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Journal articles on the topic 'Mass transfer – Mathematical models'

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Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Dyachok, Vasyl, Roman Dyachok, and Nataliy Ilkiv. "Mathematical Model of Mass Transfer from Lamina of the Leaf into Extractant." Chemistry & Chemical Technology 9, no. 1 (March 15, 2015): 107–10. http://dx.doi.org/10.23939/chcht09.01.107.

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2

Quezada-García, S., G. Espinosa-Paredes, M. A. Polo-Labarrios, E. G. Espinosa-Martínez, and M. A. Escobedo-Izquierdo. "Green roof heat and mass transfer mathematical models: A review." Building and Environment 170 (March 2020): 106634. http://dx.doi.org/10.1016/j.buildenv.2019.106634.

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3

Zhang, Tongwang, Bin Zhao, and Jinfu Wang. "Mathematical models for macro-scale mass transfer in airlift loop reactors." Chemical Engineering Journal 119, no. 1 (June 2006): 19–26. http://dx.doi.org/10.1016/j.cej.2006.03.005.

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4

Fernàndez-Garcia, D., and X. Sanchez-Vila. "Mathematical equivalence between time-dependent single-rate and multirate mass transfer models." Water Resources Research 51, no. 5 (May 2015): 3166–80. http://dx.doi.org/10.1002/2014wr016348.

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5

Kudinov, I. V., and V. A. Kudinov. "Mathematical Models For Meso- And Nano-Domain Heat, Mass, Pulse Transfer Processes." Journal of Physics: Conference Series 891 (November 10, 2017): 012351. http://dx.doi.org/10.1088/1742-6596/891/1/012351.

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6

Assis, Fernanda R., Rui M. S. C. Morais, and Alcina M. M. B. Morais. "Mass Transfer in Osmotic Dehydration of Food Products: Comparison Between Mathematical Models." Food Engineering Reviews 8, no. 2 (May 19, 2015): 116–33. http://dx.doi.org/10.1007/s12393-015-9123-1.

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7

Pyatkov, S. G. "On Evolutionary Inverse Problems for Mathematical Models of Heat and Mass Transfer." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 14, no. 1 (2021): 5–25. http://dx.doi.org/10.14529/mmp210101.

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8

Blynskaya, E. V., S. V. Tishkov, K. V. Alekseyev, and S. V. Minaev. "Mathematical models of the process of submlimationand optimization of lyophilization modes." Russian Journal of Biotherapy 17, no. 3 (November 25, 2018): 20–28. http://dx.doi.org/10.17650/1726-9784-2018-17-3-20-28.

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The purposeof this study is to analyze methods of mathematical modeling for calculating the stage of primary sublimation, as the most important stage in lyophilization technology. Presented are mathematical formulas, equations for the calculation of heat and mass transfer processes, during the removal of 90 % of all frozen ice. A model is considered that takes into account the contribution of all thermal effects, including the transient energy balance, taking into account the heat transfer through the side wall of the vial and radiation, even if they are present in a small amount. The mathematical model can be used to optimize the lyophilization cycle, and also as tools for technological monitoring (using sensors based on models). The model considered in the article is a one-dimensional nonstationary state model in which the correct comprehensive transient energy balance has been introduced to describe the heat transfer through the glass of the vial, and the results are estimated using experimental data. The equations used in the simulation describe the mass and energy balances in the dried layer, taking into account the rate of adsorption/desorption of water at the interface, mass and heat transfer at the sublimation interface, as well as the energy balance of heat transfer in the wall of vials, shelf and other factors affecting the process of sublimation. Conclusions are made on the presented mathematical models and the characteristic of the direction of the process of optimization of primary sublimation in lyophilization technology is given.

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9

Hernandez-Morales, B., and A. Mitchell. "Review of mathematical models of fluid flow, heat transfer, and mass transfer in electroslag remelting process." Ironmaking & Steelmaking 26, no. 6 (December 1999): 423–38. http://dx.doi.org/10.1179/030192399677275.

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10

Gamayunov, N. I., R. A. Ispiryan, and A. V. Klinger. "Construction and identification of mathematical models of heat transfer and mass transfer in capillary-porous bodies." Journal of Engineering Physics 50, no. 2 (February 1986): 224–27. http://dx.doi.org/10.1007/bf00870093.

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11

Khabarov, I. А., V. V. Zhurov, А. N. Zhabayeva, and S. М. Adekenov. "Modeling the extraction process of medicinal raw materials." Bulletin of the Karaganda University. "Chemistry" series 100, no. 4 (December 30, 2020): 135–44. http://dx.doi.org/10.31489/2020ch4/135-144.

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The review considers 26 mathematical models of the process of biologically active substances extraction from medicinal plant raw materials, taking into account factors affecting the extraction process: diffusion coefficient, particle size, layer porosity, extractant feed rate, raw material grinding method, pressure, temperature and duration of extraction, individual characteristics of raw materials (content of the target component) and technological equipment. In general, these models fall into four important groups: empirical models, models based on heat transfer analogies, a shrinking core model, and models based on differential mass bal-ance. Here were described problems that occur in the selection of mathematical models, first of all, associated with the imperfect behavior of the flows of extraction liquids, and the inhomogeneous cross-section of the extraction apparatus. It was shown that first of all the extraction process modeling requires mathematical models to describe the mass transfer inside solid particles. It is also important to take into account the solubility of the target substances when simulating. It is shown that for describing the extraction processes, the optimal models are Naik and Lentz, Esquivel, diffusion, H. Sovová mass transfer, damaged and undamaged cells for calculating the main factors of extraction processes.

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12

Yao, Zhiming, and Marc Le Maguer. "Mathematical modelling and simulation of mass transfer in osmotic dehydration processes. Part I: Conceptual and mathematical models." Journal of Food Engineering 29, no. 3-4 (August 1996): 349–60. http://dx.doi.org/10.1016/0260-8774(95)00045-3.

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13

Teirumnieka, Ērika, Ilmārs Kangro, Edmunds Teirumnieks, and Harijs Kalis. "The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 1 (August 6, 2015): 87. http://dx.doi.org/10.17770/etr2013vol1.833.

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The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

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14

Wäsche, S., H. Horn, and D. C. Hempel. "Mass transfer phenomena in biofilm systems." Water Science and Technology 41, no. 4-5 (February 1, 2000): 357–60. http://dx.doi.org/10.2166/wst.2000.0466.

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Mathematical models allow the simulation of microorganism growth and substrate transport in biofilm systems. Nevertheless there is still a lack of knowledge about the mass transfer of substrate in the boundary layer between biofilm and bulkphase. Several biofilms were cultivated under different substrate and hydrodynamic conditions in a biofilm tube reactor. Oxygen concentration profiles were measured with oxygen microelectrodes in the biofilm and in the boundary layer. The thickness of the concentration layer was found to depend on surface structure which depends on the substrate loading and the hydrodynamic conditions during the growth phase of the biofilm. Biofilm density and maximum substrate flux were also influenced by growth conditions. An empirical function for the concentration layer thickness was formulated for biofilms grown under different conditions to describe transport phenomena in the boundary layer.

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15

Zhao, Yu Qing, and Zhi Yong Li. "Evaporation Tower Heat and Mass Transfer Research in Saline Water Evaporation System." Advanced Materials Research 838-841 (November 2013): 1923–27. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.1923.

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In order to recycle the salt in industrial waste water, non-filler evaporation tower is used to evaporate and concentrate saline water. Based on the heat and mass transfer theory, developed a mathematical model of evaporation tower. Experiment results showed that difference of the export air dry bulb temperature values between models calculated and tested is within 5%. It is proves the correctness of the mathematical model.

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16

Chovnyuk, Yuriy, Petro Cherednichenko, Vladimir Kravchyuk, and Olga Ostapushchenko. "MASS TRANSFER PROCESSES DURING CORROSION OF CEMENT CONCRETE OF ROAD PAVEMENT AND AIRFIELD COVERINGS MODELING." Current problems of architecture and urban planning, no. 58 (November 30, 2020): 291–301. http://dx.doi.org/10.32347/2077-3455.2020.58.291-301.

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Varieties of corrosion processes under the action of various corrosive environments on the cement concretes for pavement and airfield coatings within the classification by V.M. Moskvin are considered and their distinctive features are described. It is noted in the work that the rate of destruction of cement concretes is determined by the processes of mass transfer and chemical reactions. On this basis, we provide the substantiation of a generalized methodological approach to modeling the processes of mass transfer during liquid corrosion of building materials. For corrosion types I and II, analytical solutions are obtained for specific initial and boundary conditions of the problem. Development of mathematical models of concrete corrosion processes is based on the physical models of diffusion of components that are imbedded in the porous structure of concrete and the mathematical apparatus of boundary problems of mass transfer using differential equations in partial derivatives of parabolic type. The works, to which the authors refer, provide the results of the development of mathematical models of the processes of corrosion of concrete of the first type, as well as the results of the practical application of these mathematical models. However, the results obtained cannot withstand scrutiny in terms of methods and approaches of classical mathematical physics. In this study, these errors, inaccuracies, inconsistencies and incorrectness of the abovementioned works are eliminated. At the same time, models of corrosion of concretes of the first and second types are taken into account. An undoubtedly positive aspect of the dependences obtained in the study is the possibility of solving the inverse problem, when the actual experimental data using this model make it possible to predict the numerical values of free calcium hydroxide, which, as a result, with a minimum error allows to predict the long-term durability of structures and buildings.

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17

Bulavatskiy, Vladimir M. "Some Mathematical Models of Geoinformatics for Describing Mass Transfer Processes under Time-Nonlocal Conditions." Journal of Automation and Information Sciences 43, no. 6 (2011): 49–59. http://dx.doi.org/10.1615/jautomatinfscien.v43.i6.50.

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18

LAM, KEI FONG, and HAO WU. "Thermodynamically consistent Navier–Stokes–Cahn–Hilliard models with mass transfer and chemotaxis." European Journal of Applied Mathematics 29, no. 4 (October 9, 2017): 595–644. http://dx.doi.org/10.1017/s0956792517000298.

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We derive a class of Navier–Stokes–Cahn–Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier–Stokes analogues of earlier Cahn–Hilliard–Darcy models proposed for modelling tumour growth, and are derived based on a volume-averaged velocity, which yields simpler expressions compared to models derived based on a mass-averaged velocity. Then, we perform mathematical analysis on a simplified model variant with zero excess of total mass and equal densities. We establish the existence of global weak solutions in two and three dimensions for prescribed mass transfer terms. Under additional assumptions, we prove the global strong well-posedness in two dimensions with variable fluid viscosity and mobilities, which also includes a continuous dependence on initial data and mass transfer terms for the chemical potential and the order parameter in strong norms.

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19

Kan, An Kang, Hou De Han, and Quan Ping Duan. "Heat and Mass Transfer of Cabbage in Vacuum Cooling and Experimental Research." Key Engineering Materials 467-469 (February 2011): 680–85. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.680.

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The pre-cooling device was built and the columnar cabbage was taken as the study object in this paper. The heat and mass transfer mathematical models for the cylindrical shape vegetable were built and the experimental method was introduced to prove them. The comparison and analysis, under the certain vacuum degree of the vacuum chamber, was done between the simulation and the experiment. And the differences of the vacuum degree in the chamber, the temperature change of the cabbage, the relative humidity in the chamber and the cabbage mass loss, in the experiment and the simulation, were all recorded. The reason of the parameters variance and existent deference was also analyzed in this paper. The mathematical models and the result were useful for the study on the cylindrical vegetable vacuum pre-cooling technology.

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20

Andronov, I. L. "Multiple Time Scales in Cataclysmic Variables: Observations Vs. Mathematical Models." Highlights of Astronomy 11, no. 1 (1998): 375. http://dx.doi.org/10.1017/s1539299600021250.

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Theoretical models and observational evidence for various processes in magnetic cataclysmic variables are briefly reviewed. Among them: modulation of the accretion rate by the magnetic field of the white dwarf; excitation of the orientation change of the magnetic axis of the white dwarf with respect to the secondary; structure of the accretion column and its instability; mass and angular momentum transfer; magnetic activity of the secondary; high/low luminosity state transitions; QPO’s, ”shot noise” and ”red noise” in polars, intermediate polars and nova-like objects.

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21

LOGINOVA, SVETLANA A., and ILYA N. GOGLEV. "MODELING THE KINETICS AND DYNAMICS OF MASS TRANSFER DURING VARIOUS TYPES OF CEMENT CONCRETE CORROSION." Cherepovets State University Bulletin 6, no. 99 (2020): 22–35. http://dx.doi.org/10.23859/1994-0637-2020-6-99-2.

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The article describes the features of various types of cement concrete corrosion: liquid, acid and biological corrosion, which are most often detected at the stage of inspection of concrete and reinforced concrete building struc-tures. The authors consider the possibility of using methods of mathematical modeling appli-cable to corrosion processes, which will deter-mine the intensity of mass transfer and predict the service life of concrete and reinforced con-crete structures. Mathematical models for cor-rosion of the 1st and 2nd types are given, which allow calculating the concentration of “free” calcium hydroxide depending on the thickness of the concrete structure. These mathematical models also allow us to determine the concen-tration of the transferred target component in a liquid acid-salt medium and find the average value of the concentration at any time. One of the important differences of the considered mathematical model for acid corrosion is its dependence on the concentration of the target component in the liquid phase...

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22

Larbi, Salah. "Heat and Mass Transfer with Condensation in Capillary Porous Bodies." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/194617.

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The purpose of this present work is related to wetting process analysis caused by condensation phenomena in capillary porous material by using a numerical simulation. Special emphasis is given to the study of the mechanism involved and the evaluation of classical theoretical models used as a predictive tool. A further discussion will be given for the distribution of the liquid phase for both its pendular and its funicular state and its consequence on diffusion coefficients of the mathematical model used. Beyond the complexity of the interaction effects between vaporisation-condensation processes on the gas-liquid interfaces, the comparison between experimental and numerical simulations permits to identify the specific contribution and the relative part of mass and energy transport parameters. This analysis allows us to understand the contribution of each part of the mathematical model used and to simplify the study.

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23

Galiullina, N. E., and M. G. Khramchenkov. "Mathematical Models of Mass Transfer Processes in Soils with Account for Their Interaction with Rainfall." Journal of Engineering Physics and Thermophysics 90, no. 4 (July 2017): 817–25. http://dx.doi.org/10.1007/s10891-017-1630-x.

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24

Jia, Yong Ying, and Zhi Guo Wang. "The Study of Coupled Transfer of Heat, Moisture and Air in Reservoir Porous Media." Applied Mechanics and Materials 271-272 (December 2012): 1195–200. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.1195.

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This paper studied on heat and mass transfer mechanism of steam in reservoir porous media, built coupled mathematical models for heat and mass transfer in reservoir porous media. “Black box model” and “white box model” are first proposed in heat and mass process analysis of reservoir porous media. Temperature field has been simulated by CMG-STARS software. Our work will give theoretical basis and technical support for enhanced oil recovery technology.

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25

El-Din, M. G., and D. W. Smith. "Ozone mass transfer in water treatment: hydrodynamics and mass transfer modeling of ozone bubble columns." Water Supply 1, no. 2 (March 1, 2001): 123–30. http://dx.doi.org/10.2166/ws.2001.0029.

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Most of the mathematical models that are employed to model the performance of bubble columns are based on the assumption that either plug flow or complete mixing conditions prevail in the liquid phase. Although due to the liquid-phase axial dispersion, the actual flow pattern in bubble columns is usually closer to being mixed flow rather than plug flow, but still not completely mixed flow. Therefore, the back flow cell model (BFCM), that hypothesises both back flow and exchange flow to characterise the liquid-phase axial dispersion, is presented as an alternative approach to describe the hydrodynamics and mass transfer of ozone bubble columns. BFCM is easy to formulate and solve. It is an accurate and reliable design model. Transient BFCM consists of NBFCM ordinary-first-order differential equations in which NBFCM unknowns (Yj) are to be determined. That set of equations was solved numerically as NBFCM linear algebraic equations. Steady-state BFCM consists of 3 × NBFCM non-linear algebraic equations in which 3 × NBFCM unknowns (qG,j, Xj, and Yj) are to be determined. Those non-linear algebraic equations were solved numerically using Newton–Raphson technique. Steady-state BFCM was initially tested using the pilot-scale experimental data of Zhou. BFCM provided excellent predictions of the dissolved ozone profiles under different operating conditions for both counter and co-current flow modes.

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26

Morgenroth, E., H. J. Eberl, M. C. M. van Loosdrecht, D. R. Noguera, G. E. Pizarro, C. Picioreanu, B. E. Rittmann, A. O. Schwarz, and O. Wanner. "Comparing biofilm models for a single species biofilm system." Water Science and Technology 49, no. 11-12 (June 1, 2004): 145–54. http://dx.doi.org/10.2166/wst.2004.0826.

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A benchmark problem was defined to evaluate the performance of different mathematical biofilm models. The biofilm consisted of heterotrophic bacteria degrading organic substrate and oxygen. Mathematical models tested ranged from simple analytical to multidimensional numerical models. For simple and more or less flat biofilms it was shown that analytical biofilm models provide very similar results compared to more complex numerical solutions. When considering a heterogeneous biofilm morphology it was shown that the effect of an increased external mass transfer resistance was much more significant compared to the effect of an increased surface area inside the biofilm.

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27

Eshbaev, Ulbosin, Akbarjon Nishonov, and Aziz Saodatov. "Development of mathematical models of print quality by Box-Wilson." E3S Web of Conferences 304 (2021): 03023. http://dx.doi.org/10.1051/e3sconf/202130403023.

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The transfer coefficient of ink to the printed material was determined by comparing the mass of the printed material before and after printing. The specifics of the interaction of the printed surface with the surface of the paint layer and the influence of technological factors on the graphic distortion of the image when printing on paper also affect the gradation characteristic of the image. This article states about static modeling, preliminary analysis of the color perception of offset printing on papers including synthetic polymers. On the basis of the model of color perception obtained as a result of research in offset printing on printed materials, the optimal choice is developed, which allows to make an objective assessment and predict the color perception of the printed materials.

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28

Huang, Feng, Nan Deng, Qiaoling Li, Bin Li, Ruilin Hu, Miao Liang, Dengshan Luo, and Le Wang. "Simulation of Heat and Mass Transfer of Cut Tobacco in a Batch Rotary Dryer by Multi-Objective Optimization." Beiträge zur Tabakforschung International/Contributions to Tobacco Research 29, no. 3 (December 1, 2020): 145–55. http://dx.doi.org/10.2478/cttr-2020-0013.

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Summary To simulate the drying process of cut tobacco in a batch rotary dryer, six different models of equilibrium moisture content were selected to calculate the driving force of mass transfer, and a mathematical model of heat and mass transfer was numerically solved. The multi-objective nonlinear problem of heat and mass transfer coefficients was optimized by employing a weight factor. The simulation results showed that the weight factor r was an important parameter for fitting results of moisture content and temperature. The model evaluation indices almost reached their minimal values with r at 0.1. For all the six equilibrium/classic models the fit was better for moisture content than for temperature. One model (M-Hen/C) was superior to other equilibrium/classic models and the REA (reaction engineering approach) model. This study aims for an understanding of heat and mass transfer in the tobacco drying process, and provides a theoretical framework to support the prediction of temperature and moisture in various drying situations.

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29

Bondarenko, V. I., V. V. Bilousov, F. V. Nedopekin, and J. I. Shalapko. "The Mathematical Model of Hydrodynamics and Heat and Mass Transfer at Formation of Steel Ingots and Castings." Archives of Foundry Engineering 15, no. 1 (March 1, 2015): 13–16. http://dx.doi.org/10.1515/afe-2015-0003.

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Abstract The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.

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Pacak, Anna, Demis Pandelidis, and Sergey Anisimov. "Mathematical modelling of solid desiccant systems." ITM Web of Conferences 23 (2018): 00029. http://dx.doi.org/10.1051/itmconf/20182300029.

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In this study, the mathematical model equations for solid desiccant system integrated with indirect evaporative coolers with Maisotsenko - Cycle are presented. The authors chose the modified ε–NTU method to describe heat and mass transfer processes in regenerative indirect evaporative cooler and desiccant wheel. The models based on the ε–NTU method show satisfactory agreement with experimental results. That is why this method allows to analyze and develop the performance of solid desiccant systems. In this study, the models allowed to prove that solid desiccant system with an additional heat exchanger before the desiccant wheel (System 1) obtains higher thermal COP values, higher humidity ratio drop and lower supply airflow temperatures in comparison to system with only one heat exchanger after the desiccant wheel (System 2).

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31

Basuki, Kris Tri. "MATHEMATICAL MODELING FOR THE EXTRACTION OF URANIUM AND MOLYBDENUM WITH EMULSION LIQUID MEMBRANE, INCLUDING INDUSTRIAL APPLICATION AND COST EVALUATION OF THE URANIUM RECOVERY." Jurnal Forum Nuklir 2, no. 1 (May 1, 2008): 63. http://dx.doi.org/10.17146/jfn.2008.2.1.3284.

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MATHEMATICAL MODELING FOR THE EXTRACTION OF URANIUM AND MOLYBDENUM WITH EMULSION LIQUID MEMBRANE, INCLUDING INDUSTRIAL APPLICATION AND COST EVALUATION OF THE URANIUM RECOVERY. Emulsion liquid membrane systems are double emulsion drops. Two immiscible phases are separated by a third phase which is immiscible with the other two phases. The liquid membrane systems were classified into two types: (1) carrier mediated mass transfer, (2) mass transfer without any reaction involved. Uranium extraction, molybdenum extraction and solvent extraction were used as purposed elements for each type of the membrane systems in the derivation of their mathematical models. Mass transfer in emulsion liquid membrane (ELM) systems has been modeled by several differential and algebraic equations. The models take into account the following : mass transfer of the solute from the bulk external phase to the external phase-membrane interface; an equilibrium reaction between the solute and the carrier to form the solute- carrier complex at the interface; mass transfer by diffusion of the solute-carrier complex in the membrane phase to the membrane-internal phase interface; another equilibrium reaction of the solute-carrier complex to release the solute at the membrane-internal phase interface into the internal phase. Models with or without the consideration of film resistances were developed and compared. The models developed in this study can predict the extraction rate through emulsion liquid membranes theoretically. All parameters required in the models can be determined before an experimental extraction run. Experimental data from literature (uranium extraction) and (molybdenum extraction and solvent extraction) were used to test the models. The agreements between the theoretical predictions and the experimental data were very good. The advantages of emulsion liquid membrane systems over traditional methods were discussed. The models developed in this research can be used directly for the design of emulsion liquid membrane systems. The results of this study represent a very significant step toward the practical applications of the emulsion liquid membrane technology.

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32

Ristanto, Sigit, and Choirul Huda. "Pemodelan Transfer Panas dan Massa pada Proses Pengeringan Biji-Bijian Sistem Rak Beserta Solusi Numeriknya." Jurnal Ilmiah Pendidikan Fisika Al-Biruni 5, no. 2 (October 27, 2016): 153. http://dx.doi.org/10.24042/jpifalbiruni.v5i2.115.

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Modeling of heat and mass transfer determine the form of mathematical equations obtained. The aim of this study was to obtain heat and mass transfer equation based on modeling has been prepared and finished using numerical methods. The study starts from determining assumptions, construction of models, make up the mathematical equation of heat and mass transfer, determine the type of numerical methods used, complete the heat and mass transfer equations using numerical methods that have been chosen. Grains as the dried thing modeled as porous bodies. The results shows that the numerical solutions have been successfully made with a series of requirements that must be met to stability.Pemodelan transfer panas dan massa menentukan bentuk persamaan matematis yang diperoleh. Tujuan penelitian ini adalah memperoleh persamaan transfer panas dan massa berdasarkan pemodelan yang telah disusun lalu menyelesaikannya menggunakan metode numerik.Tahapan penelitian dimulai dari menentukan asumsi-asumsi, menyusun model, menyusun persamaan matematis transfer panas dan massa, menentukan jenis metode numerik yang digunakan, menyelesaikan persamaan transfer panas dan massa menggunakan metode numerik yang telah dipilih.Biji-bijian sebagai benda yang dikeringkan dimodelkan sebagai benda porous. hasil penelitian menunjukkan bahwa solusi numerik telah berhasil disusun beserta serangkaian syarat kesetabilan yang harus dipenuhi.

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33

Susanti, Ari Diana, Wahyudi Budi Sediawan, Sang Kompiang Wirawan, and Budhijanto Budhijanto. "Mathematical Modelling of Micronutrient Recovery from Vegetable Oil by Silica-based Adsorption: Vitamin E from Palm Fatty Acid Distillate." Equilibrium Journal of Chemical Engineering 1, no. 1 (January 10, 2017): 15. http://dx.doi.org/10.20961/equilibrium.v1i1.40363.

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Mathematical modelling on kinetics of batch adsorption of vitamin E separation from palm fatty acid distillate (PFAD) has been set-up and then applied for literature experimental data. Since the sizes of adsorbent particles used are usually relatively small, the concentration in the particles is assumed to be uniform. Hence, the adsorption rate is controlled by the rate of solute mass transfer from the bulk fluid to the surface of particles. In this model, the rate of mass transfer is assumed to be proportional to the concentration deviation from the equilibrium state. Meanwhile, the equilibrium models applied were coefficient distribution, Freundlich, and Langmuir with the values of the parameters obtained from literature data. It turned out that the model set-up can quantitatively describe the experimental kinetics data from literature. The value of mass transfer coefficient per unit adsorbent mass (kca) is obtained by curve fitting. It is also observed that the model proposed quantitatively describes the batch adsorption process well. The three equilibrium models applied are suitable for the mathematical modelling. Adjustment of the values of equilibrium isotherm parameters from literature significantly improves the accuracy of the model.

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34

Krioukov, V. G., and F. K. Khaliullin. "MATHEMATICAL MODELING OF HYDRODYNAMIC AND MASS-TRANSFER PROCESSES IN THE EXTRACTOR “CROWN-MODEL”." Transactions of Academenergo 56 (September 2019): 16–38. http://dx.doi.org/10.34129/2070-4755-2019-56-3-16-38.

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35

Goreshnev, M., and E. Litvishko. "Math Modeling of Vacuum Conductive Timber Drying." Advanced Materials Research 1040 (September 2014): 478–83. http://dx.doi.org/10.4028/www.scientific.net/amr.1040.478.

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The article is devoted to the mathematical modeling of vacuum conductive timber drying. Analysis of known mathematical models allowed revealing their advantages and disadvantages. The modeling block diagram based on the drying periods is proposed. Lykov’s equations have been selected to solve heat and mass transfer problems. The comparison of experimental and calculated data has been conducted.

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Štefan, Radek, and Jaroslav Procházka. "Modelling of Hygro-Thermal Processes in Steel-Concrete Composite Columns Exposed to High Temperatures." Solid State Phenomena 249 (April 2016): 246–52. http://dx.doi.org/10.4028/www.scientific.net/ssp.249.246.

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In the paper, transport processes in heated steel-concrete composite columns are analyzed. Mathematical models of heat transfer and coupled heat and mass transfer are described with respect to the specific parameters of composite structures. Numerical formulations of the models are implemented into MATLAB environment and the applicability of the models is depicted on an illustrative example. It is shown that not only the thermal distribution, but also the moisture migration as well as the pore pressure built-up are of particular interest.

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Setford, Patrick, David Jeffery, Paul Grbin, and Richard Muhlack. "Modelling the Mass Transfer Process of Malvidin-3-Glucoside during Simulated Extraction from Fresh Grape Solids under Wine-Like Conditions." Molecules 23, no. 9 (August 27, 2018): 2159. http://dx.doi.org/10.3390/molecules23092159.

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Extraction of grape components is a key consideration for red winemaking. The impact of changing process variables on mass transfer properties of anthocyanins from fresh pre-fermentative red grape solids under forced convective conditions was explored using the dominant red grape anthocyanin, malvidin-3-glucoside (M3G) as a model solute. A two level full factorial design was implemented to investigate effects of temperature, sugar and ethanol on mass transfer properties. Factor levels were chosen to simulate conditions found at various points during the maceration and fermentation steps of the red winemaking process. A rigorous mathematical model was developed and applied to experimental extraction curves, allowing the separation of mass transport properties in liquid and solid phases in a wine-like system, for the first time. In all cases, the coefficient of determination exceeded 0.92, indicating good agreement between experimental and mathematically-solved M3G concentrations. For the conditions studied, internal mass transfer was found to limit M3G extraction and changes to the liquid phase composition and temperature influence the distribution constant. Surface response models of mass transfer parameters were developed to allow future simulations of fermentation scenarios aimed at maximising the extraction potential of M3G.

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Pereira, E. M. A., J. V. Silva, T. H. F. Andrade, S. R. de Farias Neto, and A. G. Barbosa de Lima. "Simulating Heat and Mass Transfer in Drying Process: Applications in Grains." Diffusion Foundations 3 (February 2015): 3–18. http://dx.doi.org/10.4028/www.scientific.net/df.3.3.

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The objective of this study was to investigate numerically heat and mass transport during drying of grains with particular reference to bean and rough rice. The proposed mathematical models based on the Fick’s and Fourier’s Laws consider constant physical properties and convective boundary condition at the surface of the solid. The solutions of the governing equations were performed using ANSYS CFX®software. The grains were regarded as an ellipsoid of revolution. Results of the drying and heating kinetics and moisture content and temperature distributions in the grains along the drying process are presented and analyzed.

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Xie, Yao Zhong, De Jun Fei, Ya Gu Dang, and Jian Xun Wu. "Mathematical Modeling of Chromium(Ш) Extraction by Emulsion Liquid Membrane." Advanced Materials Research 791-793 (September 2013): 315–19. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.315.

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Advancing front model, carrier-facilitated transfer model and reversible reaction model were applied to simulate extracting chromium (Ш) from wastewater by emulsion liquid membrane using di-(2-ethylhexyl) phosphoric acid as carrier and Span-80 as surfactant. Parameters of the mathematic models were gained from the designed experiments, and the reversible reaction model can be used with a reasonably accuracy as estimates of chromium (Ш) permeation. The experimental results demonstrate that the role of reversibility of the chemical reaction between internal phase and membrane phase should be considered, and the diffusion resistance is the primary resistance of the mass transfer process.

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Yunusnova, Toshkenboyevna, Sayyora, Davron Holmatov, Abdalimovich, Muhiddin Atajonov, Odiljonovich, and Ulugjon Huzanazarov. "FORMALIZATION OF THE COTTON DRYING PROCESS BASED ON HEAT AND MASS TRANSFER EQUATIONS." IIUM Engineering Journal 21, no. 2 (July 4, 2020): 256–65. http://dx.doi.org/10.31436/iiumej.v21i2.1456.

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The paper deals with the construction of a mathematical model of the cotton drying process, taking into account the thermal and mass transfer properties of raw cotton components. To determine changes in the temperature of the fibre and raw cotton seeds, the application of Fourier's law is proposed. The mathematical dependence of the change on the humidity of the cotton fibre and seeds along the length of the drum is determined. The rational value of the heat agent consumption in the process of drying raw cotton is also determined. Research methods are based on the provisions of modern trends in management theory and identification. Mathematical models are constructed using analytical methods and equations that describe the physical properties of an object. Methods for constructing a mathematical model usually rely on experimental methods, in particular, the method of acceleration curves, and as a result, the mathematical description becomes a priori inaccurate. It is shown that the mathematical model used is quite adequate for the dynamics of a real object, fully describes it, and characterizes it over the entire range of changes. The analysis of the developed mathematical model based on simulation showed the adequacy of the obtained mathematical dependence of the temperature regime of the cotton drying process with the consumption of heat agent. ABSTRAK: Kajian ini membincangkan tentang penciptaan model matematik bagi proses pengeringan kapas, dengan mengambil kira terma dan sifat-sifat pindah jisim komponen kapas mentah. Bagi mendapatkan perubahan suhu fabrik dan biji benih kapas mentah, penggunaan hukum Fourier telah dicadangkan. Kebergantungan matematik pada perubahan kelembapan fabrik kapas dan biji benih sepanjang drum telah diperolehi. Nilai bersesuaian menggunakan ejen haba dalam proses pengeringan kapas kering mentah didapati. Kaedah kajian berdasarkan tren moden dalam teori pengurusan dan pengenalpastian. Model matematik dibina dengan menggunakan kaedah analisis dan persamaan yang menerangkan ciri-ciri fizikal pada objek. Kaedah bagi membina model matematik selalunya bergantung pada kaedah eksperimen, khususnya, kaedah pecutan melengkung, dan hasilnya, penyataan penaakulan matematik menjadi tidak tepat. Model matematik yang digunakan adalah cukup bagi objek dinamik sebenar, dengan penerangan penuh dan perincian ke atas keseluruhan perubahan. Analisis model matematik yang terhasil berdasarkan simulasi, dilihat cukup kebergantungan matematik terhasil melalui proses pengeringan kapas pada aturan suhu dengan ejen haba.

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Ochoa-Martínez, C. I., and A. Ayala-Aponte. "MODELOS MATEMÁTICOS DE TRANSFERENCIA DE MASA EN DESHIDRATACIÓN OSMÓTICA MATHEMATICAL MODELS OF MASS TRANSFER IN OSMOTIC DEHYDRATION MODELOS MATEMÁTICOS DE TRANSFERENCIA DE MASA EN DESHIDRATACIÓN OSMÓTICA." Ciencia y Tecnologia Alimentaria 4, no. 5 (July 2005): 330–42. http://dx.doi.org/10.1080/11358120509487660.

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Zhao, Shibo, Yonghui Zhang, Yunqi Nie, Pengyu Qu, and Wenqiang Sun. "Performance of an internet data center refrigeration system using an evaporative cooler." E3S Web of Conferences 194 (2020): 01027. http://dx.doi.org/10.1051/e3sconf/202019401027.

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The traditional refrigeration method of internet data center (IDC) is mostly air refrigeration, which has undesired cooling effect and high power consumption. This study addresses this problem and proposes an evaporative air cooler (EAC) suitable for IDC. Given the high specific heat capacity of water, the evaporative condensing coil and spray device are added to the evaporative cooler to enhance the heat transfer effect. Heat and mass transfer mathematical models are established to analyze the heat transfer performance. The mathematical model is used to simulate the profile of the heat and mass transfer coefficient of the EAC with the amount of spray water and air flow. The results show that when the air flow changes from 10 to 20 kg/s, the air equivalent heat transfer coefficient increases by about 41%. When the air flow rate is 20 kg/s and the spray water volume is 0.00124 kg/(mꞏs), the total heat transfer coefficient is increased by about 308% compared with the case without spray water.

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Baranchuk, Vladislav A., and Sergey G. Pyatkov. "On some classes of inverse problems with point overdirection for mathematical models of heat and mass transfer." Yugra State University Bulletin 16, no. 3 (January 28, 2021): 36–46. http://dx.doi.org/10.17816/byusu2020336-46.

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The paper considers the question of the correctness in Sobolev spaces of inverse problems of recovering the function of sources of a special form for mathematical models of convection-diffusion and heat and mass transfer. Unknown time-dependent functions are included in the source function. The values of the solution in a certain set of points of the region lying both inside the region and on its boundary are considered as conditions for redefining. Conditions are given that guarantee the global correctness of the problem in Sobolev classes. The conditions for these tasks are minimal. The results are accurate.

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钱, 文斌. "A Review on the Mathematical Models about the Mass Transfer Mechanism in Static and Kinetic Adsorption Processes." Hans Journal of Chemical Engineering and Technology 09, no. 03 (2019): 288–97. http://dx.doi.org/10.12677/hjcet.2019.93041.

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Marin, Pricila, Carlos Eduardo Borba, Aparecido Nivaldo Módenes, Fernando R. Espinoza-Quiñones, Silvia Priscila Dias de Oliveira, and Alexander Dimitrov Kroumov. "Determination of the mass transfer limiting step of dye adsorption onto commercial adsorbent by using mathematical models." Environmental Technology 35, no. 18 (April 9, 2014): 2356–64. http://dx.doi.org/10.1080/09593330.2014.904445.

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Nadolin, K. A. "On a Family of Mathematical Models of Adequate Complexity, Describing Passive Mass Transfer in Calm Streambed Flowes." Bulletin of Irkutsk State University. Series Mathematics 31 (2020): 34–48. http://dx.doi.org/10.26516/1997-7670.2020.31.34.

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Łapka, Piotr, Michał Wasik, Piotr Furmański, Mirosław Seredyński, Łukasz Cieślikiewicz, Karol Pietrak, Michał Kubiś, Tomasz S. Wiśniewski, and Maciej Jaworski. "Preliminary mathematical and numerical transient models of convective heating and drying of a brick." MATEC Web of Conferences 240 (2018): 01022. http://dx.doi.org/10.1051/matecconf/201824001022.

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The paper presents the initial approach to mathematical and numerical modelling and optimization of heat and mass transfer in elements of the masonry wall. The considered single moist brick is placed in the channel through which the dry air is flowing. Only one wall of the brick is in contact with the flowing air and through this boundary heat and moisture are exchanged. The non-equilibrium mathematical model is formulated for general case with three phases of moisture present in the porous building material, i.e., water vapour in the moist air filling the pores, liquid water (bound water) adsorbed at the surface of the solid component of the material and free liquid water either in a discontinuous form (funicular) or continuous one (pendular). However, at this stage of development of the numerical model the moisture in the form of motionless liquid water and water vapour which reside in the ceramic material are considered. Moreover, the moisture and heat diffusion in the porous hydroscopic material of the brick as well as moisture and heat convection in the flowing air are assumed. The numerical model is developed with the aid of the commercial software ANSYS Fluent and its advanced customisation functionalities like the User-Defined Function, User-Defined Scalar and User-Defined Memory. Subsequently, investigation of the influence of the mass transfer coefficient between the free liquid water and moist air in the porous building material are carried out.

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Galaction, Anca Irina, Roxana Rotaru, and Dan Cascaval. "Glucose Mass Transfer Under Substrate Inhibition Conditions in a Stationary Basket Bioreactor with Immobilized Yeast Cells." International Journal of Chemical Reactor Engineering 10, no. 1 (January 3, 2012): 1–13. http://dx.doi.org/10.2202/1542-6580.2644.

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The work is dedicated to the study on the external and internal mass transfers of glucose for alcoholic fermentation under glucose inhibition limitation using a bioreactor with stationary basket beds of immobilized Saccharomyces cerevisiae cells. By means of the substrate mass balance for a single particle of biocatalysts, considering the kinetic model adapted for the inhibitory effect of glucose, specific mathematical models have been developed for describing the profiles of the substrate concentration in the outer and inner regions of biocatalysts and, implicitly, for estimating its mass flows in the liquid boundary layer surrounding the particle and inside the particle. The values of the mass flows are significantly influenced by the internal diffusion velocity of substrate and rate of the biochemical reaction of substrate consumption, but also by the position inside the basket bed. These influences cumulated led to the appearance of biological inactive region near the particle centre, its magnitude varying from 0.34 to 31% from the overall volume of particles. The presented results are the first unitary approach of the aspects of substrate mass transfer in a basket bed of immobilized biocatalysts, the proposed models being original and complex.

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Rotko, V. V. "INVERSE PROBLEMS FOR MATHEMATICAL MODELS WITH THE POINTWISE OVERDETERMINATION." Yugra State University Bulletin 14, no. 3 (December 15, 2018): 57–66. http://dx.doi.org/10.17816/byusu2018057-66.

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In the article we examine well-posedness questions in the Sobolev spaces of an inverse source problem in the case of a quasilinear parabolic system of the second order. These problem arise when describing heat and mass transfer, diffusion, filtration, and in many other fields. The main part of the operator is linear. The unknowns occur in the nonlinear right-hand side. In particular, this class of problems includes the coefficient inverse problems on determinations of the lower order coefficients in a parabolic equation or a system. The overdetermination conditions are the values of a solution at some collection of points lying inside the spacial domain. The Dirichlet and oblique derivative problems under consideration. The problems are studied in a bounded domain with smooth boundary. However, the results can be generalized to the case of unbounded domains as well for which the corresponding solvability theorems hold. The conditions ensuring local (in time) well-posedness of the problem in the Sobolev classes are exposed. The conditions on the data are minimal. The results are sharp. The problem is reduced to an operator equation whose solvability is proven with the use of a priori bounds and the fixed point theorem. A solution possesses all generalize derivatives occurring in the system which belong to the space with and some additional necessary smoothness in some neighborhood about the overdetermination points.

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Glushkov, Dmitrii O., and Pavel A. Strizhak. "Mathematical Modeling of Heat and Mass Transfer Processes with Chemical Reaction at Polymeric Material Ignition by Several Small-Size Hot Particles." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/614143.

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Numerical research of interconnected heat and mass transfer processes in the “two hot particles—polymeric material—air” system was executed. The joint effect of several local heat sources on the main integrated characteristic of ignition process (ignition delay time) was established. Two ignition models characterized by the relative positioning of hot particles on a polymeric material surface were revealed. Besides, there were established characteristics of local heat sources and the distance between them (700 K<Tp<1150 K andL>1.5orTp>1150 K and0.25<L<1.5)when regularities of heat and mass transfer processes in the “two hot particles—polymeric material—air” system are similar to regularities of heat and mass transfer processes in the “single hot particle—polymeric material—air” system.

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