Modeling and simulation of heat and mass transfer during drying of solids with hemispherical shell geometry

A heat and mass transfer model was proposed to describe the moisture and temperature evolution during drying of solid products with hemispherical shell geometry (HSG). The dimensionless form of the model was numerically solved for both several drying conditions and values of a geometrical factor related with the inner radius of the HSG to obtain their moisture and temperature profiles. In addition, average drying kinetics were calculated from the volume integration of local moisture values. A theoretical and numerical approach was used to develop a mass transfer analogy between the proposed HSG and a simpler flat slab-shaped product. These analogies provide simple mathematical expressions for drying process simulation and estimation of diffusion coefficients in solids with the proposed geometry, and may be applicable to other mass and heat transfer operations. Furthermore, the presented procedure may be used to develop similar expressions in other non-traditional or dissection geometries.     

Heat and mass transfer in multicylinder drying: Part I. Analysis of machine data

A mathematical model describing the heat and mass transfer in the dryer section of a paper machine has been applied to the production data from four paper machines. Model predictions for the machine speed are compared to actual machine speeds for a total of 163 data sets. The mathematical model assumes that the temperature and moisture content remain homogeneous in the thickness direction of the sheet. For three paper machines producing paper with basis weights ranging from 0.056 to 0.159 kg d.s./m² the model predictions are adequate. For the paper machine producing the heaviest grades with basis weights ranging from 0.189 to 0.390 kg d.s./m² the model predictions are flawed by a systematic error. For low machine velocities/high basis weights the machine velocity is over-predicted and for high machine velocities/low basis weights the machine velocity is under-predicted. This systematic error is caused by the assumption of homogeneous moisture content and temperature within the sheet being severely in error for thick sheets.     

Effects of crystal growth rate and heat and mass transfer on solute distribution

The effects of crystal growth rate and heat and mass transfer on solute distribution during solidification of binary melt have been theoretically investigated on the basis of a new theory of solute distribution proposed by the present authors. The solute distribution factor f at the solid-liquid (SL) interface is in inverse proportion to the one-half power of the dimensionless growth rate U. The growth rate U is in proportion to the second power of the normalized concentration difference between the SL interface and bulk melt. A new transport factor K, which describes heat and mass transfer in melt, gives an important contribution to the crystal growth and the solute distribution at the SL interface. The transport factor is used successfully to control the solidification of melt. The flow structure in melt exerts essential influence on the solid purity.     

Model based analysis of the drying of a single solution droplet in an ultrasonic levitator

A model for the drying of a single solution droplet into a solid, dense particle is presented and simulations are made to achieve a more fundamental understanding of the single droplet drying process relevant in connection with spray drying processes. Model predictions of drying behaviour are compared to data for the drying of aqueous solutions of maltodextrin DE 15 and trehalose from experiments conducted using an ultrasonic levitator. Model predictions are in good agreement with the experimental data, indicating that the model describes the most important physical phenomena of the process.     

Theoretical probing of the phenomenon of the formation of the outermost surface layer of a multi-component particle, and the surface chemical composition after the rapid removal of water in spray drying

Spray drying is a primary process for the manufacture of powders, which satisfy a vast array of societal demands in the areas of nutrition, health and medicine. The functionality of a spray-dried product begins with its incorporation into water (wetting followed by dispersion) Therefore, as its surface chemical composition and structure determine its first contact with water (that is, its hydrophilic nature), these are of prime concern. Laboratory studies on this first layer, which is in the order of several nm in depth from the surface, have been extensive but there is still a lack of a fundamental quantitative explanation of it. This has hampered the development of any sort of approach, which would enable industries to predict what the product may be like before conducting costly trials. This current study is an attempt to describe the on-set of solid formation around the outermost layer of a single droplet during the drying process using an innovative ‘conventional’ continuum approach, i.e. diffusion–convection equations, with a few innovative derivations. Though some complexities such as multi-component equations deduced from irreversible thermodynamics, are avoided for simplicity, some comparisons with experimental/industrial results are made. The main feature of this work is that the multi-component effect is combined with the viscosity (at the surface) effect upon the diffusivities of individual components in the solution droplets or suspension droplets. The derivations allow some extended analytical procedures to proceed in order to help make sense of the experimental observations. Comparisons are made against the data published on dairy fluids. This work provides a good basis for a fruitful area of study that will have a positive impact for spray drying industries. In particular, to help this kind of industry to forge ahead into high performing functional particle production, which are becoming increasingly popular.     

Correlations for mass transfer coefficients over blunt boards based on modified boundary layer theories

Correlations for skin friction, heat and mass transfer coefficients on the surfaces of blunt-edged flat plates have been established, based on modified boundary layer theories which take account of the influence of separation and reattachment flows. The calculated velocity profiles, skin friction, heat and mass transfer coefficients show good agreement with the data measured by previous authors.     

Heat and mass transfer characteristics in a gas-slurry-solid fluidized bed

The gas-slurry-solid fluidized bed is a unique operation where the upward flow of a liquid-solid suspension contacts with the concurrent up-flow of a gas, supporting a bed of coarser particles in a fluidized state. In the present study we measured the gas holdup, the coarse particle holdup, the cylinder-to-slurry heat transfer coefficient, and the cylinder-to-liquid mass transfer coefficient at controlled slurry concentrations. The slurry particles were sieved glass beads of 0.1 mm average diameter and their volumetric fraction was varied at 0, 0.01, 0.05 or 0.1. The slurry and the gas velocities were varied up to about 12 and 15 cm/s, respectively. The coarse particles fluidized were sieved glass beads of average diameters of 3.6 and 5.2 mm. The individual phase-holdup values were measured and served for use in correlating the heat and mass transfer coefficients. The heat and mass transfer coefficients in the slurry flow, gas-slurry transport bed, slurry-solid fluidized bed and gas-slurry-solid fluidized bed operations can be correlated well by dimensionless equations of a unified formula in terms of the Nusselt (Sherwood) number, the Prandtl (Schmidt) number and the specific power group including the energy dissipation rate per unit mass of slurry, with different numerical constants and exponent values, respectively, to the heat and mass transfer coefficients. The presence of an analogy between the heat and mass transfer from the vertically immersed cylinder in these slurry flow, gas-slurry transport bed and gas-slurry-solid fluidized bed systems is suggested.     

Experimental study and simulation of vibrated fluidized bed drying

The paper addresses numerical simulation for the case of convective drying of seeds (fine-grained materials) in a vibrated fluidized bed, analyzing agreement between the numerical results and the results of corresponding experimental investigation. In the simulation model of unsteady simultaneous one-dimensional heat and mass transfer between gas phase and dried material during drying process it is assumed that the gas-solid interface is at thermodynamic equilibrium, while the drying rate (evaporated moisture flux) of the specific product is calculated by applying the concept of a “drying coefficient”. Mixing of the particles in the case of vibrated fluidized bed is taken into account by means of the diffusion term in the differential equations, using an effective particle diffusion coefficient. Model validation was done on the basis of the experimental data obtained with narrow fraction of poppy seeds characterized by mean equivalent particle diameter (d_S,d = 0.75 mm), re-wetted with required (calculated) amount of water up to the initial moisture content (X₀ = 0.54) for all experiments. Comparison of the drying kinetics, both experimental and numerical, has shown that higher gas (drying agent) temperatures, as well as velocities (flow-rates), induce faster drying. This effect is more pronounced for deeper beds, because of the larger amount of wet material to be dried using the same drying agent capacity. Bed temperature differences along the bed height, being significant inside the packed bed, are almost negligible in the vibrated fluidized bed, for the same drying conditions, due to mixing of particles. Residence time is shorter in the case of a vibrated fluidized bed drying compared to a packed bed drying.     

Heat transfer in a particle curtain falling through a horizontally-flowing gas stream

A study of heat transfer between horizontally-flowing air and a free-falling particle curtain was reported. A steady and uniformly distributed stream of cold particles was fed through a rectangular slit and allowed to fall to form a curtain across the entire width of a horizontal duct of cross-section of 0.15 × 0.60 m. Warm air, at velocities in the range of 0.9 m/s to 1.2 m/s and with a uniform velocity profile, flowed horizontally through the duct. A range of curtain thickness (4 cm to 10 cm) and mass flow rate (0.031 kg/s to 0.040 kg/s) were used to investigate the heat transfer characteristic of the free-falling particle curtain in a uniform cross-flowing gas. Particle temperatures within the curtain and air temperatures outside the curtain were measured as a function of vertical position in the duct. A simple model based on single particle behaviour was developed. The predicted solid temperatures agreed well with the experimental results. However, the predictions for the gas temperatures were less satisfactory.     

Mass and Heat Transfer in a Continuous Plate Dryer

Abstract

A mathematical model for the mass-heat transfer in a continuous plate dryer has been developed. Along with a new mass transfer model, the formulas for several important parameters, such as height, volume of each granular heap and retention time, are provided. According to the penetration model of particle heat transfer, the average drying rate ([mdot]) is predicted together with the mean bulk temperature (T _out) and moisture content (X _out) by a straightforward stepwise calculation procedure. The only empirical parameter N _mix can be predicted by the method, provided that experimental data with various initial moisture contents (X _in) are given. According to the model, the optimization of a plate dryer should aim at the maximizing of the effective covering ratio (μ) and the total area-averaged heat transfer coefficient (α). The model and equations were applied in an experimental plant. In the result, the theoretical predictions are shown to be in satisfactory agreement with experimental data.     

Single droplet drying: Transition from the effective diffusion model to a modified receding interface model

Drying experiments on single droplets of aqueous amorphous polymer solution show morphological changes towards the end of drying that result in an under-prediction of the drying rate using an effective diffusion based model. Alternately, other researchers argue that the receding interface model more accurately reflects the physics of drying by predicting a fixed droplet radius once a specified surface condition is reached, usually the saturation concentration. However, this surface condition is not adequate for many skin forming materials. The conditions at which droplet radial contraction ceases will be determined by the balance between internal moisture loss causing a collapsing pressure and the mechanical strength of the surface skin. Because measurements and prediction of surface stress are difficult, it is proposed that they are related to the state of the polymer solution at the surface which is defined by the proximity of the surface temperature to its glass transition temperature, (T − T_g). In this work, an effective diffusion model is used to predict ideal shrinkage until a critical temperature difference or (T − T_g)_crit is reached where the surface of the droplet becomes fixed and the skin grows towards the droplet centre, that is, as a receding interface. For maltodextrin DE5, a (T − T_g)_crit of 20 °C was found to provide an accurate prediction of the drying rate. While these results show (T − T_g)_crit is indicative of mechanical stress development, it points to a need for further understanding of mechanical stress development in skin forming polymers during drying.     

Direct numerical simulations of mass transfer in square microchannels for liquid-liquid slug flow

Microreactors for the development of liquid-liquid processes are promising technologies since they are supposed to offer an enhancement of mass transfer compared to conventional devices due to the increase in the surface/volume ratio. But impact of the laminar flow should be negative and the effect is still to be evaluated. The present work focuses on the study of mass transfer in microchannels by means of 2D direct numerical simulations. We investigated liquid-liquid slug flow systems in square channel of depth. The droplet velocity ranges from 0.0015-0.25 m/s and the ratio between the channel depth and the droplet length varies between 0.4 and 11.2. Droplet side volumetric mass transfer coefficients were identified from concentration field computations and the evolution of these coefficients as a function of the flow parameters and the channel size is discussed. This study reveals that mass transfer is strongly influenced by the flow structure inside the droplet. Moreover, it shows that the confinement of the droplets due to the channel size leads to an enhancement of mass transfer compared to cases where the droplets are not constrained by the walls.     

Convective heat and mass transfer coefficient measurements and correlations for particle beds using temperature and humidity step changes with air flow through a test bed

In this paper, transient responses of a porous urea particle bed subject to a step change in the inlet temperature or humidity for a forced convective air flow through the particle bed are investigated to determine the convective heat and mass transfer coefficients inversely by comparing the measured time constant with the predicted characteristic time constant, which is a function of the convection coefficients and Reynolds number. The experimental results show, that although both the time constants for temperature and humidity step changes are dependent on Reynolds number, the temperature response time constant (35-1300 s) is much larger than the humidity response time constant (4-25 s) for the Reynolds number range of 300-5. The surface adsorption of water vapor is very rapid but the absorption inside the porous urea particle is slowed by a very low internal effective diffusion coefficient within the particles whereas the very low Biot number for heat transfer in the particles implies a complete thermal interaction with the air flow throughout each particle and a much larger time constant. Empirical correlations of the Chilton-Colburn j-factor and Nusselt number versus Reynolds number are compared with the correlations of other researchers. These new correlations, which include an uncertainty analysis, imply much lower convective coefficients than those reported previously in the literature.     

Development of a comprehensive free radical photopolymerization model incorporating heat and mass transfer effects in thick films

A comprehensive kinetic model describing photopolymerization is developed which allows variation of temperature, species concentrations, and light intensity through the thickness of a photopolymerized film. Heat and mass transfer effects are included, as is the generation of heat by both reaction and light absorption. In addition to initiation, propagation, and termination mechanisms, both primary radical termination and inhibition are incorporated into the model. The possible presence and diffusion of an inert solvent are also accounted for. Thus, the model is useful for examining complex polymerization kinetics and behavior in industrially and commercially important thick film photopolymerizations, such as the curing of contact lenses, dental restorative materials, photolithographic resists, and optoelectronic coatings. The comprehensive model is used to predict polymerization rate, temperature, and conversion profiles in a variety of systems. The effects of heat generation and the thermal boundary conditions are explored, with the result that heat generation in thick samples leads to greatly increased conversions approaching 100 percent. Increased temperature in these samples also may lead to the appearance of two rate maxima, with the first due to the temperature increase and the second caused by the autoacceleration process. The magnitude of the temperature increase, along with the resultant effects, is more pronounced in insulated systems.     

Modelling the morphological evolution of nanosuspension droplet in constant-rate drying stage

A novel mathematical model of constant-rate stage of nanosuspension droplet drying is proposed. In contrast to previously published literature studies, the developed model considers two morphologically different periods of the constant-rate drying: before the shell formation and after the shell formation; the latter was named “transition period”. The point of initial “locking” between nanoparticles on the droplet surface and beginning of the shell formation is associated with theoretical maximum of solid volume fraction. It is postulated that shrinking and thickening shell of nanoparticles occurs fast, and thus the shell virtually remains submerged in the liquid during the overall transition period. Because of the submerged shrinking shell, in the transition period, the evaporation process still takes place from the droplet surface and the drying rate remains unchanged as it was before the shell formation. Correspondingly, the droplet temperature retains at the level of equilibrium evaporation temperature. The developed theory was successfully validated by the published experiment of silica nanosuspension droplet drying. Finally, the developed model proposes a simple morphology criterion based on comparison between the calculated droplet volume at the end of transition period and the corresponding volume of solid final particle with the given porosity.     

Heat and Mass Transfer in Fry Drying of Wood

This article describes the coupled heat and mass (water, oil) transport phenomena in parallelepiped samples of beech (Fagus sylvatica) fried in peanut oil between 120 and 180°C. The aim was to evaluate the suitability of simultaneous fry drying and oil impregnation as an alternative wood treatment process. Water loss and oil impregnation were continuously assessed during the process. Temperature and pressure were measured at the center of the sample. The water in the peripheral layers of the wood vaporizes at atmospheric pressure. The water at the center of the wood vaporizes at overpressures of the order of 2.8 × 10⁵ Pa. High fluxes of water were recorded of about 0.006 kg/(m²s). The impregnated oil can amount to 20% of the mass of the removed water.     

Heat and Mass Transfer in Fry Drying of Wood

This article describes the coupled heat and mass (water, oil) transport phenomena in parallelepiped samples of beech (Fagus sylvatica) fried in peanut oil between 120 and 180°C. The aim was to evaluate the suitability of simultaneous fry drying and oil impregnation as an alternative wood treatment process. Water loss and oil impregnation were continuously assessed during the process. Temperature and pressure were measured at the center of the sample. The water in the peripheral layers of the wood vaporizes at atmospheric pressure. The water at the center of the wood vaporizes at overpressures of the order of 2.8 × 10⁵ Pa. High fluxes of water were recorded of about 0.006 kg/(m²s). The impregnated oil can amount to 20% of the mass of the removed water.     

A new model for the drying of droplets containing suspended solids

A new droplet drying model incorporating a population balance to model suspended solids is introduced. The population is evolved using a moment method with an interpolative closure employed in the case of a size dependent solids diffusion coefficient. This paper demonstrates the formulation and discusses the benefits of the new model, before presenting simulations of droplets containing colloidal silica and sodium sulphate. The results are compared with experimental data from the literature in the regime prior to shell formation.     

Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.     

Simultaneous Heat and Mass Transfer in Shrinkable Apple Slab During Drying

The goal of the study was to determine the influence of drying shrinkage on the kinetics of convection apple slab drying. The arbitrary Lagrange-Eulerian (ALE) method was used to enter a problem with moving boundaries. It was found that drying shrinkage had a major influence on the both simulated temperature and water content in the material. The lower the moisture content in particles during drying, the more pronounced the effect of shrinkage on simulation of heat and mass transfer. It was found that application of the arbitrary Lagrange-Eulerian method for shrinkage modeling leads to a relatively simple mathematical model of the drying kinetics of shrinkable materials.