Mathematical Model Of Mass Transfer Research Articles

Boronize Coatings Studied with a New Mass Transfer Model.

This study examined the development of Fe2B (diiron boronize) coatings on the surface of 35NiCrMo4 steel through the thermochemical surface hardening process called boronizing. The morphology and thickness of the boronize coatings were assessed using Scanning Electron Microscopy (SEM) and optical microscopy (OM). A novel mathematical mass transfer model was developed to estimate the diffusion coefficients of boron in hard coating. The presence of uniformly distributed boronize coatings with a typical sawtooth pattern on the surface of the substrate was confirmed. The boronize coating's chemical composition and phase constituents were analyzed utilizing X-ray energy dispersive spectroscopy (EDS) and X-ray diffraction analysis (XRD). The study confirmed the presence of a single-phase boronize coating (Fe2B). Furthermore, microhardness tests indicated that the boronized specimen's surface demonstrated an average hardness of approximately 1953 HV. The wear study were conducted using the pin-on-disk method under dry debonding conditions at room temperature to estimate the coefficient of friction (COF) of the boronized (average ≈ 0.35) and untreated (0.725) specimens. The results revealed approximately 200% improvement in wear resistance due to the boronized coating. The empirical validation of the mathematical model was carried out for two additional boronizing conditions at 1223 K for 3 h and 1273 K for 1.5 h, resulting in an estimated percentage error of around 2.5% for both conditions. Additionally, an ANOVA analysis was performed, taking into account the temperature and time factors. The findings indicate that both factors exert a substantial influence on the dependent variable (u), with temperature (T) contributing 64.68%, time (t) contributing 27.37%, and the interaction of both factors (T × t) contributing 5.13%.

Mathematical modeling of mass transfer in CO2 injection for confined fluids at near-miscible condition

Complex interaction between fluid and solid in tight formations leads to capillary confinement and interface slip. Mass transfer between oil and CO2 in CO2 flooding is essential to understand the flow complexity. Therefore, the objective of this work is to propose a comprehensive model to analyze the mass transfer during CO2 injection in the confined fluids. The modified Peng-Robinson equation of state considering the fluid-wall interaction and adsorption was established to calculate the properties of hydrocarbons and CO2. Relative permeability for the near-miscible state was then estimated using the new relative permeability model with corner flow effect. Predicted results agree well with the experimental observations. Afterwards, it was integrated with a one-dimension mathematical model to analyze the physical mechanisms of CO2 flooding in tight reservoirs. Results indicate that nanoconfinement increases the relative permeability at near-miscible condition, and confined fluid is more likely to be miscible than the bulk fluid. Additionally, nanoconfinement can reduce the velocity of CO2 front and increase the breakthrough time of CO2, which is favorable to improve the efficiency of CO2 flooding. This model provides a deep understanding of mass transfer between CO2 and hydrocarbons, and it can be integrated with compositional simulators to solve the field-scale cases including the microscale mechanism of tight reservoirs.

Molecular-Level Kinetic Model for Light Hydrocarbon Steam Cracking Based on the SU-BEM Framework.

In this work, a molecular-level kinetic model of ethane/propane steam cracking was developed by using a hybrid structural unit-bond electron matrix framework. The molecular-level simulation was conducted, creating a detailed feedstock composition, formulating the reaction rules, and automating the generation and visualization of reaction networks. Ordinary differential equations were automatically generated based on the Arrhenius equation, while the kinetic parameters were reduced via linear free energy relations (LFERs). Furthermore, proper mathematical models for mass transfer, heat transfer, and momentum transfer within the cracking furnace were integrated into the molecular-level kinetic model, enabling the simultaneous calculation of the transfer process and chemical kinetics in steam cracking. The model was validated by its precise prediction of product yields, outlet pressure, and outlet temperature, which were collected from an industrial gas-cracking furnace.

Mass transfer studies on the solvent-free lipase-catalyzed partial hydrolysis of palm oil in packed-bed reactor

Packed-bed reactor (PBR) is widely employed for enzyme-mediated reactions at an industrial scale because the reactor configuration enables reusability of the biocatalyst with ease, thereby reducing the overall operating expenses. However, mass transfer limitation remains a key challenge in fixed-bed column systems, especially at large scale. Therefore, the present study investigated the external mass transfer effects on solvent-free lipase-catalyzed partial hydrolysis reaction and aimed to develop a mass transfer model for the operation. The influence of volumetric flow rate, one of the crucial operating parameters affecting the external mass transfer resistance, was examined. Results demonstrated increasing the flow rate led to an increase in hydrolysis reaction with the highest reaction rate observed at 5 ml min-1 . A dimensionless mathematical mass transfer model of Colburn factor, JD = K(Re)n-1 which is a function of Reynolds and Schmidt numbers, was then proposed to simulate the enzymatic partial hydrolysis reaction of palm oil in PBR. The mass transfer model was analyzed with different n values and results revealed that the mass transfer correlation of JD=0.92(Re)-0.2 was able to predict the experimental data accurately. The model developed could describe the dominance of mass transfer effects besides providing useful information for the scale-up design of industrial reactor.

Multiscale Mathematical Model of Heat and Mass Transfer in a Thin Vapor Chamber

Multiscale Mathematical Model of Heat and Mass Transfer in a Thin Vapor Chamber

Parameter Identification of the Fractional-Order Mathematical Model for Convective Mass Transfer in a Porous Medium.

Fractional calculus is an essential tool in studying new phenomena in hydromechanics and heat and mass transfer, particularly anomalous hydromechanical advection-dispersion considering the fractal nature of the porous medium. They are valuable in solving the urgent problem of convective mass transfer in a porous medium (e.g., membranes, filters, nozzles, convective coolers, vibrational prillers, and so on). Its solution allows for improving chemical engineering and technology workflows, refining process models for obtaining porous granular materials, realizing the convective cooling of granular and grain materials, and ensuring the corresponding apparatuses' environmental safety. The article aims to develop a reliable convective mass transfer model for a porous medium and proposes a practical approach for its parameter identification. As a result, a general scientific and methodological approach to parameter identification of the fractional convective mass transfer model in a porous medium was proposed based on available experimental data. It mainly used Riemann-Liouville fractional time and coordinate derivatives. The comprehensive application of the Laplace obtained the corresponding general solution transform with respect to time and a coordinate, the Mittag-Leffler function, and specialized functions. Different partial solutions in various application case studies proved this solution. Moreover, the algorithm for practically implementing the developed approach was proposed to evaluate parameters for the considered model by evaluation data. It was reduced to the two-parameter model and justified by the available experimental data.

Membrane-based packed-sheet liquid desiccant dehumidification system

Humidity control plays a vital role in both buildings and greenhouses. The thermally-driven liquid desiccant dehumidification systems are getting an increasing traction because of their high moisture removal capacity and the possibility of their integration with waste-heat or renewable energy sources. In this work, a novel design concept for liquid desiccant dehumidification systems is proposed to overcome the practical challenges of the conventional systems, such as solution carryover, crystallization, and corrosion. The presented system utilizes a compact “packed-sheet” sorption bed that houses spherical membrane-based micro-absorbers with LiBr as a liquid desiccant. A bench-scale system is designed and tested under the typical dehumidification working conditions. The experimental results showed that the proposed design has up to two-fold higher moisture removal rate per volume (MRR = 75 g/s-m3) than a conventional LiBr liquid desiccant dehumidification system (MRR = 35 g/s-m3). In addition, a one-dimensional coupled heat and mass transfer mathematical model is developed to simulate the transient behavior of the proposed system. An optimization study, using the validated model, suggested that the performance of proposed design can be maximized to realize moisture removal rates of up to 135 g/s-m3 (270% higher than the conventional liquid desiccant systems) with a coefficient of performance of 0.25.

Analysis of Diffusion Coefficients of Iron Monoboride and Diiron Boride Coating Formed on the Surface of AISI 420 Steel by Two Different Models: Experiments and Modelling.

In the present work, two mathematical diffusion models have been used to estimate the growth of the iron monoboride and diiron boride coating formed on AISI 420 steel. The boronizing of the steel was carried out with the solid diffusion packing method at a boronizing temperature of 1123 K-1273 K. Experimental results show the two-coating system consists of an outer monoboride and an inner diiron boride coating with a predominantly planar structure at the propagation front. The depth of the boride coating increases according to temperature and treatment time. A parabolic curve characterizes the propagation of the boride coatings. The two proposed mathematical models of mass transfer diffusion are founded on the solution corresponding to Fick's second fundamental law. The first is based on a linear boron concentration-penetration profile without time dependence, and the second model with time dependence (exact solution). For both models, the theoretical law of parabolic propagation and the average flux of boron atoms (Fick's first fundamental law) at the growth interfaces (monoboride/diiron boride and diiron boride/substrate) are considered to estimate the propagation of the boride coatings (monoboride and diiron boride). To validate the mathematical models, a programming code is written in the MATLAB program (adaptation 7.5) designed to simulate the growth of the boride coatings (monoboride and diiron boride). The following parameters are used as input data for this computer code: (the layer thicknesses of the FeB and Fe2B phases, the operating temperature, the boronizing time, initial formation time of the boride coating, the surface boron concentration limits, FeB/Fe2B and Fe2B/Fe growth interfaces, and the mass transfer diffusion coefficient of boron in the iron monoboride and diiron boride phases). The outputs of the computer code are the constants εFeB and εFe2B. The assessment of activation energies of AISI 420 steel for the two mathematical models of mass transfer is coincident (QFeB=221.9 kJ∙mol-1 and QFe2B=209.1 kJ∙mol-1). A numerical analysis was performed using a standard Taylor series for clarification of the proximity between the two models. SEM micrographs exhibited a strong propensity toward a flat-fronted composition at expansion interfaces of the iron monoboride and diiron boride coating, confirmed by XRD analysis. Tribological characterizations included the Vickers hardness test method, pin-on-disc, and Daimler-Benz Rockwell-C indentation adhesion tests. After thorough analysis, the energies were compared to the existing literature to validate our experiment. We found that our models and experimental results agreed. The diffusion models we utilized were crucial in gaining a deeper understanding of the boronizing behavior of AISI 420 steel, and they also allowed us to predict the thicknesses of the iron monoboride and diiron boride coating. These models provide helpful approaches for predicting the behavior of these steels.

Time-Dependent Features of Mass Transfer and Transmembrane Potential in Erythrocytes During Equilibration in Cryoprotective Solutions

On the basis of the developed physical and mathematical model of mass transfer, which takes into account the transmembrane transfer of non-electrolytes, basic ions and the associated changes in the transmembrane potential, the redistribution of osmotically active substances during equilibration of erythrocytes in cryoprotective solutions was investigated. Time parameters of changes in concentrations of osmotically active substances inside and outside cells, as well as transmembrane electric potential, were calculated. It is shown that during the exposure of human erythrocytes to 1M solutions of glycerol, 1,2-propanediol (1,2-PD) and dimethylsulfoxide (DMSO), the sign of their transmembrane electric potential changes three times, and in solutions of ethylene glycol (EG) and of acetamide (AA) – once. The analysis of the obtained results showed that the most acceptable for further cryopreservation from the point of view of erythrocytes reaching a state close to equilibrium in a 1M solution of glycerol was their equilibration for 5.5 min, and in solutions of DMSO, AA, EG and 1,2-PD with the same concentration – 1 min. At the same time, the cells remain somewhat dehydrated (by 5.5–7.5%), and the concentrations of cryoprotectants inside erythrocytes change insignificantly during longer exposure. The indicated degree of dehydration does not affect cell viability, but reduces the likelihood of intracellular ice formation during subsequent freezing.

Study on the influence of borehole heat exchanger structure and soil thermal property on soil heat storage characteristics of the HST-BHE system

To effectively solve the problem of soil thermal imbalance in cold regions, a new soil heat storage system that absorbs heat from ambient air through heat source tower (HST) and injects the heat into soil through borehole heat exchanger (BHE) in the non-heating season has been proposed in author’s previous research. However, the influence of structure parameters of the BHE and soil thermal properties on soil heat storage characteristics is not deeply studied. In this paper, heat and mass transfer mathematical model of the integrated system of HST and BHE (named as HST-BHE system) was built based on the developed models of BHE and HST firstly. Then, the influence of BHE structural parameters and soil thermal properties on soil heat storage characteristics was studied. The results show that the soil heat storage capacity of the HST-BHE system and temperature difference between the inlet and outlet of BHE increase with the increases of borehole length, buried pipe spacing or soil thermal conductivity, and decrease with the increases of borehole radius under specific conditions. While the borehole wall temperature of the BHE increases with the increase of buried pipe spacing and decreases with the increase of borehole depth, borehole radius or soil thermal conductivity. Unusually, increasing the water flow velocity in BHE will decrease the temperature difference but increase the soil heat storage capacity. These soil heat storage characteristics are controlled by the heat transfer thermal resistances between water and soil in the BHE as well as water and air in the HST, and all of the impact parameters should be optimized in actual engineering applications when considering the economy of the HST-BHE system.

Experimental and modeling study of bubble absorption-based deep dehumidification using the ionic liquid: Parametric analysis on heat and mass transfer

Conventional liquid desiccant dehumidification is good at humidity control with energy conservation and stable operation, but is limited by corrosion and crystallization in deep dehumidification. Thus, it is necessary to broaden the humidity adjustment range of liquid desiccant deep dehumidification as well as avoid corrosion. Ionic liquids (ILs) with deep dehumidification potential (e.g., extremely low vapor pressure and non-corrosion) are a promising alternative to traditional salt solutions. Meanwhile, the bubble absorption-based mode can obtain a huge gas–liquid specific interfacial area, which is expected to solve the low wettability and insufficient gas–liquid transfer efficiency in traditional falling-film/packed dehumidifiers using IL. In this work, the bubble absorption-based deep dehumidification using IL (BADD-IL) is investigated. Meanwhile, the heat and mass transfer mathematical model of BADD-IL is established, and a bubble column dehumidifier using the novel IL is experimentally examined under different conditions. The results indicated that the deep dehumidification performance is strongly dependent on operating parameters, and the minimum outlet air humidity ratio is around 1.2 g/kgda. In particular, it is most sensitive to inlet air humidity ratio, followed by liquid height and superficial velocity, and the effect of solution temperature is the least. Notably, the influential mechanism of superficial velocity and solution temperature on volumetric transfer coefficient is different. The increase of superficial velocity promotes both gas–liquid specific interfacial area and heat and mass transfer coefficient. For the IL with lower temperature, its higher heat and mass transfer coefficient makes up for the poor specific interfacial area caused by high viscosity. Additionally, the Lewis factor of bubble column dehumidifier using the novel IL is basically less than 0.6, which is important for the device design and scale-up. This study clarifies the heat and mass transfer mechanism of BADD-IL, and provides guidance for the development of ILs deep dehumidification technology.

Mathematical Modeling of Mass Transfer in Complex Engineering and Biomedical Systems

We consider various analytic methods intended for the evaluation of operating parameters of the process of gas motion in the main technological objects of gas transportation systems. On the basis of these methods, we develop the mathematical models aimed at determining the parameters of the operation of the underground gas storages. In view of the similarity of hydro-, gas-, and hemodynamic processes, we extend the accumulated results to the case of modeling of the process of blood circulation in large blood vessels and soft tissues of the living organisms.

Research on heat and mass transfer characteristics of water-sprayed single-screw vapor compressor

Temperature increase in the working cavity caused by steam superheating is an important issue that affects the compressor performance in single-screw vapor compressor (SSVC). Therefore, working cavity water spraying is often accustomed to realize the cooling of pressurization process. There is a bidirectional phase change process in the SSVC water jet pressurization process, which makes the pressurization and heat transfer mechanism very complicated. To clarify the internal working mechanism, an evaporation-condensation bidirectional heat and mass transfer (HMT) mathematical model of water-vapor two-phase medium is established for the SSVC with multicolumn envelope meshing profile. The simulation results are compared and verified by the experimental data. The exhaust pressure error is within 5%. Based on the validated model, the HMT characteristics are nalysed and the influence of water-sprayed parameters are discussed. Results show that compressor performance can be significantly improved by water spraying, and the volumetric and adiabatic indication efficiency can be increased by 0.98% and 3.83%. After the vapor reaches saturation, with the continuous increase of the water spraying rate, the adiabatic indication efficiency will drop significantly. Conditions such as water-spraying temperature, pressure, suction superheat and back pressure all have an impact on compressor performance.

An Engineering Method of Analyzing the Dynamics of Mass Transfer during Concrete Corrosion Processes in Offshore Structures.

The environment of an underground structure is much more complex than the above-ground environment. Erosion processes are underway in soil and groundwater; groundwater seepage and soil pressure are also typical for underground environments. Alternating layers of dry and wet soil have a strong effect on concrete, and they reduce its durability. Corrosion of cement concretes is caused by the diffusion of free calcium hydroxide, located in the pores of concrete, from the volume of the cement stone to its surface, bordering on an aggressive environment, and the further transition of the substance through the phase boundary solid (concrete)-soil-aggressive environment (liquid). Due to the fact that all minerals in cement stone exist only in saturated or close-to-saturated solutions of calcium hydroxide, a decrease in the content of which in the pores of concrete as a result of mass transfer processes causes a change in the phase and thermodynamic equilibrium in the body of concrete and leads to the decomposition of highly basic compounds of cement stone and, consequently, to the deterioration of the mechanical properties of concrete (reduction in strength, modulus of elasticity, etc.). A mathematical model of mass transfer in a two-layer plate imitating the "reinforced concrete structure-layer of the soil-coastal marine area" system is proposed as a system of nonstationary partial derivative differential equations of the parabolic type with Newmann's boundary conditions inside the building and at the interface between the soil and the marine environment and with conjugating boundary conditions at the interface between the concrete and the soil. When the boundary problem of mass conductivity in the "concrete-soil" system is solved, expressions are obtained to determine the dynamics of the concentration profiles of the target component (calcium ions) in the volumes of the concrete and soil. As a result, one can select the optimum composition of concrete, having high anticorrosion properties, to extend the durability of the concrete constructions of offshore marine structures.

Design Selection Method of Exhaust Air Heat Recovery Type Indirect Evaporative Cooler

In order to promote the engineering application of indirect evaporative cooling (IEC) in the field of building air conditioning, as well as reduce air conditioning energy consumption and carbon emissions, this paper proposes a fresh air unit using indirect evaporative cooling to achieve heat recovery from exhaust air, which gives the recommended values of air and spray water operation parameters. The indirect evaporative cooler heat and mass transfer mathematical model and numerical solution procedure were made. In summer outdoor design conditions, the fresh air outlet state parameters, cooling capacity, fresh air cooling load, wet bulb efficiency and enthalpy efficiency were numerically solved for thirty typical cities from five climate zones of China. In addition, also based on the model results for the cities in China, two representative operating conditions points of medium and high humidity were selected. Eight models of fresh air unit coolers in the air volume range of 1000–10,000 m3/h commonly used in engineering were simulated to obtain the optimal heat transfer area and size selection of ERIEC heat exchangers for fresh air units, and economic analysis was performed. The results show that the wet bulb efficiency ranges from 0.67–0.98, and increases as the outdoor design wet bulb temperature decreases; the enthalpy efficiency ranges from 0.76–1.29, and increases as the outdoor design wet bulb temperature increases; and the fresh air load that the exhaust air heat recovery type indirect evaporative cooler can bear ranges from 55–100%, which could largely decrease the cold load of the matched surface cooler. As demonstrated, the energy-saving effect is remarkable.

Mathematical model-based performance assessment of a centrifugal humidifier under varying operating conditions

Evaporative cooling phenomenon yields a cooling and humidification process widely used in AC applications to maintain thermal comfort in the space. Present work deals with the design & construction of a dynamic humidifier that operates on the centrifugal action principle. Celdek pad is positioned inside a frame that holds the water effectively and later dispersed in the air. Heat & mass transfer mathematical model is constructed and parameters such as evaporation rate, cooling efficiency, cooling effect, coefficient of performance, specific humidity at the exit and exit temperatures are determined and validated with empirical values. Maximum Humidification efficiency of 82%, cooling effect of 3061 W and rate of evaporation of 0.82 g/s have been noticed from the experiments. Both Experimental and theoretical results agree with a maximum deviation of 8%. Also, it is found that packing in dynamic action gave maximum humidification performance compared to the stationary type except for coefficient of performance. Motor shaft speed of 150–160 rpm and the air velocity of 6.5 to 7 m/s yielded optimum results.

Modeling the release of an antimicrobial agent from multilayer film containing coaxial electrospun polylactic acid nanofibers

The research of active biodegradable multilayer materials are of current interest for developing functional and sustainable packages able to guarantee the microbiological safety of food. In this work, an active biodegradable trilayer packaging system composed of (1) an external layer of extruded polylactic acid (PLA) film, (2) an intermediate layer of electrospun PLA loaded with ethyl lauroyl arginate (LAE) and cellulose nanocrystals (CNC), and (3) an inner layer of chitosan processed by coating, was developed. Optical, structural, and thermal properties were evaluated. Furthermore, a mathematical mass transfer model focused on the fibers structure was developed to study the LAE release to aqueous and fatty food simulants. Compared to extruded PLA, the trilayer material was white and opaque with a ΔE = 2.6. Furthermore, the processing of material produced a scarce interaction between their components and its crystallinity was increased by 85%. K coefficients were lower than 100 evidencing the high affinity of LAE for both simulants, while D coefficients ≈0.5x10−17m2s−1 demonstrated the slow diffusion of LAE through the material.

Influence of salt concentration on Kimchi cabbage (Brassica rapa L. ssp. pekinensis) mass transfer kinetics and textural and microstructural properties during osmotic dehydration

The effect of salt concentration (3%, 6%, and 9%) on the mass transfer kinetics of Kimchi cabbage during osmotic dehydration was investigated, including its influence on textural and microstructural properties and salt distribution. First, kinetics was analyzed using diffusion theory to determine the impact of the factors on moisture and salt transfer. Subsequently, using the Peleg, Azuara, Henderson-Pabis, and Page models, mathematical modeling of mass transfer (water loss and salt gain) was investigated. According to the statistical analysis, the Peleg model provided the best fit for the experimental results under the operating conditions. In addition, a novel viewpoint was proposed in which the salt content of Kimchi cabbage may be indirectly forecasted by monitoring solution salinity during osmotic dehydration. Higher salt concentration resulted in decreased hardness, gumminess, and chewiness in Kimchi cabbage. Scanning electron microscopy and energy-dispersive X-ray mapping images showed an intensification of moisture and salt transport with increasing salt content, which were confirmed using modeling studies. The results could be applied in the prediction of the target salinity of Kimchi cabbage during the salting process and could facilitate the improvement of final Kimchi product quality by producing salted Kimchi cabbage with uniform salinity.

Modeling of mass transfer in complex porous environments of cylindrical form

In the work, a mathematical model of mass transfer in a complex porous medium, which has the form of a hollow cylinder of a given height, is constructed. The influence of the parameters of the porous medium on the process of pressure distribution was studied.

Вопросы численного моделирования горения в диффузионном факеле

The study is devoted to mathematical models of mass transfer during diffusion combustion of gaseous fuel. A numerical approach is presented that makes it possible to estimate the effect of combustion conditions on the length of a direct-flow diffusion flame. A simplified method for calculating the heat release in a diffusion flame is applied, taking into account the fact that the chemical reactions of combustion are concentrated in it at the flame front. Some results of numerical simulation of diffusion combustion processes and complex radiative-convective heat transfer in industrial furnaces in the production of cement clinker are presented.