer and pressure drop

phe-Figures 6 and 7 show the comparisons of the measured sure drop inside smooth and micro-fin tubes for the absence of

pres-an electrode, the presence of pres-an uncharged electrode (0 kV),and the presence of a charged electrode (2.5 kV) The test con-ditions are performed at the saturation temperature (Tsat) of

20◦C, heat flux (q”) of 10 kW/m2, and mass flux (G) of 400kg/m2s The measured pressure drop in the absence of an elec-trode is obtained by Wongsa-ngam et al [8] These figures alsoshow that the pressure drops obtained from both tubes increasewith increasing inlet quality At the same quality, the pressuredrop obtained with the presence of an uncharged electrode (0kV) is higher than that with the absence of an electrode up to

Figure 5 Electro-convection phenomenon [7].

heat transfer engineering vol 31 no 2 2010

Figure 6 Pressure drop versus inlet quality for smooth tube at Tsat = 20 ◦C,

G = 400 kg/m 2 s and q  = 10 kW/m 2

100% for smooth tube and 80% for micro-fin tube This is

be-cause the supporter and electrode obstruct the fluid flow The

pressure drop obtained with the presence of a charged electrode

is slightly higher than that with the presence of an uncharged

electrode at the same inlet quality because of the instabilities

at the liquid-vapor interface resulting from the molecules of

refrigerant disturbed by the EHD force

Figures 8 and 9 show the variation of the measured pressure

drop with inlet quality of pure R-134a during evaporation in the

smooth and micro-fin tubes for the presence of an uncharged

electrode (0 kV) and for the presence of a charged electrode

(2.5 kV) at a saturation temperature of 20◦C and heat flux of 20

kW/m2for different mass fluxes of 200, 400, and 600 kg/m2s

These figures show that the measured pressure drops obtained

from the presence of an uncharged electrode (0 kV) and the

presence of a charged electrode (2.5 kV) increase with

increas-Figure 7 Pressure drop versus inlet quality for micro-fin tube at Tsat = 20 ◦C,

on the pressure drop can be clearly seen at higher inlet quality,i.e., the pressure drop is much higher for a higher mass fluxthan that for a lower mass flux The application of EHD seems

to be negligible for almost all pressure drops obtained from thebroadest range of inlet quality

Figures 10 and 11 show the variation of the measured ration pressure drop with inlet quality in the smooth and micro-fin tubes for the presence of an uncharged electrode (0 kV) andthe presence of a charged electrode (2.5 kV) at a mass flux of 400kg/m2 s and saturation temperature of 20◦C for different heatfluxes of 10, 15 and 20 kW/m2 These figures also show that

evapo-Figure 9 The effect of mass flux on the pressure drop for micro-fin tube at

Tsat = 20 ◦C and q = 20 kW/m 2 heat transfer engineering vol 31 no 2 2010

Figure 10 The effect of heat flux on the pressure drop for smoth tube at

Tsat= 20 ◦C and G= 400 kg/m 2 s.

the pressure drops for both smooth and micro-fin tubes with

the presence of an uncharged electrode (0 kV) and the

pres-ence of a charged electrode (2.5 kV) increase with increasing

inlet quality It can be seen that pressure drop increases with

increasing heat flux This is because more vapor bubbles are

created at higher heat flux This phenomenon promotes more

agitation in the fluid flow, leading to the increase in pressure

drop Application of EHD voltage of 2.5 kV also has a slight

effect on the pressure drop in a wide range of inlet qualities

Figures 12 and 13 show the variation of the measured

evapo-ration pressure drop with inlet quality in the smooth and

micro-fin tubes for the presence of an uncharged electrode (0 kV) and

the presence of a charged electrode (2.5 kV) at a mass flux of

400 kg/m2s, heat flux of 20 kW/m2and different saturation

tem-peratures of 10, 15 and 20◦C These figures also show that the

pressure drops increase slightly with increasing inlet quality As

Figure 11 The effect of heat flux on the pressure drop for micro-fin tube at

Figures 14 and 15 show the comparisons of the average sured evaporation heat transfer coefficient obtained from thesmooth tube with that obtained from the micro-fin tube at amass flux of 400 kg/m2 s, a heat flux of 20 kW/m2, and satu-ration temperatures of 20◦C for the presence of an unchargedelectrode and a charged electrode, respectively It can be clearlyseen that the heat transfer coefficient increases with increasinginlet quality Both in the presence of uncharged electrode andcharged electrode, the heat transfer coefficient obtained from

mea-Figure 13 The effect saturation temperature on the pressure drop for fin tube at Tsat = 20 ◦C and G= 400 kg/m 2 s.

micro-heat transfer engineering vol 31 no 2 2010

Figure 14 Heat transfer coefficient versus inlet quality for the presence of an

uncharged electrode at Tsat= 20 ◦C, G= 400 kg/m 2 s, and q  = 20 kW/m 2

the microfin tube are higher than that obtained from the smooth

tube at the same inlet quality

In the case of a smooth tube, with the presence of charged

electrode, due to liquid extraction phenomenon, the liquid-vapor

interface becomes unstable This causes the average heat transfer

coefficient to be higher than in the case of uncharged electrode

In the case of micro-fin tube, due to electro-convection

phe-nomenon, the liquid interface was pulled toward the tip of the

fin causing the increase of heat transfer coefficient

Figures 16 and 17 show the heat transfer coefficient ratio

(hratio ), pressure drop ratio (
P/L) ratioand enhancement factor

((hratio )/(
P/L) ratio) with inlet quality at a saturation

tempera-ture of 20◦C, heat flux of 20 kW/m2and mass flux of 400 kg/m2

s in smooth and micro-fin tubes, respectively The heat

trans-fer coefficient ratio (hratio) is defined by havg,e/havg,o, where

havg,e is the heat transfer coefficient with the presence of a

charged electrode (2.5 kV) and havg,o is the heat transfer

co-efficient with the presence of an uncharged electrode (base

Figure 15 Heat transfer coefficient versus inlet quality for the presence of a

charged electrode at Tsat= 20 ◦C, G= 400 kg/m 2 s, and q  = 20 kW/m 2

Figure 16 The heat transfer ratio and the pressure drop ratio versus inlet quality for smooth tube at Tsat= 20 ◦C, G= 400 kg/m 2 s, and q  = 20 kW/m 2

case, 0 kV) The pressure drop ratio ((
P/L) ratio) is defined

by [(
P/L) e /(
P/L) o ], where (
P/L) eis the pressure drop with

the presence of a charged electrode (2.5 kV) and (
P/L) o isthe pressure drop with the presence of an uncharged electrode(base case, 0 kV) From these figures it can be seen that heattransfer coefficient ratio and pressure drop ratio are decreasedwith an increase in inlet quality The heat transfer coefficientratios are all higher than the pressure drop ratio The enhance-ment ratios (hratio /(
P/L) ratio) are almost always higher than 1

in the whole range of the tested inlet quality It can be explainedthat the slight pressure drop penalty is compensated by the heattransfer augmentation

Correlation for Predicting Pressure Drop

The two-phase friction pressure gradient (dp F /dz) of smoothand micro-fin tubes may be expressed in term of two-phase

Figure 17 The heat transfer ratio and the pressure drop ratio versus inlet quality for micro-fin tube Tsat= 20 ◦C, G= 400 kg/m 2 s, and q  = 20 kW/m 2 heat transfer engineering vol 31 no 2 2010

multiplier φ2l defined as follow:

φ2l =



dp F dz



/



dp F dz

where (dp F /dz)l and (dp F /dz)vare the single-phase liquid and

vapor pressure gradients (kPa/m) calculated by using the actual

phase flow as follows:

Rev= GDx

µv

(18)

Figure 18 Predicted pressure drop versus the measured pressure drop.

Figure 19 Predicted pressure drop versus the measured pressure drop.

For micro-fin tube the relative roughness (e/D) in Eqs (15)

and (17) are replaced by the equation: Cavalini and Zecchin [9]:

e/D = 0.18(e f /D t )/(0.1+ cos β) (19)

where e f is the fin height D t is the fin tip diameter β is thespiral angle

For smooth tube, empirical correlation shown in Eq (20) isdeveloped based on the presence of a charged electrode It is

created by fitting the Martinelli parameter (X) against a

ex-For micro-fin tube, the empirical correlation shown in Eq.(21) is developed based on the presence of a charged electrode

It is created by fitting the Martinelli parameter (X) against a

ex-CONCLUSIONS

The present article reports the pressure drop penalty fromthe application of EHD force on evaporation heat transfer en-hancement of R-134a in horizontal smooth and micro-fin tubes.The pressure drop obtained from the presence of an unchargedheat transfer engineering vol 31 no 2 2010

Pressure drop results from both smooth and micro-fin tubes

in-dicate that the application of an EHD voltage of 2.5 kV slightly

increases the pressure drop across the range of tested

condi-tions The enhancement ratio is almost always higher than 1

The present correlation can predict the pressure drop within a

deviation of±25% for smooth tube and ±30% for micro-fin

tube, respectively

NOMENCLATURE

A inside inside surface area of test section (m2)

A c cross section area (m2)

c p specific heat at constant pressure (J/kg-K)

D h hydraulic diameter (m)

D o outside tube diameter (m)

D f inside tube diameter (m)

e f fin height (m)

E electric field strength (V/m)

f e EHD force density (N/m3)

β spiral angle (degree)

e presence of an uncharged electrode

fg difference in property between saturated liquid and

Two-Boiling Analysis, International Journal of Heat and Mass Transfer,

vol 48, pp 5563–5579, 2005

[7] Singh, A., Ohadi, M M., and Dessiatoun, S., EHD Enhancement

of In-tube Condensation Heat Transfer of Alternate Refrigerant

R-134a in Smooth and Microfin Tubes, ASHRAE Transactions:

[9] Cavallini, A., and Zecchin, R., A Dimensionless Correlation for

Heat Transfer Coefficient in Forced Convection Condensation,

In-ternational Journal of Heat and Mass Transfer conference, pp.

193–200, 1974

heat transfer engineering vol 31 no 2 2010

Suriyan Laohalertdecha is currently a Ph.D student

at the Joint Graduate School of Energy and ronment, King Mongkut’s University of Technology Thonburi, Bangmod, Thailand He received his Mas- ter’s degree in energy technology from the same de- partment in 2005 He also received his B.Eng degree from the Department of Mechanical Engineering at the same university in 2002 Currently, his research works concern heat transfer enhancement.

Envi-Jatuporn Kaewon is currently a Ph.D student at the

Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangmod, Thailand He received his Master’s degree

in energy technology from the same department in

2003 He also received his B.Eng degree from the Department of Mechanical Engineering at the same university in 1999 He is also currently a lecturer at Thaksin University.

Somchai Wongwises is a Professor of Mechanical

Engineering at King Mongkut’s University of nology Thonburi, Bangmod, Thailand He received his Doktor-Ingenieur (Dr.-Ing.) in mechanical engi- neering from the University of Hannover, Germany,

Tech-in 1994 His research Tech-interests Tech-include two-phase flow, heat transfer enhancement, and thermal sys- tem design Professor Wongwises is the head of the Fluid Mechanics, Thermal Engineering and Multi- phase Flow Research Lab.

heat transfer engineering vol 31 no 2 2010

Experimental Characterization of an Electrohydrodynamic Micropump for Cryogenic Spot Cooling Applications

PARISA FOROUGHI,1AMIR SHOOSHTARI,1SERGUEI DESSIATOUN,1

and MICHAEL M OHADI2

1Smart and Small Thermal Systems Laboratory, Department of Mechanical Engineering, University of Maryland, College

Park, Maryland, USA

2Academic Affairs, The Petroleum Institute, Abu Dhabi, United Arab Emirates

This article presents a study on the characterization of a planar, multistage, electrohydrodynamic (EHD) ion-drag micropump

for pumping of liquid nitrogen Two designs of the pump, consisting of different emitter configurations (flat and saw-tooth),

similar emitter-collector spacing (50 microns), and similar gaps between successive electrode pairs (100 microns), were

tested at DC voltages ranging from 0 to 2.5 kV The electric currents they generated and the corresponding static pressure

heads were measured to characterize the pumping performance Pressure and current onset voltages as well as

pressure-voltage (P-V) and pressure-current (P-I) relationships were investigated The highest pressure head (30 Pa at 1700 V) was

generated with the saw-tooth design After collecting and processing the data for various prototypes, it was evident that

incorporating saw-tooth electrodes can significantly improve the performance of the micropump.

INTRODUCTION

A new electronic era began with the discovery of

high-temperature superconducting (HTSC) materials in 1987 HTSC

components, which operate in temperatures from 20 K up to

138 K, are being incorporated into communication and

elec-tronic monitoring devices to increase their signal-to-noise ratio

or their channel capacity These devices must be maintained at

cryogenic temperatures to prevent the loss of their

supercon-ducting properties and to retain their performance superiority

They are conventionally cooled via direct heat conduction to

the cold fingers of a cryocooler, which limits their spatial

con-figuration and can lead to undesirable temperature differences

among the various components being cooled [1–3]

Compact electrohydrodynamic (EHD) micropumps capable

of pumping liquid nitrogen at 77 K into liquid-cooling circuits

would enable a much more compact and lightweight method of

maintaining a uniform temperature across the cooling circuit

Besides providing precise flow control, EHD pumps, which

have no moving parts, would not vibrate the electronic devices

Address correspondence to Parisa Foroughi, Smart and Small Thermal

Sys-tems Laboratory, University of Maryland, Potomac Building (Bldg#092), Rm

1105, College Park, MD 20742 E-mail: foroughi.parisa@gmail.com

being cooled and would ultimately help to isolate them from thetypical mechanical vibrations of the cryocooler

Although a significant amount of research has been ducted on the EHD pumping phenomenon in ambient condi-tions, cited by Foroughi et al [4], the authors have found only alimited number of studies with cryogenic liquids [5, 6] There-fore, a thorough characterization of EHD micropumps for cryo-genic applications could be important for advancing the liquidcooling technology for devices containing HTSC materials, andfor bioengineering applications in which a small dose of LN2needs to be delivered to a particular spot

con-The work summarized in this article focuses on ing the feasibility of the EHD ion-drag pumping phenomenon inliquid nitrogen and on studying the effect of electrode geometry

demonstrat-on the performance A more comprehensive study demonstrat-on cal characterization of the micropump can be found in Foroughi[7]

geometri-EHD PUMPING PHENOMENON

The EHD ion-drag pumping phenomenon refers to liquid tion caused by an interaction between electric and hydrodynamic119

mo-fields in a dielectric liquid In an drag pump, the

ion-injection phenomenon is the key process for generating ions

The pumping effect occurs when a sufficiently high electric

po-tential difference is applied between a pair of electrodes, called

the emitter and collector The ions are generated mostly at the

emitter/liquid interface and move towards the collector because

of the electric force (i.e., the Coulomb force) Friction between

the moving ions and neutral molecules drags the working fluid

and induces fluid motion The Coulomb force density F

act-ing on a dielectric fluid with free space-charge density of ρe,

subjected to an electric field E is given by Melcher [8]:

For successful pressure generation, the abundance of one

ion polarity (i.e., the unipolar condition) is preferred, since the

generation of an equal number of ions of both polarities would

result in no net pumping, as positive and negative ions offset

the dragging action of each other The charge injection process

highly depends on the electrochemical characteristics of the

working liquid, the electrochemistry of the electrode material,

the strength of the electric field, and the electrode geometry

The pumping performance relies heavily on the electrical and

mechanical properties of the working fluid such as permittivity

ε, conductivity σ, and viscosity µ Generally, high permittivity

and low viscosity are required for high pumping performance

As shown in Eqs (2) and (3), demonstrated by Crowley [9, 10]

and Crowley et al [11], velocity of the fluid flow u and pressure

P are expected to show quadratic increase with electric field E

and channel depth h:

u≈ εE2h2

More studies on theoretical aspects of EHD pumping

mecha-nism can be found in Stuetzer [12, 13], Pickard [14, 15], Melcher

[8], and Seyed-Yagoobi et al [16]

For a given liquid and electrode material, geometrical

consid-erations are the most important factors in the design The shape

of the electrode and the distance between them can strongly

influence the magnitude and direction of the electric field and

therefore impact the rate of electric charge generation at the

electrode/liquid interface One example is the saw-tooth shaped

electrodes, which can substantially enhance the ion generation

due to the creation of a very high electric field [17],

some-times on the order of a few megavolts per meter at the electrode

tips

In this study, the electrode design is restricted to flat and

saw-tooth shapes for a clear comparison of the effect of electrode

geometry on the onset voltage value and pressure generation

Figure 1 Micropump components.

MICROPUMP DESIGN, FABRICATION AND PACKAGING

The micropump in this study was composed of an aluminasubstrate on which multistage gold electrodes of submicronthickness were microfabricated, a top-cover with an embeddedchannel and integrated inlet and outlet ports, and a bottom plate,

as shown in Figure 1 All the components were bonded together

by a cryogenic-compatible epoxy paste adhesive (Figure 2).Two micropump designs were selected to study the effect

of electrode geometrical pattern on the performance These signs had different emitter shapes and similar inter-electrodespacing, electrode-pair spacing, and channel heights as summa-rized in Table 1 Figure 3 displays sectional views of a couple

de-of electrode pairs with different emitter shapes

The micropumps were tested in a test rig specifically signed to measure static pressure head and electric current gen-eration (caused by the migration of ions from one electrode toanother) in a closed loop at different DC voltages

(50,100,f) 50 100, 2D el 50 —— —— f 79

Note.

-f & s: electrode shapes (flat & saw-tooth)

-D el : emitter-collector inter-electrode spacing

-D pel : electrode-pair (stage) spacing

-L el : electrode base width

-L st : saw-tooth width

-α : tooth angle

-H ch : channel height (260 µm).

shown in the figure), the micropump, a differential pressure

transducer (Validyne DP-15, range: 0–866 Pa, accuracy:± 0.1

Pa), a liquid nitrogen reservoir, and stainless steel tubing with

an outer diameter of 3.17 mm and a wall thickness of 0.25 mm

The Dewar flask with an inner diameter of 150 mm enclosed

the test loop properly A few temperature sensors were installed

inside the Dewar flask to monitor the temperatures at different

locations A foam lid isolated the interior space of the Dewar

flask from the outside environment

To prepare the test rig for the experiments, the system

ini-tially underwent a high vacuum (about 40 millitorr) and was

then completely submerged in liquid nitrogen at 77 K All the

Figure 3 Different micropump electrode designs.

components in the Dewar flask were submerged except the sure transducer, which was positioned at a higher elevation out-side the flask The external nitrogen gas tank was then used tofeed ultra-pure (99.998%) nitrogen gas into the test section Theliquid nitrogen reservoir acted as a nitrogen-gas container forliquefaction purposes The liquid nitrogen then flowed from thereservoir into the test section and filled it

pres-After the system was fully charged with liquid nitrogen, lium gas at a gauge pressure of about 120 kPa was added tokeep the LN2subcooled during tests and to prevent the forma-tion of micro-bubbles (the boiling temperature of helium at agauge pressure of 120 kPa is 5.2 K) During the experiment,the electric power consumption in the pump usually created

he-a loche-al temperhe-ature increhe-ase in the system, which could lehe-ad

to micro-bubble formation and partial discharge (PD) ing to Krahenbuhl et al [18], pressurizing the system greatlyreduces the PD intensity and raises the inception stress Theoxygen boiling point at a gauge pressure of 120 kPa is 98.3 K,much higher than that of LN2 (i.e., 84.5 K at 120 kPa gaugepressure), making it easily condensable into LN2 In addition,oxygen is a highly reactive substance and can lead to signif-icantly inaccurate measurements Since our experiments wererun in a closed, well-vacuumed system, however, the possibility

Accord-of oxygen solubility in LN2was greatly reduced

Figure 4 Schematic diagram of the test section.

heat transfer engineering vol 31 no 2 2010

Figure 5 Experimental results of a (50,100,s) design Positive voltage

polar-ity (0–1600 V) was applied to the emitter while the collector was grounded.

After the test rig was stabilized, the bypass valve was closed

and tests were performed by applying DC voltages ranging from

0 to 2.5 kV with positive polarity (unless otherwise stated) at

different increments to the micropump The pressure head of the

micropump was measured directly by the differential pressure

cell, and the generated electric current was measured by an

external electric resistant circuit and a data acquisition system

(DAS)

EXPERIMENTAL RESULTS AND ANALYSIS

Figure 5 shows an example of data taken with a (50,100,s)

design with a 260 µm channel height (Hch) The (50,100,s)

no-tation corresponds to a Del= 50 µm, and Dpel= 100 µm,

saw-tooth shaped emitter and flat collectors The static pressure head

and generated electric current (caused by the migration of ions

from one electrode to another) are plotted versus time The

pos-itive voltage polarity was applied to the emitter electrodes, and

the collector electrodes were grounded The voltage increased

slowly from 0 until the pumping onset occurred at around 1000

V From then on, the voltage was increased in increments of 100

V until it reached 1600 V To avoid the possibility of an

elec-trical breakdown, the voltage was not increased further After

a few minutes, the voltage was incrementally decreased until it

reached zero

The data set shown above was reduced by taking the time

average of pressure and current data points at each voltage

in-crement and plotting them versus the applied voltage, as shown

in Figure 6 According to the graph, the onset voltage of pressure

head and current for this design was around 1000 V

Onset Voltage

One of the determining factors in selecting the proper

mi-cropump design is the onset voltage As with most

microelec-tromechanical devices, the trend is to lower their electric power

consumption to make them compatible with microelectronic

Figure 6 P-V and I-V relationship for a micropump with saw-tooth trodes Positive voltage polarity was applied to the emitter while the collector was grounded.

elec-devices Therefore, it is necessary to have a clear estimation ofonset voltages for each micropump design and prototype.Onset voltage could not easily be calculated theoreticallydue to the complexity of the EHD phenomenon; therefore, amathematical approach was used to estimate its value from theexperimental data for every single design To do this, the equa-tion of the line connecting the first 2 data points in P-V and P-Icurves for every test was determined, and then the line inter-section with the voltage axis was calculated and defined as theonset

The onset voltages of pressure and current were calculatedseparately for many tests run with both designs and comparedagainst each other, as shown in Figures 7 and 8 Overall, themean values of pressure and current onset voltages were ex-pected to be identical, which was confirmed by the results.However, the uncertainty involved with the current was less thanthat of the pressure This could be mainly due to measurementerrors The measurement error of the current was within±1 nA,and the measurement error of the pressure was within±0.5 Pa

Figure 7 Onset voltage of pressure for different designs.heat transfer engineering vol 31 no 2 2010

Figure 8 Onset voltage of current for different designs.

A comparison of the results of the flat and saw-tooth designs

shows that the onset value of the saw-tooth shape emitter was

at least 100 V less than that of the flat shape emitter, as seen

in Figures 7 and 8 This can be explained by the difference

in their electrode geometries, which affects the local electric

field and therefore the onset value The electric field is fairly

constant between two flat electrodes with the (50,100,f) design

However, at the edge of the saw-tooth shaped emitters where the

curvature is very small, the local electric field intensity becomes

extremely high, which could eventually result in a lower onset

value compared to that of the flat electrode case

Also, these results indicate that the uncertainty of the

on-set measurement for the (50,100,f) design is much higher The

primary reason for this may be the accuracy of the onset

mea-surement The onset measurement is affected by the slope of the

P-V (or I-V) curve For flat electrodes, the pressure generation

occurs very gradually, making it difficult to define an exact

on-set value for this design On the other hand, pressure generation

elevation with saw-tooth electrodes occurs fairly rapidly at the

onset voltage, making the P-V slope quite distinguishable and

therefore more accurate

P-V Characteristic Curve

It was shown in Figure 5 that the generated pressure and

electric current relationships with voltage always resemble each

other in the general trend This clearly indicates that the ions

creating the electric current are also responsible for the pressure

generation This also demonstrates that the pressure head is

ac-curately controllable with the applied voltage, which is another

advantage of EHD micropumps

The experiment shown in Figure 5 was repeated 9 times using

the same test conditions Time-averaged pressure head values

are plotted versus applied voltage for all the tests in Figure 9

The best-fit line to the data, shown in the figure above,

re-sembles a parabola The equation of the curve is a second degree

Figure 9 Pressure data points represent the result of nine series of tests run with a (50,100,s) design when ( +) voltage polarity was applied to the emitter (0–1700 V).

polynomial function, as given by Eq (4):

in liquid nitrogen can be found in [3]

The mean values of a plotted in the figure above indicate

that at a given voltage, incorporating saw-tooth shaped emittersgenerated a much higher pressure head Both designs had similarcharacteristics in every aspect except the emitter geometry Asmentioned earlier, electrode geometry plays an important role increating ions at the emitter/liquid interface [17, 19]; therefore, a

Figure 10 Parameter of the P-V model of different designs tested with ( +) voltage polarity applied to the emitters.

heat transfer engineering vol 31 no 2 2010

Figure 11 P-I characteristic of a (50,100,s) micropump with H ch = 260 µm.

The slope is 0.014 Pa/nA.

saw-tooth shaped emitter with stronger injection sites compared

to flat shaped electrodes is expected to generate higher pressure

heads

P-I Relationship

As was shown earlier in Figure 6, the generated pressure head

as a function of applied voltage represents a trend very similar

to that of the electric current versus applied voltage As a result,

the current is expected to have a linear relationship with the

pressure, realizing both pressure and current were direct results

of ion generation and transportation To investigate this and to

demonstrate an example, all pressure values were plotted versus

their corresponding generated current at every voltage for all

nine tests run with one prototype, shown in Figure 11

These results demonstrate that the P-I slope remains

un-changed for all the tests run with one unit, although it sometimes

varied from one unit to another Therefore, it is appropriate to

say that for each micropump, the generated pressure head is a

linear function of current,

where m is the slope of the P-I line The m value is believed to be

affected by ion mobility of the working liquid and geometrical

parameters of the design such as electrode geometry, spacing,

and channel height In this article, only the effect of electrode

geometry on the performance is analyzed using designs with

different emitter shapes The slope of the P-I linear model for

both designs is plotted in Figure 12 These data points are the

averages of all the m values collected during extensive hours of

testing with many units

Comparing the m values, it is clear that at a certain current,

prototypes of the saw-tooth design generated the highest

pres-sure head This behavior, as mentioned previously should be

attributed to the lower number of ion generation sites per flat

electrodes as well as the lower electric field intensity compared

to the saw-tooth design

Figure 12 Slope of the P-I linear model.

Repeatability Analysis—Micropump Life Cycle

On many occasions, after running consecutive tests on severalmicropumps, three operation stages were observed: the initial,the intermediate, and the final stages During the initial operatingstage (the burn-in period), when the pump was being tested forthe first few times, the micropump performance was random,inconsistent, and hardly repeatable As testing on the pumpcontinued, the performance became more repeatable after a longtime, often exceeding 10 hours of operation, at which point, theintermediate stage was established The final stage set in asdegradation in the pressure head and the measured current wereobserved At this stage, keeping the pressure head as high asits previous level required increased voltage In other words,

in the final stage, the coefficient of the P-V characteristic curvedecreased and the pumping onset voltage moved to higher levels

Repeatability Analysis—Effect of Working Fluid

The main factor responsible for most of the uncertainty andnon-repeatability of the test results was believed to be impurities

in the working liquid or inside the system itself High-puritynitrogen was used in this research; however, there was still thepossibility of impurity molecules entering the system duringthe liquid charging process Dissociation of impurity moleculescreates positive and negative ions, which, under the influence

of an electric field, can not only lead to additional input powerrequirements for the pump, but also can affect the net force onthe liquid and alter the pressure head [11]

Only a few basic studies have been reported in literature onEHD phenomena in cryogenic conditions, and available infor-mation is mainly limited to electrochemical behavior of LN2under intense electric fields Byatt and Secker [20] did not findthe conduction current data in LN2 to be accurately repeatablefrom day to day Comparing their data from air and LN2, theyheat transfer engineering vol 31 no 2 2010

Ionization in Liquids,” reported “erratic and noisy emission

at low currents” and that “it was not possible to see a

well-defined tunneling regime” in LN2 Nitrogen is in fact a very

inert substance, but impurity molecules that enter the system

and which might get dissolved in the working liquid can

sub-stantially change the electrochemical properties of the liquid

and cause non-repeatable test results for consecutive runs

Generally, in ion-drag EHD pumps, high electric field

gradi-ents can affect the liquid molecular structure and cause corrosion

of the electrodes, which can affect run-to-run repeatability and

reduce the pump’s lifetime For this reason, liquid nitrogen was

expected to be a better choice for ion drag pumping compared

to other refrigerants since its molecular structure is highly

sta-ble However, during system charging, there is no practical way

to prevent all contaminants (including dissolved gases) from

entering into the system Depending on the nature of the

con-taminants under high electric voltage, the impurity molecules

can become ionized and add an unidentified number of ions into

the system or even lead to electric discharges The electric

dis-charges can result in a local temperature rise and can eventually

melt spots of the electrode This phenomenon was observed in

this investigation when the micropump was disassembled after

many hours of operation

CONCLUSIONS

This article presented an experimental study on

micropump-ing liquid nitrogen, which can have a wide range of applications

in cryogenic liquid cooling devices, as well as in bioengineering

applications where a small dose of LN2 needs to be delivered

to a particular spot Although earlier studies had claimed EHD

pumping of liquid nitrogen, the present work appears to be the

first systematic study in micropumping liquid nitrogen for spot

cooling applications

Three repetitive operation stages were recognized during

ex-periments: the initial, the intermediate, and the final stage

The relationships between pressure-current (P-I) and

pressure-voltage (P-V) for two different designs were

inves-tigated experimentally The results demonstrated that

incorpo-rating saw-tooth electrodes was effective in decreasing the

pres-sure onset voltage as well as producing higher prespres-sure heads,

since saw-tooth shaped electrodes hold more ion-injection sites

compared to flat electrodes and are effective in increasing the

electric field intensity between electrodes

NOMENCLATURE

a Leading coefficient of the P-V equation (Pa.V−2)

Del Emitter-collector inter-electrode spacing

Dpel Electrode-pair (stage) spacing

E Electric field intensity

F Coulomb force density

ductivity Motor, Journal of Physics, vol 43, pp 780–783, 2006.

[2] Walker, G., Ellison, W., and Zylstra, S., Cryocoolers for the New

High-Temperature Superconductors, Journal of

Superconductiv-ity, vol 1, no 2, pp 197–209, 1988.

[3] Foroughi, P., Dessiatoun, S., Shooshtari, A., and Ohadi, M., perimental Characterization of an EHD Ion-Drag Micropump for

Ex-Cryogenic Micro-pumping Applications, in: Proc 2007 ASME

International Mechanical Engineering Congress and Exposition,

Seattle, Washington, IMECE2007-42177, 2007

[4] Foroughi, P., Benetis, V., Ohadi, M., Zhao, Y., and Lawler, J.,Design, Testing and Optimization of a Micropump for Cryogenic

Spot Cooling Applications, 21st Annual IEEE Semi-Therm

Sym-posium, 15–17 March 2005, pp 335–340, 2005.

[5] Rada, M., Shooshtari, A and Ohadi, M., Experimental andNumeral Simulation of Meso Pumping of Liquid Nitrogen—Application to Cryogenic Spot Cooling of Sensors and Detectors,

Sensors & Actuators: A Physical, in Press.

[6] Boyarintsev, V I., Kuznetsov, S F., Molotov, P E., and Parinov,

Yu V., Investigation of the EHD Effect in Liquid Nitrogen,

trans-lated from Inzhenerno-Fizichezkii Zhurnal, October 1992, vol 63,

[9] Crowley, J M., Fundamentals of Applied Electrostatics, John

Wiley & Sons, 1986

[10] Crowley, J M., The Efficiency of Electrohydrodynamic Pumps in

the Attraction Mode, Journal of Electrostatics, vol 8, pp 171–

181, 1980

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[11] Crowley, J M., Wright, G S., and Chato, J C., Selecting a

Work-ing Fluid to Increase the Efficiency and Flow Rate of an EHD

Pump, IEEE Transactions on Industry Applications, vol 26, no.

1, pp 42–49, 1990

[12] Stuetzer, O M., Ion Drag Pressure Generation, Journal of Applied

Physics, vol 30, no 7, pp 984–994, 1959.

[13] Stuetzer, O M., Ion Drag Pumps, Journal of Applied Physics, vol.

31, no 1, pp 136–146, 1960

[14] Pickard, W F., Ion Drag Pumping I Theory, Journal of Applied

Physics, vol 34, pp 246–250, 1963a.

[15] Pickard, W F., Ion Drag Pumping II Experiment, Journal of

Applied Physics, vol 34, pp 251–258, 1963b.

[16] Seyed-Yagoobi, J., Bryan, J E., and Castaneda, J A., Theoretical

Analysis of Ion-Drag Pumping, IEEE Transactions on Industry

Applications, vol 31, pp 469–476, 1995.

[17] Benetis, V., Experimental and Computational Investigation of

Pla-nar Ion Drag Micropump Geometrical Design Parameters, Ph.D.

Dissertation, University of Maryland, College Park, USA 2005.

[18] Krahenbuhl, F., Bernstein, B., Danikas, M., Densley, J., Kadotani,

K., Kahle, M., Kosaki, M., Mitsui, H., Nagao, M., Smit, J., and

Tanaka, T., Properties of Electrical Insulating Materials at

Cryo-genic Temperatures: a Literature Review, IEEE Electrical

Insula-tion Magazine, vol 10, no 4, pp 10–22, 1994.

[19] Mirotvorsky, V O., and Y K Stishkov, Influence of

Near-Electrode Reaction on Distribution of Electric Characteristics

of Electrodes-Liquid Dielectric System, in: 12th International

Conference on Conduction and Breakdown in Dielectric Liquids

(ICDL), 1996.

[20] Byatt, S W., and Secker, P E., Electrical Conduction in Liquid

Air and Liquid Nitrogen, British Journal of Applied Physics, vol.

2, no 1, pp 1011–1017, 1968

[21] Halpern, B., and Gomer, R., Field Ionization in Liquids, Journal

of Chemistry and Physics, vol 51, no 3, pp 1048–1056, 1969.

Parisa Foroughi received her Ph.D degree in

me-chanical engineering from University of Maryland, College Park in 2008, and subsequently joined Intel Corporation as a Sr Packaging Engineer Her main research interests include MEMS and microelectron- ics packaging, and electronics cooling systems She

is a member of ASHRAE and ASME.

Amir Shooshtari received his Ph.D degree in

me-chanical engineering from University of Maryland, College Park in 2004 Since 2005, he has been a member of research faculty at the University of Mary- land His research interests include electronics cool- ing, two-phase flow, fluid flow in porous media, and modeling of electrohydrodynamics He is the author

or co-author of over 15 publications in international journals and conferences He is a member of ASME and ASHRAE.

Sergeui Dessiatoun is an Associate Research

Pro-fessor of Mechanical Engineering at the University

of Maryland, College Park He has over 30 years of extensive experience in mechanical engineering de- sign including design and development of thermal and hydraulic loops, aerospace and space cooling systems, environmental control systems, refrigera- tion and heat transfer systems, heat engines, diesel and gasoline fuel injection systems, and electronic control systems He has been intrinsically involved

in the ongoing research in the Smart and Small Thermal Systems (S2TS) ratory at the University of Maryland He is the author or co-author of over 30 patents in the area of energy transfer and conversion, including the concept of force-fed heat transfer technology.

labo-Michael M Ohadi, Professor of Mechanical

En-gineering, directs the Advanced Heat Transfer and Electronic Cooling Consortium at the Center for En- vironmental Energy Engineering at the University

of Maryland, and is the Provost and Interim dent of the Petroleum Institute of Abu Dhabi, UAE Petroleum Institute and the University of Maryland have collaborative educational and research activi- ties in the field of Energy Sciences and Engineer- ing Prof Ohadi is internationally recognized for his work in enhanced heat and mass transfer in heat exchangers and energy sys- tems, has conducted many research projects for both industry and govern- ment, and has published widely in his field of expertise He is a fellow mem- ber of both ASME and ASHRAE, and has won numerous awards from both societies.

Presi-heat transfer engineering vol 31 no 2 2010

Electrohydrodynamic Induced Flow

and Heat Transfer in Vertical

Channel with Fin Array Attached

NAT KASAYAPANAND

School of Energy, Environment, and Materials, King Mongkut’s University of Technology, Thonburi, Bangkok, Thailand

Electrohydrodynamic heat transfer enhancement of natural convection inside the finned vertical channels is investigated

via a computational fluid dynamics technique The interactions between electric field, flow field, and temperature field are

numerically determined Flow and heat transfer enhancements are significantly influenced at low Rayleigh number The

effect of electrode arrangement and number of electrodes to the average velocity and Nusselt number are expressed An

optimum inclined angle of the channel is recommended Relation between the number of fins and fin length to the augmented

flow and heat transfer is also analyzed.

INTRODUCTION

Natural convection in an asymmetrically heated open-ended

vertical channel is encountered in various applications The early

research carried out by Bodoia and Osterle [1], Levy [2], and

Aung [3] The measured-predicted Nusselt numbers for natural

convection in a vertical channel was investigated by Sparrow et

al [4] This characteristic has been presented again by [5] Aung

and Worku [6] conducted the mixed convection from an

isother-mal vertical channel by the implicit finite difference technique

Modification of heat transfer in the channels due to introduction

of obstructs and fins attached to the wall has been the subject of

investigation in recent years However, the hydrodynamic

block-age effect by the fin and the degraded convection heat transfer

on an anchoring hot wall remain a significant problem

Convective heat transfer enhancement by

electrohydrody-namic (EHD) technique is caused by the polarization of

dielec-tric fluid The method is easily implemented, i.e., using only a

transformer and electrodes, consuming only a small amount of

electric power For the typical phenomenon in air molecules, the

secondary flow or ionic wind is generated from a wire electrode

to a grounded surface propelled by the Coulomb force resulting

The author gratefully acknowledges the financial support provided by the

Thailand Research Fund and Commission on Higher Education for this research.

Address correspondence to Professor Nat Kasayapanand, School of Energy,

Environment, and Materials, King Mongkut’s University of Technology,

Thon-buri, Bangkok 10140, Thailand E-mail: nat.kas@kmutt.ac.th

increasing momentum and heat transfer This technique deals

in the interdisciplinary field with subjects concerning the teractions between electric, flow, and temperature fields Thereare some studies relating to the electrohydrodynamic, for in-stance, Yabe et al [7] examined the phenomenon of a coronawind between wire and plate electrodes under natural convectionthat increased the heat transfer from the wall surface Velkoffand Godfrey [8] performed the heat transfer over a horizontalflat plate with parallel wire electrodes and found that the ionicwind promoted the mixing of primary flow resulting to the in-crease of heat transfer coefficient The computational method inthe electrostatic precipitator has been indicated by Yamamotoand Velkoff [9] The electrohydrodynamic phenomenon on nat-ural convection inside an enclosure with Joule heating effectwas studied by Huang and Lai [10] and Yang and Lai [11].Molki and Damronglerd [12], Molki et al [13], and Molki andHarirchian [14] investigated the corona wind augmented heattransfer in various applications via a new approach by explicitartificial viscosity to improve the solution of electric charge den-sity However, there is no previous literature concerning with theelectrohydrodynamic application to natural convection inside afinned vertical channel

in-The majority of the recent study deals with the EHD inducedflow and heat transfer in channel Moreover, increasing attention

is being focused on a fin array attached Governing equations

of electrohydrodynamic phenomenon are formulated and ematical modeling is utilized to investigate the electrohydro-dynamic enhanced secondary flow and heat transfer coefficient127