Mathematical Model Of Mass Transfer Research Articles

МасоперенесеннЯ піД чаС ізОтермічнОгО ущільненнЯ карбонізованиХ ВуглепластикіВ

It is offered the mathematical model of mass transfer at the compression of carbonizated carboplastics by pyrolitical carbon. A model takes into account transporting of gaseous hydrocarbons in porous structure of carboplastic, them following decomposition and formation on the heated surfaces of pyrolitical carbon

Simulation of Trough Withering of Tea using One Dimensional Heat and Mass Transfer Finite Difference Model

One-dimensional heat and mass transfer mathematical model was developed to simulate moisture content of tea leaves during trough withering. Model solutions were approached using finite difference method with appropriate boundary conditions. A computer program written in QBASIC was used to calculate the real time moisture content of tea leaves and other psychometric parameters of conditioned air during withering. Four experiments were performed using commercial type of withering trough to validate the developed model. Leaf samples were drawn from top, middle and bottom layers of the leaf bed in the trough for one-hour time interval for 12 h of the test period. Simulated moisture data calculated by the program was compared with the experimental data. Time and space increments of the model were chosen minimizing the estimation error of moisture content. Results showed that the experimental and simulated moisture data were in close agreement for top, middle and bottom layers of the withering trough with standard errors in the range of 0.2940&ndash;1.2872, 0.7148&ndash;1.1025 and 0.7106&ndash;4.5478, respectively on percent wet basis. <strong>Keywords</strong>: Fresh tea leaves; one dimensional heat and mass transfer model; withering trough DOI: <a href="http://dx.doi.org/10.4038/tar.v22i3.3701">http://dx.doi.org/10.4038/tar.v22i3.3701</a> <em>Tropical Agricultural Research </em>22(3) (2011) 282-295

Analysis of Mass Transfer during Loose Material’s Convective Drying

Abstract. The thesis focuses on how to get the mathematical model of mass transfer under some certain simplified conditions and how to gain the moisture content of materials under drying. In this process, authors utilized phenomenological equations of heat and moisture transfer and analyzed the relationship and cross effects between force and flow, which were about various kinds of heat and mass transfer. In addition, the authors also used computer simulation in drying process. The result of the study is that drying rate depends on the speed of the internal moisture migration. The conclusions of this thesis have great significance for selecting the dryer and in the actual production.

Modeling mass transfer during osmotic dehydration of strawberries under high hydrostatic pressure conditions

Abstract Simultaneous application of high hydrostatic pressure (200–400 MPa) during osmotic dehydration of strawberries was studied in this investigation. The high hydrostatic pressure treatment improved the diffusion coefficients of water and soluble solids compared to atmospheric pressure operation. Effects of process pressure on diffusion coefficients were achieved through an Arrhenius-type equation. Mathematical modeling of mass transfer was performed applying Newton, Henderson–Pabis, Page and Weibull models. Based on statistical results, the Weibull model gave the best goodness of fit on the experimental data under the studies' operative conditions. Industrial relevance: This article deals with the mathematical modeling of mass transfer during simultaneous high hydrostatic pressure treatment and osmotic dehydration of strawberries. Transfer of water and soluble solids during this combined process were satisfactorily simulated with the Weibull model. Results indicated that application of this innovative technology improved strawberries dehydration rates compared to atmospheric pressure operation resulting in a dried fruit with intermediate moisture content ready to be used as input material of further processes.

Moisture profiles in cheese drying determined by TD-NMR: Mathematical modeling of mass transfer

A time-domain nuclear magnetic resonance (TD-NMR) method is proposed to quick and easily determine moisture profiles during cheese drying. The method consists of a combined relaxation analysis, where the magnetization at a certain time is determined by both the longitudinal and the transverse NMR relaxation processes. The drying experiments were carried out at 16 °C and 0.2–0.5 m/s for 32 days, and allowing only one-direction mass transfer. A diffusion model was formulated taking into account the external resistance to mass transfer. Both effective moisture diffusivity and external mass transfer coefficient were simultaneously identified (3.71 × 10 −11 m 2/s and 2.95 × 10 −8 m/s, respectively). The proposed model allowed a satisfactory simulation of both the drying curve (mean relative error (MRE) = 0.4% and percentage of explained variance (%var) = 99.7%) and the moisture profiles (average MRE = 4.4% and %var = 94.5%).

Mathematical Modelling of Mass Transfer and Free Convection Current Effects on Unsteady Viscous Flow with Ramped Wall Temperature

An exact analysis of the flow of an incompressible viscous fluid past an infinite vertical plate is conducted taking into account the presence of foreign mass or constant mass flux and ramped wall temperature. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. Two different solutions for the fluid velocity are obtained–one valid for the fluids of Schmidt numbers different from unity, and the other for which the Schmidt number is unity. The effects of Prandtl number (Pr), Schmidt number (Sc), time (t) and mass to thermal buoyancy ratio parameter (N) for both aiding and opposing buoyancy effects on the velocity and skin-friction are studied. Also, the heat and mass transfer effects on the flow near a ramped temperature plate have been compared with the flow near a plate with constant temperature.

Extraction separation of Cu(II) and Co(II) from sulfuric solutions by hollow fiber renewal liquid membrane

Extraction separation of Cu(II) and Co(II) from sulfuric wastewater is studied with hollow fiber renewal liquid membrane (HFRLM) technique. The organic solution of LIX 984N in kerosene is used as the liquid membrane phase to selectively separate and concentrate Cu(II) from aqueous solution; and the extractant of CYANEX 272 is used as carrier to remove and concentrate Co(II) from aqueous solution. In the selective separation process, LIX 984N has good selectivity on Cu(II); the interactions among metal ions can be negligible; the pH in the feed aqueous solution has significant influence, while the influence of hydrogen ion concentration in the stripping phase is slight. The removal efficiency of Cu(II) increases with the increasing flow rate on lumen side, while decreases with the increasing flow rate on shell side. The results of lab-scale cascade experiments show that the HFRLM technique is a promising treatment method for simulated sulfuric wastewater containing copper and cobalt with separation factor higher than 100. The Cu(II) and Co(II) concentrations in the raffinate are lower than 0.50 mg L −1 and 1.0 mg L −1, respectively, which are both below the standard of wastewater discharge in China. Based on the surface renewal theory, resistance-in-series model and mass balance law, a corresponding mass transfer mathematical model is developed; and the calculated results are in good agreement with experimental data.

Mathematical modelling of mass transfer in the concentration polarisation layer of flat‐sheet membranes during clarification of pomegranate juice

SummaryEvaluation of membrane clarification of pomegranate juice showed that a cake layer is created at the beginning of the process. This evaluation was used as the basis for modelling the solute concentration in the concentration polarisation layer to control the fouling of the membrane. The model of changes in concentration as a function of time and distance (in its dimensionless form) was solved numerically using the Forward‐Time/Central‐Space (FTCS) method. Programming was performed using MATLAB software, and the predicted concentration on the membrane surface was compared with experimental data; the prediction fit well with the experimental data. The model showed that the solute concentration increased as distance to the membrane surface decreased, time increased, transmembrane pressure increased and velocity decreased. Also, the model matched the experimental data in that it showed the cake layer to be created in the early stages of the membrane clarification process.

Mathematical model of mass transfer in an electrodialyzer with net-like spacers

Data on DC current have been recorded for EDR-III/200-0.8 electrodialysis stack available from MEGA a.s., Czech Republic, as a function of feed electrolyte (NaCl) concentration and applied voltage. The flow rates and temperature have been fixed during the tests. Spacers used between the ion-exchange membranes in the stack are of net-like type. Different approaches to the mathematical modeling of mass transfer in an electrodialyzer have been verified to select one that best fits experimental data obtained for the stack. The “turbulent flow” model has been evaluated to be the most suitable for this purpose. The model assumes uniform distribution of linear velocities, ideal cross mixing of the liquid in the flow phase and presence of the stationary diffusion layer. In addition, a correlation coefficient has been introduced into the model to take the effect of a turbulence promoter on electrical field shielding into account.

Mathematical modeling of mass transfer in a three-phase fluidized system

An algorithm and a program for calculating the driving force of the process of mass transfer and the mass fluxes of gas and liquid phases are developed on the basis of the fundamental two-parameter equation of convective diffusion taking into account the amplitude-frequency characteristics of wave packets. The algorithm and the program of engineering calculation of the processes of physical absorption and chemisorption are written.

Numerical Modeling of Mass Transfer for Solvent-Carbon Dioxide System at Supercritical (Miscible) Conditions

A numerical procedure of mathematical model for mass transfer between a droplet of organic solvent and a compressed antisolvent is presented for conditions such that the two phases are fully miscible. The model is applicable to the supercritical antisolvent (SAS) method of particle formation. In this process, solute particles precipitate from an organic solution when sprayed into a compressed antisolvent continuum. Effects of operating temperature and pressure on droplet behavior were examined. The CO2 critical locus and the conditions for which the densities of solvent and carbon dioxide are equal are identified. Calculations were performed using Peng-Robinson equation of state. The model equations were put into the form that allowed the application of the Matlab standard solver pdepe. Calculations with toluene, ethanol, acetone (solvents) and carbon dioxide (antisolvent) demonstrated that droplets swell upon interdiffusion when the solvent is denser than the antisolvent and shrink when the antisolvent is denser. Diffusion modeling results might be used for data interpretation or experiments planning of the more complex real SAS process.

Mathematical modeling of mass transfer during centrifugal filtration of polydisperse suspensions

A mass-transfer equation, the solution of which for given boundary conditions makes it possible to derive in analytical form a relationship between the extraction of the solid phase of a suspension into the centrifuge effluent and the fineness of the particles, is suggested on the basis of a model; this is of particular importance in connection with the development of a new trend in the utilization of filtering centrifuges - concentration of coal slurries by extraction into the centrifuge effluent of the finest particles, the ash content of which is substantially higher than that of particles of the coarser classes. Results are presented for production studies under conditions at an active establishment (the Neryungrinskaya Enrichment Factory); these results confirmed the adequacy of the mathematical model proposed: convergence of computed and experimental data was within the limits of the experimental error (no more than 3%). The model in question can be used to predict results of suspension separation by centrifugal filtration.

Mathematical model of mass transfer in the case of a bidispersed porous material

Consideration is given to a model (suitable for description at large times) for analysis of the heat- and massexchange processes of a porous body with two types of pores. Specifically, we are dealing with impregnation (in a sense, with the process of extraction, its converse). The solution of the problem with the most typical supplementary conditions is obtained; the kinetic impregnation (withdrawal) function and the density of the substance flux from the body are found for this problem.

Mathematical modelling of mass transfer during rehydration process of Aloe vera ( Aloe barbadensis Miller)

Aloe vera ( Aloe barbadensis Miller) slabs dried at 60 °C were rehydrated at three temperatures (20, 40 and 60 °C) in order to study the influence of temperature on the kinetics of mass transfer during rehydration phenomenon. Fick, Peleg and Weibull models were applied for rehydration modelling, as well as one new proposed model. All kinetic parameters of the models showed positive dependence on temperature, according to the Arrhenius-type equation. Weibull model and the new proposed model provided the best fit quality for each rehydration curve based on the statistical tests RMS, SSE and Chi-square. In accordance with the results, both models may be used to estimate the rehydration time of A. vera. Furthermore, two rehydration indices (RR and WHC) were analysed, which decreased as temperature increased. These indices confirm that drying process modifies the cell structure of A. vera, reducing the rehydration ability due to cellular and structural disruption that takes place during dehydration.

Mathematical Modeling of Mass Transfer during Convective Dehydration of Brown Algae Macrocystis Pyrifera

The aim of this research was to study and to model the drying kinetics of the brown algae Macrocystis pyrifera at 50, 60, 70, and 80°C. GAB equation showed a good fit on the sorption experimental data. Fick's diffusional model, together with Newton, Henderson-Pabis, Page, modified Page, logarithmic, and Midilli-Kukuc models were applied on the drying kinetics of the alga. The Dwe increased from 5.56 to 10.22 × 10−9 m2/s as temperature increased from 50 to 80°C. Midilli-Kukuc and logarithmic models obtained the best-fit quality for drying curves based on the statistical tests. In consequence, both models are excellent tools for estimating the drying time of this product.

Formation of concentration profiles of implanted ions in metallic materials under polyenergetic implantation

A physical and mathematical model of mass transfer in polycrystalline metallic materials under exposure to ion beams is proposed. Alongside bulk indiffusion from the irradiated surface, diffusion along the migrating extensive defects interacting with an impurity is considered. For a polyenergetic ion beam, the con- tribution of bulk indiffusion is presented as an integral over energy of the product of two functions; one of them describes the energy distribution of ions in a beam and the second represents the implantation profile of monoenergetic ion beam.

A macrokinetic model of aerosol deposition of a dissolved component on the surface of crystal structures under isothermal conditions

Based on kinetic ideas on the phenomena of transfer under isothermal conditions in the crystal-film-aerosol system, a mathematical model of mass transfer that accounts for the change in phase interfaces is suggested.

Physical and mathematical models of an inert macroelectrode modified with active hemispherical microelectrodes

The physical model of an inert electrode partially activated with hemispherical microelectrodes was formed by the deposition of silver grains on a graphite substrate. It is shown that the process on the microelectrodes can be under activation control despite the fact that the overall rate is determined by the diffusion layer of the macroelectrode. On the basis of this conclusion a mathematical model of mass transfer on an inert electrode partially covered with active hemispherical particles (microelectrodes) is given and verified qualitatively by appropriate experiments. It was found that the degree of activation does not depend on the size of the particles, but on the ratio of the radius of the particles to the interparticle distance. This means that the quantity of catalyst required for the transformation of an inert electrode into an active one decreases strongly with decreasing active particle size. It was also shown that the maximum current density to the activated inert electrode was equal to the limiting diffusion one to the massive active electrode, as well as that the activity of the modified inert electrode at the same coverage of catalyst strongly depends on the exchange current density of the electrochemical process taking place on it. The larger is the exchange current density, the lower is the quantity of catalyst required for the same effect on the activity of the modified electrode.

Mathematical modeling of mass transfer in symmetric heterogeneous and nanoporous media with a system of n-interface interactions

An exact analytical solution is obtained to describe mass transfer in symmetric heterogeneous and nanoporous media with a system of n-interface interactions. The Laplace integral transform and Cauchy fundamental functions are used. A solvability theorem is proved. New recurrence algorithms and computational procedures are developed to form influence matrices, which are due to heterogeneities and n-interface interactions.

Application of genetic algorithm for determination of the effective diffusivity of andrographolide in plant materials

The effective diffusivity of natural medicinal components is an important property for a detailed pharmaceutical extraction study and a proper design of the extraction process and unit. A mass transfer mathematical model for solvent extraction of andrographolide was developed and numerically solved taking into account particle geometries, solvent concentration, mass fraction of two different geometries of plant materials, external mass transfer resistance and solid–liquid equilibrium concentration. Using inverse simulation approach with genetic algorithm, unknown four key parameters in the developed model, effective diffusivity, partition coefficient, average particle size and mass fraction of leaf particles were determined at different extraction temperatures and solvent concentrations. The simulated data through the genetic algorithm-numerical model (GA-NM) and experimental data showed a good agreement ( r 2 > 0.97 and MSE < 0.0016) indicating that the scheme with genetic algorithm can be effectively used for determination of the effective diffusivity of andrographolide in plant materials.