Mass Transfer Equations Research Articles

Comparison of barrel-shaped fixed bed drying for different ventilation methods by mathematic simulation

Unsteady one-dimensional partial differential equations for heat and mass transfer in peanut drying are used in mathematical simulations to compare the drying performance of a barrel-shaped bed in three ventilation modes: bottom up, inside out and outside in. Results obtained using the finite difference scheme show that the mathematical simulation reliably predicts the drying process of peanuts, and that the drying delay of bottom-up ventilation is the most significant at the beginning of drying. This is because the drying enhancement afforded by the high average velocity of air along the ventilation direction is insufficient to offset the drying delay caused by the large ventilation thickness compared with that afforded by the inside-out and outside-in ventilation. Furthermore, as the air volume flow increases, the time consumption and moisture content difference decrease, whereas the productivity, energy consumption, and uniformity increase for all three ventilation modes, consistent with the classical ventilation drying law. Under the same air volume flow, the time and energy consumptions for the bottom-up ventilation are the lowest, followed by those for the outside-in and inside-out ventilation. The productivity afforded by the bottom-up ventilation is the highest, followed by that by the outside-in and inside-out ventilation. The outside-in ventilation indicates the least moisture content difference and the best drying uniformity. Meanwhile, the inside-out ventilation indicates the most significant moisture content difference and the worst drying uniformity.

Hybrid mechanistic approach in the estimation of flow properties in cylindrical membrane modules

A hybrid computational approach was employed for simulation of molecular separation using polymeric membranes. The considered system is a cylindrical membrane module in which the mass transfer equations were solved numerically using CFD (Computational Fluid Dynamics) to obtain the concentration of the species, and then the simulation results were used in machine learning models. Indeed, the CFD simulation results were used as the inputs for several machine learning models to obtain the hybrid model. We have a dataset with more than 2000 data points and two input features (r and z). Also, the only output is C which is the concentration of the species in the feed channel of membrane module. KNN (K nearest neighbor), PLSR (Partial Least Square Regression), and SGD (Stochastic Gradient Descent) are the models employed in this research to analyze the mentioned data set. Models were optimized with their hyper-parameters and finally evaluated with different statistical metrics. MAE error metric is 3.4, 5.1, and 5.5 for KNN, SGD, and PLSR. Also, they have 0.998, 0.997, 0.896 coefficient of determination (R2) respectively. Finally, based on the overall results, KNN with K = 8 is selected as the best model in this study for simulation of the membrane system. The final maximum error is also 1.35E+02.

Numerical simulation and experimental validation of Ti0.95Zr0.05Mn0.9Cr0.9V0.2 alloy in a metal hydride tank for high-density hydrogen storage

In order to achieve rapid hydrogen charging and discharging of high-density hydrogen storage alloys in metal hydride (MH) tank, it is key to optimize the design of MH tank by simulation based on a credible numerical model. Herein, a multi-physical field mathematical model coupled with kinetic equations and heat & mass transfer equations for the de-/hydrogenation of Ti0.95Zr0.05Mn0.9Cr0.9V0.2 alloy in MH tank is proposed. According to experimental kinetic curves, appropriate kinetic equations dominated by different rate control steps are chosen for simulating gas-solid reactions. With excellent match between experimental and simulated kinetic results under different pressure and temperature operating conditions, a novel numerical model is established to predict the local temperature variation during the de-/hydrogenation of Ti0.95Zr0.05Mn0.9Cr0.9V0.2 alloy in a self-designed hydrogen storage tank with high-density hydrogen storage of 55.1 g H2/L. Interestingly, further calculated results reveal that the temperature evolution can be accurately matched, which proves the reliability of the designed numerical model and favors to predict the de-/hydriding behaviors. This investigation provides an effective means for subsequent structure optimization and energy & mass transfer performance optimization of high-density hydrogen storage devices, and sheds light on the numerical simulation of heat & mass transfer for advanced energy storage applications.

On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review

A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined. Examples are shown in which the mechanical use of entropy production-based principles turns out to be inefficient and even contradictory. The main problem of extremal principles in the theory of irreversible processes is the impossibility of their generalization, often even within the framework of a class of problems. Alternative extremal formulations are considered: variational principles for heat and mass transfer equations and other dissipative systems. Several extremal principles are singled out, which make it possible to simplify the numerical solution of the initial equations. Criteria are proposed that allow one to classify extremal principles according to their areas of applicability. Possible directions for further research in the search for extremal principles in the theory of irreversible processes are given.

Green process of fuel production under porous γ-Al2O3 catalyst: Study of activation and deactivation kinetic for MTD process

One of the methods of industrial dimethyl ether production is the catalytic dehydration of methanol. In this research work, methanol dehydration reactor has been modeled using continuous model and its results have been compared with experimental works and Voronoi pore network model. A 1D heterogeneous dispersed plug flow model was utilized to model an adiabatic fixed-bed reactor for the catalytic dehydration of methanol to dimethyl ether. The mass and heat transfer equations are numerically solved for the reactor. The concentration of the reactant and products and also the temperature varies along the reactor, therefore the effectiveness factor would also change in the reactor. We used the the effectiveness factor that was simulated according to the diffusion and reaction in the catalyst pellet as a Voronoi pore network model. Sensitivity analysis was performed to determine the influence of T, P and weight hourly space velocity on performance of the chemical reactor. Acceptable agreement was reached between the measured and the model data. The results showed that the maximum reaction conversion was obtained about 90 % at WHSV = 10 h−1 and T = 560 K, while the inlet temperature (Tinlet) had a greater effect on methanol conversion. In addition, the effect of water in the feed on methanol conversion was quantitatively studied. Also, the deactivation kinetics of γ-Al2O3 heterogeneous-acidic catalyst in methanol to dimethyl ether dehydration process was studied using integral analysis method. Based on independent deactivation kinetics, a second order was found that accurately fitted the experimental conversion time data. The main reaction activation energies and catalyst deactivation energies were 143.1 and −102.1 kJ/mol, respectively.

STUDY OF BOREHOLE HEAT EXCHANGER HEAT TRANSFER ENHANCEMENT PARAMETERS

This paper discusses the study of parameters for improving the heat transfer of a borehole heat exchanger for a ground source heat pump application. The study of efficiency parameters was carried out based on an experimental prototype of a ground source heat pump developed by the authors. A mathematical model has been developed for calculating the efficiency of a ground heat exchanger based on three-dimensional equations of heat and mass transfer in a porous medium. The numerical solution was carried out using the COMSOL Multiphysics software. The numerical calculation algorithm was verified by comparison with experimental data from the created prototype. Calculations were made of the efficiency of a borehole heat exchanger with various geometric configurations of the pipes in the well. With an increase in the tube diameter, the heat transfer increases. With a tube diameter of 40 mm, the thermal efficiency of the heat exchanger was 42.4 W/m in the heat charging mode, which is 24% more with a diameter of 20 mm. With increasing well depth, the heat transfer efficiency increases. The influence of the thermal conductivity coefficients of the pipe material, grout material and various types of ground on the heat transfer efficiency was also studied. It was shown that with an increase in the thermal conductivity coefficients of grout and ground, the heat flux increases, but above 6.0 W/m K, the heat flux practically does not change. When the coefficient of thermal conductivity of the pipe material is higher than 1.0 W/m K, the heat fluxes almost do not change. In general, materials containing plastics are used for piping of ground heat exchangers, the thermal conductivity coefficients of which vary between 0.24-0.42 W/m K.

A comprehensive study on hygroscopic behaviour and nitrate depletion of NaNO3 and dicarboxylic acid mixtures: implications for nitrate depletion in tropospheric aerosols

Abstract. The nitrate depletion and HNO3 release in internally mixed nitrate and dicarboxylic acid (DCA) particles have been widely detected in field and laboratory studies. Nevertheless, considerable discrepancies are still present among these measurements, and the influencing factors for this acid-displacement reaction have not yet been elucidated. In this work, the hygroscopic growth and chemical composition evolution of mixtures of NaNO3 and DCAs, i.e. oxalic acid (OA), malonic acid (MA), and glutaric acid (GA), were measured using attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) and vacuum FTIR techniques. The nitrate depletion from NaNO3–OA mixtures was observed in both the measurements, owing to the relatively higher acidity of OA compared to MA and GA. At the same time, the NaNO3 phase state was found to act as a key regulator of nitrate depletion. Amorphous NaNO3 solids at relative humidity (RH) <5 % were inert to liquid OA. With increasing RH, the mixtures experienced three interesting stages of phase changes showing different HNO3 release rates; e.g. at around 15 % RH, the slow HNO3 release was detected by the vacuum IR spectra, potentially indicating the transformation of amorphous solids to semisolid NaNO3. In the second stage (sudden RH increase from ∼15 % to 61 %), the HNO3 release rate was increased by about an order of magnitude. When NaNO3 deliquescence occurred in the third stage, this displacement reaction proceeded due to more available NO3- ion formation. Compared to OA, MA and GA reacted with nitrate only in vacuum FTIR measurement, while in ATR-FTIR measurement, the mixtures tended to be effloresced completely without nitrate depletion. Further, the influences of ambient pressure, chemical composition, and water activity on HNO3 release rates were estimated via Maxwell steady-state diffusive mass transfer equation. The results showed that weaker acidity of MA and GA as well as relatively lower HNO3 diffusion rate in the ambient gas phase mainly contributed to the unobserved nitrate depletion in ATR-FTIR measurement. Our findings reveal that chemical component, phase state, and water activity of particles, as well as HNO3 gas-phase diffusion, play crucial roles in HNO3 release from nitrate and DCA mixtures. This work may provide a new perspective on nitrate depletion in the ageing processes during transport of tropospheric aerosols.

Sherwood correlation for finger-test experiments

Finger-test experiments are frequently conducted in continuous-wear investigations of ceramic materials. However, mass transfer equations accurately representing these scenarios are not yet available, which can lead to erroneous estimation of dissolution-related parameters due to poor approximations. In this study, a Sherwood correlation for finger-test experiments was developed. The equation applies to rods or nearly cylindrical specimens that are rotated in a liquid contained in a cylindrical receptacle. The equation is derived from numerical results simulating the dissolution of ceramic materials in liquid slags, where the dissolution is dominated by mass transfer in the liquid. For these simulations, surface profiles from the experimental results were employed. Based on the derived equation, a methodology for the calculation of mass transfer coefficients for dissolution processes was designed that enables diffusivity determination. This equation is also suitable for heat transfer calculations. The equation is in agreement with the results obtained by simulation and other documented heat and mass transfer equation, for the latter the fit is poorer due to differences in the experiment configuration.

Numerical calculation of temperature, velocity, and species concentration distributions in a hot filament chemical vapor deposition in a reactor using a CH4/H2 mixture

This study is a numerical modeling of transport phenomena occurring in the reaction chamber during diamond or amorphous hydrogenated carbon films growth by a hot filament chemical vapor deposition (HFCVD) technique. A two-dimensional model was adopted to study the HFCVD reactor. The equations of heat, momentum, and mass transfer were solved numerically; the simulation was performed using a program in FORTRAN language. All temperature, velocity, and species concentration distributions were similar at the filaments and they were also similar between the filaments. The results show that the gas temperature increases when the number of filaments increases from three to four filaments. We also noted an increase in the production of CH3 and C2H5 radicals near the surface; there was also an increase in the growth rate of the thin film. The concentrations of C2H6, C2H4, and C2H5 were very high. Temperature and concentrations were affected by the distance between filaments and the distance filaments-substrates.

Remarkable dynamic adsorption of Hg2+ ions on the magnetic MOF nanocomposite (CuNi-BTC@Fe3O4): Experimental and modeling using GA+CFD+ANFIS method

The magnetic bimetallic metal-organic framework (MOF) nanocomposite was fabricated using the facile preparation method for the removal of mercury ions in the fixed bed column. The several analyses including XRD, TEM, BET and VSM were also carried out to characterize the physico-chemical properties of the synthesized sample (CuNi-BTC@Fe3O4). The Langmuir model with a maximum adsorption capacity of 144.32 mg/g was fitted well with equilibrium data. The performance of the adsorption column was evaluated under the various operating conditions including length of bed (10, 15, 20 cm), flow rate of feed (10, 15, 20 ml/min) and initial concentration of mercury ions in the inlet (25, 50, 75 mg/l). The breakthrough time was measured to be about 581.1 min at the proper operating conditions including 15 cm of bed height, 50 mg/l of feed concentration and 10 ml/min of feed flow rate. The commercial models including Thomas and Yoon-Nelson were investigated for the determination of the adsorption behavior of Hg (II) in the adsorption column. The results indicated the good agreement between the experimental data and Yoon-Nelson model (R2 > 0.99). The combination model consisting of the unsteady computational fluid dynamics (CFD), an adaptive neuro-fuzzy inference (ANFIS) and genetic algorithm (GA) was developed to simulate the uptake of Hg (II) ions in dynamic bed. The employed ANFIS was also coded by using five layers to predict the source term of mass transfer equation as the most significant parameter of the modeling which must be calculated with high precision. The generated Gaussian membership functions i n the ANFIS model was optimized by applying GA. Finally, the CFD (the first order implicit) was linked with ANFIS to describe the dynasmic adsorption of mercury ions. The validation illustrated a good matching between the experimental data and the output of the combination model (R2 > 0.999).

Dimensionless Profiles of Temperature and Steam Mass Fraction in Flows of Steam-Air Mixtures on a Flat Plate

Abstract Wall functions are generally used in a turbulent analysis with a computational fluid dynamics (CFD) code and large computation cells. The logarithmic law based on the analogy between momentum, energy, and mass transfer is widely used in wall functions for turbulent flows, but its validity in the turbulent boundary layer has not been confirmed for dimensionless profiles of temperature and steam mass fraction in flows of steam and noncondensable gases. In this article, therefore, we evaluated dimensionless profiles of temperature and steam mass fraction in flows of steam and air on a flat plate by using existing data. From the heat and mass transfer equations at the condensation surface based on the gradient of temperature or steam mass fraction, we showed that the convection heat flux qconv (which is used for the definition of the dimensionless temperature T+) should include the term of condensate mass flux ms and that the dimensionless steam mass fraction Ys+ should be a function of the dimensionless distance y+ (= uτ y/ν where uτ is the friction velocity), the Schmidt number Sc and the air mass fraction (1−Xs). Values obtained from the newly defined T+ and Ys+ and the existing data agreed relatively well with the linear function near the viscous sublayer (a few data points were there) but were much smaller than the existing logarithmic law due to condensation in the turbulent boundary layer (i.e., mist generation). On the other hand, the T+ and Ys+ values obtained by using the local Nusselt number Nuy and the local Sherwood number Shy (which were proposed in our previous study), respectively, agreed well with the logarithmic law.

NUMERICAL MODELING OF AIR POLLUTION NEAR THE HIGHWAY WITH PROTECTIVE BARRIERS

Problem statement. The problem of predicting chemical pollution zones near the highway, where protective barriers are located, is considered. The protective barriers influence the aerodynamics of air flow and reduce the level of working areas chemical pollution near the highway. It is necessary to have mathematical models that allow such evaluation at the design stage in order to evaluate the effectiveness of protective barriers promptly. The purpose of the article. Development of a numerical multi-parameter model and computer program for evaluating the effectiveness of the protective barriers using near the highway to reduce the chemical contamination level of work areas. Methodology. A two-dimensional mass transfer equation is used for mathematical modeling of chemical hazardous substances spreading that are emitted from a car and spread near the highway. This simulation equation takes into account the wind direction, atmospheric diffusion, the intensity of chemically hazardous substance emission from the car, the emission source location, the car body and the location of protective barriers near the highway. The Navier − Stokes equation and the potential motion model both are used to solve the aerodynamics problem of determining the uneven air velocity field near the highway. An implicit splitting difference scheme is used to numerically integrate the vortex transfer equation. Two numerical schemes are used to numerically integrate the equation for the current function. An explicit difference scheme is used to numerically integrate the Laplace equation for the velocity potential. Based on the constructed numerical model the package of programs is developed. To solve numerically equation of pollutant transfer the finite difference schemes of splitting are used. Scientific novelty. To calculate the formation of chemical pollution areas for atmospheric air near the highway during emissions from vehicles numerical model is proposed. This model allow to estimate the protective barriers effectiveness for reducing air pollution in the working areas. Practical significance. Based on the developed model the code for quickly calculation of air pollution process both near the highway and in work areas protecting with barriers is created. Conclusions. The developed numerical model and the computer code implementing it allow to investigate the process of chemical hazardous substance spreading in the atmospheric air near the highway. The model allows to quickly determine the effectiveness of protective barriers using near the highway. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

Dynamical law of the phase interface motion in the presence of crystals nucleation

In this paper, we develop a theory of solid/liquid phase interface motion into an undercooled melt in the presence of nucleation and growth of crystals. A set of integrodifferential kinetic, heat and mass transfer equations is analytically solved in the two-phase and liquid layers divided by the moving phase transition interface. To do this, we have used the saddle-point method to evaluate a Laplace-type integral and the small parameter method to find the law of phase interface motion. The main result is that the phase interface Z propagates into an undercooled melt with time t as Z(t)=sigma sqrt{t}+varepsilon chi t^{7/2} with allowance for crystal nucleation. The effect of nucleation is in the second contribution, which is proportional to t^{7/2} whereas the first term sim sqrt{t} represents the well-known self-similar solution. The nucleation and crystal growth processes are responsible for the emission of latent crystallization heat, which reduces the melt undercooling and constricts the two-phase layer thickness (parameter chi <0).

Mathematical modeling of the dynamics of aquatic ecosystems and the possibilities of their self-cleaning at the conditions of global climate change

A detailed review of mathematical models of pollution dispersion in air, water and soil is presented in the article. The models are represented by the systems of differential equations and used for water resources management on urban landscapes. Detailed three-dimensional equations of mass, momentum and heat transfer, averaged two-dimensional dispersion models on terrain maps, one-dimensional dispersion models in river systems and zero-dimensional compartmental models have been considered. The biotic component and the impact of the effects of gradual global climate change have been taken into account. The tasks for external quality management of water, air and soil, as well as the possibilities of the ecosystem for self-management have been considered. The problems of fuzzy data for validation as well as the usage of mathematical models for practical purposes have been discussed.

Fractional diffusion model for emission and adsorption prediction of TXIB from wallpaper.

Mercury injection test shows that wallpaper is a porous building material with a complex fractal mass transfer channel. Therefore, fractional Fick's law is employed to investigate sub-diffusion of 2,2,4 trimethy1-1,3-pentanediol diisobutyrate (TXIB) from wallpaper. In view of the fact that a small amount of TXIB has been released from the wallpaper before the environmental chamber experiment, the non-uniform initial concentration is introduced. Based on fractional Fick's law, both fractional convective mass transfer equation and fractional mass balance equation have been firstly proposed. Combining the finite difference method and L1 algorithm, the fractional diffusion model is solved numerically. Numerical simulation results show that the present model matches well with the experimental data. Compared with the previous model based on Fick's law, the present model is in better agreement with experimental data of di-2-ethylhexyl phthalate(DEHP) released from polyvinyl chloride (PVC) flooring. The influence of key parameters on the concentration of TXIB is analyzed graphically. In addition, the absorption amount and absorption rate of TXIB on the environmental bulkhead are numerically simulated for the first time.

Entropy optimization of MHD Casson-Williamson fluid flow over a convectively heated stretchy sheet with Cattaneo-Christov dual flux

This work confers the comparative study of Casson-Williamson fluid flow over a heated porous stretchy sheet. The energy and mass transfer equations are modeled by Cattaneo-Christov theory. The governing flow models were altered into an ODE model with the use of suitable transformations. The HAM scheme is applied to find the series solutions. The response of diverse flow variables on fluid speed, fluid warmness, liquid concentration, skin friction coefficient, local Nusselt number, local Sherwood number, local entropy generation number and Bejan number are analyzed through graphs and charts. It is found that the fluid speed subsides when surging values of the magnetic field, porosity, Casson fluid, Williamson fluid and injection/suction parameters. The fluid warmness escalates for a high amount of radiation, convective heating and heat generation/absorption parameters and its suppresses when enriching the convective cooling parameter. The chemical reaction parameter leads to rise in the thickness of the solutal boundary layer. The higher quantity of skin friction coefficient occurs in Casson fluid compared to Williamson fluid. The local entropy generation decimates when growing the Casson and Williamson parameters and it aggravates when raising the Biot number. The Bejan number exalts when upgrading the Reynolds, Brinkman and Biot numbers.

Mathematical modeling and simulation of refractance window drying of mango pulp for moisture, temperature, and heat flux distribution

AbstractThis study aims to simulate the coupled heat and mass transfer during refractance window (RW) drying of mango pulp. A simulation model was developed by considering temperature and moisture‐dependent effective diffusivity. With the help of COMSOL Multiphysics, a three‐dimensional (3D) model was developed to solve heat and mass transfer equations. RW drying of mango pulp (6 mm thick) was executed at differe temperature of 75, 80, 85, and 90°C and air velocity of .7 m/s. There was a quick rise in product temperature, and it remained constant throughout the experiment. The drying time required to reduce mango pulp's moisture content from 5.33 to .25 (g water/g dry matter) ranged between 5.7 and 8.5 h during RW drying. Surface moisture was 28, 30, 31, and 33% lower than moisture content at the bottom of pulp after 15 min of drying when drying temperatures were 75, 80, 85, and 90°C, respectively. Diffusivity increases with increasing temperature, and values range from 2.50 × 10−10 to 3.68 × 10−10 m2/s. Out of six empirical models, page, modified page, and two‐term exponentials were the best fit for drying characteristics.Practical ApplicationsThis study explores the heat and mass transfer modeling and simulation of RW drying of mango pulp. The three‐dimensional (3D) model gave a better understanding and visualized the effect of different heat source temperature combinations on temperature profile and their distribution and moisture content and their distribution throughout the sample. The method and mode used for this experiment can enable many researchers to conduct experimental studies on RW drying products. Also, a simulation model is a precise tool for forecasting drying product characteristics, drying behaviors, and physicochemical changes during the drying process. Simulation applications for better designing processes in food industries shall be more in the coming future. The present finding can be used by food processors and researchers for predicting the drying dynamics and subsequent upscaling of the RW drying process at an industrial scale.

Thermochemical Analysis of a Packed-Bed Reactor Using Finite Elements with FlexPDE and COMSOL Multiphysics

This work presents the thermochemical analysis of a packed-bed reactor via multi-dimensional CFD modeling using FlexPDE and COMSOL Multiphysics. The temperature, concentration, and reaction rate profiles for methane production following the Fischer–Tropsch (F-T) synthesis were studied. To this end, stationary and dynamic differential equations for mass and heat transfer were solved via the finite element technique. The transport equations for 1-D and 2-D models using FlexPDE consider dispersion models, where the fluid and the catalyst can be treated as either homogeneous or heterogenous systems depending on the gradient extents. On the other hand, the 3-D model obtained in COMSOL deems the transport equations incorporated in the Porous Media module. The aim was to compare the FlexPDE and COMSOL models, and to validate them with experimental data from literature. As a result, all models were in good agreement with experimental data, especially for the 2-D and 3-D dynamic models. In terms of kinetics, the predicted reaction rate profiles from the COMSOL model and the 2-D dynamic model followed the temperature trend, thus reflecting the temperature dependence of the reaction. Based on these findings, it was demonstrated that applying different approaches for the CFD modeling of F-T processes conducts reliable results.

Numerical investigation of a squeezing flow between concentric cylinders under the variable magnetic field of intensity

The ongoing research aims to examine the mass and heat transmission phenomena of squeezing flow between two concentric cylinders under the effect of heat sources and magnetic fields. The impacts of the Lorentz force on the behavior of the liquid flow are elucidated via a magnetic field incorporated in the momentum equation. Furthermore, within concentric cylinders, the expression Q = frac{Q_0}{1-beta t} has been employed as a source/sink. The proposed model of PDEs formulates the physical phenomena of time-dependent incompressible two-dimensional squeezing flow via modified Navier-Stokes equation, energy equation, and mass transfer equation, and variable magnetic field. The proposed model involved a highly nonlinear system of PDEs, which has been reduced into a system of ODEs via Lie group of similarity transformation and subsequently solved numerically in MATLAB by Parametric Continuation Method. The direct impact of the squeezing parameter on the profile of temperature and concentration has been observed. The results shown that an increment in the heat source indicates a decline in the liquid temperature profile, that an increment in the heat source indicates a decline in the liquid temperature profile. An increment in the heat source indicates a decline in the liquid temperature prof. At the same time, an inverse relationship is observed for the concentration profile. Therefore, we have witnessed a significant increase in the velocity profiles of the flow, mainly as a result of the heat absorption coefficient. In addition, the declining effect of the Soret number on the concentration profile is noticed. It has been found that it enhanced the entropy generation rate for Pr, Omega, and Ec, while an opposite impact has been noticed at the Bejan number. The numerical outcomes of the proposed model that explain fluid flow characteristics and fluid flow characteristics are quantitatively elucidated by tables and displayed graphically. The comparison of two numerical results in the cases are found to be in good agreement, as shown in Tables.

Mathematical modeling of air pollution in working room

Purpose. Development of CFD model and computer code for the analysis and forecasting of the process of formation of areas of chemical contamination in the workplace in the event of an emergency leak of a hazardous substance, allowing to take into account the influence of obstacles and the operation of the ventilation system on this process. The methods. The masstransfer equation is used to calculate the process of formation of areas of chemical contamination in the workplace over time. Navier-Stokes equations are used to solve the problem of aerodynamics – determination of the air flow velocity field in the room. For the numerical solution of modeling equations, finite-difference splitting schemes are used. On the basis of the developed numerical model, a computer code was created for conducting computational experiments Findings. An effective CFD model and computer code were created, which allow to quickly analyze the level of chemical pollution of working areas in possible emergency situations accompanied by the emission of dangerous substances. The results of the computational experiment are presented. The originality. An effective CFD model has been developed, which allows to calculate the dynamics of the formation of areas of chemical air pollution in the workplace in the event of an emergency leak of a chemically hazardous substance Practical implementation. On the basis of the proposed CFD model, a computer code has been developed that allows determining the dynamics of the formation of areas of contamination in the workplace during the emergency emission of hazardous substances. The model can be used to analyze the risk of toxic damage to personnel in the workplace