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

Heat Transfer Engineering, 31(2):99–100, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903285294 editorial 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 improvement 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 electronics 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 electrowetting technique High voltage is applied to electrodes, and the resulting electrostatic forces reduce the contact angle of the condensate, leading to better condensate drainage Electrowetting 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 twophase heat transfer The article by Laohalertdecha et al addresses 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 is shown in the article that, for the range of parameters of this investigation, the heat transfer enhancement is sufficiently large to compensate for the pressure drop penalty Another application of EHD is in the design of micropumps for pumping liquid nitrogen In the article by Foroughi et al., two designs of a micropump are presented which differ in the shape of their emitters The pump is intended to circulate nitrogen for the cryogenic spot cooling of electronics components With this technique, a cooling strategy may be devised to apply more cooling to locations which are likely to develop hot spots The EHD technique is especially effective at low velocities, such as flows driven by the buoyancy force In the article by Kasayapanand, the technique is applied to natural convection in a finned channel where the flow and heat transfer are significantly influenced at lower values of Rayleigh number The effects of electrode arrangement and number of electrodes on flow and heat transfer are discussed, and an optimum inclination angle for the channel is recommended In the article by Kamkari and Alemrajabi we also see an example of the EHD application for convective mass transfer In this case, high voltage is applied to a wire electrode positioned above water surface to ionize the air and to generate corona wind, which leads to a higher rate of evaporation from water The enhancement of water evaporation relies on disturbing the saturated air layer over the water surface At higher air velocities, the layer is already disturbed and the enhancement effect of EHD diminishes Therefore, as is the case in buoyancy-driven flows, this technique seems to be more effective in enhancement of mass transfer at lower air velocities Address correspondence to Professor Majid Molki, Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1805, USA E-mail: mmolki@siue.edu 99 100 M MOLKI 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 exhaustive; they are intended to represent a limited set of examples from a diverse list of possible applications in thermal engineer- heat transfer engineering ing I hope you find the topics fascinating and helpful to your own research and engineering practice Majid Molki is professor of mechanical engineering at Southern Illinois University Edwardsville He received his Ph.D from University of Minnesota in 1982 With many years of teaching and research experience in thermal sciences, his research interests are electrohydrodynamic enhancement of heat transfer, electronics cooling, and flow boiling of refrigerants He has published extensively in technical journals and conference proceedings He is the Associate Editor 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 vol 31 no 2010 Heat Transfer Engineering, 31(2):101–107, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903285302 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 refrigeration 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 versatile 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 analysis by estimating the friction force as a product of the friction We are thankful for useful discussions with Hailing Wu, Michael Heidenreich and Steve Wayne of Advanced Heat Transfer LLC, and Jeffrey Bainter of Circle Prosco, Inc Address correspondence to Professor Massoud Kaviany, Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 481092125 E-mail: kaviany@umich.edu coefficient and the velocity of the contact line Little is known about the static contact line friction just prior to initiation of TCL motion Nevertheless, since liquid droplets, unlike solid objects, undergo significant topological changes in response to external forces, it is possible to estimate the force necessary to initiate motion of TCL by examining the topological observables (local radius meniscus curvature, local contact angle, etc.) at the critical inclination angle The dynamics of the static force balance at the TCL have been investigated and the three regimes (gravity dominated, intermediate and surface force dominated) have been identified as shown in Figure (Kim and Kaviany [8]) It was found that the critical inclination angle at an applied potential follows the constant Bo line which suggests that the electrostatic force reduces the contribution of the surface forces Here, we review the physics behind condensate purge using electrowetting Using this physical understanding, electrowetting technique is applied to enhance the drainage rate of a prototype heat exchanger Furthermore, ideal implementation concepts are presented for future reference THEORETICAL ANALYSIS Fundamentals of Surface Forces Liquids form a spherical cap with a well-defined equilibrium contact angle θc,o or spread across the surface as a thin film when condensed or injected onto a solid surface The precise equilibrium that determines the topology of a droplet is the balance between the liquid–gas σlg , solid–liquid σsl , and gas–solid 101 102 J KIM AND M KAVIANY Figure 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] σgs interfacial tensions This balance of forces is represented by the free energy at the contact line Fif = Ai σi − 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 Minimization 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 r2 (2) where r1 and r2 are the two principal radii of curvature of the meniscus The Laplace equation shows that for homogeneous 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 angle θc,o Figure 2a shows the contact angle and the surface tension 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 = ρgD2 sin ϕ/σlg ), where ρ is the density of the liquid, heat transfer engineering Figure 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 the droplet motion is moderately influenced by gravity For a plate inclination 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 on the receding side TCL of the advancing side is pinned due to the contact line friction and is not allowed to advance until a critical inclination angle is reached Then at the advancing side, according to Eq (2), reduction in the radius of curvature occurs and 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 difference between the advancing and receding contact angles is referred to as the contact angle hysteresis and is shown in Figure 2b As seen in the figure, the force balance at the TCL is modified due to the presence of contact line friction From the point of surface tension equilibrium at the TCL, the contact angle hysteresis can be modeled as the addition of friction, fs (per unit length), to the σsl at the advancing side and subtraction of friction, fs , at the receding side The radial component of fs varies along the azimuthal angle ζ, thus, the contact angle varies from θc,a,max to θc,o then to θc,r,min The contact angle hysteresis and the retention force (the sum of fs over the entire contact line) can be related using following equation for circular droplets, Fs = kσlg 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 receding vol 31 no 2010 J KIM AND M KAVIANY and advancing contact angles at the critical inclination angle Knowing k and using the droplet force balance, the critical 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 = 0.01Bo2 − 0.155Bo + 0.97 θc,r (5) This relationship is used to estimate the retention force over the entire range of Bond numbers 103 where, T is the Maxwell stress tensor which is written as T ik = εo ε − δik |E|2 + E i E k where δik is the Kronecker delta and n is the normal direction The tangential component of the electric field at the surface vanishes and the normal component is related to the local surface charge density through ρs = εo ε E • n Now noting that every term except the component directed along the outward surface normal vanishes, Eq (7) becomes Electrowetting ρ E ds s Fe = Extensive electrowetting studies have been done with spatial dimensions where gravity effects are negligible (Bond number tending to zero) in the areas such as microfluidics or microelectronics (Berge and Peseux [12], Srinivasan et al [13], and Yun et al [14]) Figure renders the contact angles affected by electrowetting To relate the applied voltage to the change in the effective surface tension, the thermodynamicelectrochemical, 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 introduced by Jones [16] and starts from the Korteweg-Helmholtz body force density (Landau and Lifschitz [18]) F k = ρf E − ε0 ε0 ∂ε E ∇ε + ∇ E ρ 2 ∂ρ (6) where E is the electric field vector, ρf is the fluid charge density, 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 equivalent to integrating the Maxwell stress tensor over the liquid-gas interface Fe = T • n ds (8) (9) The field and charge distribution are found by solving the electrical Laplace equation for the electrostatic potential with the appropriate boundary conditions Both the field and charge distributions diverge upon approaching the contact line [19] Therefore, the Maxwell stress is maximum at the contact line and 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 of the Maxwell stress is fe = εo ε ϕ2 2d (10) Since this force acts only on the contact line and is perpendicular to TCL, it is used in the force balance and the Young equation, i.e., σeff sl,e = σsl − ε0 ε ϕ2 2d cos θc,e = cos θc,o + ε0 ε ϕ2 2σlg d (11) (12) (7) Figure Rendering of electrowetting of the surface droplet on a dielectric coated substrate The net charge distribution is also shown heat transfer engineering where θc,e is the electrowetted contact angle, θc,o is the neutral contact angle, ε is the dielectric constant of the dielectric layer underneath the water droplet, d is the thickness of the dielectric layer, and ϕ is the applied potential between the liquid and the 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 angle saturation can be explained as an electron-discharge mechanism, together with the vertical component of the electrostatic force acting on the contact line (Kang [22]) vol 31 no 2010 104 J KIM AND M KAVIANY 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 k from 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 be written as Fx = = π −π 2Rfe cos ζdζ − Fsx π R −π εo ε ϕ cos ζdζ − 0.923σlg R(cos θc,r − cos θc,a ) d (13) We have assumed that the applied forces are concentrated at TCL, as graphically represented in Figure 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 fe becomes larger with increase in potential, the portion of the contact line which begins to slip increases Also, as the contact line begins to slip, it causes an instantaneous reduction in the advancing contact angle When the advancing contact angle is reduced, according to Eq (12), the retention force is reduced which results in lowering 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 of liquid motion under electrowetting can be described as first, at the onset of motion, the droplet is charged and experiences electrowetting which overcomes the static TCL friction When the sum of the gravity and electrowetting force is larger than the static friction over the entire contact line of the droplet, the bulk condensate motion is initiated As the droplet advances, the electrostatic energy is dissipated and dewetting becomes apparent When the droplet recovers its original topology, it experiences a rise in electrostatic energy due to its proximity to the over-hanging electrode and this sequence is repeated Using the preceding droplet physics, prediction of the electrowetting reduction of the critical inclination angle is possible by using a simple force balance at the TCL The observation indicates minimum or no advancing of receding contact line until the advancing contact line has well advanced, thus, it is reasonable to assume that the dominant criteria for the initiation of the droplet motion is the force balance at the advancing contact line (Kim [8]) As long as the droplet is not separated, this treatment of the force on the contact line is valid The retention force can be estimated 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 the inclination angle which the gravity balances, the resultant of the retention force and the electrowetting force, it is possible to obtain a theoretical prediction of the variation of the critical inclination angle with the applied potential This angle is found by solving the following equation φ = sin−1 ⎛ ⎝ π −π R εdo ε ϕ cos ζdζ − 0.923σlg (cos θc,a − cos θc,r ) ρgV ⎞ ⎠ (14) Note the underlying assumptions that friction force at the rear TCL does not contribute to the initiation of the droplet motion and that the weight of the droplet is applied to the front half of the droplet EXPERIMENTAL ANALYSIS Implementation of Electrowetting in Heat Exchangers Figure Graphical representation of balance between the retention and electrowetting forces, at the advancing TCL heat transfer engineering The theoretical analyses in the preceding sections have indicated that by using electrowetting droplet motion initiation at vol 31 no 2010 J KIM AND M KAVIANY low Bond numbers is possible This would significantly increase the drainage rate in heat exchangers To extend the theoretical prediction to practical application, a series of experiments were designed and performed Figure presents a detailed picture of an electrowetting assisted droplet purge in prototype heat exchangers 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 Image of initiation of droplet purge using electrowetting using vertical 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 heat transfer engineering 105 ternal acrylic frame Then the heat exchangers were connected to a refrigeration unit and were operated under 80% humidity condition for 60 The heat exchanger surface temperature TH X was measured to be 0.2◦ C When condensation began to form, electric potential of 600 V was applied The experiment was photographed using a DSLR camera with a 1:1 macrolens The figure shows that there exists clear contrast between the fins which have been subjected to electrowetting forces and the ones which were not The droplets which were formed under heat exchanger operations have either been purged or on the verge of purge for the fins which have electrodes, whereas significant droplet retention is observed on the fins which not have electrodes Figure shows the drainage rate (mass of water drained per unit time) normalized with respect to base (no coat) heat exchanger of different passive and active surface treatments The data show approximately 150% improvement in drainage rate compared to heat exchanger with no coat Also, for manual target excitation (where electrodes were manually brought in proximity to the droplets), there was approximately 290% increase in the drainage rate showing significantly improved drainage potential when optimization is achieved In light of previously shown potential-improvement of drainage rate in heat exchangers, we present a ideal conceptual design in which the electrowetting assisted drainage can be implemented in a full scale heat exchanger Figure shows one of the optimized implementations of electrowetting technique in heat exchangers The heat exchanger is coated with a hydrophobic dielectric coating and the electrodes are suspended between the fins via external frame The electrodes are vertically oriented to minimize the blockage of liquid droplets Although there Figure 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 vol 31 no 2010 106 J KIM AND M KAVIANY pose an electrode-heat exchanger design which will enhance the current performance of the evaporator By using the new electrowetting implemented heat exchanger design and overcoming the following challenges: need for enhanced electrical insulation, high performance dielectric coating and polished find tip, it is expected that the evaporator performance will increase by many folds NOMENCLATURE A Bo D E Fif fs g k n p R r1 T THX V area, m2 bond number diameter, m electric field strength, V/m total force, N friction force, N gravitational acceleration, m.s−2 retention force constant unit vector pressure drop, Pa droplet radius, m minuscule radius, m Maxwell stress tensor, Pa Temperature, ◦ C Volume, m3 Greek Symbols Figure 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 Kronecker delta azimuthal angle, ◦ contact angle, ◦ Lagrange multiplier mass density, kg/m3 liquid charge density, C/m3 surface charge density, C/m3 i − j interfacial tension, N/m δik ζ θc λ ρ ρf ρs σij Subscripts CONCLUSION Electrowetting purged surface condensate in evaporators has been investigated using physics of the force balance at the threephase contact line Using a prototype heat exchanger, the theory was applied to investigate the improvement of drainage under 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 elecrowetting as the means of condensate purge Based on the theoretical insight and the preliminary experimental investigation, we proheat transfer engineering c,a c,e c,o c,r g HX if l max s advancing contact angle electrowetted contact angle equilibrium contact angle receding contact angle gas heat exchanger interface liquid maximum minimum static or solid vol 31 no 2010 J KIM AND M KAVIANY REFERENCES [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 Actuators B, vol 87, pp 201–206, 2002 [4] Adamson, A., Physical Chemistry of Surfaces, 4th edition, Wiley, New York, 1982 [5] deGennes, P G., On Fluid/Wall Slippage, Langmuir, vol 18, pp 3413–3414, 2002 [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 Motion, 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 European 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 Low-Voltage and LowPower Operations, Journal of Microelectromechanical Systems, vol 11, pp 454–461, 2002 heat transfer engineering 107 [15] Berge, B., Electrocapillarity and Wetting of Insulator Films by Water, Comptes Rendus De l’Academie des Science., Series II: Mec., Phys., Chim., Scie.Terre Univers, vol 317, pp 157–163, 1993 [16] Jones, T B., On the Relationship of Dielectrophoresis and Electrowetting, Langmuir, vol 18, pp 4437–4443, 2002 [17] Jones, T B., An Electromechanical Interpretation of Electrowetting, Journal of Micromechanics and Microengineering, vol 15, pp 1184–1187, 2005 [18] Landau, L D., and Lifschitz, E M., Electrodynamics of Continuous 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 Angle 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 Engineering, 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 antiStokes luminescence Massoud Kaviany is Professor of Mechanical Engineering and Applied Physics at University of Michigan, since 1986 His Ph.D is from University of California-Berkeley His education-research field is heat transfer physics vol 31 no 2010 144 B KAMKARI AND A.A ALEMRAJABI at air velocity of U = 0.125 m/s and electrode spacing of L = cm, evaporation is enhanced 3.2 folds by consuming 0.071 W electrical power This reduces to 1.2 fold as air velocity increases to 1.75 m/s Evaporation enhancement increases steeply at low electrical powers and gently at higher electrical powers which highlights the effect of electric field at lower power consumptions Since corona wind velocity is the main mechanism in heat and mass transfer augmentation, considering that P = V I , one can combine Eqs (2) and (4) to get Ue ∝ P 1/3 which supports the steep increase of evaporation enhancement at lower powers Results also show that while evaporation enhancement is a function of air velocity, it is nearly independent of electrode spacing for fixed electrical power consumption Electric power consumption is equal to the multiplication of voltage and current Using the preceding derivations, i.e., Eqs (17) and (18), the relationship between electrical power consumption and evaporation enhancement can be expressed as P 1/3 Sh ∝ Sh0 U (20) This relationship shows that if evaporation enhancement is presented as a function of electrical power, it would be independent of electrode spacing which is in good agreement with the experimental data in Figure Coefficient of Thermal Performance of electrohydrodynamic (COTPEHD ) technique is defined here as the ratio of increase in the heat absorbed by the evaporated water in the presence of the electric field to the electrical power consumption ˙ eva0 )λ ˙ eva − m (m (21) VI ˙ eva0 are the rates of water evapo˙ eva and m In this equation m ration with and without electric field, respectively λ is the latent heat of evaporation for water As shown in Figure 9, an increase in applied voltage and a decrease in electrode spacing both lead to a decrease in COTPEHD However these results shouldn’t be confused with earlier results presented in Figure 3, which show that an increase in applied voltage and a decrease in electrode spacing are two effective parameters which result in augmentation of evaporation enhancement These results imply that electrical energy is more effectively used at a lower applied voltage and the thermal performance coefficient falls sharply for higher voltages As it is seen, COTPEHD , like evaporation enhancement, is a function of both corona wind velocity and axial air flow velocity, so it seems to be possible to correlate the values of COTPEHD to corona wind and axial air flow velocities This has been performed in Figure 10 In this figure, COTPEHD values for air velocities greater than U = 0.75 m/s and different electrode spacings are plotted versus corona wind, also the effect of primary air velocity is considered As it is seen, they can be correlated well by the following relation: 12.4 U > 0.75 m/s (22) COTPEHD = Ue1.4622 × U 0.5 Figure COTPEHD versus voltage for different electrode spacings According to the previous statements, this relation shows that corona wind is more effective at lower air velocities COTPEHD = heat transfer engineering UNCERTAINTY ANALYSIS The experimental uncertainty of the present work was determined for Sherwood number The uncertainties corresponding to the measured parameters are approximately: air velocity (±0.1 m/s), air temperature (±0.2◦ C), air relative humidity Figure 10 Relation between COTPEHD , corona wind velocity and primary air velocity Curve line is the result of the correlation of experimental data vol 31 no 2010 B KAMKARI AND A.A ALEMRAJABI • 145 Applying EHD technique at voltages near corona inception voltage can lead to a considerable amount of heat and mass transfer enhancement with a very small amount of electrical power but its performance decreases with increasing the applied voltage However, this shouldn’t be confused with the earlier statement that evaporation enhancement increases with applied voltage What actually is emphasized here is that the electrical energy usage is more effective at lower applied voltages NOMENCLATURE Figure 11 numbers Uncertainty bands and reproducibility of experimental Sherwood (±1%), voltage and current (±1% of the reading) The uncertainty bars corresponding to the above parameters are presented in Figure 11, with a maximum uncertainty of 11% The experiments were repeated three times to ensure that the data presented are reproducible and trends are not caused by the experimental uncertainty As it is seen all data placed well within the uncertainty bands It is observed that the data scattered as the voltage increases This should be attributed to the unsteady behavior of corona discharge at high voltages, especially close to the breakdown voltage CONCLUSIONS This experimental research revealed the level of evaporation enhancement in the wind tunnel that can be achieved by applying the corona wind The effects of corona wind velocity, electrode spacing and air flow velocity on evaporation enhancement have been examined The emitting electrode was a thin copper wire suspended above a copper plate covered with a thin layer of water and charged with positive DC high voltage The results could be summarized as follows: A At b C COTPEHD D d E Fe hm I L ˙ eva m ˙ eva0 m ˙ dry air m NEHD P Pa Pg qe Sh Sh T U Ue V surface area of plate electrode, (m2 ) cross sectional area of wind tunnel, (m2 ) positive ion mobility, (1.43 × 10−4 m2 /V s) water vapor concentration, (kgw /m3 ) EHD coefficient of thermal performance mass diffusivity of water vapor, (m2 /s) characteristic length, (m) electric field intensity, (V /m) electrohydrodynamic force, (N/m3 ) mass transfer coefficient, (m/s) electric current, (A) electrode spacing, (m or cm) rate of water evaporation with electric field, (kgw /s) rate of water evaporation without electric, field (kgw /s) mass flow rate of dry air, (kga /s) EHD number, Eq (14) electrical power, (W ) air pressure, (kP a) saturated pressure of water vapor, (kP a) free electric charges density, (1/m3 ) dimensionless Sherwood number, Eq (8) Sh − Sh0 air temperature, (◦ C) axial air flow velocity, (m/s) corona wind velocity, Eq (4) (m/s) electrical voltage, (V ) • The evaporation enhancement increases with increasing voltage and decreases with increasing the electrode spacing at a fixed applied voltage • It’s found that as the air flow velocity over the water surface increases, EHD enhancement reduces, which implies that EHD effectiveness on evaporation enhancement gradually diminishes by increasing the air flow velocity Maximum enhancement ratio was 7.3 obtained at air velocity of 0.125 m/s • It can be deduced that evaporation enhancement is nearly independent of electrode spacing at a fixed corona wind velocity This result strengthens the postulate that corona wind velocity is the main mechanism in evaporation enhancement • Except for very low air flow velocities, evaporation enhancement is a linear function of EHD number heat transfer engineering Greek Symbols dry air density, (kga /m3 ) humidity ratio, Eq (5) (kgw /kga ) relative humidity, (%) electric permittivity of vacuum, 10−12 F /m) ρa ω φ εo Subscripts m w mean value surface of the water vol 31 no 2010 (8.85 × 146 W BT B KAMKARI AND A.A ALEMRAJABI wet bulb temperature inlet of the wind tunnel outlet of the wind tunnel at the presence of air flow, without electric field [13] [14] REFERENCES [15] [1] Rashkovan, A., Sher, E., and Kalman, H., Experimental Optimization of an Electric Blower by Corona Wind, Applied Thermal Engineering, vol 22, pp 1587– 1599, 2002 [2] Panofsky, H., Wolfgang, K., and Philips, M., Classical Electricity and Magnetism, Addison-Wesley, New York, 1977 [3] Molki, M., and Bhamidipati, K L., Enhancement of Convective Heat Transfer in the Developing Region of Circular Tubes Using Corona Wind, International Journal of Heat and Mass Transfer, vol 47, pp 4301–4314, 2004 [4] Bhattacharyya, S., and Peterson, A., Corona Wind Augmentation Natural Convection, Part1: Single Electrode Studies, Journal of Enhanced Heat Transfer, vol 9, pp 209–219, 2002 [5] Owsenek, B L., Seyed-yagoobi, J., and Page, R H., Experimental Investigation of Corona Wind Heat Transfer Enhancement With a Heated Horizontal Flat Plate, Journal of Heat Transfer, vol 117, pp 309–315, 1995 [6] Sadek, S E., Fax, R G., and Hurwitz, M., The Influence of Electric Fields on Convective Heat and Mass Transfer From a Horizontal Surface Under Force Convection, Journal of Heat Transfer, vol 94, no 2, pp 144–148, 1972 [7] Sadek, H., Robinson, A J., Cotton, J S., Ching, C Y., and Shoukri, M., Electrohydrodynamic Enhancement of In-Tube Convective Condensation Heat Transfer, International Journal of Heat and Mass Transfer, vol 49, pp 1647–1657, 2006 [8] Liu, Y., Li, R., Wang, F., and Yu, H., The Effect of Electrode Polarity on EHD Enhancement of Boiling Heat Transfer in a Vertical Tube, Experimental Thermal and Fluid Science vol 29, pp 601–608, 2005 [9] Alemrajabi, A A., and Lai, F C., EHD-Enhanced Drying of Partially Wetted Glass Beads, Drying Technology, vol 23, pp 597– 609, 2005 [10] Lai, F C., and Sharma, R K., EHD-Enhanced Drying With Multiple Needle Electrode, Journal of Electrostatics, vol 63, pp 223–237, 2005 [11] Wong, D S., and Lai, F C., EHD-Enhanced Drying With Auxiliary Heating From Below, Journal of Energy Resources Technology, vol 126, pp 133–139, 2004 [12] Cao, W., Nishiyama, Y., and Koide, S., Electrohydrodynamic Drying Characteristics of Wheat Using High Voltage Electrostatic heat transfer engineering [16] [17] [18] [19] [20] Field, Journal of Food Engineering, vol 62, no 3, pp 209–213, 2004 Wonly, A., Intensification of The Evaporation Process by Electric Field, Chemical Engineering Science, vol 47, no 3, pp 551–554, 1992 Barthakur, N N., Electrohydrodynamic Enhancement of Evaporation From NaCl Solutions, Desalination, vol 78, pp 455–465, 1990 Zhanga, J., and Adamiak, K., A multi-species DC stationary model for negative corona discharge in oxygen; point-plane configuration, Journal of Electrostatics, vol 65, no 7, pp 459–464, 2007 Robinson, M., Movement of Air in the Electric Wind of the Corona Discharge, AIEE Transactions, vol 80, pp 143–150, 1961 Steutzer, O M., Ion Drag Pressure Generation, Journal of Applied Physics, vol 30, no 7, pp 984–994, 1959 Kamkari, B., Experimental Investigation of Water Evaporation Enhancement Using Electrohydrodynamic, M.Sc Thesis, Department of Mechanical Engineering, Isfahan University of Technology, 2008 Chaker, M., and Cyrus, B., Inlet Fogging of Gas Turbine Engines—Part I: Fog Droplet Thermodynamics, Heat Transfer, and Practical Considerations, Journal of Engineering for Gas Turbines and Power, vol 126, pp 545–558, 2004 Bansal, P K., and Xie, G., a Unified Empirical Correlation for Evaporation of Water at Low Air Velocities, International Communications in Heat and Mass Transfer, vol 25, no 2, pp 183– 190, 1998 Babak Kamkari received his M.Sc in mechanical engineering from Isfahan University of Technology, Iran in 2008 He is currently a Ph.D student at Tehran University, Iran Ali Akbar Alemrajabi is associate professor of energy conversion at the Isfahan University of Technology, Iran He received his Ph.D in 1988 from Birmingham University, England His main research interests are heat transfer enhancement and renewable energies vol 31 no 2010 Heat Transfer Engineering, 31(2):147–156, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903285427 Electrohydrodynamically-Enhanced Forced Convection in a Horizontal Channel with Oscillatory Flows FENG C LAI and KONGKEE TAY School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma, USA Prior studies on electrohydrodynamically enhanced forced convection in a horizontal channel have revealed the existence of oscillatory flows These oscillatory flows are the product of interactions between the electric body force and flow inertia of the primary flow It has also been shown that heat transfer can be significantly enhanced when operating in this oscillatory flow mode It is speculated that heat transfer may be further enhanced by exciting the primary flow in a frequency similar to those observed for the oscillatory flows (i.e., the so-called resonant effect) To verify this speculation, computations have been performed for primary flows excited with a frequency that is either a fraction or multiple of the natural frequency observed in the original oscillatory flows The results show that an inlet flow excited at the natural frequencies produces the best heat transfer enhancement in the single-cell regime, and the enhancement increases with the Reynolds number However, the results show an opposite trend in the multiple-cells regime INTRODUCTION Air is a common working fluid When in use, one is usually facing a challenging problem to increase its heat transfer to a higher rate that is normally limited by its low thermal conductivity It has been long demonstrated that heat transfer can be significantly enhanced using electrohydrodynamics (EHD) [1–4] When it is applied to air, an electric field can provide a novel solution to the challenge mentioned above The mechanism for this heat transfer enhancement technique is generally attributed to the electrically induced secondary flow, which is also known as ionic wind or corona wind The EHD-induced secondary flow can be thought of as a micro jet issued from the charged electrode to the grounded heat transfer surface The net effect of this secondary flow is additional mixing of the fluid and destabilization of the thermal boundary layer, thus leading to a substantial increase in the heat transfer coefficient Prior studies on EHD-enhanced forced convection in a horizontal channel have revealed the existence of oscillatory flows due to the interaction between electric body force and uniform inlet flow [5–8] Particularly, the results obtained by the authors Address correspondence to Professor Feng C Lai, School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma E-mail: flai@ou.edu [7, 8] have shown that the flow and temperature fields may become steady, periodic or non-periodic, depending on the flow Reynolds number and EHD number In addition, heat transfer enhancement produced by oscillatory flows is found to be more effective than steady flows [8] Since these EHD-induced oscillatory flows are similar to those self-sustained flows observed in grooved channels [9–12], it is speculated that further heat transfer enhancement may be attainable if the flow introduced at the inlet is also oscillatory Therefore, it is the objective of the present study to investigate if a resonant effect can be achieved through the excitation of the inlet flow and the heat transfer enhancement this may bring about To this end, numerical calculations are performed for inlet flows with a frequency that is either a fraction or multiple of the natural frequency observed in the original oscillatory flows FORMULATION AND NUMERICAL METHOD The geometry considered is a two-dimensional horizontal channel with a wire electrode placed at the center This channel, which has exactly the same dimensions as that of the previous study [13], is chosen so that the previously reported electric field data can be used in the present numerical calculations While the wire is charged with dc high voltage, the channel walls are 147 148 F.C LAI AND K TAY are given by [7, 8] ∂2 ∂2 + =− , ∂X2 ∂Y2 (5) ∂2 ∂2 + ∂X2 ∂Y2 ∂ ∂ ∂ ∂ ∂ = − + ∂τ ∂X ∂Y ∂Y ∂X ReEHD Figure 25.8 cm) A horizontal channel with one wire electrode (d = cm and L = electrically grounded and maintained at a constant temperature Tw (Figure 1) Only positive corona discharge is considered in the present study Since the positive corona discharge is uniformly distributed along the length of the wire, it permits a two-dimensional analysis Air at a uniform temperature Ti and a specified velocity ui is introduced at the channel inlet The inlet velocity is assumed to have the following form, ui = ui0 (1 + a cos(2πft)), (1) where a is the amplitude of the oscillatory component and f is the frequency of the oscillatory flow For the problem considered, the governing equations of the electrical field are given by [8] ρ ∂ V ∂2 V + = − c, ∂x2 ∂y2 ε0 + ¯ ∂ρc ¯ ∂ρc ∂V ∂V − ∂Y ∂X ∂X ∂Y ∂θ ∂ ∂θ ∂ ∂θ = − + ∂τ ∂X ∂Y ∂Y ∂X PeEHD ρ2c = ε0 X = 0, V=0 ¯ = u¯ i0 (1 + a cos(2πfτ))Y, θ = 0, ∂ = 0, ∂X ∂ = 0, ∂X ∂θ = 0, ∂X (8b) (3) (4a) along the channel wall (y = d) = 0, (8a) Y = 1, at the wire , (7) (2) with the boundary conditions given by V = V0 , ∂2 θ ∂2 θ + ∂X2 ∂Y2 where ReEHD and PeEHD are both based on the electric characteristic velocity ue The last term on the right side of Eq (6) represents the body force term due to the electrical field For the geometry considered, the electric current involved is very small (on the order of 10−5 A based on the measurements of Yamamoto and Velkoff [13]) over the range of voltage applied, which justifies the neglect of Joule heating The boundary conditions for the flow and temperature fields are given by ¯ X = L, ∂ρc ∂V ∂ρc ∂V , + ∂x ∂y ∂y ∂x (6) , (4b) ∂V = 0, ∂y along the horizontal centerline (y = 0) (4c) ∂V = 0, ∂x along the vertical centerline(x = L/2) (4d) For the operating conditions considered in the present study, the ion drift velocity is about two orders of magnitude higher than the air velocity such that the contribution of convective flow to the current density can be neglected [6, 13] Also, the electrodynamic and fluid dynamic equations can be uncoupled for the same reason Thus, the solution of the electric field can be obtained independently of the flow equations Although this has been accepted as a common practice, the so-called one-way coupling approach has been verified only recently [7] For the flow and temperature fields, the dimensionless governing equations in terms of the stream function and vorticity heat transfer engineering = ∂2 , ∂Y2 ¯ = u¯ i0 (1 + a cos(2πfτ)), Y = −1, = θ = 1, (8c) ∂2 , ∂Y2 ¯ = −¯ui0 (1 + a cos(2πfτ)), θ = (8d) At the channel exit, gradients of stream function, vorticity and temperature are set to zero These boundary conditions are less restrictive and are widely accepted For the solution of the electric field, the numerical procedure used is identical to that proposed by Yamamoto and Velkoff [13] Electric potential and space charge density are determined by iterations on Eqs (1) and (2) with an assumed value of space charge density at the wire (ρc0 ) The validity of the solution is checked by comparing the calculated total current with the measured current at the corresponding voltage If the currents not match, a new value of space charge density at the wire is assumed and the calculations are repeated The solutions of the flow and temperature fields are obtained using the standard procedure for the stream function-vorticity formulation, which vol 31 no 2010 F.C LAI AND K TAY is well documented in most numerical textbooks and is omitted here for brevity The computational domain (the shaded area in Figure 1) is one half of the channel due to the symmetry about the horizontal centerline Accordingly, the boundary condition at the bottom wall, Eq (8d), is replaced by the symmetric condition at the centerline Since the radius of the electrode wire (10−4 m) is small as compared to the grid spacing used (9.375 × 10−4 m), it is appropriate to treat the wire as a nodal point Numerical solution starts with the calculations of electric field, then is followed by solving the flow and temperature fields simultaneously Since the test of grid dependence has been documented in the previous studies [7–8, 13], there is no need to repeat it here Uniform grids (225 × 33) are used in the present study to be consistent with the previous calculations [7, 8] The dimensionless time step chosen is × 10−4 so as to guarantee numerical stability and accuracy The stability criterion for the numerical scheme used is given by Jaluria and Torrance [14], t≤ 2ν ( x)2 + ( y)2 + |u| x + |v| y (9) To verify that the observed oscillations are not due to numerical instability, the computation has been repeated with a reduced time step ( τ = × 10−4 ) The results obtained are identical to those using the time step of τ = × 10−4 To closely monitor the development of the flow and temperature fields, the computation is continued for at least 1,000 dimensionless time, which would normally take about 100 hours CPU time on a Pentium personal computer To examine the interaction between the flow and electric fields, it is convenient to use a parameter which can represent the ratio of electrical body force to flow inertia For the present study, the parameter used is the EHD number proposed by Davidson and Shaughnessy [15], which is given by NEHD = Id βρu2i A 149 Nusselt number which is given by Nu= ¯hDh = k L¯ L¯ Nux dX = log(1/θ0 ) L¯ − θ0 L¯ ∂θ ∂Y dX Y=1 (12) For periodic flows, the time-averaged Nusselt number is determined by averaging the Nusselt number over a period of oscillation and is given by Nu = τP τ+τP Nu dτ, (13) τ where τP is the period of the oscillation and Nu is determined from Eq (12) at each time step To validate the numerical solutions thus obtained, the present code has been first tested against forced convection in a horizontal channel without the presence of electrical field The average Nusselt number obtained in general agree well with the empirical correlation reported by Shah and London [16] The discrepancy found varies from one to six percent, depending on the Reynolds number As reported in the previous studies [7–8], when an electric field interacts with a uniform flow in a horizontal channel, the flow and temperature fields may not always reach a steady state for the range of parameters considered (i.e., 10 ≤ V0 ≤ 17.5 kV and 75 ≤ Re ≤ 4800) The results show that flow and temperature fields may become oscillatory at certain electrical conditions when the flow Reynolds number is small (i.e., a high EHD number) For example, one such case is shown in Figures and for a complete cycle of oscillation As observed, when interacting with the primary flow from the inlet, corona wind produces a sizable recirculating cell directly above the wire (Figure 2) As time advances, there is a visible change in the strength of the recirculating cell (in terms of the increasing number of streamlines that constitute the cell), which in turn produces considerable effect on the thermal boundary layer (Figure 3) The temperature field is distinguished by a wave-like (10) where I is the total current and A is the surface area of the channel wall It is clear that it increases with the applied voltage and decreases with an increase in the Reynolds number A high EHD number thus implies that the flow field is dominated by electric body force On the other hand, a small EHD number indicates that the flow field is controlled by flow inertia To evaluate the heat transfer performance, one needs to calculate the heat transfer coefficient The local heat transfer coefficient in terms of the local Nusselt number is given by Nux = qDh Dh (∂T/∂y) hDh = = k k(Tw − Tm ) Tw − Tm (11) In the above expression, Dh is the hydraulic diameter and Tm is the fluid bulk temperature at the given location The average heat transfer coefficient can then be determined from the overall heat transfer engineering Figure Oscillatory flow fields at V0 = 17.5 kV and Re = 1200 (NEHD = 5.87), (a) τ = 1034, (b) τ = 1043, (c) τ = 1052, (d) τ = 1061, (e) τ = 1070 vol 31 no 2010 150 F.C LAI AND K TAY the flow and temperature fields may first stabilize during this interval, but become oscillatory again if the EHD number is increased further As reported by Lai et al [6], the oscillatory flow frequency cannot be completely characterized by the EHD number In fact, it also depends on the flow structure (i.e., single cell or double cells) It has been correlated with the EHD number and is given by [6] f0 = 0.60 + 0.70[log(NEHD )] for oscillatory flows with single cell (14a) f0 = −0.49 + 1.15[log(NEHD )] for oscillatory flows with double cell Figure Oscillatory temperature fields at V0 = 17.5 kV and Re = 1200 (NEHD = 5.87), (a) τ = 1034, (b) τ = 1043, (c) τ = 1052, (d) τ = 1061, (e) τ = 1070 appearance of the thermal boundary layer at the downstream of the wire Because of the disruption of the thermal boundary layer development, there is an increase in the total heat transfer rate A steady state can only be reached when the flow Reynolds number becomes sufficiently large (i.e., a small EHD number) In fact, the transition of flow and temperature fields is a rather complicated function of EHD number as indicated in Figure To determine if flow and temperature fields are steady or periodic, computations have to be performed over a sufficiently long time (τ ≥ 1000) until a repeated pattern in the flow and temperature profiles as well as the variation of heat transfer coefficient (i.e., the Nusselt number) can be clearly identified As shown, the flow and temperature fields are always stable when Nehd < and become oscillatory when Nehd > 200 No definite conclusion can be drawn on the flow stability when < Nehd < 200 For example, for an applied voltage at 12.5 kV, (14b) It is interesting to note that the frequency of EHD-induced secondary flows with a single cell is usually higher than that with double cells To investigate the possible resonant effect, an excited inlet flow is applied to those cases in which oscillatory secondary flows were produced when a uniform inlet flow had been introduced For convenience, the frequencies of these oscillatory flows induced by a uniform inlet flow are called the fundamental frequencies f0 and the corresponding flow patterns are called the baseline flow patterns RESULTS AND DISCUSSION Since frequency is the most important factor in forming a resonant effect, two types of frequency are considered for the excitation of the inlet flow While the first one has a fractional value of the fundamental frequency (e.g., 0.25f0 , 0.5f0 , and 0.75f0 ), the second one is a multiple of the fundamental frequency (e.g., 2f0 , 3f0 , and 4f0 ) For all calculations, an amplitude is fixed at 75% of the corresponding uniform inlet velocity (i.e., a = 0.75 in Eq (1)) In this case, the magnitude of the inlet velocity will change with time, but not its direction Other values of amplitude (a = 0.25 and 0.5) have been tried as well and their trends are basically the same [17] As with the previous studies [7, 8], EHD number will be used to characterize the flow structure and heat transfer enhancement However, for the present study, the inlet velocity varies with time and so does the EHD number As such, an average EHD number, N¯ EHD , is used instead Oscillatory Inlet Flows with Fractional Fundamental Frequency Figure Transition of flow fields under the influence of electric field heat transfer engineering The interaction between the oscillatory inlet flow and EHDinduced secondary flow is first shown in Figure for a complete cycle when the inlet flow is excited at a full fundamental frequency As observed, a weak secondary cell appears at τ = 1032 when the inlet flow has the highest velocity One also observes vol 31 no 2010 F.C LAI AND K TAY Figure Oscillatory flow fields excited at f = f0 (V0 = 17.5 kV and Re = 1200), (a) τ = 1032, (b) τ = 1041.5, (c) τ = 1051, (d) τ = 1060.5, (e) τ = 1070 that in the first half of the cycle (from τ = 1032 to τ = 1051), the inertia of the primary flow decreases as time advances (which is indicated by a reduction in the streamline number of the inlet flow) and thus the influence of the electrical body force becomes more important (which is indicated by an increase in the number of streamlines for the secondary cells) The gradual changes in the fundamental flow pattern can be clearly observed When the inlet flow is at its minimum velocity, the electric body force becomes most dominant at the center of the channel and the EHD-induced secondary flow is at its peak strength However, with an increase in the inlet flow velocity in the second half of the cycle (from τ = 1051 to τ = 1070), the secondary flow is suppressed and forced downstream The strength of the secondary cells becomes the weakest when the inlet flow is at its maximum velocity This complete out-of-phase interaction between the inlet flow and EHD-induced secondary flow produces the best heat transfer enhancement It produces a resonance-like effect that one would like to take advantage of the heat transfer enhancement Due to this effect, the wavy flow motion downstream is amplified, which induces more recirculating cells to further increase the fluid mixing The thermal boundary layer is compressed distinctly by the resultant flow (Figure 6) When the inlet flow is excited at a fractional fundamental frequency, a similar result is observed The baseline flow pattern is retained during the flow restructuring period as long as the mean velocity of the inlet flow is the same as that of the uniform flow However, since the interaction between the primary flow and EHD-induced secondary flow is not completely out of phase, there is a slight change in the flow restructuring process For example, Figures and show a complete cycle of variation for an inlet flow excited at f = 0.5f0 The figures indicate that the flow restructuring process consists of two parts For the first part (from τ = 1006 to τ = 1044), the flow field has a similar pattern as those shown in Figure It is observed that the cycle begins with an inlet velocity that is close to its mean value heat transfer engineering 151 Figure Oscillatory temperature fields excited at f = f0 (V0 = 17.5 kV and Re = 1200), (a) τ = 1032, (b) τ = 1041.5, (c) τ = 1051, (d) τ = 1060.5, (e) τ = 1070 Since the inlet velocity is decreasing with time, the inertia of the primary flow is getting weaker In the second part of the flow restructuring process which starts right after τ = 1044, the inlet velocity increases to a maximum value and then reduces Figure Oscillatory flow fields excited at f = 0.5f0 (V0 = 17.5 kV and Re = 1200), (a) τ = 1006, (b) τ = 1015.5, (c) τ = 1025, (d) τ = 1034.5, (e) τ = 1044, (f) τ = 1053.5, (g) τ = 1063, (h) τ = 1072.5, (i) τ = 1082 vol 31 no 2010 152 F.C LAI AND K TAY Figure Oscillatory temperature fields excited at f = 0.5f0 (V0 = 17.5 kV and Re = 1200), (a) τ = 1006, (b) τ = 1015.5, (c) τ = 1025, (d) τ = 1034.5, (e) τ = 1044, (f) τ = 1053.5, (g) τ = 1063, (h) τ = 1072.5, (i) τ = 1082 to its mean value During this period of time, secondary flow is greatly suppressed Thus, the contribution to heat transfer enhancement by the secondary flow is significantly reduced Although the secondary flow has some contributions to the heat transfer enhancement in the first half of the cycle, its overall performance is less effective than when the inlet flow is excited at a full fundamental frequency f0 The interaction between an oscillatory inlet flow with a fractional fundamental frequency and EHD-induced single-cell secondary flow can also be examined through the variation of Nusselt number with time (Figure 9) For reference, the variation of inlet velocity is also included in the figure One observes that when excited at a frequency of f0 , the variation of Nusselt number shows a complete phase shift (180 degree) from that of inlet velocity (Figure 9(a)), which is consistent with the observation discussed earlier in Figure This observation applies to all cases for which the baseline flow pattern is characterized by single-cell On the other hand, the resultant flows are neither in phase nor out of phase with the inlet flow when the latter is excited at other fractional frequencies Since the inlet flow excited at f = f0 produces the strongest secondary flows among all other cases with a fractional fundamental frequency, it produces the best result for heat transfer heat transfer engineering Figure Variation of Nusselt number and inlet velocity with time (V0 = 17.5 kV and Re = 1200) for inlet flow excited at (a) f = f0 , (b) f = 0.5f0 enhancement This can also be verified from the isotherm distribution in the thermal boundary layer (Figure 6) For this case, isotherms are compressed more uniformly along the wall than the other three cases (0.25f0 , 0.5f0 , and 0.75f0 ) As the inlet flow frequency decreases, the effect of the secondary flow is reduced and the wavy flow motion is minimized In short, the variation of the inlet flow needs to match that of the secondary flow A precise match of these two flows will produce the resonance-like effect and generate additional flow mixing that further enhances the heat transfer rate The cases examined above are for oscillatory flows whose baseline flow pattern is characterized by a single cell When the flows with a baseline flow pattern of double cells are excited, the resulting flow patterns are less distinguishable The presence of additional secondary cells may offset the heat transfer enhancement brought about by the baseline flow pattern Figure 10 shows the heat transfer enhancement for inlet flows excited with the fundamental frequency and three fractional frequencies The heat transfer enhancement is defined here as the ratio between the average Nusselt number resulting from the oscillatory inlet flow and that from the uniform inlet flow As observed, different excitation frequencies produce various degrees of heat transfer enhancement In general, for baseline flows with single-cell structure, inlet flow excited at the fundamental frequency produces the best result The maximum heat transfer enhancement vol 31 no 2010 F.C LAI AND K TAY 153 Figure 10 Heat transfer enhancement due to oscillatory inlet flow excited at various fractional natural frequencies, (a) V0 = 10 kV, (b) V0 = 12.5 kV, (c) V0 = 15 kV, (d) V0 = 17.5 kV can be as high as 1.5 times that already produced by EHD with a uniform inlet flow However, for baseline flows with double cell structure, an opposite trend is observed Although an oscillatory inlet flow in some cases may produce a heat transfer result less than that of uniform inlet flow, one should be reminded that the minimum heat transfer enhancement produced by EHD with uniform inlet flows is about 1.6 times that of forced convection alone [8] Therefore, heat transfer by EHD with oscillatory inlet flows is always greater than that of forced convection alone heat transfer engineering Oscillatory Inlet Flows with Multiple Fundamental Frequency A higher excitation frequency will produce more disturbances to the baseline flow pattern For instance, an inlet flow excited with f = 3f0 will complete three oscillatory cycles within a period of that excited by the fundamental frequency From the results shown, the timing for the velocity change in the inlet flow does not match well with the baseline flow pattern Also noticed is that the flow pattern in each subsidiary cycle induced by the vol 31 no 2010 154 F.C LAI AND K TAY Figure 12 Heat transfer enhancement due to oscillatory inlet flow excited at multiple natural frequencies (V0 = 17.5 kV) CONCLUSIONS Figure 11 Variation of Nusselt number and inlet velocity with time (V0 = 17.5 kV and Re = 1200) for inlet flow excited at (a) f = 2f0 , (b) f = 3f0 , (c) f = 4f0 oscillatory inlet flow is different from all others Although the interaction between the inlet flow and EHD-induced secondary flows produces several additional weaker cells both upstream and downstream, their change in the temperature field is small and is mostly confined to the region downstream close to the exit Figure 11 presents the variations of Nusselt number with time for an inlet flow excited at various multiple frequencies The figure clearly illustrates how the inlet flow oscillation induces a change in the heat transfer cycle For f = 2f0 , every two complete cycles of inlet flow produce a cycle of change in the Nusselt number Similarly, three and four distinct velocity cycles are required for 3f0 and 4f0 to produce a complete cycle of change in the Nusselt number Figure 12 shows the heat transfer enhancement achieved by each multiple fundamental frequency Basically, there are two trends observed; heat transfer enhancement decreases with an increase in the excitation frequency for baseline flows with single cell, but the result is reversed for baseline flows with double cells Again, it is noticed that there are some cases in which oscillatory inlet flow excited at multiple natural frequencies does not produce further heat transfer enhancement than uniform inlet flow heat transfer engineering The characteristics of oscillatory flows are critically examined in the present study The results have revealed the importance of the excitation frequency of the inlet flow in creating a resonant effect to further enhance heat transfer It has been observed that the interaction between the oscillatory inlet flow and the electrical body force can modify the flow characteristics (i.e., period and flow structure) of the original flows Nevertheless, the baseline flow pattern can still be recognized from the superimposed flow In addition, it is observed that an oscillatory inlet flow will produce a resonant effect if its frequency matches that of the baseline flow When excited at the fundamental frequencies, the motion of secondary flows will be amplified When the inlet flow is excited at a fractional fundamental frequency, the resultant period follows the relation Ps = f0 P0 /f On the other hand, the resultant period remains the same as its fundamental period when the excitation frequency is a multiple of the fundamental frequency In the single-cell regime, the inlet flow excited at the fundamental frequencies produces the best heat transfer enhancement and increases with the Reynolds number In the multiple-cells regime, the results show an opposite trend All the heat transfer enhancements produced by the flows excited at the fundamental frequencies are lower than that of uniform inlet flow Since the minimum heat transfer enhancement by EHD with uniform inlet flow is about 1.6 times that of forced convection alone, one can conclude that heat transfer with EHD and oscillatory inlet flow is always greater than that of forced convection alone The present study has shown a new way to further enhance heat transfer using electric field Particularly, for applications with air as the working fluid, the present results have provided a novel approach to enhance heat transfer However, as vol 31 no 2010 F.C LAI AND K TAY indicated by the results, the relation between the heat transfer enhancement and its excitation frequency can be very complicated Caution is advised when the operating condition is outside the range examined in the present study NOMENCLATURE A b d Dh g h h¯ I k ¯ L NEHD Nu ¯ Nu Nux Nu0 PeEHD Pr Re ReEHD t Ti Tw u ue ui ui V ¯ V V0 v X,Y x, y α ε θ θ0 ν ρ ρc ρc ρc0 τ surface area of channel wall, [m2 ] ion mobility of air, b = 1.4311 × 10−4 m2 /V · s distance between wire and plate, [m] hydraulic diameter, [m] acceleration due to gravity, [m/s2 ] local heat transfer coefficient, [W/m2 · K] average heat transfer coefficient, [W/m2 · K] total electric current, [A] thermal conductivity of air, [W/m · K] dimensionless channel length, L/d EHD number, defined in Eq (12) overall Nusselt number, h¯ Dh /k time-averaged Nusselt number local Nusselt number, hDh /k overall Nusselt number without the application of electric field, h¯ Dh /k Peclet number, ue d/α Prandtl number, ν /α flow Reynolds number, 2ui d/ν EHD Reynolds number, ue d/ν time, [s] inlet air temperature, [K] wall temperature, [K] velocity in x-direction, [m/s] characteristic velocity of ionic wind, ρc0 V0 /ρ , [m/s] inlet velocity, [m/s] dimensionless inlet velocity of air, ui /ue electric potential, [V] normalized electrical potential, V/V0 electric potential at the wire, [V] velocity in y-direction, [m/s] dimensionless Cartesian coordinates, X = x/d, and Y = y/d Cartesian coordinates, [m] thermal diffusivity, [m2 /s] permitivity of air, [F/m] dimensionless temperature, (T - Ti )/(Tw - Ti ) dimensionless mean outlet air temperature kinematic viscosity of air, [m2 /s] density of air, [kg/m3 ] ionic space charge density, [C/m3 ] dimensionless space charge density, ρc /ρc0 ionic space charge density at the wire, [C/m3 ] dimensionless time, ue t/d dimensionless stream function dimensionless vorticity heat transfer engineering 155 REFERENCES [1] Jones, T B., Electrohydrodynamically Enhanced Heat Transfer in Liquids—A Review, Advances in Heat Transfer, vol 14, pp 107–148, Academic Press, New York, 1978 [2] Davidson, J H., Kulacki, F A., and Dunn, P F., Convective Heat Transfer with Electric and Magnetic Fields, Handbook of SinglePhase Convective Heat Transfer, eds S Kakac, R K Shah and W Aung, Wiley, pp 9.1–9.48, New York, 1987 [3] Yabe, A., Mori, Y., and Hijikata, K., Active Heat Transfer Enhancement by Utilizing Electric Fields, Annual Review of Heat Transfer, vol 7, pp 193–244, 1996 [4] Seyed-Yagoobi, J., and Bryan, J E., Enhancement of Heat Transfer and Mass Transport in Single-Phase and Two-Phase Flows with Electrohydrodynamics, Advances in Heat Transfer, vol 33, pp 95–186, Academic Press, New York, 1999 [5] Takimoto, A., Tada, Y., Yamada, K., and Hayashi, Y., Heat Transfer Enhancement in a Convective Field with a Corona Discharge, Transaction of JSME, Series B, vol 54, pp 695–703, 1988 [6] Lai, F C., McKinney, P J., and Davidson, J H., Oscillatory Electrohydrodynamic Gas Flows, Journal of Fluids Engineering, vol 117, pp 491–497, 1995 [7] Huang, M., and Lai, F C., Numerical Study of EHD-Enhanced Forced Convection Using Two-Way Coupling, Journal of Heat Transfer, vol 125, pp 760–764, 2003 [8] Lai, F C., and Mathew, J., Heat Transfer Enhancement by EHDInduced Oscillatory Flows, Journal of Heat Transfer, vol 128, pp 861–869, 2006 [9] Ghaddar, N K., Magen, M., Mikic, B B., and Patera, A T., Numerical Investigation of Incompressible Flow in Grooved Channel Part Resonance and Oscillatory Heat Transfer Enhancement, Journal of Fluid Mechanics, vol 168, pp 541–567, 1986 [10] Amon, C H., and Mikic, B B., Numerical Prediction of Convective Heat Transfer in Self-Sustained Oscillatory Flows, Journal of Thermophysics and Heat Transfer, vol 4, pp 239–246, 1990 [11] Amon, C H., Herman, C V., Majumdar, D., Mayinger, F., Mikic, B B., and Sekulic, D., Numerical and Experimental Studies of Self-Sustained Oscillatory Flows in Communicating Channels, International Journal of Heat and Mass Transfer, vol 35, pp 3115–3129, 1992 [12] Azar, K., Enhanced Cooling of Electronic Components by Flow Oscillation, Journal of Thermophysics and Heat Transfer, vol 6, pp 700–706, 1992 [13] Yamamoto, T., and Velkoff, H R., Electrohydrodynamics in an Electrostatic Precipitator, Journal of Fluid Mechanics, vol 108, pp 1–8, 1981 [14] Jaluria, Y., and Torrance, K E., Computational Heat Transfer, Hemisphere, New York, 1986 [15] Davidson, J H., and Shaughnessy, E J., Turbulence Generation by Electric Body Forces, Experiments in Fluids, vol 4, pp 17–26, 1986 [16] Shah, R K., and London, A L., Laminar Flow Forced Convection in Ducts, Supplement 1, Advances in Heat Transfer, Academic Press, New York, 1978 [17] Tay, K K., Enhanced Forced Convection in Horizontal Channels by Electric Field and Flow Oscillation, M.S Thesis, University of Oklahoma, 1998 vol 31 no 2010 156 F.C LAI AND K TAY Feng C Lai is an Associate Professor in the School of Aerospace and Mechanical Engineering at the University of Oklahoma He received his Ph.D in Mechanical Engineering from the University of Delaware in 1988 He is most well known for his work in heat and mass transfer in porous media as well as EHD-enhanced heat and mass transfer He has published more than 120 technical papers in archival journals and conference proceedings He has received numerous awards for his contribution in research and teaching He is an Associate Fellow of AIAA and a Fellow of ASME heat transfer engineering Kongkee Tay is currently employed as a mechanical engineer with Kingsley Tools, Inc., Garland, Texas He received his B.S and M.S in Mechanical Engineering from the University of Oklahoma in 1996 and 1998, respectively vol 31 no 2010 Heat Transfer Engineering, 31(2):157–158, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903346971 new products UNIFIN ANNOUNCES REMOVABLE COVER PLATE GENERATOR COOLERS: RCPTM coolers provide effective, reliable performance in demanding applications Unifin announces its line of Removable Cover Plate (RCPTM ) generator coolers for superior performance in the most demanding applications Unifin RCPTM coolers are widely used in new and existing power generation installations, from nuclear to hydro-electric to gas turbine power Applications include both air cooled and hydrogen cooled generators Today’s electrical generators produce not only electricity, but also heat from conductor resistance and from friction losses in the bearings Unifin’s RCPTM coolers effectively and reliably remove this heat, in a system that is easy to clean and maintain The RCPTM coolers feature Unifin’s industry-best plate fin technology, which provides optimal heat transfer efficiency and exceptional durability Other fin surfaces are also available from Unifin A removable, bolt-on cover plate facilitates access for cleaning while keeping the cooler installed, without disturbing the piping Unifin RCPTM coolers deliver enhanced reliability A unique leak detector configuration is available to prevent catastrophic failure of the motor or generator The detector senses moisture before it can leak into the air The Unifin leak detector system consists of a unique full double-tube construction, which provides additional protection against possible leaks caused by tube erosion For more information on Unifin International and its complete line of heat transfer products, visit http://www.unifin.com or call 1-888-451-0310 UNIFIN OFFERS CARDINAL PUMPS FOR DEMANDING TRANSFORMER OIL APPLICATIONS: Rugged Pumps Perform in Extreme Temperatures Unifin offers its line of transformer oil pumps, manufactured under the company’s Cardinal brand Cardinal pumps are the industry’s only pumps that are specifically designed to meet the demanding requirements of transformer oil applications To meet the extreme temperature requirements, Cardinal pumps are rated for continuous duty operating temperature ranges from –40◦ C (–104◦ F) to 100◦ C (212◦ F) The Cardinal pumps also have other special features for transformer oil applications, such as the capability to permit thermo-siphon flow when the pump is not operating, allowing natural convection even when the pump is completely shut off For long life in the field, all Cardinal pumps offer rugged split casing design with heavy-duty class 30 cast iron used for the pump casting, motor enclosures, impellers and volutes Large thrust face sleeve bearings also extend life, minimize wear, and reduce maintenance Cardinal offers three bearing types: standard sleeve bearing, the HarleyTM sleeve bearing by Cardinal, and the HarleyTM sleeve bearing with TecSonicsTM bearing wear monitoring As a result of their design, Cardinal pumps are low maintenance and long-lasting With no mechanical seals, repair and upkeep is reduced in utilizing two gasket seals on each pump Cardinal pumps are durable and resilient as a result of a design that allows transformer oil flow back through the motor and bearings, thereby providing cooling and lubrication All Cardinal pump and motor units are subjected to extensive testing, including pressure tests to 50 PSIG to ensure the integrity of the complete unit Motor windings are all tested for 60 seconds at (2x voltage + 1000) to ensure electrical integrity and continuity, 157 158 addition to achieving global standardization, Chromalox has redesigned the heating element layout, bussing and housing on the new line of heaters to achieve more even heat distribution, improved fluid flow and easier installation and service “Our customers are looking to standardize on products that can be deployed globally and we are committed to supporting those efforts while also providing unsurpassed quality, reliability and performance,” said Scott Dysert, CEO of Chromalox “Our products have achieved more certifications than any other line of heaters so it was a natural progression for us to move to global standardization.” This global design also streamlines manufacturing processes to increase production flexibility and reduce turnaround times Features of the new product line include: • with winding resistance taken both before and after the pump is built All Cardinal pumps are also meggar tested to ensure the integrity of the insulation The Cardinal Pumps division of Unifin manufactures hundreds of different pump configurations used in all of Unifin’s wide range of transformer oil coolers The Cardinal Pumps division also manufactures a line of heavy-duty transformer oil valves ranging from 2" to 8", including ANSI standard and OEM-specific flange configuration bolt hole patterns For more information on Unifin International and its complete line of heat transfer products, visit http://www.unifin.com or call 1-888-451-0310 Chromalox Introduces Global Design for ANSI Flange and Circulation Heaters Chromalox introduced new line of ANSI Flange and Circulation Heaters with a standardized design that meets all major global certifications, eliminating the need for global organizations to deploy different designs in different parts of the world The new line of immersion heaters also features a number of enhancements that increase product functionality and performance Chromalox ANSI Flange and Circulation Heaters are designed to be mounted in pipes or vessels to efficiently and precisely heat liquids and gasses in a variety of process industries, including petrochemical, oil and gas, alternative fuels, and bio-pharmaceuticals In heat transfer engineering Octobox Housing Design — The Octobox design offers maximum flexibility for wiring options It works with both NPT and Gland Plate Style connectors, offers six different angles to bring conduit into the housing, and the removable plate design allows the installer to choose the exact connection size needed to match the conduit runs The housing is fully removable, providing unrestricted access to the bussing arrangement, thermowell and circuit identification • Triangular Element Pattern — The heating element patterns has been completely redesigned to achieve more even heat distribution, resulting in cooler elements, less pressure drops and a longer life for the unit • Element Bussing/Power Connections — A new style of ‘vertical bussing’ is used that simplifies installation while providing more robust configuration to support higher amperage, stronger power connection points, and cooler bussing temperatures • Fully Configurable — The new design is driven by the Chromalox Configurator, which can reduce engineering time by more than 90 percent This means that, in most cases, a custom design will reach the production floor the same day it is ordered “As we were working on creating a global heating platform, we reviewed every component in the system and asked ourselves, can this be improved?” said Mark Wheeler, manager, packaged systems for Chromalox “The result is a new generation of flange and circulation heaters that deliver better performance and easier installation than any line of heaters.” For more information on ANSI Flange and Circulation Heater product lines and Chromalox visit http://www.chromalox.com vol 31 no 2010