Mixed convection heat and Mass transfer in a vertical channel with film evaporation

Numerical results are presented for effects of latent heat transport associated with film vaporization on laminar mixed convection heat and mass transfer in a vertical channel with a half channel width b = 0.01 m. The influences of the inlet liquid mass flowrate and wall temperature on the film vaporization and the associated heat and mass transfer characteristics are examined for air-water and air-ethanol systems with gas Reynolds number Re_g = 2000. 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 in Lin et al. (1988) and Yan and Lin (1989) is only valid for systems having small liquid mass flow rates. Additionally, it is found that the interfacial heat flux is predominantly determined by latent heat transfer connected with film evaporation.     

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.     

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.     

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.     

The influence of liquid-side mass transfer on heat transfer and selectivity during surface and nucleate boiling of liquid mixtures in a falling film

Experimental studies using a falling film apparatus and a theoretical analysis of heat and mass transfer for mixtures lead to the following results.During nucleate boiling the separation effect, that is, the selectivity, and the heat transfer are influenced to a great extent by liquid-side mass transfer resistances. The selectivity diminishes significantly with increasing heat flux. The heat transfer coefficients for boiling mixtures can be much lower than for pure substances. For the calculations liquid-side mass transfer resistances were assumed to be the only reason for the reduction of both the selectivity and the heat transfer coefficients. No further physical explanations were needed.During surface boiling the reduction of the heat transfer coefficients is negligible for practical applications. The selectivity is mainly controlled by the thermodynamic equilibrium. The liquid-side mass transfer coefficients are of the same order of magnitude as found in physical absorption and absorption with chemical reactions, i.e. (2–5) × 10⁻⁴ ms⁻¹.The effect if liquid-side mass transfer resistances on heat transfer and selectivity during partial evaporation of the binary refrigerant mixture R11–R113 in a falling film apparatus was investigated by varying the heat flux, the film Reynolds number and the liquid composition. During surface boiling the reduction of the heat transfer coefficients in negligible for technical applications, because of the minor deviations from evaporation which are mainly controlled by thermodynamic equilibrium. Nevertheless, the liquid-side mass transfer coefficients, which can be determined by the measured vapour and liquid mole fractions, are of the same order of magnitude as in physical absorption and absorption with chemical reactions, i.e. β_ℓ = (2–5) × 10⁻⁴ m s⁻¹. The coupled heat and mass transfer during falling film evaporatation of mixtures, condensation and absorption [17,19] can be calculated with the same relationships as for the hydrodynamics of falling films.During nucleate boiling the selectivity diminishes significantly and heat transfer is influenced to a great extent by liquid-side mass transfer resistances. There is considerable deviation form evaporation controlled exclusively by thermodynamic equilibrium. The heat transfer coefficients α for the R11–R113 mixture as well as for ten other binary and two ternary mixtures could be calculated assuming the mass transfer resistances to be the only reason for the reduction of the heat transfer coefficient α during boiling of mixtures. No other physical explanations were needed. The calculation method is easily extendable to multicomponent mixtures, if the corresponding vapour-liquid equilibria are available.     

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.     

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.     

Heat transfer control by dispersed metallic particles in glassy mold flux film for continuous steel casting

To assess the effect of metallic particles (MPs) on heat transfer in glassy mold flux, a structurally stable glassy mold flux system composed of CaO–Al₂O₃–CaF₂ was examined with 0, 2, or 5 wt% of FeO or Fe MPs. The change of extinction coefficient by Mie Scattering of the Fe particles and absorption by FeO was quantified using Fourier transformation infrared ray spectroscopy and an Ultraviolet/Visible spectrometry. Thermal conductivity of mold flux film with dispersed MPs was quantified using laser flash technique. One-dimensional Debye temperature was calculated, and particle morphology and size distribution were observed using image analysis to explain variations in thermal conductivity among the glass samples. Finally, to simulate the heat transfer ratio by both the conduction and radiation, the actual heat flux through mold flux film was measured using an Infrared Emitter Technique. The overall heat transfer rate across liquid flux film could be reduced significantly by a dispersion of MPs.     

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.     

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.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

Hydrodynamics and mass transfer of gas–liquid flow in a falling film microreactor

In this article, flow pattern of liquid film and flooding phenomena of a falling film microreactor (FFMR) were investigated using high‐speed CCD camera. Three flow regimes were identified as “corner rivulet flow,” “falling film flow with dry patches,” and “complete falling film flow” when liquid flow rate increased gradually. Besides liquid film flow in microchannels, a flooding presented as the flow of liquid along the side wall of gas chamber in FFMR was found at high liquid flow rate. Moreover, the flooding could be initiated at lower flow rate with the reduction of the depth of the gas chamber. CO₂ absorption was then investigated under the complete falling flow regime in FFMR, where the effects of liquid viscosity and surface tension on mass transfer were demonstrated. The experimental results indicate that k_L is in the range of 5.83 to 13.4 × 10^?5 m s^?1 and an empirical correlation was proposed to predict k_L in FFMR. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

An experimental investigation of heat transfer to water in film flow Part I – non-boiling runs with and without induced swirl

Local heat transfer coefficients have been measured in the range of Reynolds Numbers 3,000-20,000 for non-boiling heat transfer to water flowing down the inside of a copper tube. The tube was 0.948-in. Inside diameter and 8-ft long, heated in 15 sections 6-in. long, by electrical resistance heaters wound on the outside of the tube. Thermocouples measured the wall temperature at the midpoint of each section. Coefficients obtained for downward, non-swirling, full tube flow were correlated by the Dittus Boelter equation, with a correction for heat flux. An experimental correlation was obtained for the improved coefficients resulting from the use of a swirl generator in full tube flow. Non-swirling falling film data were correlated by an equation: h_LA = 3.9 Re_LA^0.05 It is to be noted that the exponent on Re_LS is higher than the value of 0.1-0.33 found by previous workers. The effect of swirl on falling film heat transfer was complex; increased coefficients were noted at ReL below 10,000 but much reduced coefficients were obtained at R_L above 15,000 in the lower parts of the tube.     

Mass Transfer and Liquid‐Film Formation in a Spray Tower for SO2 Removal in Sodium Hydroxide Solution

Spray towers allow for controlling air pollution in which a liquid is sprayed in small droplets to produce a large interfacial area for mass transfer between a gas and a liquid phase. An experimental study of a spray tower for removing SO₂ is described. The experiments were carried out under different operating conditions by varying the gas velocity, liquid flow rate, and SO₂ concentration. SO₂ removal efficiency, volumetric mass transfer coefficient, and liquid‐film formation as a result of the collision of droplets against the tower wall are investigated. Removal efficiency and volumetric mass transfer coefficient are analyzed as a function of gas velocity, liquid flow rate, and SO₂ concentration, while liquid‐film formation is evaluated as a function of tower height. The results indicate high removal efficiency. Correlations to predict the volumetric mass transfer coefficient are also proposed.     

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Bed‐to‐wall heat transfer properties of a vertical heat tube in a fluidized bed of fine fluid catalytic cracking (FCC) particles are measured systematically using a specially designed heat tube. Two important surface hydrodynamic parameters, i.e. the packet fraction (δ_pa) and mean packet residence time (τ_pa) based on the packet renewal theory, are determined by an optical fiber probe and a data processing method. The experimental results successfully reveal the axial and radial profiles of heat‐transfer coefficient, the effects of superficial gas velocity, and static bed height on heat‐transfer coefficient, most of which can be explained successfully by the measured τ_pa, an indicator of packet renewal frequency. τ_pa is found to play a more dominant role than δ_pa on bed‐to‐wall heat transfer. With a fitted correction factor, the modified Mickley and Fairbanks model is able to predict the heat‐transfer coefficients with enough accuracy based on the determined packet parameters. © 2014 American Institute of Chemical Engineers AIChE J, 61: 68–83, 2015     

Simulation of Adsorption of Uranium from Seawater Using Liquid Film Mass Transfer Controlling Model

Abstract

A liquid film mass transfer control model was applied to the batch adsorption of uranium from seawater with an amidoxime-group-containing polymeric adsorbent made by the radiation-induced grafting method. The adsorption amount was calculated by changing two parameters, equilibrium adsorption amount q_o and liquid film mass transfer coefficient k, to obtain the best fit between the observed and calculated values. The index of a Freundlich-type isotherm was obtained as 1.6, which is similar to the previously observed value with hydrous titanium oxide adsorbent. The plot of k vs 1/T provided the activation energy as 10.0 kcal/mol. Both q_o and k showed an approximately first-order dependency on the amidoxime group content in the adsorbent. The simulation made it clear that the increase in k brought about by mixing amidoxime groups with carboxyl groups was due to a synergistic effect of these groups     

EFFECTS OF SURFACE TENSION ON LAMINAR FILMWISE CONDENSATION ON A HORIZONTAL PLATE IN A POROUS MEDIUM WITH SUCTION AT THE WALL

The problem of two-dimensional, steady-state film condensation on an isothermal finite-size horizontal plate embedded in a porous medium is studied for the case in which the plate faces upward into a region of dry saturated vapor. Due to surface tension effects, a two-phase zone is formed between the liquid film on the horizontal plate and the vapor zone. The effects of surface tension are shown to reduce the thickness of the liquid film and hence to increase the heat transfer performance of the horizontal plate. Furthermore, the results show that the dimensionless heat transfer coefficient depends on the Darcy number Da, the Jacob number Ja, the effective Rayleigh number Ra_e, the effective Prandtl number Pr_e, the wall suction parameter Sw, and the surface tension parameter Bo_c. When the surface tension effects are neglected and there is no suction at the wall, a closed-form correlation for the Nusselt number can be established.     

Gas–liquid interfacial area and mass transfer coefficient in a co‐current down flow contacting column

The gas–liquid interfacial area and mass transfer coefficient for absorption of oxygen from air into water, aqueous glycerol solutions up to 1.5% (w/w) and fermentation medium containing glucose up to a 3% concentration were determined in a co‐current down flow contacting column (CDCC; 0.05 m i.d. and 0.8 m length). Experimental studies were conducted using various nozzle diameters at different gas and re‐circulation liquid rates. Specific interfacial area (a) is determined from the fractional gas hold‐up (ε_G) and the average bubble diameter (d_b). Once the interfacial area is determined, the volumetric mass transfer coefficient (k_La) is then used to evaluate the film mass transfer coefficient in the CDCC. The effects of operating conditions and liquid properties on the specific interfacial area were investigated. The values of interfacial area in air–aqueous glycerol solutions and fermentation media were found to be lower than those in the air–water system. As far as experimental conditions were concerned, the values of interfacial area obtained from this study were found to be considerably higher than those of the literature values of conventional bubble columns. The penetration theory is used to interpret the film mass transfer coefficient and results match the experimental k_L data reasonably well. Copyright © 2006 Society of Chemical Industry     

Heat transfer in trickle bed column with constant and modulated feed temperature: Experiments and modeling

Heat transfer was investigated in an insulated packed bed column with co-current downflow of gas and liquid under constant and periodically modulated gas–liquid feed temperature. Bed temperatures at three axial positions were assessed at steady state for different insulating systems, different gas and liquid flow rates and system pressure. The experimental profiles recorded were modeled with a dynamic pseudo-homogeneous one parameter model to analyze the effect of operating conditions and to deduce coefficients of overall (U) and bed to wall (h_W) heat transfer. It appears that the heat transfer is strongly affected by the system pressure, whereas the liquid flow rate has a smaller influence. The experimental data of h_W were correlated with the operating conditions leading to a small average error of 7% in the correlation. Condensation of water vapor occurring in the column seems to contribute to the heat transfer inside the packed bed. Several dynamic experiments modulating the feed temperature were also conducted and described with the help of the dynamic model. Predictions with the fitted values of U were in good agreement with experiments and give confidence to apply this model in the investigation of the catalytic wet air oxidation of phenol over carbon conducted in a trickle bed reactor under temperature feed modulation.     

Marangoni instability in non-isothermal first order gas—liquid reactions—evaluations of Cl2—toluene and CO2—sodium hydroxide systems

A necessary condition for surface tension driven interfacial convection in non-isothermal gas—liquid reaction processes is that the interface be at a higher temperature than the adjacent liquid. In many important practical applications the interface is, however, hotter than the liquid, unless the liquid looses heat to the gas. The magnitude of the dimensionless quantity Biot number, (Bi), is a measure of the rate of this heat transfer. Its critical value Bi_crit is defined as that value which makes the temperature gradient at the interface vanishes. Thus when Bi ? Bi_crit the temperature gradient at the interface is positive. It is assumed here that Bi_crit constitutes a lower bound of the Biot number below which Marangoni type instability is not possible. Bi_crit is evaluated here from the governing unperturbed state equations. This analysis is presented for liquids of both finite and infinite depths.For system conditions which result in a positive temperature gradient at the gas—liquid interface, the results for critical Marangoni number are obtained using small perturbation analysis. Stationary neutral stability curves for chlorine—toluene systems and the relation between independent system parameters and the critical Marangoni number are outlined. The critical Marangoni number shows a curious U-type relation with Biot number. Practical significance of the stability results to the chlorine—toluene system is discussed.