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.     

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.     

Study on flow and heat transfer characteristics of heat pipe with axial “Ω”-shaped microgrooves

A theoretical model of fluid flow and heat transfer in a heat pipe with axial “Ω”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.     

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     

Research on a new heat transfer model for liquid film convective evaporation in annular flow

Based on the phenomenon of turbulence restraint in liquid‐vapor interface, an analytical model is proposed for annular flow with a velocity distribution. The liquid‐vapor interface affecting district mixing length model was amended, and a new liquid film convective evaporation heat transfer model at the annular flow was developed. Compared with the experimental data, the results show that the new model is better than the model based on full tube flow velocity distribution. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 524–530, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10051     

A study on flow and heat transfer characteristics for saturated falling-film evaporation of liquid oxygen in a vertical channel

In this study, a mathematical model for the laminar falling film is presented in order to simulate the evaporation heat transfer characteristics in falling liquid oxygen films. The model takes into account the effect of the interfacial shear. The values of the film thickness, the heat transfer coefficient as well as the interfacial shear are obtained under given conditions by solving the model with an iteration method. The influences of the inlet Reynolds number, channel length and the interfacial shear on the flow and heat transfer characteristics of the falling film evaporation are analyzed in detail. Effects of key factors on the circulation ratio of the inlet fluid mass flow rate to the generated vapor mass flow rate, an important design parameter for reboilers/condensers, are particularly analyzed. In addition, the variations of the average vapor velocity and interfacial film velocity are also discussed. The analysis results could provide theoretical guidance for the simulation and design of downflow reboilers/condensers applied in air separation units.     

Condensation heat transfer studies for stratified,cocurrent two-phase flow in horizontal tubes

Condensation heat transfer inside horizontal tubes is investigated for a stratified, cocurrent two-phase flow of vapor and liquid. The analysis takes into account the effects of interfacial shear, axial pressure gradient, saturation temperature level, driving temperature difference and the development of the stratified angle associated with the accumulated condensate layer at the bottom of the tube. The influence of these parameters is evaluated with respect to the peripheral condensate film heat transfer performance for the practically interesting laminar flow range of operating conditions of water-vapor flow. A theoretical predictive method is developed to obtain the overall heat transfer coefficient along the tube length. Results of the theoretical predictions are found to agree favorably with the reported experimental data which cover a variety of fluids with a relatively wide range of operating conditions. A simple, predictive heat transfer coefficient correlation is proposed from the numerical solution by means of regression analysis.     

Theoretical research of convective condensation heat transfer for mixture gas on a horizontal tube

The mechanism of convective condensation heat transfer of moist mixed gas across a horizontal tube was studied in this paper. The models referring to how the liquid film flows and the heat transfers on the tube are set up by combining modified film model and Nusselt condensation theory. The effects of Re number, wall temperature, and water vapor concentration on condensation heat transfer are discussed. Results predict that the film thickness profile on the tube is influenced greatly by vapor shear force on liquid film. Local Nusselt number depends remarkably on gas phase heat resistance, which is different from pure vapor and very similar to single‐phase gas. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 324–333, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20169     

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

horoductiouInveshgation on heat tI'ansfer meehanism ofcaPillny is the basis of designing Iniero and highefficiency evaPOratO. Some investigatOrs modeled thesitUations of smooth wall[1x.MicroscoPically, the wall sho of the caPillny isrough to some extellt. Some concave and protrUdingndwtef Of difftw sizes on the sdse are formedin the PIDCess Of manufacturing caPillny and thecaPllary gnved stheMs of heat PiPesl'l. In addition,some Inicro Inarks ealst due tO erosion and dePositionon tb…     

剪切层流蒸发液膜的传热特性

为克服理论分析中气液界面对流换热难以计算的问题,基于气相传热模型,建立了在同向或反向切应力作用下层流饱和蒸发液膜的传热模型,推导出无量纲液膜厚度和壁面对流换热系数与流动长度、界面切应力和初始雷诺数间的理论关系式.研究表明,受液膜蒸发的影响,液膜厚度沿流动长度不断减小,换热传热系数不断增加;同向切应力具有减薄液膜厚度和增大传热系数的作用;反向切应力则具有相反的作用,其影响更为明显.这一理论模型可以反映层流饱和蒸发液膜的传热特性.     

Two-Phase Flow and Boiling Heat Transfer in Small-Diameter Tubes

For the development of a high-performance heat exchanger using small channels or minichannels for air-conditioning systems, it is necessary to clarify the characteristics of vapor‐liquid two-phase flow and heat transfer of refrigerants in small-diameter tubes. In this keynote paper, the related research works that have already been performed by the author and coworkers are introduced. Based on the observations and experiments of R410A flowing in small-diameter circular and noncircular tubes with hydraulic diameter of about 1 mm, the characteristics of vapor‐liquid two-phase flow pattern and boiling heat transfer were clarified. In low quality or mass flux and low heat flux condition, in which the flow was mainly slug, the “liquid film conduction evaporation” heat transfer peculiar to small-diameter tubes prevailed and exhibited considerably good heat transfer compared to nucleate boiling and forced convection evaporation heat transfer. The effects of the tube cross-sectional shape and flow direction on the heat transfer primarily appeared in the region of the “liquid film conduction evaporation” heat transfer. A new heat transfer correlation considering all of three contributions has been developed for small circular tubes.     

A theoretical study of evaporative heat transfer in high‐velocity two‐phase flow of air–water in a small vertical tube

A theoretical study was performed to investigate the evaporative heat transfer of high‐velocity two‐phase flow of air–water in a small vertical tube under both heating conditions of constant wall temperature and constant heat flux. A simplified two‐phase flow boundary layer model was used to evaluate the evaporative heat transfer characteristics of the annular two‐phase flow. The analytical results show that the gravitational force, the gas–liquid surface tension force, and the inertial force are much smaller than the frictional force and hence can be neglected for a small tube. The evaporative heat transfer characteristics of the small tube with constant wall temperature are quite close to those of the small tube with constant heat flux. The mechanism of the heat transfer enhancement is the forced convective evaporation on the surface of the thin liquid film. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 430–444, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10110     

The formation of rising liquid thin film on the fluted surface of a horizontal tube

The purpose of this study is to investigate the mechanism of the formation of the rising liquid thin film and its flow characteristics on the fluted surface of a horizontal tube. By analyzing the wetting behaviors of the fluted tube, which was primarily responsible for the formation of the rising liquid thin film, a numerical model of one‐phase fluid was established to analyze the distribution of the velocity and thickness of the rising liquid thin film during its evaporation. The behaviors of the flow characteristics were discussed and the results showed that geometric properties of the fluted surface of a horizontal tube and surface tension of the fluid were essential for the formation of a continuous and uniform liquid thin film. Theoretical analysis suggested that the capillary force created by the fluid surface tension was a key value for the formation of the thin film. The heat and mass transfer characteristics of the formed thin film also had an effect on the formation of the rising film. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 396–406, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20075     

Two-phase flow of refrigerants during evaporation under constant heat flux in a horizontal tube

This paper presents the results of simulations using a two-phase separated flow model to study the heat transfer and flow characteristics of refrigerants during evaporation in a horizontal tube. A one-dimensional annular flow model of the evaporation of refrigerants under constant heat flux is developed. The basic physical equations governing flow are established from the conservation of mass, energy and momentum. The model is validated by comparing it with the experimental data reported in literature. The present model can be used to predict the variation of the temperature, heat transfer coefficient and pressure drop of various pure refrigerants flowing along a horizontal tube. It is found that the refrigerant temperature decreases along the tube corresponding to the decreasing of its saturation pressure. The liquid heat transfer coefficient increases with the axial length due to the reducing thickness of the liquid film. The evaporation rate of liquid refrigerant tends to decrease with increasing axial length, due to the decreasing latent heat transfer through the liquid–vapor interface. The developed model can be considered as an effective tool for evaporator design and can be used to choose appropriate refrigerants under designed conditions.     

Heat transfer and flow characteristics of flow boiling of CO2‐oil mixtures in horizontal smooth and micro‐fin tubes

Experiments were carried out on the flow pattern, heat transfer, and pressure drop of flow boiling of pure CO₂ and CO₂‐oil mixtures in horizontal smooth and micro‐fin tubes. The smooth tube is a stainless steel tube with an inner diameter of 3.76 mm. The micro‐fin tube is a copper tube with a mean inner diameter of 3.75 mm. The experiments were carried out at mass velocities from 100 to 500 kg/(m²·s), saturation temperature of 10 °C, and the circulation ratio of lubricating oil (PAG) was from 0 to 1.0 mass%. Flow pattern observations mainly showed slug and wavy flow for the smooth tube, but annular flow for the micro‐fin tube. Compared with the flow patterns in the case of pure CO₂, an increase in frequency of slug occurrence in the slug flow region, and a decrease in the quantity of liquid at the top of the tube in the annular flow region were observed in the case of CO₂‐oil mixtures. With pure CO₂, the flow boiling heat transfer was dominated by nucleate boiling in the low vapor quality region, and the heat transfer coefficients for the micro‐fin tube were higher than those of the smooth tube. With CO₂‐oil mixtures, the flow boiling heat transfer was dominated by convective evaporation, especially in the high vapor quality region. In addition, the heat transfer coefficient decreased significantly when the oil circulation ratio was larger than 0.1 mass%. For the pressure drop characteristics, in the case of pure CO₂, the homogeneous flow model agreed with the experimental results within ±30% for the smooth tube. The pressure drops of the micro‐fin tube were 0–70% higher than those predicted with the homogeneous flow model, and the pressure drops increased for the high oil circulation ratio and high vapor quality conditions. The increases in the pressure drops were considered to be due to the increase in the thickness of the oil film and the decrease in the effective flow cross‐sectional area. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20287     

Cross Vapor Stream Effect on Falling Film Evaporation in Horizontal Tube Bundle Using R134a

The falling film evaporation of R134a with nucleate boiling outside a triangular-pitch (2-3-2-3) tube bundle is experimentally investigated, and the effects of saturation temperature, film flow rate and heat flux on heat transfer performance are studied. To study the effect of cross vapor stream on the falling film evaporation, a novel test section is designed, including the tube bundle, liquid and extra vapor distributors. The measurements without extra vapor are conducted at the saturation temperature of 6, 10 and 16°C, film Reynolds number of 220 to 2650, and heat flux of 20 to 60 kWm^?2. Cross vapor stream effect experiments are operated at three heat fluxes 20, 30, and 40 kWm^?2 and two film flow rates of 0.035 and 0.07 kgm^?1s^?1, and the vapor velocity at the smallest clearance in the tube bundle varies from 0 to 2.4 ms^?1. The results indicate that: film flow rate, heat flux and saturation temperature significantly influence the heat transfer; the cross vapor stream either promote or inhibit the falling film evaporation, depending on the tube position, film flow rate, heat flux and vapor velocity.     

Zero‐flux zone model analysis of a single bubble in boiling liquid

We start from a bubble, the basic unit of boiling, to explore liquid boiling. Research indicates that the heat and mass transfer between liquid and vapor is the determinant factor of boiling heat transfer. We have analyzed interfacial vaporization and condensation of a single bubble in boiling liquid based on a zero‐flux zone model. We have deduced the expression of zero‐flux angle and discussed the relationship between zero‐flux zone and the other parameters in order to comprehend the mechanism of boiling heat transfer. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(4): 249–256, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10026     

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.     

Heat transfer research on vapor‐gas mixture with condensation in a vertical tube

The convection‐condensation heat transfer of vapor‐gas mixtures in a vertical tube was studied theoretically and experimentally. The effects of the condensation of a small amount of water vapor (8 to 20%) on heat transfer in a vertical tube were discussed. Comparisons show that theoretical solutions obtained through modified film model and experimental results are in good agreement. The results show that the condensation heat transfer of a small amount of water vapor and single‐phase convection heat transfer in the vapor‐gas mixtures are of the same order of magnitude, and these two modes of heat transfer could not be neglected. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 531–539, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10055     

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.