Effects of surface roughness of capillary wall on the profile of thin liquid film and evaporation heat transfer

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Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger

The complex physicochemical phenomena occurring in the contact line region of an evaporating meniscus are described using a unique combination of high-resolution experimental data and three complementary models. The following were used: (1) high-resolution experimental liquid profile data (thickness, slope, curvature and curvature gradient) to obtain the pressure gradient in the evaporating pentane meniscus in a vertical constrained vapor bubble (VCVB); (2) macroscopic outside surface temperature profile data; (3) a finite element model to obtain the two-dimensional heat conduction profile in the solid substrate wall (macro-model) and the solid–liquid interfacial temperature profile in the evaporating meniscus region; (4) a continuum fluid-dynamics model (micro-model) to obtain the liquid–vapor interfacial temperature, mass flow rate, Marangoni stresses, and evaporative heat flux profiles along the length of the evaporating meniscus; and (5) the Kelvin–Clapeyron model to obtain the vapor temperature profile (liquid–vapor interfacial temperature jump) in the evaporating meniscus region.The retarded dispersion constant and high-resolution thickness, slope, curvature and curvature gradient profiles were obtained from the experimental reflectivity profiles. There was a substantial increase in the measured curvature in the transition region, where the evaporation rate and flux are a maximum. To obtain numerical closure between the three complementary models, the continuum fluid dynamics model (micro-model) required slip at the solid–liquid interface to support the observed high mass flow rates in the evaporating pentane meniscus. Mass flow rates due to Marangoni stresses, capillary pressure and disjoining pressure are compared. Depending on the liquid thickness, Marangoni stresses can either enhance or hinder fluid flow towards the contact line for the evaporating pure pentane meniscus. Due to the high heat removal rate by the evaporating pentane meniscus in the transition region, dips in the vapor, liquid–vapor and solid–liquid interface temperature were obtained. The results demonstrate and describe the sensitivity and complexity of the phase change process in micro-regions.     

Evaporation heat transfer of steady thin film in micro capillary tubes of micron scale

This paper reports that the heat transfer mechanism of phase change in a capillary tube belongs to liquid film conduction and surface evaporation. The surface evaporation is influenced by vapor temperature, vapor‐liquid interfacial temperature, and vapor‐liquid pressure difference. In the vapor‐liquid flow mechanism, flow is effected by both the gradient of disjoining pressure, and the gradient of capillary pressure. The mechanism of vapor‐liquid interaction consists of the shear stress caused by momentum transfer owing to evaporation, and frictional shear stress due to the velocity difference between vapor and liquid. In the model presented for a capillary tube, the heat transfer, vapor‐liquid flow, and their interaction are more comprehensively considered. The thin film profile and heat transfer characteristics have close relations with a capillary radius and heat transfer power. The results of calculation indicate that the length of the evaporating interfacial region decreases to some extent with decreasing capillary radius and increasing heat transfer power. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 513–523, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ).DOI 10.1002/htj.10050     

DISJOINING PRESSURE EFFECT ON THE WETTING CHARACTERISTICS IN A CAPILLARY TUBE

A mathematical model capable of predicting the wicking height formed by a wetting liquid in a vertical, heated capillary tube was developed. The model incorporates the disjoining pressure, the fluid flow and heat transfer in the thin film region, and the thermocapillary effects. Evaluation of the modeling predictions indicates the meniscus radius of curvature at the vapor - liquid interface increases significantly with increasing heat flux, resulting in an increase in the contact angle due to the surface tension variation, disjoining pressure, and fluid flow in the evaporating thin film. The increase in the contact angle is shown to be the principal reason that the static wicking height in capillary tubes is typically greater than the dynamic wicking height observed during dynamic flow conditions. In addition to the individual contributions of the dynamic flow effect and the contact angle variation, both of these parameters are presented and discussed as a function of the tube diameter. In order to verify the analytical model, comparisons with previously obtained experimental data are made. The verified analytical model presented and developed here provides a better understanding of the wetting phenomena occurring in a heated capillary tube and has applicability in a wide range of applications.     

EFFECTS OF THE POLARITY OF WORKING FLUIDS ON VAPOR-LIQUID FLOW AND HEAT TRANSFER CHARACTERISTICS IN A CAPILLARY

For one polar and several apolar working fluids, the vapor-liquid flow and the heat transfer characteristics in a capillary tube are obtained and compared. The polarity of the working fluid has a close relation to the disjoining pressure, which affects the formation of the liquid film profile greatly. For a polar working fluid (water), the length of the evaporating interfacial region is much longer than those for apolar working fluids. And the thickness of its liquid film increases relatively more gently at the end of the evaporating interfacial region. For different apolar working fluids, the calculation results are similar and the above-mentioned lengths are shorter. The difference is due mainly to the fact that the stronger polar working fluid leads to much stronger disjoining pressure, and the evaporation is choked because the liquid molecules of polar working fluids on the vapor-liquid interface are strongly attracted by the solid wall. The effects of other factors on the length of the evaporating interfacial region and the profile of the vapor-liquid interface are more secondary.     

Characteristics of an evaporating thin film in a microchannel

An evaporating meniscus in a microchannel is investigated through an augmented Young–Laplace model and the kinetic theory-based expression for mass transport across a liquid–vapor interface. The complete expression for mass transport is employed without any approximations and boundary conditions for the film profile are developed. The thin film and the intrinsic-meniscus regions are distinguished based on the disjoining pressure variation along the meniscus. While heat transfer in the thin-film region is found to be relatively insensitive to channels larger than a few micrometers in radius, that in the intrinsic meniscus is quite sensitive to channel size. The role of evaporation suppression due to capillary pressure in both regions is discussed. Compared to the relatively small contribution to overall heat transfer from the thin-film region, the micro-region (defined here as extending from the non-evaporating region to a location where the film is 1 μm thick) is found to account for more than 50% of the total heat transfer.     

Evaporation heat transfer characteristics of a grooved heat pipe with micro-trapezoidal grooves

A detailed mathematical model predicting the effect of contact angle on the meniscus radius, thin film profile and heat flux distribution occurring in the micro-trapezoidal grooves of a heat pipe has been presented. The model can be used to determine the maximum evaporating heat transfer rate in the evaporator including the effects of disjoining pressure and surface tension. The equation of meniscus radii calculation in the evaporator at given heat load based on the liquid wicks configuration has been put forward. The numerical results show that while the capillary limitation governs the maximum heat transport capability in a grooved heat pipe, the thin film evaporation determines the effective thermal conductivity in a grooved heat pipe. The ratio of the heat transfer through the thin film region to the total heat transfer through the wall to the vapor phase decreases when the contact angle increases. The superheat effects on the heat flux distribution in the thin film region also have been conducted and the results show that the disjoining pressure plays an important role in this region. The current investigation will result in a better understanding of thin film evaporation and its effect on the effective thermal conductivity in a grooved heat pipe.     

Effects of the liquid polarity and the wall slip on the heat and mass transport characteristics of the micro-scale evaporating transition film

A mathematical model is developed to describe the micro-/nano-scale fluid flow and heat/mass transfer phenomena in an evaporating extended meniscus, focusing on the transition film region under non-isothermal interfacial conditions. The model incorporates polarity contributions to the working fluid field, a slip boundary condition on the solid wall, and thermocapillary stresses at the liquid-vapor interface. Two different disjoining pressure models, one polar and one non-polar, are considered for water as the working fluid so that the effect of polar interactions between the working fluid and solid surface can be exclusively examined on heat and mass transfer from the thin film. The polar effect is examined for the thin film established in a 20-μm diameter capillary pore. The effect of the slip boundary condition is separately examined for the thin film developed in a two-dimensional 20-μm slotted pore. The analytical results show that for a polar liquid, the transition region of the evaporating meniscus is longer than that of a non-polar liquid. In addition, the strong polar attraction with the solid wall acts to lower the evaporative heat transfer flux. The slip boundary condition, on the other hand, increases evaporative heat and mass flux and lowers the liquid pressure gradients and viscous drag at the wall. The slip effect shows a more pronounced enhancement as superheat increases. Another thing to note is that the slip effect of elongating the transition region can counteract the thermocapillary action of reducing the region and a potential delay of thermocapillary driven instability onset may be anticipated.     

Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels

A model based on the augmented Young–Laplace equation and the Clausius–Clapeyron equation was developed to describe the extended evaporating meniscus in a microchannel. The effects of the adsorbed film thickness, channel height and temperature-dependent thermophysical properties of the fluid are included in the model at wall superheats up to 50 K. The liquid flow is coupled with the vapor flow to obtain the mass transport across the liquid–vapor interface. The results show that the constant thermophysical property model greatly overestimates the liquid pressure difference and the total thin film heat transfer rate at higher superheats compared with the variable thermophysical property model. The adsorbed film thickness, which is controlled by the disjoining pressure limit, reaches a minimum near about 20 K superheat for water. The maximum film curvature and liquid pressure difference then decrease at superheats larger than 20 K. The effects of the capillary pressure limit produced by the channel height can be reduced by increasing the superheat.     

Slip and micro flow characteristics near a wall of evaporating thin films in a micro channel

The microscopic liquid flow and heat transfer characteristics near the solid–liquid interface in the evaporating thin film region of a mini channel were investigated based on the augmented Young–Laplace equation and kinetic theory. A physical model using the boundary layer approximation and a constant slip length was developed to obtain the solid–liquid interfacial thermal resistances and interfacial temperatures. The results show that the ordered micro layer and micro flow near the wall reduce the effective liquid superheat and the liquid pressure difference mainly due to the reduced capillary pressure gradient. The solid–liquid interfacial thermal resistances and U‐shaped temperature drops tend to reduce the thin film spreading and heat transfer. The effects of the solid–liquid interfacial thermal resistances on the thin film evaporation outweigh the effects of the thermal conductivity enhancement due to the liquid ordering. The concepts of the micro flow and ordered adsorbed flowing micro layer are clarified to express the Kapitza resistance analytically in terms of the slip length and micro layer thickness. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 460–474, 2010; Published online 3 June 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20310     

Flow and heat transfer characteristics of the evaporating extended meniscus in a micro-capillary channel

A mathematical model is developed to predict the transport phenomena during evaporation in the extended meniscus region of a micro-capillary channel. In this model, the vapor pressure variation and the disjoining pressure effect are included and the friction force at the liquid-vapor interface is considered as well. The results show that the local heat transfer coefficient has an extremely large value in the thin film region. The heat transfer rate, however, is larger for the meniscus than for the thin film region. The maximum liquid velocity appears at approximately 40% of the extended meniscus region and the variation of the heat flux has a negligible effect on the maximum liquid velocity. It is also found that the length of the extended meniscus region is affected by the heat flux, the channel height and the dispersion constant.     

Second law analysis for microscale flow and heat transfer

In phase change transport devices, capillary forces drive overall circulation of working fluid from an evaporator section to a condenser section, whereas the thin film flows at the evaporating meniscus are driven by capillary and disjoining pressure gradient. An analysis has been provided for the microscale fluid flow and heat transfer in an evaporating extended meniscus. Using the second law of thermodynamics, the entropy generated has been investigated. The geometric configuration that corresponds to the minimization of entropy generated and minimization of fluid flow resistance is identified.     

Numerical investigation of heat and mass transfer from an evaporating meniscus in a heated open groove

The process of evaporation from a meniscus into air is more complicated than in enclosed chambers filled with pure vapor. The vapor pressure at the liquid–gas interface depends on both of the evaporation and the vapor transport in the gas environment. Heat and mass transport from an evaporating meniscus in an open heated V-groove is numerically investigated and the results are compared to experiments. The evaporation is coupled to the vapor transport in the gas domain. Conjugate heat transfer is considered in the solid walls, and the liquid and gas domains. The flow induced in the liquid due to Marangoni effects, as well as natural convection in the gas due to thermal expansivity and vapor concentration gradients are simulated. The calculated evaporation rates are found to agree reasonably well with experimentally measured values. The convection in the gas domain has a significant influence on the overall heat transfer and the wall temperature distribution. The evaporation rate near the contact lines on either end of the meniscus is high. Heat transfer through the thin liquid film near the heated wall is found to be very efficient. A small temperature valley is obtained at the contact line which is consistent with the experimental observation.     

Effects of wall slip and temperature jump on heat and mass transfer characteristics of an evaporating thin film

A new mathematical model is developed to predict heat and mass transport characteristics of the evaporating thin film. The model considers effects of velocity slip and temperature jump at the solid-liquid interface, disjoining pressure, and surface tension. Three-dimensional nonequilibrium molecular dynamics simulations for coupling between the momentum and heat transfer at the nanoscale solid-liquid interface are performed to obtain the slip length and interfacial thermal resistance length. It is found that both slip length and interfacial thermal resistance length decrease significantly with the decreasing interface wettability of the liquid to the wall. Velocity slip and temperature jump at the solid-liquid interface intend to reduce the superheat degree of the evaporating thin film, and thus result in a sharp decrease of the heat and mass transport characteristics of the evaporating thin film. It is also noted that velocity slip and temperature jump at the solid-liquid interface show a more pronounced effect as the superheat degree increases.     

Numerical study of convective flow with condensation of a pure fluid in capillary regime

A stationary 2-phase flow model with condensation in the capillary regime, based on a separate flow approach was developed. One of the specificities of the model is that it takes into account the coupling between a cylindrical interface (region with a thin film of liquid) and a hemispherical interface (main meniscus at the end of the condensation region). A specific algorithm was developed for numerical resolution to overcome the difficulty related to the presence of a free boundary condition. Analysis of the liquid–vapour interface profiles and the various local parameters allowed us to establish the heat and mass transfer laws for the particular type of regime studied. We analysed the dominant effects of this type of flow, which are characterised by dimensionless numbers Ca (capillary number) and Bo (boiling number), representing the competition between the capillary, viscous and phase-change effects. The effects due to the difference in density between the two phases and to the Reynolds number were also studied. We show that the mean heat transfer coefficients are driven by the profile of the interface. Hence, in certain situations, even when the liquid film becomes thinner on average an unexpected lowering of the efficiency of heat transfer is obtained. These effects are closely related to the coupling between the thin liquid film region and the main meniscus.     

Theoretical analysis of film condensation heat transfer inside vertical mini triangular channels

An analytical model is presented for predicting film condensation of vapor flowing inside a vertical mini triangular channel. The concurrent liquid-vapor two-phase flow field is divided into three zones: the thin liquid film flow on the sidewall, the condensate flow in the corners, and the vapor core flow in the center. The model takes into account the effects of capillary force induced by the free liquid film curvature variation, interfacial shear stress, interfacial thermal resistance, gravity, axial pressure gradient, and saturation temperatures. The axial variation of the cross-sectional average heat transfer coefficient of steam condensing inside an equilateral triangular channel is found to be substantially higher than that inside a round tube having the same hydraulic diameter, in particular in the entry region. This enhancement is attributed to the extremely thin liquid film on the sidewall that results from the liquid flow toward the channel corners due to surface tension. The influences of the inlet vapor flow rates, the inlet subcooling, and the channel size on the heat transfer coefficients are also examined.     

Numerical study of liquid-gas and liquid-liquid Taylor flows using a two-phase flow model based on Arbitrary-Lagrangian–Eulerian (ALE) formulation

The liquid-gas and liquid-liquid Taylor flows in circular capillary tubes are numerically studied using a mathematical model developed in the frame of Arbitrary-Lagrangian–Eulerian (ALE), where the interface is tracked so that the important interfacial curvature and forces for Taylor flow can be accurately estimated. It is found that for liquid-gas Taylor flow, thin film thickness predicted by the present numerical model agrees very well with the benchmark experimental data both in visco-capillary and visco-inertia flow regimes. Thin film thicknesses decreases first and then increases as Reynolds number (Re) increases at relatively large capillary numbers (Ca). With the increase of Ca, classical pressure drop correlations become inaccurate, because of strong internal circulation inside liquid slug, the appearance of waves at rear meniscus, as well as the deviation from semi-spherical shape of head meniscus. For liquid-liquid flow, when Ca is small, thin film thickness correlations for liquid-gas flow can be used since the disperse phase has negligible effects, while when Ca is relatively large, the viscosity ratio and density ratio of continuous phase to disperse phase become two additional influencing factors. The larger are the viscosity ratio and the density ratio, the thicker is the film thickness. Different from stagnant thin film in liquid-gas flow, the flow in thin film of liquid-liquid flow is not stagnant and has a large contribution to pressure drop. The numerical model developed in this study is shown to be a powerful and accurate tool to study both the liquid-gas and liquid-liquid Taylor flows.     

Transport phenomena in the thin-film region of a micro-channel

A mathematical model to predict the flow and heat transfer characteristics for a thin film region of a micro-channel is proposed. Gradient of the vapor pressure and the capillary force are considered. The effects of channel height, heat flux and slip boundary condition at the solid-liquid interface are investigated. The length of the thin film region is calculated by comparing the magnitude of the capillary and disjoining pressures. The length and the thickness of the thin film region decrease exponentially with increasing heat flux. The channel height has no effect on the shape of film thickness. In the case of slip condition, the decreased film thickness causes the capillary and disjoining pressures to increase.     

Contribution of thin-film evaporation during flow boiling inside microchannels

Flow boiling through microchannels is characterized by nucleation and growth of vapor bubbles that fill the entire channel cross-sectional area. As the bubbles nucleate and grow inside the microchannel, a thin film of liquid or a microlayer gets trapped between the bubbles and the channel walls. The heat transfer mechanism present at the channel walls during flow boiling is studied numerically. It is then compared to the heat transfer mechanisms present during nucleate pool boiling and in a moving evaporating meniscus. Increasing contact angle improved wall heat transfer in case of nucleate boiling and moving evaporating meniscus but not in the case of flow boiling inside a microchannel. It is shown that the thermal and the flow fields present inside the microchannel around a bubble are fundamentally different as compared to nucleate pool boiling or in a moving evaporating meniscus. It is explained why thin-film evaporation is the dominant heat transfer mechanism and is responsible for creating an apparent nucleate boiling effect inside a microchannel.     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.