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Guest Editorial

J. Heat Transfer. 2015;137(8):080301-080301-1. doi:10.1115/1.4030441.

The 18th Heat Transfer Photogallery was sponsored by the K-22 Heat Transfer Visualization Committee for the 2014 International Mechanical Engineering Congress and Exhibition (IMECE) held in Montreal, Canada on November 14–20, 2014. The Photogallery sessions at 2014 IMECE presented a total of 19 entries and the peer-reviewed evaluation conducted by the participants has identified the 12 final entries for publication in this ASME Journal of Heat Transfer August issue of 2015.

Topics: Heat transfer
Commentary by Dr. Valentin Fuster

Photogallery

J. Heat Transfer. 2015;137(8):080901-080901-1. doi:10.1115/1.4030442.

The condensation and evaporation of hydrogen under cryogenic conditions is visualized by using neutron imaging at the BT-2 Beam Facility at the National Institute of Standards and Technology (NIST). The condensation and evaporation are controlled by adjusting temperature (20 K ~ 23 K) and pressure (1.3 ~ 1.95 bar absolute). The hydrogen contained in the aluminum test cell inside the cryostat has a large attenuation coefficient due to its large scattering cross section. The high sensitivity of neutron radiography to hydrogen allows the visualization of a meniscus and a contact line of evaporating hydrogenated cryogenic propellants. The graphic represents the temperature, pressure and corresponding images of liquid hydrogen in the test cell. The test cell is made of Aluminum 6061 with an inner diameter of 12 mm. The captured images are then median filtered and post-processed in order to find the volume of liquid hydrogen in the test cell as a function of time. The condensation/evaporation rates obtained from neutron imaging along with corresponding temperature and pressure are used to validate the evaporation model being developed by the authors.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080902-080902-1. doi:10.1115/1.4030446.

The freezing characteristics of small diameter eicosane (Tmelt = 37°C) droplets are studied here for their use in novel dry-cooling strategies based on spray freezing of recirculating phase change materials (PCM). PCM can be used to store thermal energy with relatively small changes in temperature (due to latent heat), as well as volume (due to small density changes). 4.2 mm diameter eicosane droplets are superheated to 40°C, placed on a cold stage at 10°C, and imaged during freezing (a). Similarly, liquid eicosane is enclosed within a custom-built experimental package creating a 5 mm diameter, 100 μm thick disc geometry with a temperature controlled boundary that is rapidly dropped from 40°C to 10°C (b). In both cases the liquid-solid interface is tracked, as well as the formation and growth of long dendrite structures which have been observed to play a critical role in the freezing process. (c) and (d) show the vertical position normalized by the droplet height , y/H, and the radial position (measured inward) normalized by the disc radius, r/R, of both the interface location and the average dendrite tip location. The total freezing time is observed visually, resulting in characteristic Fourier numbers of Fo = 0.55 ± 0.15 (droplet) and Fo = 3.5 ±0.15 (disc) at identical Stefan numbers of St = 0.3 ± 0.03, where the characteristic lengths are taken as the ratio of the eicosane volume to the cooled surface area.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080903-080903-1. doi:10.1115/1.4030449.

The study of evaporation dynamics of droplets is of scientific interest and has numerous practical applications. Here, we studied the evaporation of small condensate droplets on structured surfaces with one-tier microscale roughness and two-tier micro/nanoscale roughness (the top and valley of micropillars are covered by nanograss), respectively. On both surfaces, the micropillar arrays are arranged in a radical lattice with the decreasing pillar-to-pillar spacing towards the center of the surface (The first figures in Figs. 1 and 2). The condensate droplets on structured surfaces were formed by conducting condensation inside environmental scanning electron microscope (ESEM, Philips XL-30, ~4.9 Torr, stage temperature ~ 3°C). The condensate droplet on the one-tier surface stays in a Cassie-state (0 s in Fig. 1). However, owing to the preferential droplet nucleation on the smooth sidewall of micropillars, the condensate droplet on the two-tier surface maintains in the composite state (0 s in Fig. 2). To visualize the evaporation dynamics of condensate droplet, we gradually decreased the vapor pressure in the chamber from ~4.9 Torr to ~4.2 Torr. On the one-tier surface (Fig. 1), the droplet first evaporates in a constant contact radius mode (CCR, 0-124 s), followed by a constant contact angle mode (CCA, 136-166 s), and a mixed mode of both CCR and CCA (188-224 s). By contrast, on the two-tier surface (Fig. 2), the condensate droplet first evaporates in the CCR mode, with the solid-liquid contact line remain pinned until the formation of a flat liquid-air interface at the top of micropillars at ~86 s. After that, the liquid-air interface at the top of surface remains flat and the liquid evaporation is dominant in the lateral direction (96-170 s), with the liquid cylinder symmetrically shrinking towards the center of the surface. The presence of a stable and flat liquid/air interface at the top of surface is due to the stabilization effect rendered by the nanograss on the micropillars.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080904-080904-1. doi:10.1115/1.4030451.

Engineering surfaces that sustain continuous dropwise condensation, and are composed of materials commonly employed in heat transfer applications, are of great interest for scaled-up industrial systems. We fabricate hierarchical micro/nano-structured superhydrophobic surfaces on copper substrates. Condensate droplet growth dynamics on the as-fabricated samples were investigated using an environmental scanning electron microscope (ESEM; FEI Quanta 3D, ~6 torr, ~3 °C stage). Time-lapse ESEM images show that the condensate droplets preferentially nucleate at the bases of the hill-shaped microstructures (40 s). The droplets at the microstructure bases coalesce; merged droplets rise and appear to be suspended atop adjacent microstructures (180-220 s). These droplets, when triggered by coalescence, can gain sufficient kinetic energy by a reduction in droplet surface area/energy to spontaneously depart from the substrate. This droplet motion sweeps additional droplets in the trajectory and exposes fresh space for formation of new droplets (220-250 s). These droplet growth and departure dynamics are facilitated by the combination of microscale and nanoscale roughness features on the surface, and the behavior provides important insight into surface design requirements for sustaining dropwise condensation in thermal management applications.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080905-080905-1. doi:10.1115/1.4030452.

Super-bi-philic surfaces have been fabricated and characterized using environmental scanning electron microscopy (ESEM) to demonstrate spatial control of microscale droplets during condensation. The surfaces are composed of biotemplated nickel nanostructures based on the self assembly and metalization of the Tobacco mosaic virus. They are then functionalized using vapor-phase deposition of trichlorosilane, and lithographically patterned to create engineered nucleation sites. The resulting surfaces are primarily superhydrophobic (θ ≈ 170°) with arrays of superhydrophilic islands (θ ≈ 0°) with diameters of 3 μm and center-to-center pitches varying from 10 – 50 μm. During condensation the superhydrophilic islands promote nucleation resulting in spatial control of the condensate, which forms into ordered rectangular arrays (a,b). This spatial control has been shown to produce efficient jumping-mode condensation for pitches greater than 15 μm, as well as promote multi-droplet events (c). Additionally, super-bi-philic surfaces have been shown to delay the transition to a flooded state at high supersaturations, as compared to superhydrophobic designs.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080906-080906-1. doi:10.1115/1.4030453.

For occurring dropwise condensation, the droplet growth behavior such as single droplet growth, coalescence, and fall-off of large droplets play a major role in regard to condensation heat transfer and water harvesting. The present study visualized the droplet growth behavior of dropwise condensation which might be controlled by the surface tension. We used three copper plate with different hole area fraction (i.e., ϕ=0, 0.148 and 0.439). Surface texturing was conducted by using a μ-computer numerical control (μ-CNC) machine and composed of micro-holes (diameter: 300 μm, depth: 200 μm) with 691 μm, 401 μm pitch. To make the hydrophobic surfaces, the copper surfaces were coated self-assembled monolayer (SAM). From the results, it was found that for only SAM coated surface, random coalescence occurred and affected the droplet growth significantly, whereas for textured SAM coated surfaces, the droplet started to be grown up at the textured holes and coalesced near the holes, indicating that capillary effects might affect the droplet growth mechanism. In particular, the fall-off time at which a coalesced droplet is removed away from the surface increased when the textured surfaces was used, because of surface tension effect increased by the textured holes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080907-080907-1. doi:10.1115/1.4030454.

Recent advances in condensing surfaces with hybrid architectures of superhydrophobic/hydrophilic patterns allow us to decrease the nucleation energy barrier and spatially control the water condensation. However, the condensed water is susceptible to the large pinning force of the hydrophilic area, leading to an ultimate flooding. Here, we demonstrate a hierarchical nanostructured surface with patterned high wetting contrast to achieve a natural transition from filmwise-to-dropwise condensation, which reconciles the existing problems. The energy-dispersive X-ray spectroscopy (EDX) indicates that the fluorinated hydrophobic coating conformably covers the nanostructures except for the tops of micropillars, which are covered by hydrophilic silicon dioxide (FIG 1), resulting in an extreme wetting contrast. Condensation on the hybrid surface was observed in the environmental scanning electron microscope (ESEM) and ambient conditions with controlled humidity. Water preferentially nucleates on the top of micropillars and exhibits a rapid droplet growth (FIG 2). The enhancement is attributed to the filmwise-to-dropwise transition induced by the unique architectures and wetting features of the hybrid surface (FIG 3). The water embryos initially nucleate on the hydrophilic tops and quickly grow to a liquid film covering the whole top area. Since the superhydrophobic surrounding confines the spreading of condensed water, the localized liquid film gradually transits to an isolated spherical droplet as it grows. Remarkably, the condensate morphology transition activates an unusual droplet self-propelling despite the presence of abundant hydrophilic patches. It is important to note that such coalescence-induced jumping is dependent on the size of hydrophilic patches, that is, for larger hydrophilic patches, the energy released by coalescence may not overcome the increased droplet pinning, resulting in an immobile coalescence (FIG 4). The droplet departure ensures the recurrence of filmwise-to-dropwise transition, thus prevents the water accumulation in continuous condensation. These visualizations reveal the undiscovered impact of heterogeneous wettability and architectures on the morphology transition of the condensed water, and provide important insights into the surface design and optimization for enhanced condensation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080908-080908-1. doi:10.1115/1.4030472.

Superhydrophilic Nano-Structured Coatings (SHNC) were discovered during pool boiling experiments using nanofluids with alumina nanoparticles. During nucleate boiling, the nanoparticles are deposited on the heater surface, forming a uniform oxide coating. These coatings have been demonstrated to greatly decrease the liquid contact angle observed on the surfaces, both by increased surface roughness and increased surface energy. An illustration of this roughness, within 1 μm thickness, can be seen in the 3-D optical microscope mapping of a SHNC surface, top right. These highly wetting structures can greatly enhance macro-level mass transfer effects, such as capillary action. The series of images on the left depict the wickability enhancement achieved by SHNC coating inside a 0.92 mm internal diameter aluminum tube. In the tube coated with SHNC, a 21 μl water droplet disappeared in 183 milliseconds, resulting in an average wicking speed along the pipe of 17 cm/sec. The bare aluminum tube does not wick at all, even as it is pushed into the droplet. The bottom right sequence shows the wettability enhancement responsible for this behavior; an 8 μl water droplet is dropped onto both a SHNC-coated and a bare aluminum surface from a height of 1 cm. The droplet on the SHNC-coated surface spreads instantaneously due to the high wettability of the SHNC, while the droplet on the bare aluminum remains aggregated as a hemisphere.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080909-080909-1. doi:10.1115/1.4030473.

This study aims to experimentally examine rebounding characteristics of a free-fall droplet which impacts on a static droplet with a spherical-cap shape in a low Weber number range. Two well-aligned high-speed cameras were used for visualization of droplet behaviors after impact. From the image analysis, the influence of impact velocity, offset distance and static droplet volume on the rebound characteristics was examined. The results show that the dynamic contact angle and the contact diameter of a static droplet change significantly with time after impact. In particular, a substantial change in dynamic contact angles for different offset distances is also observed. Contact diameters are also varied larger with the increase in the impact velocity. It is thought that occurrence of droplet rebound may be because of air-gap formation at the interface inhibiting viscous film drainage, coming from droplet oscillation before impact.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080910-080910-1. doi:10.1115/1.4030474.

The time-and space-resolved water jet impingement heat transfer on stationary hot steel plate was measured by a novel experimental technique that has a function of high-temperature heat flux gauge. The simultaneous visual observation was helpful to understand the complex heat transfer regimes occurring on a stationary hot steel plate cooled from 900°C by a circular water jet. The heat transfer regimes adjacent to a circular water jet impinging on a hot steel plate were known as to be classified into 5 distinct regimes; (I) single phase forced convection, (II) nucleate and transition boiling, (III) forced convection film boiling, (IV) agglomerated pools, (V) radiation and natural convection to surroundings. The observed images of water jet impingement boiling were well agreed with the measured cooling curve and boiling curve, so this study can provide the benchmark data for validating the 5 distinct regimes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080911-080911-1. doi:10.1115/1.4030475.

A simple use of Venturi might be used to measure two-phase flow rate within relatively low GVF(gas volume fraction). Upstream flow entering Venturi can be improved with installed flow homogenizer which is easily fabricated by 3-dimensional printer with multiple holes. Simultaneous measurement between high-speed flow visualization and dynamic differential pressure measurement was made to find visual criteria for two-phase flow rate measurement with different GVF ranged from 0% to 30%. It was observed that the two-phase flow rate can be reliably measured up to 15% of GVF using flow homogenizer. FFT(Fast-Fourier Transform) results proved that the long flow homogenizers (type 2 and 4) showed a lower amplitude of differential pressure (Δp) than the short flow homogenizers (type 1 and 3) respectively. So the optimized flow homogenizer can be useful to measure two-phase flow rate at low GVF.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):080912-080912-1. doi:10.1115/1.4030476.

The growth dynamics of isolated gas bubbles from a submerged capillary-tube orifice in a pool of aqueous solution of Cetyl Trimethyl Ammonium Bromide (CTAB) was studied by multi-scale modeling. The macro-scale bubble ebullience is controlled by the molecular scale surfactant adsorption/desorption on the liquid-gas interface. Molecular dynamics simulations were carried out to predict the interfacial adsorption/desorption kinetics. The results of the molecular dynamics simulations were input to the volume-of-fluid based macro-scale computations. The size and shape of bubbles from incipience to departure were measured using high speed videography for model validation. Predictions of the multi-scale model agree with the experimental measurements of bubble size evolution and bubble diameter at departure. The surfactant mass transfer and adsorption on the liquid gas interface gives rise to dynamic surface tension. As a result of the surfactant presence, the bubble departure diameters were smaller in CTAB solution compared to pure water. Furthermore, dynamic surface tension behavior of CTAB makes the bubble departure diameter a function of bubble Reynolds number (Re based on the orifice diameter and air flow rate). At low flow rates or low Re, the bubble departure diameters are smaller than those in water. As the air flow rate increases, the bubble departure diameters tend towards those in pure water. The authors gratefully acknowledge funding from AFOSR Thermal Science Program and AFRL DoD Supercomputing Resource Center for computing time and resources.

Commentary by Dr. Valentin Fuster

Research Papers: Electronic Cooling

J. Heat Transfer. 2015;137(8):081401-081401-10. doi:10.1115/1.4028243.

Integrating the cooling systems of power electronics and electric machines (PEEMs) with other existing vehicle thermal management systems is an innovative technology for the next-generation hybrid electric vehicles (HEVs). As such, the reliability of PEEM must be assured under different dynamic duty cycles. Accumulation of excessive heat within the multilayered packages of PEEMs, due to the thermal contact resistance between the layers and variable temperature of the coolant, is the main challenge that needs to be addressed over a transient thermal duty cycle. Accordingly, a new analytical model is developed to predict transient heat diffusion inside multilayered composite packages. It is assumed that the composite exchanges heat via convection and radiation mechanisms with the surrounding fluid whose temperature varies arbitrarily over time (thermal duty cycle). As such, a time-dependent conjugate convection and radiation heat transfer is considered for the outer-surface. Moreover, arbitrary heat generation inside the layers and thermal contact resistances between the layers are taken into account. New closed-form relationships are developed to calculate the temperature distribution inside multilayered media. The present model is used to find an optimum value for the angular frequency of the surrounding fluid temperature to maximize the interfacial heat flux of composite media; up to 10% higher interfacial heat dissipation rate compared to constant fluid-temperature case. An independent numerical simulation is also performed using Comsol Multiphysics; the maximum relative difference between the obtained numerical data and the analytical model is less than 6%.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2015;137(8):081501-081501-7. doi:10.1115/1.4030245.

The present research is an experimental study for the enhancement of boiling heat transfer using microporous coatings. Two types of coatings are investigated: one that is bonded using epoxy and the other by soldering. Effects on pool boiling performance were investigated, of different metal particle sizes of the epoxy-based coating, on R-123 refrigerants, and on water. All boiling tests were performed with 1 cm × 1 cm test heaters in the horizontal, upward-facing orientation in saturated conditions at atmospheric pressure and under increasing heat flux. The surface enhanced by the epoxy-based microporous coatings significantly augmented both nucleate boiling heat transfer coefficients and critical heat flux (CHF) of R-123 relative to those of a plain surface. However, for water, with the same microporous coating, boiling performance did not improve as much, and thermal resistance of the epoxy component limited the maximum heat flux that could be applied. Therefore, for water, to seek improved performance, the solder-based microporous coating was applied. This thermally conductive microporous coating, TCMC, greatly enhanced the boiling performance of water relative to the plain surface, increasing the heat transfer coefficient up to ∼5.6 times, and doubling the CHF.

Commentary by Dr. Valentin Fuster

Research Papers: Experimental Techniques

J. Heat Transfer. 2015;137(8):081601-081601-8. doi:10.1115/1.4028901.

The thermal conductivity of silica aerogel developed in this research program was measured using the transient hot-wire technique. The thermal conductivity of monolithic samples drops significantly from 9.3 mW/m · K to 3.2 mW/m · K with modest pressure reduction from 1 atm to 0.1 atm. The same aerogel in granular form has a thermal conductivity of 15.0 mW/m · K at ambient gas pressure with a modest compression applied to compact the granules and reduce the air void sizes. Radiation heat transfer in the hot-wire test may not be representative of its contribution in large scale applications. Measurements of the monochromatic extinction coefficient over the wavelengths of interest resulted in a Rosseland mean extinction coefficient of 2400 m−1 at 300 K. The small thermal penetration distance during the hot-wire measurements suggest that in actual use radiation could contribute approximately 2.5 mW/m · K with a possible upper limit of 3.0 mW/m · K to the effective thermal conductivity over that measured using the transient hot-wire method.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2015;137(8):081701-081701-9. doi:10.1115/1.4030246.

A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group parameters.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Transfer in Manufacturing

J. Heat Transfer. 2015;137(8):082101-082101-9. doi:10.1115/1.4029086.

The effects of entrainment accompanying mass, momentum, and energy transport from the keyhole wall on keyhole collapse during high-power-density laser or electron beam drilling are theoretically and systematically investigated in this study. High intensity beam drilling is widely used in components, packaging and manufacturing technologies, micro-electromechanical-systems (MEMS), rapid prototyping manufacturing, and keyhole welding. This study proposes a quasi-steady, one-dimensional transport model to predict supersonic and subsonic flow behavior of the two-phase, vapor–liquid dispersion in a keyhole and applies the Young–Laplace equation to calculate the keyhole shape. The results show that the keyhole collapse, representing decreased or vanished radius, is susceptible to mass ejection at the base and entrainment from the side wall. Deposition of a mixture of gas and droplets in the keyhole stabilizes deformation of the keyhole. Enhanced energy and decreased axial component of momentum associated with entrainment are also apt to keyhole collapse. The predicted results agree with axial variations of transport variables of a compressible flow through a divergent and convergent nozzle, and their exact analytical solutions in the absence of friction, energy absorption, and entrainment. An understanding of the effects of ejected and entrained mass in the keyhole on drilling efficiency is therefore provided.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2015;137(8):082102-082102-9. doi:10.1115/1.4029039.

This study theoretically investigates the effects of the entrainment accompanying mass, momentum, and energy transport on pore size during high power density laser and electron beam welding processes. The physics of macroporosity formation is not well understood, even though macroporosity often occurs and limits the widespread industrial application of keyhole mode welding. This work is an extension of a previous work dealing with collapses of keyholes induced by high intensity beam drilling. In order to determine the pore shape, this study, however, introduces the equations of state at the times when the keyhole is about to be enclosed and when the temperature drops to melting temperature. The gas pressure required at the time when keyhole collapses is determined by calculating the compressible flow of the two-phase, vapor–liquid dispersion in a vertical keyhole with varying cross sections, paying particular attention to the transition between annular and slug flows. It is found that the pore size increases as entrainment fluxes decrease in the lower and upper regions of the keyhole containing a supersonic mixture. The pore size also increases with decreasing total energy of entrainment and an increasing axial velocity component ratio between entrainment and mixture through the core region. With a subsonic mixture in the keyhole, the final pore size increases with entrainment fluxes in the lower and upper regions. This work provides an exploratory and systematical investigation of pore size induced by entrainment accompanied by mass, momentum, and energy transport during keyhole mode welding.

Commentary by Dr. Valentin Fuster

Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2015;137(8):082401-082401-7. doi:10.1115/1.4030170.

Thermal transport across interfaces can play a critical role in nanosystems for thermal management and thermal energy conversion. Here, we show the dependence of the thermal boundary conductance (G) of the interface between a 70-nm Al transducer and a Si substrate on the size of a laser pump diameter (D) in the time-domain thermoreflectance (TDTR) experiments at room temperature. For D ≥ 30 μm, G approaches to a constant where diffusion dominates the heat transfer processes. When D decreases from 30 μm to 3.65 μm, G decreases from 240 to 170 MW/m2K due to the increasing nonlocal effects from nondiffusive heat transport. This finding is vital to our understanding of the thermal boundary conductance: it depends not only on inherent interfacial conditions but also on external heating conditions, which makes the accurate measurements and theoretical predictions of thermal transport across interfaces in micro/nanosystems more challenging.

Commentary by Dr. Valentin Fuster

Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2015;137(8):082901-082901-9. doi:10.1115/1.4029270.

Thermosolutocapillary convection within a rectangular cavity with dynamic free surface is numerically investigated in the absence of gravitational effects. Both the temperature and solute concentration gradients are applied horizontally. The free surface deformation is captured by the level set method. Two cases of the ratio of thermal to solutal Marangoni number Rσ < −1 and Rσ = −1 are considered. For Rσ< −1, the free surface bulges out near the left wall and bulges in near the right wall; with the increase of Marangoni number, the free surface deformation decreases and with the increase of capillary number and aspect ratio, it increases. For Rσ= −1, the free surface bulges out near the left and right walls and bulges in at the central zone; with the increase of Marangoni number, the free surface deformation mode is changed and with the increase of capillary number and aspect ratio, the free surface deformation increases.

Commentary by Dr. Valentin Fuster

Announcement

J. Heat Transfer. 2015;137(8):088001-088001-1. doi:10.1115/1.4030477.

NA

Commentary by Dr. Valentin Fuster

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