Numerical investigation of an evaporating meniscus in a channel

A detailed numerical model is developed that describes heat and mass transfer from a meniscus to open air. The model accounts for the effects of evaporation at the interface, vapor transport through air, thermocapillary convection, and natural convection in air. Evaporation at the interface is modeled using kinetic theory, while vapor transport in air is computed by solving the complete species transport equation. Since the vapor pressure at the liquid–gas interface depends on both evaporation and the vapor transport in air, the equations are solved in an iterative manner. Evaporation is strongest at the triple line due to the highest local vapor diffusion gradient in this region. This differential evaporation, coupled with the low thermal resistance near the triple line, results in a temperature gradient along the interface that creates thermocapillary convection. The numerical results obtained show satisfactory agreement with experimental data for the evaporation rate and the temperature profile. Additionally, results from a simplified model neglecting thermocapillary convection are compared with the full solution, thus delineating the importance of thermocapillary convection-induced mixing in the energy transfer process. The present generalized model may easily be extended to other geometries and hence may be used in the design of two-phase cooling devices.     

A microscale model for thin-film evaporation in capillary wick structures

A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.     

Effects of radius and heat transfer on the profile of evaporating thin liquid film and meniscus in capillary tubes

The physical and mathematical models are established to account for the formation of evaporating thin liquid film and meniscus in capillary tubes. The core vapor flow is due to gradient of vapor pressure, which is mainly contributed by the shear stress at vapor-liquid interface. The liquid film flow is owing to gradients of capillary pressure and disjoining pressure. The heat transfer is composed of liquid film conduction and evaporation at vapor-liquid interface. The mass balance of vapor flow is considered to obtain the vapor velocity, this can evade directly solving the rarefied gas velocity field.In regard to the capillary tubes of micron scale, the calculation results show that, the bigger the inner radius or the smaller the heat flow, the longer the evaporating interfacial region will be. There only exists meniscus near the wall, and nearby the axial center is flat interface. While as to the capillary tubes of scale about 100 μm, the evaporating interfacial region will increase with heat flux. Compared with capillaries of micron scale, the meniscus region will extend to the center of capillary axis. These can be tentatively explained as strong influence of the thin liquid film.For the capillary tubes of radius about 100 μm, the experimental results indicate that the apparent contact angles and meniscus profiles can almost coincide with those of the theoretical values.     

Thin-liquid-film evaporation at contact line

When a liquid wets a solid wall, the extended meniscus near the contact line may be divided into three regions: a nonevaporating region, where the liquid is adsorbed on the wall; a transition region or thin-film region, where effects of long-range molecular forces (disjoining pressure) are felt; and an intrinsic meniscus region, where capillary forces dominate. The thin liquid film, with thickness from nanometers up to micrometers, covering the transition region and part of intrinsic meniscus, is gaining interest due to its high heat transfer rates. In this paper, a review was made of the researches on thin-liquid-film evaporation. The major characteristics of thin film, thin-film modeling based on continuum theory, simulations based on molecular dynamics, and thin-film profile and temperature measurements were summarized.     

Transient heat and mass transfer at the ignition of vapor and gas mixture by a moving hot particle

The processes of heat and mass transfer at the ignition of air and typical combustible liquid vapors mixture by a moving single metal particle heated till high temperatures are numerically investigated. The researches are carried out on the base of gas phase ignition model considering processes of heat conductivity, liquid evaporation, diffusion and convection of fuel vapors in oxidizing medium, ignition source crystallization, kinetic of evaporation and ignition processes, dependences of thermo physical properties of interacting substances from temperature, air humidity, heating source movement in vapor and gas mixture. The dependences of main characteristic of investigated process – ignition time delay from rate of particle motion, air humidity and temperature, distance between heating source and liquid surface, initial temperature and sizes of particle are determined.     

The effect of three-phase contact line speed on local evaporative heat transfer: Experimental and numerical investigations

In pool boiling or flow boiling devices or e.g. during meniscus evaporation within capillary structures the local heat flux and evaporation rate at the position where the liquid–vapor interface meets the solid wall can be extremely high. This three-phase contact line region is characterized by a thin liquid film with a very low heat resistance. Depending on the application the contact line can move with velocities of several meters per second, either in receding (dewetting) or in advancing (wetting) direction. In this paper, experimental and numerical results on the influence of three-phase contact line speed on the local heat transfer in the contact line region during pool boiling and during meniscus evaporation are presented and analyzed. It is shown that the local heat flux can be one or more orders of magnitude higher than the mean heat flux supplied to the system. This local heat transfer peak is almost independent of the contact line speed in the case of a receding contact line while it significantly increases with contact line speed for an advancing contact line. This behavior could be observed in different evaporation configurations and with different fluids. Experimental and numerical results agree well and allow a characterization of the transient heat transfer phenomena in the contact line region during evaporation.     

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.     

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.     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.     

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     

Capillary-assisted flow and evaporation inside circumferential rectangular micro groove

To introduce capillary-assisted evaporation from micro-size fields to normal-size fields, an inclined circumferential micro groove with rectangular cross sections is investigated analytically and a systematic mathematical model is developed. The model is composed of five sub-models: a natural convection model, a liquid axial flow model, a heat transfer model in and below the intrinsic meniscus, an evaporation thin film region model and an adsorbed region model. In this model, for the extended meniscuses formed at groove cross sections, both the intrinsic meniscus and evaporation thin film region are considered when calculating heat absorbing. Through solving the model, the influences of dynamic contact angle on the heat absorbing in the intrinsic meniscus and evaporation thin film region are investigated. Moreover, the factors affecting the whole-groove equivalent heat transfer coefficient have been investigated.     

High resolution measurements of wall temperature distribution underneath a single vapour bubble under low gravity conditions

Heat transfer performance in nucleate boiling crucially depends on a circular thin film area near the foot of a vapour bubble where high heat fluxes and thus high local evaporation rates occur. The corresponding wall temperature drop close to the tiny thin film area is computed using an existing nucleate boiling model. To verify the predicted temperature distribution, an experiment is designed with a thin electrically heated wall featuring two-dimensional, high resolution temperature measurement using unencapsulated thermochromic liquid crystals. By means of temperature measurements during a parabolic flight under low-g conditions, the validity of the model used to calculate the temperature distribution in the tiny thin film area could be confirmed.     

Temperature measurements near the contact line of an evaporating meniscus V-groove

Evaporation from a meniscus of heptane liquid in a V-groove geometry is experimentally investigated. A thin layer of titanium coated on the backside of the fused quartz groove is electrically heated to provide a constant heat flux. The temperature profile in the evaporating thin film region of the extended meniscus is measured using high-resolution infrared thermography and the temperature suppression in this region is obtained as a function of liquid feeding rate. The meniscus shape is captured using a goniometer. A temperature suppression of ～0.2 K in the 150 μm region surrounding the contact line on each side indicates the efficacy of evaporation in the extended meniscus. At a given axial location, the fraction of total meniscus heat transfer which takes place in a 50 μm sub-region measured from the contact line is estimated by an approximate heat balance analysis to be ～45% for the range of liquid feeding rates explored.     

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.     

Convection and evaporation of microlayer underneath bubbles under microgravity

The multidimensional heat transfer and fluid flow in the microlayer region below a vapor bubble formed during boiling in microgravity are investigated by numerically solving the Navier–Stokes equations with the energy equation. The flow is driven by Marangoni flow due to the surface tension gradient along the bubble surface that results from the temperature gradient. The model also includes condensation and evaporation at the bubble surface. The flow field and heat transfer are calculated for microlayer thicknesses from 0.01 mm to 10 mm to investigate the effect of microlayer thickness. The results show that the velocities are small and have only a small effect on the temperature distribution as compared to the solution for pure conduction in the liquid. Natural convection is shown to have a negligible effect on heat transfer. For less than ideal evaporative heat transfer at the bubble interface, Marangoni convection caused the heat transfer to increase several percent. The flow in the microlayer is shown to agree with the lubrication analogy only for thin, relatively flat interfaces. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 1–10, 2001     

Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

Rapid vaporization of subcooled liquid in a capillary structure

A novel process is introduced for rapid vaporization of subcooled liquid in a capillary structure. The process consists of a low-thermal-conductivity porous wick, heated from a downward-facing grooved heating block that is in intimate contact with the upper surface of the wick structure. For such a specially configured heat transfer device, measurements show that vapor can be generated rather quickly once a sufficient amount of heat was applied. The mechanisms leading to the rapid vaporization of liquid are numerically investigated. It is found that the low thermal conductivity of the capillary structure and the presence of the extremely steep temperature gradients at the fin/porous structure interface due to the rather weak natural convection, reflected by small-scale secondary flow cells below the heated fins, are responsible for the rapid vaporization of subcooled liquid.     

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.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

The effect of heated wall thickness and materials on nucleate boiling at high heat flux

The present work is to numerically investigate the effect of heater side factors on the nucleate boiling at high heat flux, which is characterized by the existence of macrolayer. Two-region equations are proposed to study both thermo-capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical results indicate that the thermo-capillary driven flow in the macrolayer and evaporation at the vapor-liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. For a very thin wall and/or wall with a poor thermal conductivity (heat side factors) are found to have significant effect on flow pattern in the liquid layer and the temperature distribution in the heated wall.