The effect of liquid film vaporization on natural convection heat and mass transfer in a vertical tube

A numerical analysis was carried out to investigate the effects of film vaporization on natural convection heat and mass transfer in a vertical tube. Results for interfacial Nusselt and Sherwood numbers are presented for air-ethanol and air-water systems for various conditions. Predicted results show that heat transfer along the gas-liquid interface is dominated by the transport of latent heat in association with the vaporization of the liquid film. Additionally, the 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 Chang et al. (1986) and Yan and Lin (1990) is only valid for systems with small liquid mass flow rates. For systems with a high liquid film Reynolds number, Re₁₀, the assumption of an extremely thin film is seriously in error.     

Natural convection heat transfer enhancement through latent heat transport in vertical parallel plate channel flows

A numerical analysis is carried out to investigate the effects of latent heat transfer, in connection with the vaporization of a liquid film, on natural convection heat transfer in a vertical parallel plate channel. Major nondimensional groups identified are Gr_T, Gr_M, Pr and Sc. Results for Nusselt and Sherwood numbers are specifically presented for the air-water and air-ethanol systems under various heating conditions to illustrate the heat transfer enhancement through latent heat transfer during the evaporation processes. Considerable enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

Mixed convection heat transfer enhancement through latent heat transport in vertical parallel plate channel flows

A detailed numerical study has been performed to examine the heat transfer enhancement through latent heat transport, in conjunction with the evaporation of a liquid film, in laminar mixed convection channel flows. Results for Nusselt numbers are presented for the air–water and air–ethanol systems under various conditions. Considerable augmentation in heat transfer due to the exchange of latent heat during the evaporation process was clearly demonstrated. The results show that the heat transfer is dominated by the transport of latent heat exchange.     

Post extrusion heat and solvent transfer from polymeric film

The problem of heat and solvent transfer from plasticized film is considered. The transport equations are solved by a numerical method. The formulation of the model includes the temperature dependence of diffusivity, the dependence of diffusivity on decreasing solvent concentration, as solvent leaves the film, and the latent heat of vaporization of the solvent. The Flory-Huggins theory is used as a model for vaporliquid equilibrium. Heat and mass transfer coefficients are taken either as constants (to simulate extrusion with blowing at the film surface) or from analytical solutions to the appropriate boundary layer equations (to simulate extrusion into a stationary medium.) The boundary layer theory takes into account the effect of rapid vaporization on heat and mass transfer coefficients. Several numerical solutions were obtained for cases corresponding to extrusion of polyvinylacetate, plasticized with acetone, extruded into air.     

The effect of liquid viscosity and modeling of mass transfer in gas–liquid slug flow in a rectangular microchannel

Both chemical (by adding 0.05 M NaOH) and physical absorption of CO₂ into aqueous glycerol solutions with viscosity up to 45.6 mPa·s in a microchannel are investigated. The concentration distribution pattern, absorption time, and mass transfer coefficient are analyzed and discussed. A new concentration distribution pattern is observed with the lowest concentration locating at the channel center. It is shown for the first time that presents a positive relationship with liquid viscosity, which is explained by the essential role of the mass exchange between the liquid film and bulk liquid slug. This mass exchange may lead to a rise in k _L when increasing the liquid viscosity under some cases in chemical absorption. A mass transfer model is successfully applied to predict the bubble size evolution in physical absorption. The model also shows about 10–46% of the mass transfer contribution from liquid films before saturation.     

Intensification of G/L absorption in microstructured falling film. Application to the treatment of chlorinated VOC's - part II: Modeling and geometric optimization

The falling film microabsorber developed by the Institut für Mikrotechnik Mainz is used to study its performance for the treatment of VOC-containing gases. The technique used is the gas/liquid absorption. The gas (mixture of air and tetrachloroethylene) and the solvent (Di(ethyl-2-hexyl) adipate, DEHA) flow counter-currently in the microabsorber. The solvent streams by gravity on a plate structured by microchannels. This technique makes it possible to miniaturize the process by increasing the mass transfer flow per volume unit as explained in Part I. Experiments are presented and a model is developed from equations of mass and momentum transfers. Results show a competition between two transport phenomena: diffusion and convection. The mass transfer rate is also studied with respect to the structure of microabsorber. It is also shown that it is possible “to optimize” the geometry of the apparatus in order to intensify the transfer so as to miniaturize the process. In the case of physical absorption, mass transfer intensification (Murphree Efficiency) increases when the number of transfer unit NTU_G (=τ/t_transfer) increases too. It is mainly due to the small volume of the apparatus where the gas phase residence time must be taken into account in the study of the mass transport towards the gas/liquid interface: the radial and the axial distances for the mass transfer and the mass transport have the same order of magnitude.     

Liquid (melt) heat capacities and heats of vaporization of oligomers of poly(hexamethylene sebacate)

The liquid heat capacities and heats of vaporization of three linear esters of poly(hexamethylene sebacate) with hexylcapped end groups (M(mol. wt.) = 370, 655, and 939) have been determined. The heats of vaporization of the oligomers measured at a mean temperature were corrected to 323.15 to 523.15°K by use of the experimental liquid (melt) heat capacities and the calculated gas heat capacities. The corrected heats of vaporization were fitted to the equation ΔH_v = S(T)M^α + I(T), where the temperature dependence of the slope and intercept are represented, respectively, as S(T) = ClnT + K_o and I(T) = a T + b_o, and α is an exponent. The results indicate (at corresponding molecular weights and constant temperature) that the ratio of the liquid heat capacities of the oligomer ester and the n-alkane, and similarly the ratio of the heats of vaporization, depend on the number of carboxyl groups in the oligomer ester chain.     

Predicting inter-phase mass transfer for idealized Taylor flow: A comparison of numerical frameworks

Four numerical frameworks were derived to investigate the impact of underlying assumptions and numerical complexity on the predicted mass transfer between a Taylor bubble and liquid slug in circular capillaries. The separate influences of bubble velocity and film length, slug length, and bubble film thickness on k_La were compared to empirical and CFD-based predictions from existing literature. Reasonable agreement was obtained using a Slug Film model, which accounted for diffusion-limited mass transfer between the slug film and circulating bulk without the need for an iterative numerical solution. Subsequent investigation of the relative contributions of film and cap mass transport for industrially relevant conditions suggests that both mechanisms need to be accounted for during the prediction of k_La.     

Heat Transfer from Immersed Vertical Cylinders in Gas‐Liquid and Gas‐Liquid‐Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid‐solid and gas‐liquid‐solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt‐% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface‐to‐liquid heat transfer coefficients in the liquid‐solid and gas‐liquid‐solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j_H‐factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1 %. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr^1/3, and the specific power group including energy dissipation rate per unit mass of liquid, E^1/3D^4/3/ν_l, within a smaller error of 24.7 %. It is also confirmed that a good analogy exists between the surface‐to‐liquid heat transfer and mass transfer on the immersed cylinder in the liquid‐solid and gas‐liquid‐solid fluidization systems.     

Etude numérique de l'influence de l'inclinaison sur l'évaporation d'un film liquide s'écoulant sur une paroi plane isotherme ou à flux de chaleur imposé

The authors study numerically, by using an implicit centred difference method with non-uniform grid, the effects of inclination on the evaporation of liquid film flowing on a horizontal or inclined isotherm flat plate with the assumption of existing two-dimensional laminar boundary-layers with variable physical properties. In the case of an humid air-water system, they compare their results with those of other authors and study the influence of the entrance air velocity and the inclined angle of plate. They show that for an isotherm plate, the inclined angle effects heat and mass transfer, especially for low flow air velocity and for an inclined angle less than 10°. In this domain, the interfacial temperature is so high as the inclined angle increases which causes an increase of the density of flux of vapor, of the latent heat of vaporization and a reduction of draining length. For the heated plate, it is always for an inclined angle than 10°, that the effects of this parameter and air velocity are very important on the film thickness and its interfacial velocity. Opposite to the case of an isotherm plate, air velocity increase causes a reduction of interfacial temperature; inclined angle has less effect on temperature, density of latent heat of vaporisation and on heat and mass transfer at the interface. Generally, for an isotherm or heated plate, heat transfer is dominated by liquid-vapor phase transition.     

Impact of water film thickness on kinetic rate of mixed hydrate formation during injection of CO2 into CH4 hydrate

In this work, nonequilibrium thermodynamics and phase field theory (PFT) has been applied to study the kinetics of phase transitions associated with CO₂ injection into systems containing CH₄ hydrate, free CH₄ gas, and varying amounts of liquid water. The CH₄ hydrate was converted into either pure CO₂ or mixed CO₂?CH₄ hydrate to investigate the impact of two primary mechanisms governing the relevant phase transitions: solid‐state mass transport through hydrate and heat transfer away from the newly formed CO₂ hydrate. Experimentally proven dependence of kinetic conversion rate on the amount of available free pore water was investigated and successfully reproduced in our model systems. It was found that rate of conversion was directly proportional to the amount of liquid water initially surrounding the hydrate. When all of the liquid has been converted into either CO₂ or mixed CO₂?CH₄ hydrate, a much slower solid‐state mass transport becomes the dominant mechanism. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3944–3957, 2015     

Wall-to-bed heat transfer in liquid—solid and gas—liquid—solid fluidized beds part I: Liquid—solid fluidized beds

Experimental work was conducted to investigate the effect of particle size and particle density upon the wall-to-bed heat transfer characteristics in liquid—solid fluidized beds with a 95.6 mm column diameter over a wide range of operating conditions. The radial temperature profile was found to be parabolic, indicating the presence of a considerable bed resistance. The effective radial thermal conductivity and the apparent wall film coefficient were obtained on the basis of a series thermal resistance model. The modified Peclet number of the radial thermal conductivity decreases upon the onset of fluidization, has a minimum at a bed porosity of 0.6 to 0.7 and increases with further increase of bed porosity. The modified Peclet number decreases considerably with decreasing particle size or increasing particle density. The apparent wall heat transfer coefficient can be represented well by a Colburn j-factor correlation over a wide range of data as follows: j′_H = 0.137 Re′^?0.271 A close analogy is found to exist between the modified j-factor for wall heat transfer coefficient and that for wall mass transfer coefficient, in liquid—solid fluidized beds.     

Etude numérique de l'évaporation dans un courant d'air humide laminaire et turbulent d'un film d'eau ruisselant sur une plaque inclinée

The authors have proposed an appropriate model based on the liquid film transfer equations which are one‐dimensional, partially two‐dimensional and two‐dimensional. They have compared their results with those of other works and studied the influence of the liquid mass flow rate and the inclined angle. They have shown that the interracial heat transfer is dominated by the latent heat transfer; the contribution of the sensible heat is only important in the turbulent region where the interfacial temperature and the evaporating mass flux are practically constant and the thickness of the liquid film is uniform. For the adiabatic plate, the liquid mass flow rate and the inclined angle have no influence on the transfers. For the isothermal or the heated plate, the liquid mass flow rate essentially influences the turbulent region by reducing the interrfacial temperature and the heat and mass transfer coefficients. However, the inclination angle affects mainly the laminar region by increasing the interfacial velocity, reducing the film thickness and has little effects on the transfer coefficients.     

竖直窄矩形通道内环状流的流动传热特性

为了研究竖直窄矩形通道内环状流的流动传热特性,建立了窄矩形通道内环状流的数学物理模型,并进行了实验验证。通过数值求解环状流的数学物理模型得到了环状流区域的压降梯度、沸腾传热系数和液膜内的速度分布。结果表明窄矩形通道内的环状流模型能够很好地预测环状流区域的压降梯度和沸腾传热系数,而且环状流液膜内速度在法向的分布是非线性的,在层流边界层区速度梯度较大。热通量和窄矩形通道的尺寸对液膜的流速有很大影响,随热通量的增加和窄矩形通道尺寸的减小液膜的流速逐渐增加,然而质量流速对液膜流速的影响较小,而且随质量流速的增加液膜的速度逐渐减小。     

Mass Transfer Flux of CO2 into Methyldiethanolamine Solution in a Reactive-Absorption Process

The mass transfer parameters of both gas and liquid phases affect the mass transfer flux of CO₂ in absorption processes. In this study, an accurate correlation is proposed to calculate the CO₂ mass transfer flux in an absorption-reactive process by methyldiethanolamine (MDEA) solution using the Buckingham π theorem. The various parameters include film parameter, CO₂ loading, concentration ratio, partial-to-total pressure ratio, film thickness ratio, and diffusion ratio which are incorporated in the model. An average absolute relative error of 4.4 % for the calculation of mass transfer flux was stated.     

Hydrogen reduction of chromium chlorides: A kinetic investigation

The reduction of single pellets of chromic and chromous chlorides by hydrogen has been studied kinetically. The reaction 2 CrCL₃ + H₂ →2 HCl + 2 CrCl₂ was investigated over the temperature range 475?615°C. The rate controlling factor in the range of 475?493°C. is vaporization of chromic chloride; the activation energy was found to be 67.8 K.cal./mole. Between S10 and 615°C, the reaction rate is evidently controlled by heat and internal mass transfer processes. In this case the apparent activation energy is 16.6 K.cal./mole. Reduction of chromous chloride, CrCl₂ + H₂ → 2 HCl + Cr, was investigated over the temperature range 675?800°C. This reaction is also controlled by heat and mass transfer and involves vaporization of the chromous chloride. The apparent activation energy is 25.5 K.cal./mole.     

Numerical simulation on the falling film absorption process in a counter-flow absorber

Falling liquid film is commonly employed in variety of industrial systems, such as LiBr/H₂O absorption heat pump or chiller. In this paper, the falling film absorption in aqueous lithium bromide solution was investigated numerically using CFD software package-Fluent. The practical convective boundary condition at the cooling water side was considered. The heat transfer coefficient is assumed constant, and the coolant temperature changes linearly along its flow path. The numerical results indicate that the profile of temperature is exponential and their gradients are high due to the distinct heat effect associated with the absorption at the interface and the cooling effect of coolant at the wall at small downstream distance. As the downstream distance increases, the profile of temperature is nearly linear. The absorption heat and mass fluxes reach a maximum at the inlet region and decrease at the outside of the inlet region. Specially, the effect of variable physical properties on the absorption process was considered and discussed. The prediction of the total absorption mass transfer rate is about 6.5% higher when assuming constant properties.     

Analytical solution using a pore diffusion model for a pseudoirreversible isotherm for the adsorption of basic dye on silica

An analytical solution for a two resistance mass transfer model explaining the adsorption of Astrazone Blue dye (Basic Blue 69) onto Sorbsil silica has been developed. The model includes a film mass transfer coefficient, k_f1 = 80 × 10⁻⁶cm·s−1, and an internal effective diffusivity, D_eff = 18×10⁻⁹cm²·s⁻¹ which controls the internal mass transport processes based on a pore diffusion mechanism.     

Heat transfer from a horizontal smooth tube to a laminar falling film

For the case in which the liquid, freely falling between two adjacent horizontal tubes, forms a liquid sheet, Rogers (1981) gave an analysis of the heat transfer from the tube to the liquid. The flow within the film was assumed to be laminar. Some of the results obtained by Rogers are extended and discussed in the present paper. In particular, a simple relation is given for the angle θ_d, at which the thermal boundary layer intersects the film surface. This relation provides an easy means for calculation of the heat transfer coefficient and for determination of the range of parameters in which Rogers' analysis is applicable.     

Influence of current density on oxygen transfer in an electroflotation cell

The objective of this work is to study the transfer of oxygen from gas to liquid phase in an electroflotation cell. The measurements were performed in a laboratory scale cell using insoluble electrodes, titanium coated with ruthenium oxide as anode and stainless steel as cathode. The volumetric mass transfer coefficient K _L a, was characterized for clean tap water as liquid phase for different values of current density (J). The global coefficient of mass transfer based on the liquid film, K _L , and the specific interfacial area, a, were characterized. A model which relates K _L a to current density was established. Different evaluation criteria of oxygen transfer in electroflotation process were determined and compared with other aeration process.