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

Heat Transfer Engineering, 32(7–8):525–526, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.506388 editorial Selected Papers from the Seventh International Conference on Nanochannels, Microchannels, and Minichannels SATISH G KANDLIKAR Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York, USA It gives us great pleasure to present this special issue highlighting some of the papers presented at the ASME Seventh International Conference on Nanochannels, Microchannels, and Minichannels, held at the Pohang University of Science and Technology (POSTECH), in Pohang, South Korea, June 22–24, 2009 The conference was held under the sponsorship of ASME and was co-hosted by Dr Moo-Hwan Kim, professor and director of the Two Phase Flow Laboratory at POSTECH On behalf of the conference organizing committee and the participants, we would like to thank him and his team of students and staff for putting together a world-class event Pohang, home of the Pohang Steel Corporation, is a prosperous port city on the eastern side of Korea As one of Korea’s top universities dedicated to science and engineering, POSTECH offers 4-year programs in 10 departments and POSTECH’s Graduate School offers programs in 14 departments The excellence of the university extends far beyond the campus, as POSTECH has international cooperative agreements in place with 68 sister universities We had more than 150 papers presented over days in 24 sessions The conference theme of interdisciplinary research was once again showcased with researchers working in diverse areas such as traditional heat and mass transfer, labon-chips, sensors, biomedical applications, micromixers, fuel Address correspondence to Professor Satish G Kandlikar, Mechanical Engineering Department, Rochester Institute of Technology, James E Gleason Building, 76 Lomb Memorial Drive, Rochester, NY 14623-5603, USA E-mail: sgkeme@rit.edu cells, and microdevices, to name just a few Selected papers in the field of heat transfer and fluid flow are included in this special volume There are 19 papers included in this special volume The topics covered include review of cooling technology using microchannels, single-phase flow in microchannels with porous/fibrous structures, boiling and bubble dynamics, Tjunction micromixers for two-phase flow, capillary filling, wetting in microgrooves with liquid metals, gas flow in rough nanochannels, effect of ultrasound on subcooled flow boiling, explosive boiling, flow patterns, and falling film flow on periodic structures These topics indicate that the microchannels are now being used in many diverse applications The conference organizers are thankful to all authors for participating enthusiastically in this conference series Special thanks are due to the authors of the papers in this special issue The authors have worked diligently in meeting the review schedule and responding to the reviewers’ comments The reviewers have played a great role in improving the quality of the papers The help provided by Enrica Manos in the Mechanical Engineering Department at Rochester Institute of Technology with this special issue is gratefully acknowledged We thank Professor Afshin Ghajar for his dedication to this field and his willingness to publish this special issue highlighting the current research going on worldwide He has been a major supporter of this conference series, and I am indebted to him for this collaborative effort 525 526 EDITORIAL Satish G Kandlikar is the Gleason Professor of Mechanical Engineering at Rochester Institute of Technology (RIT) He received his Ph.D degree from the Indian Institute of Technology in Bombay in 1975 and was a faculty member there before coming to RIT in 1980 His current work focuses on heat transfer and fluid flow phenomena in microchannels and minichannels He is involved in advanced singlephase and two-phase heat exchangers incorporating heat transfer engineering smooth, rough, and enhanced microchannels He has published more than 180 journal and conference papers He is a fellow of the ASME, associate editor of a number of journals including ASME Journal of Heat Transfer, and executive editor of Heat Exchanger Design Handbook published by Begell House and Heat in History Editor for Heat Transfer Engineering He has received RIT’s Eisenhart Outstanding Teaching Award in 1997 and Trustees Outstanding Scholarship Award in 2006 Currently he is working on a Department of Energy-sponsored project on fuel cell water management under freezing conditions vol 32 nos 7–8 2011 Heat Transfer Engineering, 32(7–8):527–541, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.506390 A Review of Cooling in Microchannels JAMI F TULLIUS, ROBERT VAJTAI, and YILDIZ BAYAZITOGLU Department of Mechanical Engineering and Material Science, Rice University, Houston, Texas, USA Advancements in electronic performance result in a decrease in device size and increase in power density Because of these advancements, current cooling mechanisms for electronic devices are beginning to be ineffective Within the localized hot spots, the materials of the components are reaching temperature values that can lead to improper functioning of the device Many techniques have been successful in the past, such as heat sinks, cavities or grooves, micro pin-fins, etc., but still not provide adequate cooling necessary to maintain temperature values low enough for the electronic components to operate Microchannels, with their large heat transfer surface to volume ratio, cooled with either gas or liquid coolant, have shown some potential By modifying the walls of the microchannel with fins, pins, or grooves, the cooling performance can be improved A possible fin material used to increase the surface area of a microchannel is carbon nanotubes, which possess excellent thermal and mechanical properties Numerical and computational methods needed to analyze flow at the micro- and nano-scale are also introduced The numerical methods such as lattice Boltzmann, molecular dynamics, and computational fluid dynamics may lessen the cost and time that often accompany experimentation INTRODUCTION Electrical gadgets are continuously advancing in society by creating larger computing power in more reduced physical dimensions than ever before The heat produced per unit area has increased, because of the reduction of the size of these electronic devices With the increase in power and heat, overheating of these electrical components has caused concern [1] The overall well-being of the component, as well as its proper functioning, is being threatened by the elevated temperatures Semiconductor components must maintain a relatively low constant surface temperature Therefore, the development of electronic technology is limited by the efficient cooling methods necessary to maintain the operation of the mechanisms Many techniques have been studied, such as thermal interface materials, heat spreaders and heat sinks, and microchannels A method of appropriate cooling is necessary to allow for more advancement in the years to come while maintaining proper functioning This paper provides a brief overview on the thermal cooling of microchannels Microchannels have been proven effective in cooling small surfaces of electrical components such as microchips These This work was partially supported by LANCER directed research funds from Lockheed Martin POTT0715421 and Alliances for Graduate Education and the Professoriate (AGEP) program through the NSF grant HRD-0450363 Address correspondence to Professor Yildiz Bayazitoglu, Department of Mechanical Engineering and Material Science, Rice University, 6100 Main, Houston, TX 77005-1827, USA E-mail: bayaz@ruf.rice.edu channels act as heat exchangers or heat sinks, which can efficiently cool the microchip The high temperatures can be dissipated through the modified surfaces of the microchannel with natural or forced convection of the fluid flowing within the channel [2–6] Microchannels contain a much higher heat transfer surface area to fluid volume ratio, which allows the convection to be enhanced when compared to the macro-scale systems As the hydraulic diameter decreases in a microchannel, the heat transfer coefficient increases, providing an excellent cooling mechanism However, these small channels experience a very high pressure drop A basic microchannel with a smooth wall surface has demonstrated to cool a heat flux of approximately 790 W/cm2 at a temperature of 71◦ C, while the pressure drop was roughly 214 kPa In altering the channel surface with small cavities or fins, the performance of the channel can improve with a slight increase in pressure drop [7, 8] The most commonly used fluids in microchannels are air, water, and refrigerants; however, there are limitations to their heat transferring capabilities due to their transport properties Air has been a preferred fluid used in microchannels to cool electronic components However, with heat fluxes going beyond 100 W/cm2, air cooling methods have become inadequate for most applications Liquids have a much higher convection heat transfer coefficient providing a better performance in cooling [7, 9] Fluids with higher convection heat transfer coefficients and higher specific heats are more effective in reducing heat from the surface The increase of the heat transfer coefficient or the surface area of the finned structures can help reduce convection 527 528 J F TULLIUS ET AL Figure Thermal properties of different fluids of convection flow Adapted from [11], [12], and [13] resistances [10] In Figure 1, a qualitative comparison of different heat transfer coefficients is presented [11–13] Two-phase systems have an advantage over one-phase systems, because of the latent heat during the phase change process [1] Nanofluids consist of small nanosized particles usually no bigger than 100 nm in size in a base fluid such as water, ethylene glycol, engine oil, or refrigerant In recent studies, nanofluids have emerged, having unique properties that consist of a very high thermal conductivity and maintaining stability Metallic materials that have been used for these nanoparticles are oxide ceramics (Al2 O3 , CuO), nitride ceramics (AlN, SiN), carbide ceramics (SiC, TiC), metals (Cu, Au, Ag), semiconductors (SiC, TiC2 ), carbon nanotubes, and some composite materials (Al70 Cu30 ) The most common materials used are the oxide ceramics These nanofluids increase the thermal conductivity and will in turn increase the heat transfer performance Although adding nanoparticles to a base fluid can influence the cooling process positively, there are still challenges These fluids leave sedimentation of particles, fouling, high pressure drop, and erosion, and may even clog the channel over time [14–19] This paper reviews the effects of a microchannel with various fluids as it flows in both one and two phases Many methods have been proven to be efficient by thermally enhancing the channel Some methods include treating the surface with cavities, fins, micro pin-fins, and increasing the roughness on the surface Carbon nanotubes (CNT) are considered to improve the heat dissipation in a microchannel with their excellent thermal and mechanical properties A section describing the mechanical behaviors of CNT will also be discussed At the nanoscale, Navier–Stokes equations (NS) are proven to be inaccurate because the assumptions made at the continuum level are no longer valid A review of the mathematical methods needed to calculate micro- and nano-scale problems is discussed heat transfer engineering SINGLE-PHASE FLUID Single-phase fluids such as air and liquid, before it reaches the saturation temperature, have been used in microchannels to effectively enhance performance Fluids flowing through the channel can convectively transfer heat from the bottom surface and, as shown in Figure 1, different fluid properties can influence the amount of heat that can be cooled due to their heat transfer coefficients Microchannels can be influenced by many factors other than the different fluid properties, including the shape of the channel, the surface roughness of the channel walls, the cavities machined on the channel surface, etc The shapes of the cross-sectional area of the microchannels themselves can affect cooling Sadeghi et al [20] examined a laminar forced convection channel with an annular cross section while maintaining a uniform temperature at the inner wall and an adiabatic outer wall With lower slip velocity, the exchange of momentum at the liquid/solid interface is also lowered, providing a decrease of the friction factor and an increase of the Knudsen number (Kn) Because of the thermal resistance at the interface, the Nusselt number (Nu) in the smooth channel decreases [20] Nonino et al [21] investigated a developing laminar flow in a microchannel with different cross sections and uniform wall heat flux Channel cross-sectional shapes of a rectangle, trapezoidal, and hexagonal were examined for this study Nonino et al discovered that viscous dissipation close to the entrance and the temperature dependent viscosity should not be ignored The Nu is greatly affected by the viscosity The shape of the channel can influence how well the channels performance can be; however, it does not have much influence on the effect of pressure drop, which is mainly influenced by the temperature-dependent viscosity The channel shape can influence the cooling performance of the microchannel vol 32 nos 7–8 2011 J F TULLIUS ET AL Surface roughness is also a major factor in optimizing the thermal performance Microchannels can have smooth surface walls or can contain small structures meant to disturb the fluid as it flows Shokouhmand et al [22] studied the surface roughness effects of a fully developed, laminar, rough rectangular microchannel analytically using the Gaussian technique The aspect ratio was varied from to and the relative roughness from to 0.15 For roughness values less than 0.01, there was little effect on the friction factor; however, for roughness values between 0.01 and with an aspect ratio of 1, there was an increase of 11.3%, with an aspect ratio 0.5 there was a 5.5% increase of the friction factor, and for an aspect ratio of 0.1 there was a 1.7% increase For the convective heat transfer coefficient, there is a parabolic profile with the values of the lower aspect ratio close to and the higher aspect ratio near being high and the values with the aspect ratio of 0.5 reaching a minimum Decreasing the relative roughness of the channel, the heat transfer coefficient also decreases slightly For a relative roughness of 0.01, the aspect ratio has little effect As the relative roughness value increases, so does the friction factor, while Nu is not dependent on the roughness scale With an increase in surface roughness the convection heat transfer coefficient will increase slightly [22] A method used to impact the cooling performance is applying small grooves to the surface Lee and Teo [8], Solovitz [23], and Baghernezhad and Abouali [9] all adjusted the wall surface of a microchannel with grooves These openings can induce more disturbances in the flow, providing a more effective cooling mechanism When applying gaps in the surface, the pressure drop was maintained—that is, it did not increase from a smooth microchannel—and the heat transfer performance was increased by roughly 12% The spacing and the size of the grooves are still being tested to obtain the maximum efficiency of the channel [8] Solovitz [23] modeled a two-dimensional (2D) simulation with a small dimple-like groove imbedded in the channel surface When varying the dimensions of the cavity and the Reynolds number, there was a 70% increase in the heat transfer performance with only a 30% increase in pressure drop when compared to a smooth base model using a depth/diameter ratio of 0.4 and a Reynolds number of 1000 The depth of the cavity was proportional to the cooling performance of the channel Baghernezhad and Abouali [9] compared the shapes of the grooves used to disrupt the flow A rectangular groove and an arc-shaped groove were compared, and it was found that both shapes can improve the cooling performance but the arc-shaped one is more effective This is probably due to the aerodynamics of the flow past the gap From these studies, grooves can increase performance while maintaining pressure drop Micro pin–fins, micro-studs, pillars, and square pin–fins are all synthetically engineered structures, usually made of silicon but also of other thermally conducting materials, which have shown significant improvements in removing heat These structures protrude out of the surface, increase the wall surface area, and interrupt the steady flow of the fluid They can take different shapes and sizes and be placed in different patterns heat transfer engineering 529 Figure Different shapes used for fins on the surface of the microchannel to improve the thermal heat transfer performance Vanapalli et al [24] investigated the pillar “fin” shape, which contains the lowest friction factor with nitrogen gas flowing through the microchannel These pillars are used to increase the contact between the surface and the fluid with minimal thermal resistance The geometries tested were circles, squares, rhombus, elliptical, eye-shaped, and sine-shaped cross sections in staggered arrangements across the surface Pillars with the sine-shaped cross sections, when compared to all of the other geometries, have the lowest friction factor A three-dimensional (3D) representation of similar shapes that Vanapalli et al [24] used is shown in Figure Shapes of the fins can affect the motion of flow When the pillars are aerodynamic in shape, there is less separation of the fluid from the solid body, creating less thermal resistance at the interface Lee et al [25] implemented oblique fins into a microchannel to understand the effects of the local and overall heat transfer performance and pressure drop By introducing the oblique silicon fins to replace the conventional microchannel heat sink with continuous fins, the thermal boundary layer development along the channel surface is disrupted and a secondary flow of the fluid is created The opening between the fins disrupts the momentum and the trailing edge of the thermal boundary layer of each oblique fin This causes the leading edge to redevelop, allowing the flow to remain in the developing state This in turn enhances the heat transfer performance Also the secondary flow can produce mixing of the flow as the fluid flows through the fin opening, improving the performance The heat transfer coefficient of the channel with the oblique fins was enhanced by 80% when compared to the conventional channel Within this investigation, Lee et al [25] studied the pressure drop effects of the oblique finned channel and a conventional channel Minimal differences were obtained With the oblique fins, and the working conditions already described, there was a significant heat transfer performance enhancement with little effects on pressure drop A key factor that can influence the performance of heat transfer is the thermal conductivity of the fins, pins, and micro pin–fins used on the surface of the microchannel With a material that has a higher thermal conductivity, the thermal resistance is decreased and the temperature decreases Zhong et al [2] investigated the effects of varying the properties of an vol 32 nos 7–8 2011 530 J F TULLIUS ET AL array of microstructures placed along the bottom surface of the channel When the thermal conductivity of the microstructures was varied, the temperature decreased and the pressure drop remained fairly constant With a material with a higher thermal conductivity, the resistance at the interface decreases and the convection heat transfer performance is increased Pasupuleti and Kandlikar [1] have applied many of these factors—fluid properties, material properties, fin shape, etc.—to their investigation where they studied the effects of refrigerant R-123 as the working fluid in a single-chip module setup A single-chip module is essentially a heat sink on a silicon microchip The silicon wall is coated with mini ellipse-shaped fins to increase the surface area In contrast to water, this refrigerant is considered a safe working fluid for electronic devices that not require corrosion inhibiters or biocide The results of refrigerant R-123 were compared to those of water and it was found that they had similar results [1] Countless modifications to the surfaces of microchannels have been extensively studied and tested to improve the performance of the cooling devices Surface roughness, grooves, and microfins are among the few alterations made to the microchannels in order to remove temperature from the surface using a single-phase laminar flow Despite these encouraging effects, microchannels with single-phase fluids are still not enough to keep up with the innovations of the electronic industry TWO-PHASE FLOW Phase change of a fluid can cause a substantial amount of heat to be absorbed When a liquid turns into a gas or a gas into a liquid, the temperature reaches a constant temperature until the percentage composition of the fluid is either solely liquid or solely vapor The evaporation of fluid can result in the absorption of heat during the phase change between liquid and vapor More evaporation of the fluid flowing though the microchannel can result in a higher heat flux [26] The fluid surrounding the component reaches a temperature that exceeds the fluid saturation temperature, and vapor bubbles originate in the small cavities or pores on the surface There are two types of boiling occurrences: pool boiling and flow boiling Pool boiling is the thermal cooling of a surface with a stagnant fluid that can effectively remove heat Flow boiling refers to boiling where the liquid has a high-velocity flow field Both techniques are limited in the nucleate boiling regime by the critical heat flux (CHF), which is the maximum point of operation for engineering system To influence the flow boiling and pool boiling process, one should consider reducing the boiling incipience temperature and increasing the CHF in efforts to improve the boiling process [12] Pool Boiling Pool boiling is the boiling of an inert liquid At low heat flux levels, natural convection is dominant, but at high heat flux heat transfer engineering levels, nucleate superheating begins to occur Nucleate boiling is the means by which vapor bubbles form and escape the heated surface A larger bubble size on a nucleation site for a given amount of time results in a more effective thermal performance More liquid is being evaporated as the bubble size increases [27, 28] When boiling is initiated, the growth of the bubble from one cavity extends to other nucleation sites, causing those to initiate The boiling spreads rapidly over the surface, increasing the convective heat transfer coefficient and decreasing the surface temperature [29] Using liquids with low boiling points, phase change from a liquid to a gas occurs more quickly, more heat can be removed, and the pressure drop decreases Nucleate boiling initiates when the temperatures of the fluids are few degrees higher than the saturation temperature, where small surface defects appear As the microchip is heated, the boiling incipience appears but only with a few vapor bubbles Bubbles are generated between the gaps of the fins or surface cavities With the evaporation of the surrounding liquid, the bubble grows in between the fins that are confining it As the vapor grows, the thin film surrounding the bubble evaporates with a high heat transfer coefficient value With its increasing size, the bubble forces itself to the top of the fin surface Liquid from under the rapidly growing bubble attracts the remaining liquid surrounding the fins This process enhances the microconvection of the liquid along the walls of the fins With this suction reaction, there is an increase in evaporation, which effectively enhances effective heat transfer With increasing heat flux, there is an increase in nucleation sites When there are more nucleation sites, a domino effect is triggered, creating more vapor bubbles [27, 28] When compared to a smooth surface, the optimal effect of the phase change phenomena ideally produced by microstructures or microcavities in the surface is to have a lower boiling incipience, decrease the surface temperature, increase the CHF, and increase the evaporation to obtain more nucleation bubbles [28, 30] Many factors must be considered when attempting to optimize the performance of the cooling method Surface roughness, orientation of the microchip relative to the flowing fluid, and geometry or configuration of the fin arrays can all alter the effect of cooling A higher thermal conductivity, an enlargement of the interface surface area, and optimization of fin placement, geometry, and dimensions are needed to improve the efficiency and performance of microstructures [2] The orientation of the channel can influence the thermal performance A comparison of a vertically and a horizontally mounted chip was observed for a smooth surface and a finned surface using FC-72 The surface orientation of the chip increases the heat transfer performance in the nucleate boiling regime as the angle increases toward a vertical position for a smooth surface It is believed that gravity assists the increase in performance as the chip is mounted in a relatively vertical direction For a treated surface, however, the orientation of the chip has little or no effect on the heat transfer performance [27, 29] vol 32 nos 7–8 2011 J F TULLIUS ET AL Surface roughness can also influence the thermal performance for a pool boiling process Testing of surfaces with different degrees of roughness using FC-72 was performed by Honda and Wei [31] A high surface roughness lowered the boiling incipience, increases the CHF, and increases nucleate boiling Shokouhmand et al [22] studied numerically the effects of surface roughness in microchannels on convective heat transfer in fully developed, laminar flow With increasing relative roughness, the friction factor increases, the Nu remains unchanged, and the convective heat transfer coefficient slightly increases The use of small cavities is one of the techniques that increase the heat transfer area In this process, an array of holes with precise dimensions is drilled into the silicon surface; in effect, these holes act as nucleation cavities and enhance nucleate boiling An investigation of the thermal performance on artificial micro cavity surfaces was conducted by Yu et al [12] using a dielectric fluid, FC-72 as the working fluid The 16 × 16, 25 × 25, and 33 × 33 arrays of microcavities were tested varying the heat flux, diameter, and depth When increasing the diameter of the cavity at moderate and high heat fluxes, an earlier decay and low peak value of the heat transfer coefficient were experienced Varying the cavity depth too much can lead to the overall heat transfer coefficient’s rapid decline Also, because of the larger flow resistance created by the deeper cavities, the rewetting of the surface diminishes The test section with a 33 × 33 array of cavities results in an increase of the CHF by a factor of 2.5 when compared to that of the plain silicon surface with a heat flux value of 30 W/cm2 Micro pin-fins, micro-studs, pin-fins, and square pin-fins are manually manufactured structures, usually silicon, proven to significantly enhance nucleate boiling Wei et al [27] submerged two different pin-fin geometries in FC-72 to monitor the pool boiling performance These fin types, each in its different topology and shape, improve thermal convection when they are submerged in the liquid These cooling mechanisms, because of the increase of chip surface area, allows for a higher heat flux to be used These microchannel modifications have proven to be effective in decreasing the boiling incipience and surface temperature and improving the CHF The use of nanofluids as the working fluid supplements heat transfer performance with its higher thermal conductivity than a pure fluid–air, water, or fluorochemicals [32] Nanofluids are colloidal nanoscale metallic or nonmetallic particles in a base fluid [32–37] By adding nanoparticles to the volume of fluid, thermal conductivity can be increased by about 40% [38] Kedzierski [39] investigated the effect that CuO nanoparticle concentration had on a roughened horizontal flat surface A 2% and a 4% volume concentration of CuO in R-134a were compared in this study On average the mixtures with a 4% CuO volume concentration had a 140% larger value for boiling heat flux than the mixture with only 2% volume [39] CHF is enhanced up to 45% with a 1% volume concentration of alumina nanofluid at a mass flux of 2500 kg/m2 [33] Wright et al [40] studied the effects of the percentage of metal particles in the nanofluid using CNT to increase the thermal conductivity of the heat transfer engineering 531 fluids If the concentration of the metal particles is too low, there are no significant improvements At 1% volume concentration of CNT, there was about a 10–20% increase in the thermal conductivity The higher concentration of these metal particles inside the fluids increases the viscosity, making it more difficult for the fluid to flow through microstructures [40, 41] An explanation for the amount of metallic nanoparticles is that the orientation and alignment of the CNT are random in the fluid and the CNT need physical contact with each other in order to increase the thermal conductivity With a low concentration, there is minimal contact as there are fewer metallic particles [40] Gold nanoparticles have also been placed in refrigerant R-141b to increase the CHF Boiling coefficients of the fluid increase with an increased concentration of nanoparticles For only a 1% volume concentration of nanosized Au particles in refrigerant R-141b, the heat transfer coefficient doubled when compared to the fluid without nanoparticles Nanosized Au particles can significantly increase pool boiling heat transfer when placed in refrigerant R-141b, but the surface roughness and the particle size aged after one test, decreasing the effects [42] Using nanofluids will improve the heat transfer due to the nanoparticle interaction with the surface roughness when compared to those without nanoparticles In general, the wettability of the surface can play a critical role in improving the heat transfer performance Truong et al [30] used nanofluids to investigate how the surface wettability affects the CHF and the heat transfer coefficient Minimum wettability contact angle will maximize the CHF To achieve a high heat transfer coefficient, the optimal surface is one with low wettability containing many nucleation sites Surfaces should be hydrophilic, having an intrinsic contact angle no higher than 90◦ Too much surface roughness can cause a higher contact angle, leading to a smaller CHF and a hydrophobic surface Nanoparticles suspended in fluids will not directly affect the heat transfer coefficient through the contact angle; rather, the nanoparticles can create many microcavities and therefore nucleation sites The heat transfer coefficient strongly depends on the number of active nucleation sites available for vaporization [30] Many modifications to microchannel surfaces have been tested in enhancing the cooling performance For pool boiling, increasing surface roughness and adding small cavities or fins to the channel walls can lower the boiling incipience, increase the CHF, and increase the nucleate boiling of the system To further enhance the thermal performance, nanofluids with an optimal amount of volume concentration of particles can be used Because of the continuous advancements in electronic components, further enhancements of the microstructure materials, configurations, geometry, etc still need to be investigated Flow Boiling Flow boiling has the capability of increasing the thermal performance of the microchannel; it can provide a much higher heat transfer coefficient than both the single-phase flow and the pool boiling Flow boiling is a two-phase process that convectively removes heat as a fluid that is flowing with some given velocity vol 32 nos 7–8 2011 532 J F TULLIUS ET AL Figure Flow patterns in flow boiling To understand the flow boiling process, it is essential to understand how it relates to the macro-scale assumptions Among many of the previous works done regarding flow boiling, there is a controversy about the dominant mechanism driving the heat transfer at the micro-scale Is it the conventional nucleate boiling that is dominant in the macro-scale, or is it the forced convection of the vapor bubble that transfers the most heat? In nucleate boiling, the heat transfer coefficient is affected by the heat flux inputted into the system but it is independent of the fluid flow rate and vapor quality On the other hand, convective boiling is driven by the fluid’s flow rate and the vapor quality and is not a function of the inputted heat flux [43] Thome et al [44] believe flow boiling has the most heat transfer from convection At the macro-scale, experimental studies have concluded that nucleate boiling is the dominant factor in removing heat with little effect of the convective flow; however, at the micro-scale, the heat transfer is mainly affected by a thin liquid film that surrounds the elongated vapor bubbles, not nucleate boiling [45] Because of this, using macro-scale assumptions in microchannels is not realistic when predicting the flow boiling coefficients The principal flow regimes in flow boiling are bubbly, elongated bubble (slug), churn, annular, mist, and flows with partial dry-out Figure displays a schematic of the main flow patterns that may be experienced with a constant heat flux Flow patterns in a small channel can vary slightly, depending on the orientation of the channel because of the effects of gravity For a horizontal channel, when the fluid reaches temperatures just above the saturation temperature, small bubbles begin to nucleate This is known as the bubbly regime As vapor bubbles increases, a flow pattern develops that entraps the vapor bubbles in the main flowing liquid, known as plug flow With more heat, the bubbles grow to be within a few micrometers of the channel’s hydraulic diameter The bubble is now confined by the microchannel and it can no longer grow in diameter, but elongates, growing in length This is now the elongated bubble regime or the slug regime This pattern is the dominant regime for flow boiling where the most heat is transferred convectively Separating the growing elongated bubbles is a section of fluid also known as liquid slug There is a small thin film of liquid surrounding the vapor bubble separating it from the microchannel wall If the liquid film enclosing the elongated bubble reaches a minimum thickness, the region is considered dried out, also known as the vapor slug As the length of the vapor continues to grow, it swallows up the liquid slug until the elongated bubble emerges to the next cycle or the next patch of vapor This is shown in Figure When the dominant flow is vapor and has a small film of liquid surrounding the bubble, this is known as the annular regime This flow pattern may have small droplets of liquid dispersed throughout the vapor core The vertical channel is very similar as it experiences the slug, churn, annular, and mist pattern It initiates with the bubbly flow and quickly the vapor pockets grow to a slug regime The vapor bubble continues to grow into churn, then annular, and then mist fashion Because of the influence of gravity, the horizontal flow patterns are more likely to have intermittent drying and rewetting of the upper surfaces of the tube for slug and annular patterns [44, 46, 47] Figure shows a model used to describe the elongated bubble flow regime in the flow boiling process At a fixed reference frame, a liquid slug of some length will pass, followed by an elongated bubble, and if the thin film dries out before it reaches the next liquid slug, there will pass a vapor slug This cycle repeats itself until the vapor is continuous throughout the channel [44, 46] To better understand the flow boiling profiles, Thome et al [44] developed a three-zone model in an effort to qualitatively and quantitatively describe the heat transfer effects due to flow boiling in microchannels This model describes the evaporation of the elongated bubble as it flows through a microchannel and predicts the local heat transfer coefficient in the liquid slug, evaporating elongated bubble, and a vapor slug or the dry-out region The three-zone model takes into account the frequency of the vapor bubbles with respect to time, the minimum liquid film thickness as dry-out occurs, and the liquid film thickness When Figure Model used to describe the flow boiling process heat transfer engineering vol 32 nos 7–8 2011 J F TULLIUS ET AL compared to the liquid slug region, the heat transfer coefficient in the thin film evaporation region (elongated bubble) is several times higher The values for the vapor slug region, annular, are almost negligible as the heat transfer coefficient of air is much lower Like in single-phase flow and pool boiling, adding microstructures to the surfaces of microchannels can enhance the cooling performance Chien et al [48] added square pin-fins of dimension 400 µm × 400 µm × 400 µm (width × thickness × height) to a rectangular 20 mm × 25 mm Cu plate and investigated the heat transfer effects when varying the heat flux and the flow rate For both a smooth and pin-finned surface, water and FC-72 were used as the working fluids in the microchannel For water, the performance is influenced by the flow rate for heat flux lower than 60 W/cm2 At low flow rates, the heat transfer coefficients increase with increasing heat flux However, at high flow rates, the heat flux is almost negligible with minimal effect to the heat transfer coefficient For lower heat fluxes the performance is driven by the nucleate boiling, and for higher flow rates, the forced convection is dominant However, when using FC-72 as the working fluid, the most influential parameter is the heat flux When varying the flow rate, the heat transfer coefficient curves were similar, implying that the boiling heat transfer is the more dominant effect, rather than the forced convection With the saturation temperature in FC-72 (56◦ C) being much lower than that of water (100◦ C), one should expect to see the nucleation start sooner More vapor bubbles are observed with Fluorinert For low heat fluxes, the heat transfer coefficient increases as the flow rate decreases, but for lower flow rates, partial dry-out was observed during the experiments, which drastically degrades the performance The pin-finned surface increases the heat transfer coefficient by about 30% and contains a greater CHF for a fixed flow rate when compared to the smoothed surface The convective heat transfer was greater at low flow rates (80–160 mL/min) and heat fluxes (18–35 W/cm2) for FC-72 than for water Water, however, had a superior performance compared with FC-72 for higher flow rates [48] Chien et al [49] in another investigation compared the effect of FC-72 cooling fluid flow boiling through two different square pin-fin geometries A comparison was conducted of square pin-fins with geometries of 400 µm × 400 µm × 400 µm and 200 µm × 200 µm × 200 µm with various flow rates (80–960 mL/min) and heat fluxes (18–50 W/cm2) Similar to the previous investigation, the heat flux is the driving force influencing the heat transfer coefficient, as opposed to the flow rate, because of the dominant nucleate boiling effect With the square pin-fins, the partial dry-out only occurred at the lowest flow rate (80 mL/min), unlike with the smoothed surface, because the gaps of the fins prevent the drying out by the liquid it retains on the surface Therefore, the structured surface had a significantly higher heat transfer performance because the surface was kept from drying out for lower flow rates and high heat fluxes At high flow rates, both geometries contain similar results, but at the lowest flow rate tested (80 mL/min), the geometry with the smaller square pin-fins had a 5–10% higher heat transfer coefficient For both pin-finned surfaces, there is heat transfer engineering 533 a 10–20% increase in the heat transfer coefficient when compared to the smooth surface as the flow rates were between 320 and 960 mL/min [49] Similar results were found in the study conducted by Lie et al [50] Cetegen et al [51] used refrigerant R-245fa and passed it through a force-fed evaporation element and a microgrooved surface using three mass flow rates From the results, for all mass flow rates, there was no variance in the trend below a heat flux of 320 W/cm2 For lower heat fluxes in this experiment, the heat transfer coefficient was due to the variance of the heat flux Therefore, it can be concluded that the dominant heat transfer mechanism was nucleate boiling with negligible convective boiling At a heat flux of 320 W/cm2 there was a huge temperature jump and a drop in heat transfer coefficient where it is believed to have reached the CHF Grooved surfaces, like finned surfaces, can also influence the thermal performance of flow boiling process For space applications, the effects of gravity on flow boiling through microchannels can be very useful Kandlikar and Balasubramanian [52] varied the orientation of a six-parallelmicrochannel system with flow boiling of water in three different directions: horizontal, vertical with an upward flow, and vertical with a downward flow, all while maintaining the heat and mass flux conditions For all directions, the flow regimes encountered were bubbly flow, thin film nucleation, plug flow, churn flow, and annular flow The flow patterns seem to be similar for all orientations of the channel, except the shapes of the vapor bubbles in the vertical down flow orientation are more bullet-shaped, while there was an elongated circular shape for the horizontal orientation A flow reversal effect was also encountered for all orientations, but was more noticeable in the vertical downward flow case Similar results of the heat transfer performance for the vertical up flow and the horizontal flow case were better than that of the vertical down flow case due to this higher flow reversal encountered Luciani et al [53] compared the effects of microgravity to terrestrial gravity in a single vertical microchannel using a transparent, nonflammable and nonexplosive fluid with a low boiling temperature A microchannel was placed in an Airbus A300 Zero G, flying in a parabolic fashion, starting from terrestrial gravity and peaking at microgravity At microgravity, vapor patterns lead to larger bubble sizes than in terrestrial gravity Churn and slug flow patterns were dominant, while in terrestrial gravity, for the same conditions, bubbly flow and some slug flow patterns were visible The heat transfer coefficient in microgravity was much higher Because of the larger vapor bubbles and the higher heat transfer coefficient, Luciani et al [53] concluded his heat transfer performance was driven by the convective flow and not nucleate boiling Gravity has little effect on the heat transfer performance at a terrestrial level, which seems to be influenced by nucleate boiling At microgravity levels, the forced convection of the fluid guides the heat transfer performance As stated earlier, nanofluids can effectively enhance the thermal performance of microchannels Peng et al [54] investigated vol 32 nos 7–8 2011 K.-S YANG ET AL 699 placed at any position above the square microchannel To minimize the effect of maldistribution caused by the inlet, an inlet plenum is made at the entrance of the test section whereas the inlet is placed at the bottom of the plenum, as seen in Figure 3c With this design, the working fluid enters into the plenum and rises gradually before it distributes quite evenly into the multiport microchannels Similarly, a downstream plenum having a similar configuration is exploited to reduce the effect from the downstream A 10-mm-thick layer of rubber insulation is wrapped around the cold plate and Bakelite board to minimize the heat loss to the surrounding At the inlet and outlet of the cold plate, a precise differential pressure transducer having an accuracy of 0.1% is used to measure the pressure drop across the cold plate DATA REDUCTION The measured temperatures at the nine locations underneath the microchannels were first corrected to obtain the corresponding wall temperature at the inner wall surface via a onedimensional conduction equation, i.e., Q δw T¯wall = T¯b,wall − ks A (1) where T¯wall is the average surface temperature of cold plate whereas T¯b.wall is the average surface temperature beneath the cold plate and δw is the thickness of the cold plate; ks is the corresponding thermal conductivity of cold plate (copper); and Q’ is the heat transfer into the cold plate, and is obtained by subtracting the heat loss from the input power: Q = Q input − Q loss Figure Configuration of the microchannels heat sink test section × 25.4 mm with the corresponding rectangular microchannels with a hydrodynamic diameter of 480 and 790 µm, respectively Its detailed dimensions along with the inlet location of the heat sink are shown in Figures 3a and b Thermocouples are used to measure the surface and fluid temperature A total of nine T-type thermocouples are placed beneath the cold plate for measurement of the average surface temperature, whereas two thermocouples are used to record the inlet and outlet temperatures of HFE-7100 across the cold plate The thermocouples were precalibrated with an accuracy of 0.1◦ C The test cold plate is located above a well-fitted Bakelite board A transparent piece of glass is placed on top of the test section Observations of flow patterns are obtained from images produced by a high-speed camera, type Redlake Motionscope PCI 8000s The maximum camera shutter speed is 1/8000 s The high-speed camera can be heat transfer engineering (2) where Qinput (I × V) is the supplied input power and Qloss is the heat lost across the Bakelite segment, which can be estimated from the one-dimensional heat conduction equation from the measured temperature difference of the thermocouples that were placed above and below the Bakelite segment The average heat transfer coefficient can be obtained as follows: Q (3) h= A Tm where A is total surface area and Tm is the effective mean temperature difference, and is calculated from the following: Tm = T¯wall − Ts (4) During the two-phase experiment, the inlet vapor quality is controlled by a double-pipe heat exchanger that is circulated with controlled water temperature by a thermostat Note that the HFE-7100 is initially subcooled before entering the preheater Hence the corresponding thermodynamic quality can be estimated from the simple energy balance from the preheater: xin = ˙ p,H F E7100 Tsub Q water − mc ˙ fg mi vol 32 nos 7–8 2011 (5) 700 K.-S YANG ET AL Notice that Tsub is the inlet subcooling of HFE7100, and ifg the latent heat of HFE-7100 The test conditions within the test sample are all at saturated state RESULTS AND DISCUSSION Figure presents the two-phase convective heat transfer coefficient versus vapor quality subject to the influence of heat flux for the two test microchannels (Dh = 480 and 790 µm) with G = 100, 200, and 400 kg m−2 s−1 The saturation pressure is fixed at 110 kPa before entering the test section and the prescribed heat flux is 25 kW m−2 or 37.5 kW m−2, respectively Normally the heat transfer coefficients for Dh = 480 µm exceed those of Dh = 790 µm The results are in line with recent studies [8, 9]) On the other hand, for a moderate mass flux of 200 and 400 kg m−2 s−1, the heat transfer coefficients are relatively invariant with the heat flux and vapor quality, whereas a noticeable influence of heat flux on the heat transfer coefficient is encountered for Dh = 790 µm, but it still holds comparatively unchanged with respect to mass flux and vapor quality Upon the influence of heat flux, the two distinct trends for the two test channels imply different mechanisms behind them The appreciable influence of heat flux on the heat transfer coefficient for Dh = 790 µm implies that the nucleate boiling plays an essential role By contrast, for a smaller hydraulic diameter of 480 µm, a confinement effect takes control and the generated bubbles easily occupying the channel engender early establishment of a churn/annular flow pattern In this regard, bubble nucleation is not the sole heat transfer mechanism, and the thin film evaporation for the annular flow and the microlayer evaporation between elongated bubble and wall also contribute to the heat transfer As a consequence, one can see a rather small influence of heat flux on the heat transfer performance for Dh = 480 µm, whereas a detectable influence of heat flux is seen for Dh = 790 µm For a better interpretation of the aforementioned argument, a typical progress of flow pattern with G = 400 kg m−2 s−1 subject to the influence of heat flux and channel size is shown in Table For the smaller size channel (Dh = 480 µm), the dominant flow pattern, except that for x = 0.12 and q = 25 kW m−2, is almost annular throughout the test range Conversely, the flow pattern develops from elongated bubble, to slug, to churn, and finally into annular flow for Dh = 790 µm as the vapor quality is increased Thus, the smaller channel reveals a rather small influence of heat flux, while the latter one is prone to being influenced by heat flux A sharp decline of the heat transfer coefficient is seen for G = 200 kg/m2-s at q = 37.5 kW m−2 and x > 0.7 This is apparently due to the early dryout of working fluid within the microchannel However, for a smaller mass flux like G = 100 kg m−2 −1 s , the heat transfer coefficients for both channels reveal a quite different characteristic than those for larger mass flux Despite the heat transfer coefficient for the smaller channel still exceeding that of the larger channel, the larger channel does not reveal an apparent dependence of heat flux, while the smaller channel with q = 37.5 kW m−2 shows an appreciable decline heat transfer engineering Figure Two-phase heat transfer coefficient versus vapor quality subject to influence of heat flux for G = 100, 200, and 400 kg m−2 s−1 with the rise of vapor quality A close examination of the flow visualizations indicates that it is also related to the flow pattern In fact, the decline of heat transfer coefficient for Dh = 480 µm at G = 100 kg m−2 s−1 with q = 37.5 kW m−2 is caused by the vol 32 nos 7–8 2011 K.-S YANG ET AL 701 Table Flow pattern for both test channels with G = 400 kg m−2 s−1 presence of flow reversal in some part of the multiport channels The flow reversal is found to be strongly related to the applied heat flux and is especially pronounced when the mass flux is low Some typical photos showing the progress of vapor slug within the microchannel for G = 100 kg m−2 s−1, Dh = 480 µm, are seen in Table 2a As depicted in the photos, for a higher heat flux of 37.5 kW m−2, one can find that within some channels the vapor slug is moving backward, yet it expands with time due to heat addition Conversely, for a lower heat flux of 25 kW/m2, the vapor slug moved with the main flow direction regardless of the vapor slug still expanding along the flow direction Wang et al [10] found that at a given heat flux and inlet water temperature, depending on the mass flux, stable and unstable flow boiling regimes existed For a 186-µm microchannel, they identified that the stable/unstable flow regime is related to the ratio of q/G Unstable flow boiling persists when q/G > 0.96 kJ/kg Though the present oscillation flow conditions not quantitatively agree with the q/G ratio reported by Wang et al [10], they are quite similar to the Wang et al results to some extent The flow oscillation is quite complex, for it resorts to the difference in working fluid, operating conditions, and channel size Generally, a larger value of q/G will be prone to oscillation On the other hand, the flow reversal phenomenon is not seen for Dh = 790 µm at q = 37.5 kW m−2 and G = 100 kg m−2 s−1 heat transfer engineering as shown in Table 2b Therefore, one can see that there is no apparent decline of heat transfer coefficient when x < 0.5 However, a larger heat flux still may bring about local early partial dryout within the microchannel, leading to some deteriorations of heat transfer performance; the effect offsets the influence of heat flux and results in an insignificant variation of the heat transfer coefficients for Dh = 790 µm at G = 100 kg m−2 s−1 The flow reversal within some microchannels implies that some other channels must have a much higher mass flux, for the average mass flux is fixed during the experiments Note that the origin of the flow reversal is due to the expansion of vapor slug during heat addition With a higher heat input, the onset of forming vapor slugs is rather violent and it can easily fill up the channel The resultant phenomenon pushes the liquid at the tail of the expanding slug, and this acts like a roadblock to the main flow within the microchannel As a consequence, flow reversals occur in some of the channels An analogous phenomenon was also reported by Kandilikar et al [11] This phenomenon becomes even more severe when the heat flux is further raised, thereby leading to an appreciable decline of heat transfer coefficient versus vapor quality Figure depicts the two-phase convective heat transfer coefficient versus vapor quality subject to the influence of mass flux for the two test microchannels (Dh = 480 and 790 µm) vol 32 nos 7–8 2011 702 K.-S YANG ET AL Table 2a Progress of the flow pattern with G = 100 kg m−2 s−1 and xave = 0.4 for Dh = 480 µm Figure Effect of mass flux on the two-phase heat transfer coefficient generally slightly lower than that of G = 300 kg m−2 s−1 It is not totally clear about this phenomenon but it is likely that the decrease in heat transfer coefficient may be associated with the suppression of nucleate boiling caused by the contribution of forced convection The measured heat transfer coefficients are compared with the Cooper correlation [12] The correlation is given as h C = 55q 0.67 M −0.5 Prm (− log10 Pr )−0.55 m = 0.12 − 0.2 log10 R p with G = 100, 200, 300, and 400 kg m−2 s−1 The saturation pressure is also fixed at 110 kPa, having a prescribed heat flux of 37.5 kW m−2 As illustrated in the figure, except for G = 100 kg m−2 s−1 where flow reversal may occur, the effect of mass flux on the heat transfer coefficient is not as evident as that of heat flux This is applicable for both test channels In the meantime, for Dh = 480 µm, despite the fact that there is no significant difference upon the measured heat transfer coefficients subject to mass flux variation, it is interesting to know that the heat transfer coefficients for G = 400 kg m−2 s−1 are Table 2b Progress of the flow pattern with G = 100 kg m−2 s−1 and xave = 0.4 for Dh = 790 µm heat transfer engineering (6) (7) As reported by Stephan and Abdelsalam [13], the commercial-finish copper tubes generally have a surface roughness of 0.4 µm Therefore, the surface roughness, Rp , is given as 0.4 µm in the present calculation The overall deviation amid the predicted values versus the measurements for Dh = 790 µm is within ±30% On the other hand, for Dh = 480 µm, the Cooper correlation is found to considerably underpredict the measurements, ranging from 35% to approximately 85% Notice that the Cooper correlation was originally developed for nucleate boiling and did not contain the effect of mass flux The good agreement between Cooper correlation and the measurements for Dh = 790 µm implies a dominance of nucleate boiling Results of the comparisons confirm with the discussions already drawn from the discussion of Figure The results are also analogous to those reported by Bertsch et al [14], who performed a comparative analysis of heat transfer coefficients against various correlations They had compiled 1847 measurements from 10 independent sources with hydraulic diameter ranging from 0.16 mm to 2.01 mm, and performed comparisons with the database against 12 correlations Their comparisons indicated that the Cooper correlation gives the best overall predictive ability However, it should be mentioned that for a smaller size like Dh = 480 µm, the Cooper correlation considerably underpredicts the present test data due to a significant change of flow pattern This trend is also reported by Harirchian and Garimella [9] vol 32 nos 7–8 2011 K.-S YANG ET AL CONCLUSIONS This study examines the heat transfer characteristics of the dielectric fluid HFE-7100 within multiport microchannel heat sinks having hydraulic diameters of 480 µm and 790 µm, respectively Flow visualization is also conducted in this study For the same heat flux and mass flux, the test results indicate that the heat transfer coefficient for the smaller channel is generally higher than that of the larger channel Depending on the channel size, the test results show that the heat transfer coefficients are roughly independent of heat flux and vapor quality for a modest mass flux ranging from 200 to 400 kg m−2 s−1 for a channel size of 480 µm Conversely, a noticeable increase of heat transfer coefficient with heat flux for Dh = 790 µm is observed The corresponding flow visualization confirms that the difference arises from flow pattern The major flow pattern for the smaller channel is dominated by churn/annular flow, leading to a negligible influence of heat flux, yet for a larger channel the flow pattern develops from bubbly, to elongated bubble, slug, and churn/annular, which brings about a detectable influence of heat flux However, for a smaller mass flux of 100 kg m−2 s−1, the presence of flow reversal at an elevated heat flux for Dh = 480 µm is seen, leading to an appreciable drop of heat transfer coefficient For a larger channel size of 790 µm, though the flow reversal is not observed at a larger heat flux, some local early partial dryout still occurs to offset the heat flux contribution, and results in an unconceivable influence of heat flux The measured heat transfer coefficients for Dh = 790 µm are well predicted by the Cooper correlation However, the Cooper correlation considerably underpredicts the test data by 35–85% for Dh = 480 µm For the same heat flux, the influence of mass flux on the heat transfer coefficient is quite small, and this is applicable for both microchannels (Dh = 480 µm and 790 µm) NOMENCLATURE A cp Dh G h hC I ifg ks m m˙ Pr q Q’ Qinput Qloss Rp surface area (m2) specific heat (J kg−1 K−1) hydraulic diameter (m) mass flux (kg m−2 s−1) heat transfer coefficient (W m−2 K−1) boiling heat transfer coefficient for Copper correlation (W m−2 K−1) current (A) latent heat of HFE-7100 (J kg−1) thermal conductivity of cold plate (W m−1 K−1) molecular weight (kg/kmol) mass flow rate (kg s−1) reduced pressure heat flux (W m−2) heat transfer into the cold plate (W) supplied input power (W) heat loss across backlite (W) surface roughness (µm) heat transfer engineering t Ts T¯wall T¯b,wall V x xave time (s) saturation temperature (K) average surface temperature of cold plate (K) average surface temperature beneath the plate (K) voltage (V) vapor quality average vapor quality of inlet and outlet 703 cold Greek Symbols δw thickness of the cold plate (m) Tm effective mean temperature difference (K) Tsub inlet subcooling of HFE-7100 (K) REFERENCES [1] Thome, J R., Boiling in Microchannels: A Review of Experiment and Theory, International Journal of Heat and Fluid Flow, vol 25, pp 128–139, 2004 [2] Kandlikar, S., Garimella, S., Li, D., Colin, S., and King, M R., Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier Science, Oxford, UK, 2006 [3] Ribatski, G., Wojtan, L., and Thome, J R., An Analysis of Experimental Data and Prediction Methods for Two-Phase Frictional Pressure Drop and Flow Boiling Heat Transfer in Micro-Scale Channels, Experimental Thermal & Fluid Science, vol 31, pp 1–19, 2006 [4] Thome, J., State-of-the-Art Overview of Boiling and TwoPhase Flows in Microchannels, Heat Transfer Engineering, vol 27, pp 4–19, 2006 [5] Cheng, P., Wu, H Y., and Hong, F J., Phase-Change Heat Transfer in Microsystems, Journal of Heat Transfer, vol 129, pp 101–107, 2007 [6] Chen, T., and Garimella, S V., Effects of Dissolved Air on Subcooled Flow Boiling of a Dielectric Coolant in a Microchannel Heat Sink, ASME Journal of Electronic Packaging, vol 128, pp 398–404, 2006 [7] 3M, Thermal Management Fluids and Services, 3M, St Paul, MN, 2003 [8] Qi, S L., Zhang, P., Wang, R Z, and Xu, L X., Flow Boiling of Liquid in Micro-Tubes: Part II—Heat Transfer Characteristics and Critical Heat Flux, International Journal of Heat and Mass Transfer, vol 50, pp 5017–5030, 2007 [9] Harirchian, T., and Garimella, S V., The Critical Role for Channel Cross-Sectional Area in Microchannel Flow Boiling Heat Transfer, International Journal of Multiphase Flow, vol 35, pp 349–362, 2009 [10] Wang, G., Cheng, P., and Wu, H., Unstable and Stable Flow Boiling in Parallel Microchannels and in a Single Microchannel, International Journal of Heat and Mass Transfer, vol 50, pp 4297–4310, 2007 vol 32 nos 7–8 2011 704 K.-S YANG ET AL [11] Kandlikar, S G., Kuan, W K., Willistein, D A., and Borrelli, J., Stabilization of Flow Boiling in Microchannels Using Pressure Drop Elements and Fabricated Nucleation Sites, Journal of Heat Transfer, vol 39, pp 159–167, 2006 [12] Cooper, M G., Heat Flow Rates in Saturated Nucleate Pool Boiling—A Wide-Ranging Examination Using Reduced Properties, Advances in Heat Transfer, vol 16, pp 157–239, 1984 [13] Stephan, K., and Abdelsalam, M., Heat Transfer Correlations for Natural Convection Boiling, International Journal of Heat and Mass Transfer, vol 23, pp 73–87, 1980 [14] Bertsch, S S., Groll, E A., and Garimella, S V., Review and Comparative Analysis of Studies on Saturated Flow Boiling in Small Channels, Nanoscale and Microscale Thermophysical Engineering, vol 12, pp 187–227, 2008 Kai-Shing Yang is a scientific researcher at the Green Energy & Environment Research Laboratories, ITRI, Taiwan He received his M.S and Ph.D in mechanical engineering from National Yunlin University of Science and Technology, Taiwan, during 1998–2004 and joined the Energy & Environment Research Lab., Industrial Technology Research Institute, Hsinchu, Taiwan, during 2004–2009 His research areas include enhanced heat transfer and multiphase system technology heat transfer engineering Yeau-Ren Jeng is a professor in the Department of Mechanical Engineering, National Chung Cheng University, Taiwan He received his Ph.D from the Department of Mechanical Engineering, Case Western Reserve University, Cleveland, OH His research areas include tribology, nanomechanics, nanotechnology, surface texture, electrical packaging, and semiconductor fabrication Chun-Min Huang is a master’s degree student in the Department of Mechanical Engineering, National Chung Cheng University, Taiwan His current research is in the microscale heat transfer technology Chi-Chuan Wang is a professor in the Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan He received his B.S., M.S., and Ph.D from the Department of Mechanical Engineering of National Chiao-Tung University, Hsinchu, Taiwan, during 1978–1989 He then joined the Energy & Environment Research Lab., Industrial Technology Research Institute, Hsinchu, for about 20 years (1989–2009), conducting research related to enhanced heat transfer, multiphase systems, microscale heat transfer, membrane separation, and heat pump technology He is also a regional editor of the Journal of Enhanced Heat Transfer and an associate editor of Heat Transfer Engineering vol 32 nos 7–8 2011 Heat Transfer Engineering, 32(7–8):705–713, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.509775 Long-Wave and Integral Boundary Layer Analysis of Falling Film Flow on Walls With Three-Dimensional Periodic Structures ¨ TATIANA GAMBARYAN-ROISMAN,1,2 HONGYI YU,1 KARSTEN LOFFLER, 1,2 and PETER STEPHAN Institute for Technical Thermodynamics, Technische Universit¨at Darmstadt, Darmstadt, Germany Center of Smart Interfaces, Technische Universit¨at Darmstadt, Darmstadt, Germany Falling films exhibit very complex wavy patterns, which depend on the properties of the liquid, the Reynolds number, the wall inclination angle, and the distance from the film inlet The film hydrodynamics governs the heat and mass transfer in the liquid films Our vision is to control and enhance heat and mass transport by using walls with specific microscale topographies that influence the falling film flow, stability, and wavy pattern In this work, long-wave theory and integral boundary layer approximation are used for modeling the falling film flow on walls with three-dimensional periodic microstructures The wall topography is periodic both in the main flow direction and in the transverse direction Examples of such microstructures are longitudinal grooves with sinusoidal path (or meandering grooves) and herringbone structures The effects of the Reynolds number, the wall inclination angle, and the longitudinal and transverse periods of the structure on the shape of liquid–gas interface are investigated It is shown that, as opposed to straight grooves in longitudinal direction, grooves with meandering paths may lead to significant interface deformations INTRODUCTION Thin liquid films frequently appear in various technological processes used for thermal management of electronic devices and other components, water desalination, distillation, powder production, chemical reactions, coating, etc., where they play a major role in defining performance and efficiency The advantages of falling liquid films include high heat and mass transfer rates at low liquid flow rate and short contact time between the liquid and the solid wall Falling films are unstable to long-wave disturbances [1–3] The instabilities lead to development of waves which are often characterized by a very complex structure The hydrodynamics The authors acknowledge the support of the German Science Foundation, DFG, through the Emmy Noether Program and through the Collaborative Research Center 568 Address correspondence to Dr Tatiana Gambaryan-Roisman, Institute for Technical Thermodynamics and Center of Smart Interfaces, Technische Universit¨at Darmstadt, Petersenstr 30, 64287, Darmstadt, Germany E-mail: gtatiana@ttd.tu-darmstadt.de of wavy film has been a focus of numerous experimental and theoretical investigations [4–9] Heat and mass transport in falling films are strongly coupled with the film hydrodynamics [10–12] Therefore, controlling the film hydrodynamics is an important step toward controlling and enhancing the heat and mass transfer in devices utilizing falling films One of the ways to influence the hydrodynamics and heat transfer in liquid films is using microstructured walls Several mechanisms of the wall topography influence on film hydrodynamics and heat transfer have been described Wall topography promotes the rivulet flow regime characterized by intensive evaporation in the vicinity of contact lines [13–16] Grooves arranged normal to the main flow direction may lead to appearance of vortices that intensify heat transfer through the mixing of liquid [17] The vortex flow pattern on walls with topography may also be developed as a result of the Marangoni effect [18] The wall (micro)structure also significantly affects the film stability and dynamics [13, 14, 16, 19–22] 705 706 T GAMBARYAN-ROISMAN ET AL One of the most extensively studied types of wall topography is comprised of grooves arranged normal to the main flow direction [17, 19–21, 23–27] Bontozoglou and Papapolymerou [25] and Wierschem et al [27] have performed linear analysis for small amplitude of the wall corrugation to compute the steady deformation of the liquid–gas interface (free surface) in the waveless falling film flow They have studied the free surface amplification, defined as the ratio between the amplitude of the free surface deformation and the amplitude of the wall corrugation, as well as the phase shift between the wall corrugation and the free surface deformation A linear resonance phenomenon has been predicted that manifests itself in a peak of the free surface amplification at a certain Reynolds number, depending on the period of the wall corrugation This phenomenon cannot be predicted on the basis of the creeping flow analysis Trifonov [20, 21] has studied the steady deformation of the liquid—gas interface for arbitrary amplitude of the wall corrugation by direct solution of Navier–Stokes equations and in the framework of the integral boundary layer (IBL) approach first introduced by Shkadov [28] Additionally, he has performed stability analysis of the film flow over a corrugated wall It has been found that, depending on the parameters of the wall corrugation and on the Reynolds and Kapitza number, the wall topography may have a stabilizing or a destabilizing effect on the film flow Experimental works report about a significant effect of the wall corrugation on the velocity field in the film [17] and on the free surface deformation and development of waves [19] The wall topography comprised of straight longitudinal grooves does not lead to steady-state deformations of the free surface as long as the topography is completely flooded by the liquid In this case the wall topography always stabilizes the film flow [13, 14, 22] If the liquid flow rate is low and the wall topography crests are dry, the deformation of the free surface is determined by the grooves geometry and by the flow rate [29] These flow regimes are characterized by a long cumulative length of the triple contact line and are therefore advantageous for evaporation process [13–15] In numerous industrial applications three-dimensional wall topographies are used [30, 33] In spite of the industrial relevance, theoretical and numerical investigations of film flow on three-dimensional mini- and microstructures are very rare Trifonov [32] has simulated steady deformations of the liquid–gas interface of falling film flowing along a wall with threedimensional topography This topography is a superposition of minigrooves arranged oblique to the main flow direction (rough corrugation with amplitude much higher than the Nusselt film thickness) and fine-grooved texture It has been found that in the range of moderate Reynolds numbers the free surface deformation can be adequately described on the basis of integral boundary layer approximation Hydrodynamics and heat transfer in falling liquid films over heated plates with three-dimensional topography has been experimentally studied by L¨offler et al [34, 35] Two structures of plates have been used in the experiments The first structure heat transfer engineering Figure Structured plates [35]: (a) plate with meandering mini-grooves; (b) plate with zigzag mini-grooves (herringbone structure) has been comprised of grooves with meandering path arranged along the main flow direction (Figure 1a) The main idea behind this topography is prevention of film dry-out at elevated heat fluxes and the increase of the cumulative contact line length in the low flow rate regimes, which may lead to essential intensification of evaporation The second plate has herringbone structure (Figure 1b) This kind of structure can induce a complex vortex flow pattern that is very advantageous for liquid mixing [31] and for heat transfer enhancement In this article, the deformation of liquid–gas interface in falling liquid films on three-dimensional topography is studied in the framework of long-wave theory and integral boundary layer approach The model is applied to two- and threedimensional periodic structures that are close to those studied experimentally by L¨offler et al [34, 35] THEORETICAL MODEL AND NUMERICAL METHOD Modeling of hydrodynamics and transport processes in liquid films is generally a very challenging task In addition to the velocity components and the pressure, the position of the free surface has to be determined Analytical treatment in most vol 32 nos 7–8 2011 T GAMBARYAN-ROISMAN ET AL 707 where ρσh ∗ h l gh ∗3 sin β, S = , H = ∗, L = ∗, F = H + L 3ν2 3µ2 h h y tgh ∗ sin β x X = ∗, Y = ∗, τ = h h 3ν (2) Here g is the gravity acceleration, σ is the surface tension, ρ the density, and µ the dynamic and ν the kinematic viscosity Re denotes the Reynolds number and S is an inverse crispation number The function F (X, Y, τ) describes the interface position The indices τ and X denote partial differentiation with respect to these variables The time-independent form of Eq (1) describes the steady deformation of the liquid–gas interface in the waveless falling film flow If the wall is unstructured or if the wall topography is a function of y only (longitudinal grooves or fins), then the interface in the absence of waves remains smooth [13] If the wall topography is periodic in x, the interface deforms Re = Figure Falling film geometry and coordinate system practically relevant cases is not possible The application of numerical methods is difficult and time-consuming due to the high aspect ratio between the lateral extent of the film and the film thickness These difficulties make large-scale three-dimensional direct numerical simulation of the film flow impractical In the following sections two asymptotic methods commonly used for studying the film hydrodynamics are described Long-Wave Theory If the characteristic film thickness h∗ is much smaller than the characteristic wave length of the film thickness variation, and if the Reynolds number of the flow is of the order of unity, the film dynamics can be described by a nonlinear partial differential equation in the framework of the long-wave theory [36] The velocity field inside the film can be uniquely determined from the film thickness distribution The liquid films on microstructured walls have also been modeled using the long-wave theory [13, 14, 16, 29, 37–39] In this case the film thickness should be much smaller than the scale of the wall topography variation This is possible if the height-to-width ratio of the topographical features is small Consider a wall with a three-dimensional topography described by a function l(x, y), where the coordinate axis x is directed along the gravity-driven flow, the coordinate axis y lies in the plane of the wall normal to the main flow direction, and the coordinate axis z is perpendicular to the wall (Figure 2) The inclination angle between the wall and the horizon is β The evolution equation for the dimensionless film thickness H has the form of modified Benney equation [13, 36, 40]: Hτ + 3H H X − +∇· H ∇ 27 S(H Hτ ) X − Re(H H X ) X 40 S ∇ F − cot βF Re =0 Integral Boundary Layer Approximation The applicability of the long-wave theory is limited by the Reynolds numbers of unity order The integral boundary layer approximation first introduced by Shkadov [28] allows relieving this limitation The classical integral boundary layer approach is based on the assumption of a parabolic velocity profile persisting at moderate Reynolds numbers It has been shown that this assumption is valid for Reynolds numbers up to 30 [6, 41] The parabolic velocity profile is substituted into the boundary-layer momentum equations and integrated between the wall and the liquid–gas interface This procedure yields the following system of simultaneous partial differential equations: ∂ ∂ Q1 + ∂τ ∂X Q 21 H + ∂ ∂Y Re Q1 H2 − ∂F ∂∇ F cot βH + W eH (3) Re ∂X ∂X = H− ∂ Q2 ∂ + ∂τ ∂X =− Q1 Q2 H + Q1 Q2 H ∂ ∂Y Q 22 H Q2 ∂F ∂∇ F cot βH + W eH − Re H Re ∂Y ∂Y ∂ Q1 ∂ Q2 ∂F + + =0 ∂X ∂Y ∂τ (4) (5) where (1) heat transfer engineering We = (3Fi)1/3 , Re5/3 (sin β)1/3 vol 32 nos 7–8 2011 Fi = σ3 gρ3 ν4 (6) 708 T GAMBARYAN-ROISMAN ET AL In these equations Q and Q denote the dimensionless local liquid flow rates in x and y direction, respectively We denotes the Weber number, and Fi denotes the film number [6, 20] ∗3 The value gh3ν sin β = Reν has been chosen as the flow rate scale The system of Eqs (3)–(5) appeared first in the work of Demekhin and Shkadov [42] A version of the same system of equations accounting for the three-dimensional topography has been reported by Trifonov [32] The solution of the time-independent version of Eqs (3)–(5) describes the steady deformation of the liquid–gas interface caused by the wall topography If the amplitude of the wall corrugation is small (max |L| 1), then the interface deformation, as well as the deviation of the liquid flow rate in the x direction from an average value are small The time-independent version of the system of Eqs (3)–(5) can be linearized to obtain the following form: 3 (ϕ1X − δ X + L X ) = (3δ − 3L − ϕ1 ) − cot βδ X Re Re + W e(∇ δ) X (7) 3 ϕ2X = − ϕ2 − cot βδY + W e ∇ δ Re Re ϕ1X + ϕ2Y = Y (8) (9) form: 2π Y − Y p (X ) (11a) D where the function Y p (X ) describes the sinusoidal groove path: L (X, Y ) = −A cos Y p (X ) = A p cos (10a) Q (X, Y ) = + ϕ1 (X, Y ) (10b) Q (X, Y ) = ϕ2 (X, Y ) (10c) (11b) In the preceding, A denotes the amplitude of the groove, D denotes the distance between two adjacent grooves (the groove period), Ap denotes the amplitude of the groove path, and Dp denotes the period of the groove path If A p = 0, then Y p (X ) = 0, and Eqs (11a) and (11b) describe the longitudinal grooves with straight path and sinusoidal cross section Falling film flow, heat transfer, and stability on the walls with longitudinal grooves have been studied numerically and experimentally by our group [13–15, 22, 29, 39, 43] The herringbone structure is comprised of grooves with a zigzag path The main axis of these grooves is oriented normal to the flow direction In our simulations we use a topography function that preserves most of the features of the herringbone structure but replaces the zigzag groove path (which cannot be used in connection with the long-wave theory or integral boundary layer approach) with a sinusoidal path The equation describing this topography is very similar to that describing the meandering grooves: where the following linear approximations for F, Q1 and Q2 have been used: F (X, Y ) = + δ (X, Y ) 2πX Dp L (X, Y ) = −A cos 2π X − X p (Y ) D (12a) where X p (Y ) = A p cos 2πY Dp (12b) where the absolute values of the functions δ (X, Y ), ϕ1 (X, Y ), and ϕ2 (X, Y ) are small The linear system of Eqs (7)–(9) can be applied for investigation of the effect of the flow parameters and the wall topography on the free surface amplification and the linear resonance phenomenon at moderate values of the Reynolds number [25, 27] If A p = 0, then X p (Y ) = 0, and Eqs (12a) and (12b) describe the wall with grooves oriented normal to the main flow direction The falling film flow and stability on this type of topography have been extensively studied [17, 19–21, 25–27] In this work the time-independent versions of Eqs (1) and (7)–(9) have been solved in the domain determined by the periods of the topography in x and y directions The equations have been solved with spectral method using trigonometric functions for computation of the differentiation matrices [44] Wall Topography RESULTS AND DISCUSSION In this work we consider the wall topographies that capture the most important features of the two structures shown in Figure However, we are not aiming at an exact description of the structures tested in our experiments For example, instead of nearly rectangular cross-section of the grooves with rounded corners, we assume sinusoidal groove cross-section in our models The simplest equation describing a prototype of the meandering groove structure (Figure 1a) has the following Free Surface Deformation on Walls With Grooves Normal to Main Flow Direction heat transfer engineering In this section we assess the applicability of the long-wave theory and the integral boundary-layer approximation to computation of the free surface deformation in falling liquid films Figure depicts the calculated ratio between the maximal and minimal film thickness over a period of the wall corrugation as a function of the groove amplitude for a falling liquid film along a vol 32 nos 7–8 2011 T GAMBARYAN-ROISMAN ET AL 709 1.6 1.5 1.4 1.4 Re = Amplification hmax /hmin 1.2 1.3 1.2 1.1 d =10 mm 0.8 d =5 mm 0.6 Re = 20 0.4 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Wall topography amplitude, mm Figure Ratio between the maximal and minimal film thickness over the wall corrugation period calculated on the basis of the long-wave theory (solid line) and by integral boundary layer approximation (dashed line, [20]) The wall corrugation period is d = 1.57 mm vertical wall with topography given by Eqs (12a) and (12b) with A p = The computations are performed for a water–glycerin mixture characterized by the film number Fi = 7.249 · 106 and the viscous-gravitational length scale (3ν2 /g)1/3 = 0.251 mm Solid lines represent the results of our computations on the basis of the long-wave theory, and the dashed lines depict the results of Trifonov [20] obtained using the integral boundary layer approximation As expected, the ratio h max /h increases with increasing of the wall topography amplitude and decreases with increasing Reynolds number At Re = the results of the long-wave theory and of the integral boundary layer analysis are in good agreement At Re = 20, when the effect of inertia is important, the discrepancy between the predictions of two models is higher Figure illustrates the free surface amplification as a function of the Reynolds number for a liquid falling film flowing down an inclined corrugated plate The inclination angle isβ = 30◦ The computations are performed for water at 20◦ C The free surface amplification characterizes the influence of the wall topography on the deformation of the free surface of the liquid film The topography is described by Eqs (12a) and (12b) with A p = The computations have been performed for the wall corrugation periods of mm, mm, and 10 mm A small value of the wall corrugation amplitude has been chosen (A 1), so that the free surface amplification is independent of A Bontozoglou and Papapolymerou [25] have shown that the solution of the creeping flow equations predicts a monotonous decrease of the free surface amplification with increasing Re The solution of Navier–Stokes equations with inertial terms retained predicts a decrease of the amplification with increasing Re at small values of the Reynolds number However, in a certain range of the Reynolds numbers, which depends on the period of wall corrugation, the free surface amplification increases, reaches a peak, and decreases again The authors have named this phenomenon linear resonance We have performed simulations of the film deformation using two asymptotic methods: long-wave theory (dashed lines in Figheat transfer engineering d =3 mm 0.2 0 10 15 20 25 30 35 40 Reynolds number Figure Free surface amplification for the falling film flowing along a wall with β = 30◦ The wall topography is given by Eqs (12a) and (12b) with Ap = 0, A Solid lines: integral boundary layer approximation; dashed lines: long-wave theory ure 4) and integral boundary layer approach (solid lines in Figure 4) Both methods agree well with the results of Bontozoglou and Papapolymerou [25] for small values of the Reynolds number It can be easily seen that the amplification increases with increasing period of the wall topography at small Re It is also evident that for d = mm the agreement between the predictions of two theories is perfect up to Re ≈ 20 For d = mm the discrepancy between the two theories reaches 10% already at Re = Note that this value is a commonly accepted upper limit of applicability of the long-wave theory (Benney equation) The free surface amplification predicted by the integral boundary layer depends on Re in a nonmonotonic way The curves describing amplification versus Reynolds number are characterized by a minimum (practically invisible for d = 10 mm) It can be conjectured that this curve has a maximum at a higher value of Re However, the range of Reynolds numbers 80 < Re < 300 corresponding to the most pronounced amplification peaks predicted in [25] is beyond the applicability range of the integral boundary layer approximation Free Surface Deformation on Walls With Three-Dimensional Topography In this section we present the long-wave simulation results for the deformation of the free surface of falling films on topographies comprised of meandering mini-grooves along and normal to the main flow direction Figure illustrates the wall topography and corresponding distribution of the steady-state free surface deformation for the falling film flow over a plate with topography described by Eqs (11a) and (11b) (prototype of meandering mini-grooves shown in Figure 1a) Light colors correspond to an elevation of the wall topography or an elevation of the free surface, and dark colors correspond to a depression of the wall topography or vol 32 nos 7–8 2011 710 T GAMBARYAN-ROISMAN ET AL Figure Meandering mini-grooves arranged normal to the main flow direction (prototype of herringbone structure) (a) Wall topography with d = mm, ap = mm, dp = mm; (b) amplification of the free-surface for Re = 4, β = 30◦ Figure Meandering mini-grooves arranged along the main flow direction (a) Wall topography with d = mm, ap = mm, dp = 20 mm; (b) amplification of the free-surface for Re = 4.2, β = 30◦ a depression of the free surface One period of wall structure in x and y directions is presented in the figure (0 ≤ x ≤ d p , −d/2 ≤ y ≤ d/2) It is clearly seen that although the main features of the wall topography are reflected in the free surface shape, these two shapes differ from each other First, a phase shift between the wall topography and the corresponding free surface deformation can be identified The positions of the maximal free surface elevation are located upstream of the corresponding positions of the maximal topography elevation In the vicinity of the line x = d p /2, where the groove path is locally parallel to the main flow direction, the shape of the free surface is qualitatively different from the wall topography The reader is invited to examine the details of these differences using Figure 5b The local difference in shape is due to the known fact that falling film flow over longitudinal grooves does not lead to the free surface deformation Figure represents the free surface amplification for the falling film flow on structures described by Eqs (11a) and (11b) as a function of the Reynolds number for different values of the groove path amplitude a p Note that a p = corresponds to the case of straight longitudinal grooves, for which amplification is equal to zero (no free surface deformation) In the range of Re represented in the figure, the free surface amplification decreases with increasing Re This trend is similar to the case of straight grooves normal to the flow direction predicted for the same range of Reynolds numbers The dependence of amplification on a p is nonmonotonic For the structures in which the groove path only slightly deviates from a straight line (a p /d p 1) the amplification increases with increasing a p The highest values of amplification for the given set of parameters are predicted for a p = mm For higher values of the path amplitude (a p = mm and a p = mm) the free surface amplification decreases with increasing a p The wall topography described by Eqs (12a) and (12b) (prototype of the herringbone structure shown in Figure 1b) and the corresponding steady-state free surface deformation are shown in Figure As in the case with meandering grooves (Figure 5), one structure period is presented (0 ≤ x ≤ d, −d p /2 ≤ y ≤ d p /2) It is seen that the positions corresponding 0.35 0.5 0.3 0.4 0.25 Amplification Amplification a p = mm 0.3 mm 0.2 mm mm 0.1 0.5 mm ap= 0.2 0.15 0.5 mm 0.1 mm 0.05 mm 0 Reynolds number Figure Free surface amplification for the falling film flowing along a wall with β = 30◦ The wall topography is given by Eqs (11a) and (11b) with d = mm, dp = 20 mm heat transfer engineering Reynolds number Figure Free surface amplification for the falling film flowing along a wall with β = 30◦ The wall topography is given by Eqs (12a) and (12b) (prototype of herringbone structure) with d = mm, dp =5 mm vol 32 nos 7–8 2011 T GAMBARYAN-ROISMAN ET AL to the maximal free surface elevation are located upstream of the corresponding positions of the wall topography elevation (negative phase shift) The maximal elevation of the film free surface occurs at the plate locations where the groove path is normal to the flow direction (y = 0) It can be conjectured that the deviation of the groove path from a straight line leads to decreasing of the free surface amplification Figure illustrates the free surface amplification for the falling film flowing down inclined plates (β = 30◦ ) with topography described by Eqs (12a) and (12b) as a function of Re at different a p Similar to the case of meandering grooves along the main flow direction, the free surface amplification decreases with increasing Re in the relevant range The case of a p = corresponds to straight grooves normal to the flow direction In this case the free surface amplification is maximum Deviation of the groove path from a straight line leads to the decrease of the film surface deformation The free surface amplification decreases with increasing of a p Of course, not every flow regime for which the steady-state surface deformation is predicted in this work can be physically realized, since they may be unstable to disturbances Therefore, stability analysis of the falling film flow has to be performed in the next step 711 NOMENCLATURE A a D d F f Fi g H h h∗ L l Q1 , Q2 dimensionless amplitude of the wall topography amplitude of the wall topography, m dimensionless period of the wall topography period of the wall topography, m dimensionless interface position interface position, m film number gravity acceleration, m/s2 dimensionless film thickness film thickness, m characteristic film thickness, m dimensionless wall topography function wall topography function, m dimensionless volumetric flow rates in x and y directions, respectively Re Reynolds number S inverse crispation number We Weber number X, Y, Z dimensionless coordinates x, y, z coordinates, m Greek Symbols CONCLUSIONS Deformation of the liquid–gas interface in falling liquid films on walls with periodic three-dimensional structures has been modeled using long-wave theory (modified Benney equation) and the integral boundary layer approach The integral boundary layer approach can predict the peak of the free surface amplification for the falling film flows over plates with grooves normal to the main flow direction Longwave theory adequately describes the free surface deformation of the falling film flowing along structured plates for Re < Falling film flow over walls with meandering grooves arranged along the main flow direction leads to substantial deformation of the free surface of the film This deformation depends on the amplitude of the groove path deviation from the straight line in a nonmonotonic way Falling film flow over walls with meandering grooves arranged normal to the main flow direction is also characterized by the free surface deformation This deformation decreases with increasing amplitude of the groove path deviation from the straight line Stability analysis of the predicted falling film flow regimes and simulations of the wave patterns on periodic threedimensional structures are needed for complete understanding of the wall topography effect on the film behavior After that, the effect of the three-dimensional topography on the heat transport in the falling film should be described numerically heat transfer engineering β δ µ ν ρ σ τ ϕ1 , ϕ2 plate inclination angle auxiliary function defined in Eq (10a) dynamic viscosity of the liquid, kg/(m-s) kinematic viscosity of the liquid, m2/s density of the liquid, kg/m3 surface tension, N/m dimensionless time auxiliary functions defined in Eqs (10b) and (10c) Subscript p path REFERENCES [1] Yih, C.-S., Stability of Parallel Laminar Flow with a Free Surface, Quarterly of Applied Mathematics, vol 13, pp 434–439, 1955 [2] Yih, C.-S., Stability of Liquid Flow Down an Inclined Plane, Physics of Fluids, vol 6, no 3, pp 321–334, 1963 [3] Benjamin, T B., Wave Formation in Laminar Flow Down an Inclined Plane, Journal of Fluid Mechanics, vol 2, pp 554–574, 1957 [4] Kapitza, P L., Wave Flow of Thin Layer of Viscous Fluid (in Russian), Zhurn Eksper Teor Fiz., vol 18, no 1, pp 3–28, 1948 [5] Telles, A S., and Dukler, A E., Statistical Characteristics of Thin, Vertical, Wavy, Liquid Films, Industrial & vol 32 nos 7–8 2011 712 [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] T GAMBARYAN-ROISMAN ET AL Engineering Chemistry Fundamentals, vol 9, no 3, pp 412–421, 1970 Alekseenko, S V., Nakoryakov, V E., and Pokusaev, B G., Wave Flow of Liquid Films, Begell House, New York, 1994 Adomeit, P., and Renz, U., Hydrodynamics of ThreeDimensional Waves in Laminar Falling Films, International Journal of Multiphase Flow, vol 26, pp 1183–1208, 2000 Nosoko, T., and Miyara, A., The Evolution and Subsequent Dynamics of Waves on a Vertically Falling Liquid Film, Physics of Fluids, vol 16, pp 1118–1126, 2004 Drosos, E I P., Paras, S V., and Karabelas, A J., Characteristic of Developing Free Falling Films at Intermediate Reynolds and High Kapitza Numbers, International Journal of Multiphase Flow, vol 30, pp 853–876, 2004 Chun, K R., and Seban, R A., Heat Transfer to Evaporating Liquid Films, ASME Journal of Heat Transfer, vol 93, pp 391–396, 1971 Schmerler, J A., and Mudawar, I., Local Heat Transfer Coefficient in Wavy Free-Falling Turbulent Liquid Films Undergoing Uniform Sensible Heating, International Journal of Heat and Mass Transfer, vol 31, no 1, pp 67–77, 1988 Al-Sibai, F., Leefken, A., and Renz, U., Local and Instantaneous Distribution of Heat Transfer Rates through Wavy Films, International Journal of Thermal Science, vol 41, pp 658–663, 2002 Gambaryan-Roisman, T., and Stephan, P., Analysis of Falling Film Evaporation on Grooved Surfaces, International Journal of Enhanced Heat Transfer, vol 10, no 4, pp 445–457, 2003 Gambaryan-Roisman T., and Stephan P., Falling Films in Micro- and Minigrooves: Heat Transfer and Flow Stability, Thermal Science & Engineering, vol 11, no 6, pp 43–50, 2003 Helbig, K., Alexeev, A., Gambaryan-Roisman, T., and Stephan, P., Evaporating of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces, Flow, Turbulence and Combustion, vol 75, pp 85–104, 2005 Kabova, Yu O., Alexeev, A., Gambaryan-Roisman, T., and Stephan, P., Marangoni-Induced Deformation and Rupture of a Liquid Film on a Heated Microstructured Wall, Physics of Fluids, vol 18, 012104, 2006 Wierschem, A., and Aksel, N., Influence of Inertia on Eddies Created in Films Creeping over Strongly Undulated Surfaces, Physics of Fluids, vol 16, no 12, pp 4566–4574, 2004 Alexeev, A., Gambaryan-Roisman, T., and Stephan, P., Marangoni Convection and Heat Transfer in Thin Liquid Films on Heated Walls with Topography: Experiments and Numerical Study, Physics of Fluids, vol 17, 062106, 2005 Vlachogiannis, M., and Bontozoglou, V., Experiments on Laminar Film Flow along a Periodic Wall, Journal of Fluid Mechanics, vol 457, pp 133–156, 2002 heat transfer engineering [20] Trifonov, Yu Ya., Stability and Nonlinear Wavy Regimes in Downward Film Flows on a Corrugated Surface, J Appl Mech Tech Phys., vol 48, no 1, pp 91–100, 2007 [21] Trifonov, Y Y., Stability of a Viscous Liquid Film Flowing down a Periodic Surface, International Journal of Multiphase Flow, vol 33, pp 1186–1204, 2007 [22] Helbig, K., Nasarek, R., Gambaryan-Roisman, T., and Stephan, P., Effect of Longitudinal Mini-Grooves On Flow Stability and Wave Characteristics of Falling Liquid Films, ASME Journal of Heat Transfer, vol 131, 011601, 2009 [23] Wang, C Y., Liquid Film Flowing Slowly Down a Wavy Incline, AIChE Journal, vol 27, pp 207–112, 1981 [24] Pozrikidis, C., The Flow of a Liquid Film Along a Periodic Wall, Journal Fluid Mechanics, vol 188, pp 275–300, 1988 [25] Bontozoglou, V., and Papapolymerou, G., Laminar Film Flow Down a Wavy Incline, International Journal of Multiphase Flow, vol 23, no 1, pp 69–79, 1997 [26] Trifonov, Y Y., Viscous Film Flow Down Corrugated Surfaces, Journal of Applied Mechanics and Technical Physics, vol 45, pp 389–400, 2004 [27] Wierschem, A., Bontozoglou, V., Heining, C., Uecker, H., and Aksel, N., Linear Resonance in Viscous Films on Inclined Wavy Planes, International Journal of Multiphase Flow, vol 34, pp 580–589, 2008 [28] Shkadov, V Y., Wavy Modes of Gravity-Driven Viscous Thin-Film Flow, Izd Akad Nauk SSSR, Mekh Zhidk Gasa, vol 1, pp 43–51, 1967 [29] Gambaryan-Roisman, T., and Stephan, P., Flow and Stability of Rivulets on Heated Surfaces with Topography, ASME Journal of Heat Transfer, vol 131, 033101, 2009 [30] Chamra, L.M., Webb, R L., and Randlett, M R., Advanced Micro-Fin Tubes for Evaporation, International Journal of Heat and Mass Transfer, vol 39, no 39, pp 1827–1838, 1996 [31] Stroock, A D., Dertinger, S K W., Ajdari, A., Mezic, I., Stone, H A., and Whitesides, G M., Chaotic Mixer for Microchannels, Science, vol 295, pp 647–650, 2002 [32] Trifonov, Y Y., Viscous Liquid Film Flows Over a Periodic Surface, International Journal of Multiphase Flow, vol 24, pp 1139–1161, 1998 [33] Webb, R L., and Kim, N.-H., Principles of Enhanced Heat Transfer, Taylor & Francis, Boca Raton, FL, 2005 [34] L¨offler, K., Yu, H., Gambaryan-Roisman, T., and Stephan, P., Hydrodynamics and Heat Transfer of Thin Films Flowing Down Inclined Smooth and Structured Plates, Proc 4th International Berlin Workshop—IBW4 on Transport Phenomena with Moving Boundaries, Berlin, Germany, September 27–28, 2007 [35] L¨offler, K., Yu, H., Gambaryan-Roisman, T., and Stephan, P., Flow Patterns and Heat Transfer in Thin Liquid Films on Walls with Straight, Meandering and Zigzag Mini-Grooves, Proc 6th International Conference on Nanochannels, Microchannels and Minichannels, Darmstadt, Germany, ICNMM2008–62318, June 23–25, 2008 vol 32 nos 7–8 2011 T GAMBARYAN-ROISMAN ET AL [36] Oron, A., Davis, S H., and Bankoff, S G., Long-Scale Evolution of Thin Liquid Films, Review of Modern Physics, vol 69, pp 931–980, 1997 [37] Stillwagon, L E., and Larson, R G., Leveling of Thin Films Over Uneven Substrates During Spin Coating, Physics of Fluids A, vol 2, pp 1937–1944, 1990 [38] Gramlich, C M., Kalliadasis, S., Homsy, G M., and Messer, C., Optimal Leveling of Flow Over OneDimensional Topography by Marangoni Stresses, Physics of Fluids, vol 14, pp 1841–1850, 2002 [39] Gambaryan-Roisman, T., and Stephan, P., Evaporation of Gravity- and Gas Flow-Driven Thin Liquid Films in Micro- and Minigrooves, Proc 2nd International Conference on Microchannels and Minichannels, Rochester, NY, pp 551–558, June 17–19, 2004 [40] Benney, D J., Long Waves on Liquid Films, Journal of Mathematics & Physics, vol 45, pp 150–155, 1966 [41] Demekhin, E A., Kaplan, M A., and Shkadov, V Y., Mathematical Models of the Theory of Viscous Liquid Films, Izv Akad Nauk SSSR, Mekh Zhidk Gaza, vol 6, pp 73–81, 1987 [42] Demekhin, E A., and Shkadov, V Y., On ThreeDimensional Nonstationary Waves in a Falling Liquid Film, Izv Akad Nauk SSSR, Mekh Zhidk Gaza, vol 5, pp 21–27, 1984 [43] L¨offler, K Gambaryan-Roisman, T., and Stephan, P., Wave Patterns in Thin Films Flowing Down Inclined Smooth and Structured Plates, Proc 6th International Conference on Multiphase Flow, ICMF 2007, Leipzig, Germany, July 9–13, 2007 [44] Trefethen, L N., Spectral Methods in MATLAB, SIAM, Philadelphia, 2000 Tatiana Gambaryan-Roisman is a Privatdozent and a research group leader at the Institute for Technical Thermodynamics, Technische Universit¨at Darmstadt, in Germany In 1998 she earned her D.Sc degree in mechanical engineering from TechnionIsrael Institute of Technology, Haifa, Israel From 1998 to 2000 she was a Minerva Research Fellow (Max Planck Society) at the Material Science Department of the University Erlangen-Nuremberg, Erlangen, Germany Since 2000 she has been working at Technische Universit¨at Darmstadt In 2003 she founded an Emmy NoetherJunior Research Group “Evaporation of Thin Films on Structured Surfaces.” In 2007 she founded together with colleagues a research center, “Center of heat transfer engineering 713 Smart Interfaces.” In 2008 she earned a Habilitation degree from the Faculty of Mechanical and Process Engineering, Technische Universit¨at Darmstadt Her research interests include heat and mass transfer, interfacial phenomena in liquids and solids, multiphase flows, phase change, hydrodynamic and thermal instabilities, micro- and nanoscale transport phenomena, and transport phenomena in porous media Hongyi Yu is a Ph.D student at Technische Universit¨at Darmstadt in Germany He studied mechanical engineering at Technische Universit¨at Darmstadt and received his diploma in 2005 His doctoral research is focused on numerical simulation of wave development and heat transfer in thin falling films on structured plates Karsten L¨offler is a Ph.D student in mechanical engineering at Technische Universit¨at Darmstadt in Germany He received his diploma in chemical engineering at Clausthal University of Technology and worked on heterogeneous reaction systems and simulation of pulverized coal combustion His doctoral research at the Chair of Technical Thermodynamics is focused on the experimental investigation of falling liquid films on structured surfaces Peter Stephan is professor and director of the Institute for Technical Thermodynamics at Technische Universit¨at Darmstadt in Germany He studied mechanical engineering at the Technical University of Munich From 1989 to 1992 he was a Marie-Curie Research Fellow at the Joint Research Centre of the European Commission in Ispra, Italy In 1992 he received his Ph.D from the University of Stuttgart From 1992 to 1997 he was working as a senior process engineer and research and development manager in the Mercedes-Benz group Since 1997 he has been at Technische Universit¨at Darmstadt His main fields of research are phase change heat transfer and boiling, microscale heat and mass transfer, interfacial phenomena, heat pipe technology, and drying and freezing processes Specific interests lie in multiscale approaches and the combination of numerical and experimental studies From 2007 to 2009 he was the dean of the Mechanical Engineering Faculty In 2007 he founded together with colleagues a new interdisciplinary research centre with a focus on smart fluid boundaries He received the IIR Sadi Carnot Prize in 1995 and the SFT Prize for Excellence in Heat Transfer Research in 2002, and an ASME outstanding researcher award He is president of the German Heat Transfer Association, editor-in-chief of the VDI Heat Atlas, and an editorial board member of Journal of Heat and Mass Transfer, Journal of Experimental Heat Transfer, and Journal of Experimental Thermal and Fluid Science vol 32 nos 7–8 2011 [...]... mass flux increasing heat transfer engineering vol 32 nos 7 8 2011 H Z CAO ET AL 5 47 Figure 8 (a) pressure in inlet-tank and outlet-tank; (b) temperature in inlet-tank and outlet-tank; (c) wall temperature; (d) wall temperature distribution along the channel heat transfer engineering vol 32 nos 7 8 2011 548 H Z CAO ET AL Figure 8 (Continued) heat transfer engineering vol 32 nos 7 8 2011 H Z CAO ET AL... 50 4.48 6.2 7. 79 4.06 5.85 7. 55 3.82 5.33 7. 3 0.23 0. 17 0.16 0.25 0. 178 0.16 0.265 0.196 0.16 0.683 0 .72 6 0 .77 2 0. 674 0 .72 2 0 .77 4 0.654 0 .70 8 0 .78 2 23.8 23.85 23.5 24.2 23.9 23 24.12 24.2 23.5 0.588/21 0.584/20.8 0. 577 /20.1 0.564/19.6 0.551/18.8 0.541/18.4 0.531/ 17. 9 0.529/ 17. 6 0.526/ 17. 4 Part 3 Part 5 Part 5 Part 3 Part 5 Part 5 Part 3 Part 3 Part 5 0. 674 /25.45 0.646/24 0.651/24.3 0.6 67/ 25.06 0.648/24.13... Presentaheat transfer engineering [45] [46] [ 47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [ 57] 539 tion of the Model, International Journal of Heat and Mass Transfer, vol 47, pp 3 375 –3385, 2004 Jacobi, A M., and Thome, J R., Heat Transfer Model for Evaporation of Elongated Bubble Flows in Microchannels, Journal of Heat Transfer, vol 124, no 6, pp 1131–1136, 2002 Takeuchi, G., Fujiwara, A., Abe, Y., and... interests include microchannel heat transfer, heat pumps, automobile air conditioning, and new technology for the built environment He has co-authored four books and more than 80 papers vol 32 nos 7 8 2011 Heat Transfer Engineering, 32 (7 8):554–565, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145 -76 32 print / 1521-05 37 online DOI: 10.1080/014 576 32.2010.506399 A Numerical Analysis of the Fiber... Effect of Nano-Particles on Pool Boiling Heat Transfer of Refrigerant 141b, Proceedings of ASME ICNMM20 07 30221, Puebla, Mexico, 20 07 [43] Celata, C P., Microscale Heat Transfer in Single- and TwoPhase Flows: Scaling, Stability, Transition, Turbulence, Heat and Mass Transfer, vol 6, pp 16, 2009 [44] Thome, J R., Dupont, V., and Jacobi, A M., Heat Transfer Model for Evaporation in Microchannels Part... Tainan, Taiwan, 2008 Chien, L., Pei, S Y., and Wu, T Y., Convective Heat Transfer Performance of FC -72 in a Pin-Finned Channel, Proceedings of ASME ICNMM2008–622 98, Darmstadt, Germany, 2008 Lie, Y M., Ke, J H., Chang, W R., Cheng, T C., and Lin, T F., Saturated Flow Boiling Heat Transfer and Associated Bubble Characteristics of FC -72 on a Heated Micro-PinFinned Silicon Chip, International Journal of Heat. .. Mechanical Engineering in the Department of Mechanical Engineering and Materials Science She received her M.S and Ph.D degrees from University of Michigan, Ann Arbor Her current research interests include containerless processing of materials, solution to electromagnetic radiation equation, molecular dynamics studies for nano heat transfer, microchannel fluid and heat transfer, and bio heat transfer. .. and Buongiorno, J., Surface Modifications Using Nanofluids for Nucleate Boiling Heat Transfer and CHF Enhancements, Proceedings of ASME ICNMM2008–62085, Darmstadt, Germany, 2008 vol 32 nos 7 8 2011 J F TULLIUS ET AL [31] Honda, H., and Wei, J J., Advances in Enhanced Boiling Heat Transfer From Electronic Components, JSME International Journal, Series B, vol 46, no 4, pp 479 –490, 2003 [32] Shokouhmand,... 0.661/24 .78 0.648/24.13 0.698/26.6 0. 676 /25.55 2.9 27. 4 23.23 55 22 0. 37 27. 15 22.4 40 40 2.46 26.66 22.2 40 31 1.38 27. 1 22.33 55 51 heat transfer engineering 0.51 27. 12 21.46 40 64 5.31 27 21.6 40 44 vol 32 nos 7 8 2011 0 27. 52 21.02 55 64 5.08 28 22.1 55 55 5.9 28 .76 21.48 40 58 546 H Z CAO ET AL Figure 6 Flow pattern while pump power frequency is 50 Hz: (a) heat power is 8 W and mass flux 7. 79 kg/h;... and Ajayan, P., Substrate-Site Selective Growth of Aligned Carbon Nanotubes, Applied Physics Letters, vol 77 , no 23, pp 376 4– 376 6, 2000 heat transfer engineering [73 ] Wei, B Q., Vajtai, R., Jung, Y., Ward, J., Zhang, R., Ramanath, G., and Ajayan, P M., Assembly of HighlyOrganized Carbon Nanotube Architectures by Chemical Vapor Deposition, Chemical Materials, vol 15, no 8, pp 1598–1606, 2003 [74 ] Vajtai,