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     

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…     

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.     

Interfacial suction effects of a porous layer on filmwise condensation heat transfer enhancement

Considering the liquid transverse suction effect at the porous layer interface, a mathematical model was presented to investigate the influence of the porous layer characteristic parameters on condensation heat transfer. The results revealed that the enhancement ratio increased with the increase of the porous layer thickness and permeability. The effective thermal conductivity of the porous layer was, however, of little significance for condensation heat transfer enhancement. Also, the enhancement mechanism was analyzed by comparing the thermal resistances within the external condensate film and the porous layer. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 568–577, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10058     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

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.     

Study on high performance evaporator with micro‐grooves (Measurement of capillary force in a single groove and modeling of heat and mass transfer)

A micro‐grooved evaporator is composed of µm‐wide grooves on a heat transfer plate in which the inter‐line regions at the liquid–vapor meniscus of coolant become identifiable. The high‐heat performance of the evaporator is realized by this inter‐line region (ILR) where the liquid thin film reduces the thermal resistance on the heat transfer surface. In this report, we propose a numerical simulation model of heat and mass transfer in a single groove to predict its capillary force and heat flux. The capillary force performance (capillary‐rise length in a groove) of a single groove was measured for samples of varying width, superheat, and inclination. The performance was found to be a maximum at a specific groove width of 200–400 µm, which is in good agreement with the predicted results calculated by the proposed model. For a better prediction of capillary‐rise length, the effective capillary force and the effective flow resistance were considered. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20257     

A study on the thermal resistance over solid–liquid–vapor interfaces in a finite-space by a molecular dynamics method

Molecular dynamics of argon atoms in a nano-triangular channel which consists of (111) platinum walls were studied. The molecular dynamics simulations aim to gain understanding in the heat transfer through the channel including the influence of the contact resistances which become important in small-scale systems. The heat transfer properties of the finite-space system were measured at a quasi-steady non-equilibrium state achieved by imposing a longitudinal temperature gradient to the channel. The results indicate that the total thermal resistance is characterized not only by the thermal boundary resistances of the solid–liquid interfaces but also by the thermal resistance in the interior region of the channel. The overall thermal resistance is determined by the balance of the thermal boundary resistances at the solid–liquid interfaces and the thermal resistance attributed to argon adsorption on the lateral walls. As a consequence, the overall thermal resistance was found to take a minimum value for a certain surface potential energy. A rich solid–liquid interface potential results in a reverse flow along the wall which gives rise to a stationary internal flow circulation. In this regime, the nanoscale-channel functions as a heat-pipe with a real steady state.     

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.     

A study on thermal conductivity of a quasi‐ordered liquid layer on a solid substrate

In the present paper, a study on thermal conductivity of a quasi‐ordered liquid layer on a solid surface was performed by molecular dynamic simulation. Results showed that the motion of the molecules and their radial distribution function in the quasi‐ordered liquid layer were similar to those of solid molecules. By using the Green–Kubo formula, the thermal conductivity of the layer was calculated. It was found that it increased with the increase of the parameters of ordering. The size effect and the influence of the boundary condition were also discussed. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(7): 429–434, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20171     

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.     

Film condensation in presence of non-condensable gases: Interplay between variable radius of curvature and interfacial slip

A theoretical study has been executed to investigate the implications of interfacial slip in presence of non-condensable species in the bulk mixture of vapour on heat transfer characteristics in film condensation over horizontal tubes with varying radius of curvature. A polar surface comprising a segment of an equiangular spiral in the form of Rp = ae^mθ (a and m being parametric constants), generated symmetrically on a vertical chord, has been considered. We reveal that there is a substantial enhancement in the rate of condensation heat transfer due to an effective interfacial slip at the solid–liquid interface. The enhancement in condensation heat transfer due to solid–liquid interfacial slip is more pronounced in the case of vapour with non-condensable species, but less pronounced for higher values of m (a surface profile parameter).     

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.     

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     

Molecular dynamics simulations of heat and momentum transfer at a solid–fluid interface: Relationship between thermal and velocity slip

The thermal resistance of a model solid–liquid interface in the presence of laminar shear flow is investigated using molecular dynamics simulations. Two model liquids – a monoatomic liquid and a polymeric liquid composed of 20 repeat units – are confined between walls which are modeled as idealized lattice surfaces composed of atoms identical to the monomers. We find that in the absence of a velocity slip (discontinuity) at the solid–fluid interface, the mass flow does not affect the thermal interfacial resistance, but the presence of velocity slip results in an increase in the interfacial thermal resistance by about a factor of two.     

Mechanism research of convective condensation heat transfer for a gas mixture flowing over a horizontal tube

The modified film model combined with Nusselt's condensation theory are used for the study of convective condensation heat transfer on a horizontal tube with moist mixed horizontal gas flows at a given speed. A theoretical model considering gas boundary layer separation was set up. The liquid film flows and the heat transfer on the tube are presented. The effects of the flow direction on condensation heat transfer are discussed. The results predict that the condensate film is so thin that the liquid phase heat resistance can be ignored. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20238     

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.     

Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non‐Newtonian fluid from a semi‐infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non‐dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21115     

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.     

Direct simulation of spray cooling: Effect of vapor bubble growth and liquid droplet impact on heat transfer

Numerical modeling of multiphase flow using level set method is discussed. The 2-D model considers the effect of surface tension between liquid and vapor, gravity, phase change and viscosity. The level set method is used to capture the movement of the free surface. The detail of incorporating the mechanism of phase change in the incompressible Navier–Stokes equations using the level set method is described. The governing equations are solved using the finite difference method. The computer model is used to study the spray cooling phenomenon in the micro environment of about 40 μm thick liquid layer with vapor bubble growing due to nucleation. The importance of studying the heat transfer mechanism in thin liquid film for spray cooling is identified. The flow and heat transfer details are presented for two cases: (1) when the vapor bubble grows due to nucleation and (2) merges with the vapor layer above the liquid layer and when a liquid droplet impacts the thin liquid layer with vapor bubble growing.