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Journal articles on the topic 'Chemical engineering – Mathematical models'

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Published: 4 June 2021

Last updated: 29 January 2023

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1

Kurpatenkov, A. V., V. M. Polyaev, and A. L. Sintsov. "Mathematical models of transpiration cooling." Journal of Engineering Physics 53, no. 2 (August 1987): 914–19. http://dx.doi.org/10.1007/bf00872416.

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2

Orazbayev, B. B., K. N. Orazbayeva, and B. E. Utenova. "Development of mathematical models and modeling of chemical engineering systems under uncertainty." Theoretical Foundations of Chemical Engineering 48, no. 2 (March 2014): 138–47. http://dx.doi.org/10.1134/s0040579514020092.

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3

Maksimova, Nadezhda N. "INVESTIGATION OF MATHEMATICAL MODELS OF THE CHEMICAL REACTIONS KINETICS." Messenger AmSU, no. 97 (2022): 6–12. http://dx.doi.org/10.22250/20730268_2022_97_6.

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4

Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Numerical Investigation of Brusselator Chemical Model by Residual Function Using Mathematica Software." Journal of Computational and Theoretical Nanoscience 17, no. 7 (July 1, 2020): 2947–54. http://dx.doi.org/10.1166/jctn.2020.9324.

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In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathematica software includes Adams method, Backward differential formula (BDF) and Implicit Runge-Kutta method which works well on stiff systems. The graphical results are on interval of 0 ≤ t ≤ 30.

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5

Oliveri, Hadrien, and Alain Goriely. "Mathematical models of neuronal growth." Biomechanics and Modeling in Mechanobiology 21, no. 1 (January 7, 2022): 89–118. http://dx.doi.org/10.1007/s10237-021-01539-0.

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AbstractThe establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

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6

Dul'nev, G. N., and P. A. Korenev. "Synthesis of thermostating devices. II. Mathematical models." Journal of Engineering Physics 51, no. 4 (October 1986): 1243–49. http://dx.doi.org/10.1007/bf00870856.

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7

Prishchenko, Olga, Nadezhda Cheremskaya, Tetyana Chernogor, and Svetlana Bukhkalo. "INNOVATIVE METHODS OF TEACHING THE DISCIPLINE HIGHER MATHEMATICS TO STUDENTS STUDYING CHEMICAL TECHNOLOGY AND ENGINEERING." Bulletin of the National Technical University "KhPI". Series: Innovation researches in students’ scientific work, no. 1 (October 2, 2022): 30–37. http://dx.doi.org/10.20998/2220-4784.2022.01.05.

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The article discusses some innovative methods that can be used in practical classes in higher mathematics, teaching students of chemical specialties. The possibilities for the development of competencies in complex interuniversity projects are closely related to the issues of classifying all types of interrelationships of disciplines within the framework of courses according to curricula, as well as the choice of additional universal competencies. Mathematics for chemical process engineers is, first of all, a useful tool for solving many chemical and technological problems and tasks. The typical curriculum takes into account the modern needs of related and special disciplines in the mathematical education of students, and consists of four main sections: the foundations of algebra and analytical geometry, mathematical analysis, differential equations, probability theory and mathematical statistics. When writing the article, many years of experience in teaching students of chemical specialties by the department 'Higher Mathematics' of the National Technical University «KhPI» were used. The purpose of the scientific research of teachers and students presented in the article is to increase the competitiveness of Ukrainian technical education in the world market by developing and implementing innovative models and methods. When writing this article, the authors pursued three goals. First, to give the general course of mathematics for students of chemical and related specialties an appropriate professional orientation; secondly, to form in students of the first years of study ideas about the mathematical apparatus, information technologies and the mathematical modeling of modern chemistry and, thirdly, to instill in students the primary skills of building mathematical models of the simplest physical and mathematical processes when studying a mathematics course.

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8

Gumnitsky, Jaroslav, Lubov Venger, Vira Sabadash, Dmytro Symak, Anna Hyvlud, and Zoriana Gnativ. "Physical and Mathematical Models of Target Component Extraction from Rectlinear Capillaries." Chemistry & Chemical Technology 16, no. 1 (February 20, 2022): 112–17. http://dx.doi.org/10.23939/chcht16.01.112.

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The extraction of the solid component from the rectilinear capillary has been investigated. The presence of two extraction zones (convective and molecular diffusion) was confirmed. The effect of the system vacuumizing on the extraction rate has been studied. The convection zone during vacuumizing was found to be increased due to the appearance of the vapor phase bubbles. The mass transfer coefficients for the convective zone have been determined. A mathematical model of the molecular diffusion stage is given, taking into account the nonlinear change in the component concentration in the liquid due to the displacement of the extraction boundary. The molecular diffusion coefficients in the capillary have been determined.

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9

Negiz, Antoine, Eric S. Lagergren, and Ali Cinar. "Mathematical Models of Cocurrent Spray Drying." Industrial & Engineering Chemistry Research 34, no. 10 (October 1995): 3289–302. http://dx.doi.org/10.1021/ie00037a015.

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10

Monakov, A. A., and A. A. Tarasenkov. "Comparative Analysis of Mathematical Models of Tracking Radio Altimeters." Journal of the Russian Universities. Radioelectronics 25, no. 4 (September 29, 2022): 72–80. http://dx.doi.org/10.32603/1993-8985-2022-25-4-72-80.

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Introduction. Tracking radio altimeters of low altitudes are widely used in civil aviation. These devises use periodic frequency modulated continuous wave (FMCW) signals, while altitude measurements are based on processing the beat signal processing. For this purpose, a closed automatic control loop is arranged to maintain the frequency of the beat signal at a fixed level by changing parameters of the transmitted signal (the frequency deviation or the modulation period). An alternative approach to arranging the tracking loop for altitude variations is based on the use of a phase locked loop (PLL), which adjusts the reference signal – a copy of the emitted signal – to obtain the maximum cross-correlation of the beat and reference signals. А comparative analysis of short-range radio altimeters with other currently known tracking radio altimeters for various types of frequency modulation of the transmitted signal seems to be a relevant research task.Aim. An analysis of the influence of the type of frequency modulation on the accuracy of altitude estimation in a PLL-based radar altimeter, as well as a comparative analysis of this altimeter with other known tracking altimeters.Materials and methods. Mathematical models of tracking radio altimeters are proposed, and a computer simulation of their performance is carried out for the case of altitude estimation over a smooth flat surface.Results. The conducted comparative analysis of tracking radio altimeters confirmed the effectiveness of the PLL when processing signals of different frequency modulation type (sawtooth, triangular, and harmonic FM). Altitude estimates produced by PLL-based radar altimeters are unbiased, with their standard deviation not exceeding 3 cm for the signalto-noise ratio of greater than 10 dB and under the scenario parameters adopted in the work. The conducted comparison with other tracking altimeters showed that estimation errors of this radar altimeter are an order of magnitude smaller.Conclusion. A PLL-based tracking radar altimeter can be used to estimate the height of the aircraft flight. The quality of altitude estimates produced by this device is higher than those produced by other known tracking radio altimeters. Further research and field tests will investigate the accuracy of altitude estimation when working over a rough surface.

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11

Alekseev, M. V., N. G. Sudobin, A. A. Kuleshov, and E. B. Savenkov. "Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (91) (August 2020): 4–23. http://dx.doi.org/10.18698/1812-3368-2020-4-4-23.

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The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration

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12

Stepova, Kateryna, Yaroslav Gumnitskyy, and Duncan Maquarrie. "Mechanism and Mathematical Model of Н2S Chemisorption on Modified Bentonite." Chemistry & Chemical Technology 3, no. 3 (September 15, 2009): 169–72. http://dx.doi.org/10.23939/chcht03.03.169.

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New H2S adsorbent was synthesized on the basis of bentonite. It was analyzed using elemental and BET surface area analysis. Models and mathematical representations of mechanisms that govern the chemisorption of hydrogen sulfide on the chemically treated bentonite were presented. The models adequacy was assessed by means of statistic t-criterion.

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13

Ovchinnikov, P. "Mathematical models for fine grinding of powders." Advanced Powder Technology 4, no. 3 (1993): 179–89. http://dx.doi.org/10.1016/s0921-8831(08)60641-x.

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14

Mantzaris, Nikolaos V., Prodromos Daoutidis, Friedrich Srienc, and Arnold G. Fredrickson. "Growth processes in a cascade of bioreactors: Mathematical models." AIChE Journal 45, no. 1 (January 1999): 164–76. http://dx.doi.org/10.1002/aic.690450114.

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15

Xing, W., Huu Hao Ngo, S. H. Kim, W. S. Guo, and P. Hagare. "Physico‐Chemical Processes for Landfill Leachate Treatment: Experiments and Mathematical Models." Separation Science and Technology 43, no. 2 (January 2008): 347–61. http://dx.doi.org/10.1080/01496390701787214.

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16

Zhang, Fangyuan, Brittany Macshane, Ryan Searcy, and Zuyi Huang. "Mathematical Models for Cholesterol Metabolism and Transport." Processes 10, no. 1 (January 13, 2022): 155. http://dx.doi.org/10.3390/pr10010155.

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Cholesterol is an essential component of eukaryotic cellular membranes. It is also an important precursor for making other molecules needed by the body. Cholesterol homeostasis plays an essential role in human health. Having high cholesterol can increase the chances of getting heart disease. As a result of the risks associated with high cholesterol, it is imperative that studies are conducted to determine the best course of action to reduce whole body cholesterol levels. Mathematical models can provide direction on this. By examining existing models, the suitable reactions or processes for drug targeting to lower whole-body cholesterol can be determined. This paper examines existing models in the literature that, in total, cover most of the processes involving cholesterol metabolism and transport, including: the absorption of cholesterol in the intestine; the cholesterol biosynthesis in the liver; the storage and transport of cholesterol between the intestine, the liver, blood vessels, and peripheral cells. The findings presented in these models will be discussed for potential combination to form a comprehensive model of cholesterol within the entire body, which is then taken as an in-silico patient for identifying drug targets, screening drugs, and designing intervention strategies to regulate cholesterol levels in the human body.

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17

Hernowo, Pandit, Carolus B. Rasrendra, Yogi W. Budhi, Jenny Rizkiana, Anton Irawan, Septhian Marno, Yana Meliana, Oki Muraza, and Yazid Bindar. "Volatile State Mathematical Models for Predicting Components in Biomass Pyrolysis Products." Journal of Engineering and Technological Sciences 54, no. 1 (February 2, 2022): 220108. http://dx.doi.org/10.5614/j.eng.technol.sci.2022.54.1.8.

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Volatile state mathematical models for quantifying the chemical components in volatile biomass pyrolysis products were developed. The component mass yield Yi rate depends linearly on its pseudo kinetic constant and the remaining mass yield. The mass fraction rate of each component was modeled from the derivation of its mass yield rate equation. A new mathematical model equation was successfully developed. The involved variables are: biomass number, temperature, heating rate, pre-exponential factor, and pseudo activation energy related to each component. The component mass fraction yi and the mass yield were predicted using this model within a temperature range. Available experimental pyrolysis data for beechwood and rice husk biomass were used to confirm the developed model. The volatile products were separated into bio-pyrolysis gas (BPG) and a bio-pyrolysis oil (BPO). Five components in the BPG and forty in the BPO were quantified. The pseudo activation energy for each pseudo chemical reaction for a specific component was modeled as a polynomial function of temperature. The component mass fraction and yield are quantifiable using this developed mathematical model equation within a temperature range. The predicted component mass fractions and yields agreed excellently with the available experimental data.

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18

Asprey, Steven P., and Yuji Naka. "Mathematical Problems in Fitting Kinetic Models. Some New Perspectives." JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 32, no. 3 (1999): 328–37. http://dx.doi.org/10.1252/jcej.32.328.

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19

Leonzio, Grazia. "Mathematical modeling of a methanol reactor by using different kinetic models." Journal of Industrial and Engineering Chemistry 85 (May 2020): 130–40. http://dx.doi.org/10.1016/j.jiec.2020.01.033.

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20

Gao, Ming, and Mark E. Orazem. "The development of advanced mathematical models for continuous glucose sensors." Electrochimica Acta 382 (June 2021): 138226. http://dx.doi.org/10.1016/j.electacta.2021.138226.

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21

Parrouffe, Jean-Michel, and Arun S. Mujumdar. "Bibliography on Mathematical Models of Drying and Dryers." Drying Technology 6, no. 2 (June 1988): 305. http://dx.doi.org/10.1080/07373938808916379.

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22

Lyashenko, Viktor, Elena Kobilskaya, and Tetiana Nabok. "APPLICATION OF MATHEMATICS SOFTWARE FOR SOLVING APPLIED PROBLEMS." Transactions of Kremenchuk Mykhailo Ostrohradskyi National University, no. 3(128) (June 11, 2021): 11–16. http://dx.doi.org/10.30929/1995-0519.2021.3.11-16.

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Purpose. To show the possibilities of using mathematics software in solving problems arising in the construction of mathematical models of various processes and, thus, to reveal the importance of realizing the professional orientation of the mathematical training of students of natural and engineering specialties. Methodology. A number of mathematical models that are presented in the form of a Cauchy problem for a common first-order differential equation are considered in this paper. Mathematical models considered in this paper describe chemical and ecological processes. Euler's numerical method is used to solve the problems that describe the proposed models. This method is implemented in special mathematical software (Mathcad, Matlab). Findings. It is shown how the use of special functions designed to solve the Cauchy problem solves the problems proposed in mathematical models. Graphs are built in Mathcad and Matlab, including graphs that can be used to compare analytical and numerical solutions of problems obtained by Euler's method. Originality. The paper concludes that mathematical models of many technological and physical processes in different industries can be represented by the Cauchy problem for a common differential equation. Practical value. The considered mathematical models show the importance of realization of professional orientation of mathematical training of students of natural and engineering specialties. Conclusions. Mathematical modeling allows you to study and evaluate various processes (physical, economic, environmental), and therefore knowledge of the basics of modeling and special mathematical software is very important in the training of modern specialists in various specialties. The problems presented in the article are used in teaching the courses of numerical methods and computer mathematics in the study of the topic «Numerical Solution of Differential Equations». References 10, tables 2, figures 9.

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23

Kato, K. "Classification of wear mechanisms/models." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 216, no. 6 (June 1, 2002): 349–55. http://dx.doi.org/10.1243/135065002762355280.

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Wear mechanisms may be briefly classified by mechanical, chemical and thermal wear whose wear modes are further classified into seven. Some of them have wear models and mathematical expressions of wear rate, but many of them have not satisfactory wear models and wear equations for reliable predictions. This paper reviews such present understanding on wear mechanisms and models.

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24

Sevast'yanov, P. V. "Structural parametric method of identification of mathematical models of technological processes." Journal of Engineering Physics 57, no. 3 (September 1989): 1080–84. http://dx.doi.org/10.1007/bf00870822.

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25

Orazbayev, B. B., E. A. Ospanov, K. N. Orazbayeva, and L. T. Kurmangazieva. "A Hybrid Method for the Development of Mathematical Models of a Chemical Engineering System in Ambiguous Conditions." Mathematical Models and Computer Simulations 10, no. 6 (November 2018): 748–58. http://dx.doi.org/10.1134/s2070048219010125.

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26

Popov, S., S. Shumykin, and Н. Laptieva. "Mathematical simulation of welded deposit layers as for adaptation of materials to failure in quasidissipative tribosystems." Innovative Materials and Technologies in Metallurgy and Mechanical Engineering, no. 2 (March 18, 2021): 82–87. http://dx.doi.org/10.15588/1607-6885-2020-2-11.

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Purpose. To establish mathematical models for the adaptation of materials under conditions of activation of a metastable structural-phase state of quasi-dissipative tribosystems. Determination and substantiation of factors for planning an active experiment due to which it is possible to create mathematical models of stable forecasts for increasing the wear resistance of materials. Research methods. When conducting the experiments, a priori data were used in combination with our own scientific developments of mathematical models of the dependences of the influence of the chemical composition of alloys during manual and automatic electric arc surfacing on the physical and mechanical properties of the surface layer of the material, which is destroyed under tribosystem conditions. It was decided to use mathematical planning of research on the basis of an active experiment with the creation of models for the numerical description of the mathematical expectation in the form of regression equations. Obtained results. On the basis of theoretical and practical scientific research with planning a passive and active experiment, a set of relevant knowledge has been obtained, which makes it possible to determine the main criterion requirements for the sensitivity of deposited steels and alloys to adaptation under the action of external mechanical and energy influences and allows to mathematically describe the characteristics of the alloy and provide a numerical estimate of the correlation parameters among themselves. On the basis of the theory of scientific mathematical planning of the experiment, a set of corresponding experiments was carried out, which made it possible to build spatial graphic models. Scientific novelty. For the first time, theoretical and practical scientific research is presented with the reproduction of a systemic multivariate analysis of the parameters of mathematical models and processes leading to the martensitic ( γ → α ) transformation and determines the substantiation of the chemical composition of the deposited materials to increase fracture resistance under conditions of quasi-dissipative and dissipative tribosystems. Practical meaning. The obtained results of the above studies allow, within the framework of technical and technological accuracy, which is necessary within the framework of practical engineering forecasts, to determine the physical and mechanical properties of wear-resistant deposited alloys under conditions of quasi-dissipative and dissipative tribosystems.

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27

Phanawadee, Phungphai, Monrudee Phongaksorn, Nalinee Chaimongkol, Attasak Jaree, and Jumras Limtrakul. "Mathematical analysis of TAP models for porous catalysts." Chemical Engineering Journal 115, no. 1-2 (December 2005): 51–62. http://dx.doi.org/10.1016/j.cej.2005.09.010.

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28

Jannelli, Alessandra. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences." Mathematics 8, no. 2 (February 8, 2020): 215. http://dx.doi.org/10.3390/math8020215.

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This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.

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29

Gordeev, L. S., A. V. Koznov, A. S. Skichko, and Yu L. Gordeeva. "Unstructured mathematical models of lactic acid biosynthesis kinetics: A review." Theoretical Foundations of Chemical Engineering 51, no. 2 (March 2017): 175–90. http://dx.doi.org/10.1134/s0040579517020026.

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30

ASSAWARACHAN, RITTICHAI, and ATHAPOL NOOMHORM. "MATHEMATICAL MODELS FOR VACUUM-MICROWAVE CONCENTRATION BEHAVIOR OF PINEAPPLE JUICE." Journal of Food Process Engineering 34, no. 5 (November 19, 2009): 1485–505. http://dx.doi.org/10.1111/j.1745-4530.2009.00536.x.

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31

Sanecki, Przemysław T., Piotr M. Skitał, and Krzysztof Kaczmarski. "The mathematical models of the stripping voltammetry metal deposition/dissolution process." Electrochimica Acta 55, no. 5 (February 2010): 1598–604. http://dx.doi.org/10.1016/j.electacta.2009.10.032.

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32

Bobkov, Vladimir I., Margarita V. Chernovalova, and Andrey M. Sokolov. "Mathematical Models for an Energy Intensive Multistage Roasting Process of Pelletized Industrial Waste from Apatite-Nepheline Ores." Materials Science Forum 1052 (February 3, 2022): 473–81. http://dx.doi.org/10.4028/p-0i5ger.

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In this article, we describe mathematical and computer models for the complex, energy-consuming, multistage, integrated chemical and power engineering processes of calcination and sintering of pelletized industrial waste from apatite-nepheline ores, accumulated in the dumps of mining and processing plants. The models take into account the negative effect of vitrification and the subsequent destruction of pellets in case the operating temperature condition in the high-temperature roasting zone of indurating conveyor furnaces is violated during the implementation of these thermally activated processes. Experimental and analytical methods have been developed for the analysis of integrated, thermally activated processes in a dense multilayer mass of pellets obtained from apatite-nepheline ores waste, taking place in indurating furnaces. The possibility of complex phenomena accounting for polymorphic transformations, chemical reactions in solid phases, reactions involving a liquid phase, as well as the formation of new phases and solid solutions as a result of reactions, must be considered when modeling these processes. This analysis makes it possible to increase the strength of pellets during sintering and the degree of calcination as a result of carbonates dissociation, as well as to detect and use the potential of increasing energy and resource efficiency in a complex, environmentally safe, chemical and power engineering system for the processing of industrial waste of apatite-nepheline ores from dumps of mining and industrial plants.

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33

Nikolaevich, Karpenko Vasily, Yuriy Starodub, and Andrii Havrys. "Computer Modeling in the Application to Geothermal Engineering." Advances in Civil Engineering 2021 (August 10, 2021): 1–23. http://dx.doi.org/10.1155/2021/6619991.

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In the article, investigation is given of the developed mathematical models of nonequilibrium in time and distributed in space thermodynamic state of Earth’s matter from its center to its surface depending on the cases of the presence and absence of an internal source of thermal energy concentrated in the center of mass taking into account known geophysical data about the nucleus, mantle, lithosphere and atmosphere, and endogenous and exogenous heat fluxes. The objects of research are as follows: mathematical models of geothermal energy of the Earth, its internal source, and heat balance of endogenous and exogenous heat fluxes on the Earth’s surface. Research methods used are as follows: thermometry in deep wells, ground and remote sensing of heat fluxes of the Earth and the planets of the Solar System, mathematical modeling of heat exchange and thermoelastic processes from compression of Earth’s matter by gravitational field energy information and classical physical and mathematical methods, and computer modeling. The aim of research: in computer modeling to provide new mathematical models that determine the geophysical parameters of geothermal energy, which are aimed on solving problems of energy, environmental and economic security of society, using modern technical means of calculating ground and remote sensing data development of geothermal resources, and regulation of the heat balance of the ecosystem, namely: (i) study of the geological structure of the lithosphere to a depth of 10 km by remote sensing to determine the physical parameters of its layers more accurately than ground methods; (ii) development of projects of geothermal power plants on the basis of single isolated wells of a given depth with a capacity of up to 2 ÷ 3 mW of electricity on continents of the globe; (iii) real-time monitoring and forecasting of the temperature field of the atmosphere according to its physical and chemical composition. The novelty of the obtained research results: (i) developed the mathematical model of the physical process of origin and distribution in the bowels of the density of geothermal energy of the Earth from the surface to its center, which is the density of internal energy of an elementary geological object, and which increases when approaching the center of the planet; (ii) developed the mathematical model of the thermal energy source of infrared (IR) waves of the elementary geophysical object of the Earth’s interior depending on the depth of its occurrence, which allows to determine the stable generation of geothermal energy by rocks in a deep well for extraction and conversion into electricity and to study the geological structure and physical properties of the Earth’s interior; (iii) the mathematical model of heat exchange between the layers of the Earth’s subsoil with the thermal energy of infrared waves according to the laws of Fourier thermal conductivity and Stefan–Boltzmann heat transfer, which together with the geothermal energy source model allows to determine a thermal capacity of rocks in a deep well; (iv) developed the mathematical model of stable action of a source of thermal energy in the center of mass of the Earth, in the absence of which it is hard to explain the power of its endogenous infrared heat flux, parameters of geothermal energy distribution in the Earth, and the current thermodynamic state of the atmosphere, and the change in temperature of which depends on the thermophysical parameters of the physical-chemical composition of the atmosphere more than on changes in the thermal activity of the Sun; (v) determination of new numerical values: thermophysical parameters of the Earth’s interior; kinetic, potential and own gravitational energy of the Earth and own gravitational energy of the planets of the Solar System.

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34

Gil'man, A. A. "Analogy between two mathematical models in the theory of two-phase filtration." Journal of Engineering Physics 55, no. 5 (November 1988): 1251–53. http://dx.doi.org/10.1007/bf00872620.

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35

Beschkov, V., T. Sapundzhiev, K. Petrov, and E. Vasileva. "Mathematical Modeling for Studying Microbial Processes – Some Examples." Serdica Journal of Computing 4, no. 1 (March 31, 2010): 19–28. http://dx.doi.org/10.55630/sjc.2010.4.19-28.

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Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or to reject kinetic models for certain processes, or to evaluate the importance of some transport phenomena on the net chemical or biochemical reaction rate. In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processes accomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products, like enzymes, lactic acid, gluconic acid, etc. By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial process is also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.

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36

Longhi, Daniel Angelo, Francieli Dalcanton, Gláucia Maria Falcão de Aragão, Bruno Augusto Mattar Carciofi, and João Borges Laurindo. "Microbial growth models: A general mathematical approach to obtain μ max and λ parameters from sigmoidal empirical primary models." Brazilian Journal of Chemical Engineering 34, no. 2 (April 2017): 369–75. http://dx.doi.org/10.1590/0104-6632.20170342s20150533.

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Nguyen, Nhu Tuong An, Vinh Quang Do, The Thinh Pham, and Tuan Tran Nguyen. "Application of different control algorithms on a ‘home-made’ temperature control lab kit." Can Tho University Journal of Science 14, no. 1 (March 30, 2022): 62–73. http://dx.doi.org/10.22144/ctu.jen.2022.007.

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Providing enough facilities for students to do laboratory activities is important. An existing useful kit was proposed for students learning a variety of control engineering topics. A temperature control lab kit is made from scratch using common electronics components as a replacement for the original TCLab introduced by Hedengren (Hedengren et al., 2019). Mathematical models of the system derived from theoretical and experimental methods are simulated in Matlab/Simulink to verify their accuracy to the physical kit. Different control algorithms such as: On/Off, PID, Fuzzy are then applied on the Kit as well as its mathematical models to illustrate their control feasibility. Human machine interface (HMI) is also designed using Matlab GUI allowing an operator to select a control algorithm, tune control parameters and monitor parameters of the process. Experimental results show that the derived models can reflect quite well dynamics of the physical kit with temperature deviation among them in the range of ±3°C. This confirms that the kit is well-suited for teaching different control topics such as system modelling, system identification, classical control and advanced control algorithms.

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Rakovitis, Nikolaos, Nan Zhang, Jie Li, and Liping Zhang. "A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy." Frontiers of Chemical Science and Engineering 13, no. 4 (November 7, 2019): 784–802. http://dx.doi.org/10.1007/s11705-019-1858-4.

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Abstract The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

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Khaghanikavkani, Elham, and Mohammed M. Farid. "Mathematical Modelling of Microwave Pyrolysis." International Journal of Chemical Reactor Engineering 11, no. 1 (October 31, 2013): 543–59. http://dx.doi.org/10.1515/ijcre-2012-0060.

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Abstract This study deals with a detailed numerical investigation of the microwave heating process in plastic pyrolysis. The pyrolysis of high-density polyethylene (HDPE) was studied using a single-mode microwave cavity, TE10 mode, at 2.45 GHz with two different absorbents, as carbon and silicon carbide, and the results were compared. The temperature distribution inside the sample was determined by solving the conservation equations coupled with the microwave and chemical kinetic equations. Lambert’s law was applied to describe the electromagnetic field in the microwave cavity. The effective heat capacity method was used to account for the latent heat in the melting range of plastic. The heat of the reaction was taken into account using first-order kinetic equations assuming a single-step reaction. One-dimensional model equations were solved using the finite difference method utilising MATLAB codes. The model developed in this study provides a better understanding of the fundamental mechanisms of the microwave pyrolysis of HDPE based on a combination of electromagnetic field and thermal models. The primary focus was to incorporate and investigate the effect of the phase changes and reaction during microwave pyrolysis. The results show that the temperature profile strongly depends on the physical properties of the material. Silicon carbide provides more uniform heating distribution compared with carbon.

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Kumar, Rajiv, A. K. Gupta, and M. Naveen. "Compartment Fires: BFD Curve and Mathematical Models." Journal of Applied Fire Science 17, no. 1 (January 1, 2007): 73–95. http://dx.doi.org/10.2190/af.17.1.e.

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Kontoravdi, Cleo, Efstratios N. Pistikopoulos, and Athanasios Mantalaris. "Systematic development of predictive mathematical models for animal cell cultures." Computers & Chemical Engineering 34, no. 8 (August 2010): 1192–98. http://dx.doi.org/10.1016/j.compchemeng.2010.03.012.

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Nguyen, Ngoc Hung, Van Phan Do, and Hoa Tien Vu. "Estimating Disturbance Torque Effects on the Stability and Control Performance of Two-Axis Gimbal Systems." Journal of the Russian Universities. Radioelectronics 25, no. 4 (September 29, 2022): 63–71. http://dx.doi.org/10.32603/1993-8985-2022-25-4-63-71.

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Introduction. Two-axis gimbal systems are applied for stabilizing and controlling the line of sight (LOS) of an optical or imaging system mounted on a moving vehicle. Gimbal systems are intended to isolate various disturbance torques and control the LOS toward the direction of a target. Two-axis gimbals can be of two main types, namely Yaw-Pitch and Swing-Roll type. In this article, we focus on investigating mathematical models of two-axis gimbals, which describe the impact of cross-disturbance torques on their stability and control performance. Simulations were conducted to compare advantages and disadvantages of the two types of two-axis gimbals.Aim. To study mathematical models describing the impact of cross-disturbance torques on the stability and control performance of two-axis gimbals.Materials and methods. Mathematical models of two-axis gimbal systems were synthesized by the Lagrange method. The operation of two-axis gimbal systems was simulated in the Matlab-Simulink environment. Results. Mathematical models and structural diagrams of the synthesized Yaw-Pitch and Swing-Roll gimbals were obtained. The conducted simulations of typical cases revealed different cross-disturbance effects.Conclusion. Motion equations for Swing-Roll and Yaw-Pitch gimbals were derived using similar methodology. The impact of cross-disturbance torques on gimbal systems was evaluated. The obtained results form a basis for selecting an optimal structure of tracking systems meeting the desired characteristics.

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Egorova, S. V., O. V. Makhnenko, G. Yu Saprykina, and D. P. Sineok. "Mathematical models of the dependence of mechanical properties on chemical composition of steels for ESW." Avtomatičeskaâ svarka (Kiev) 2021, no. 1 (January 28, 2021): 50–60. http://dx.doi.org/10.37434/as2021.01.09.

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van Odyck, Daniel E. A., John B. Bell, Franck Monmont, and Nikolaos Nikiforakis. "The mathematical structure of multiphase thermal models of flow in porous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2102 (November 4, 2008): 523–49. http://dx.doi.org/10.1098/rspa.2008.0268.

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This paper is concerned with the formulation and numerical solution of equations for modelling multicomponent, two-phase, thermal fluid flow in porous media. The fluid model consists of individual chemical component (species) conservation equations, Darcy's law for volumetric flow rates and an energy equation in terms of enthalpy. The model is closed with an equation of state and phase equilibrium conditions that determine the distribution of the chemical components into phases. It is shown that, in the absence of diffusive forces, the flow equations can be split into a system of hyperbolic conservation laws for the species and enthalpy and a parabolic equation for pressure. This decomposition forms the basis of a sequential formulation where the pressure equation is solved implicitly and then the component and enthalpy conservation laws are solved explicitly. A numerical method based on this sequential formulation is presented and used to demonstrate some typical flow behaviour that occurs during fluid injection into a reservoir.

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Moshinskii, A. I. "One-dimensional discrete mathematical models of extraction from a porous material." Theoretical Foundations of Chemical Engineering 44, no. 1 (February 2010): 43–51. http://dx.doi.org/10.1134/s0040579510010069.

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Bassioni, Ghada, Mohammed Mohammed Ali, Ali Almansoori, Gabriele Raudaschl-Sieber, and Fritz E. Kühn. "Rapid determination of complex oil well cement properties using mathematical models." RSC Advances 7, no. 9 (2017): 5148–57. http://dx.doi.org/10.1039/c6ra26045d.

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Lutovska, Monika, Vangelce Mitrevski, Ivan Pavkov, Vladimir Mijakovski, and Milivoj Radojcin. "Mathematical modelling of thin layer drying of pear." Chemical Industry and Chemical Engineering Quarterly 22, no. 2 (2016): 191–99. http://dx.doi.org/10.2298/ciceq150122032l.

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In this study, a thin - layer drying of pear slices as a function of drying conditions were examined. The experimental data set of thin - layer drying kinetics at five drying air temperatures 30, 40, 50, 60 and 70?C, and three drying air velocities 1, 1.5 and 2 m s-1 were obtained on the experimental setup, designed to imitate industrial convective dryer. Five well known thin - layer drying models from scientific literature were used to approximate the experimental data in terms of moisture ratio. In order to find which model gives the best results, numerical experiments were made. For each model and data set, the statistical performance index, (?), and chi-squared, (?2), value were calculated and models were ranked afterwards. The performed statistical analysis shows that the model of Midilli gives the best statistical results. Because the effect of drying air temperature and drying air velocity on the empirical parameters was not included in the base Midilli model, in this study the generalized form of this model was developed. With this model, the drying kinetic data of pear slices can be approximated with high accuracy. The effective moisture diffusivity was determined by using Fick?s second laws. The obtained values of the effective moisture diffusivity, (Deff), during drying ranged between 6.49 x 10-9 and 3.29 x 10-8 m2 s-1, while the values of activation energy (E0) varied between 28.15 to 30.51 kJ mol-1.

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Faisal Siddique, Hafiz, Adnan Mazari, Antonin Havelka, Zdenek Kus, David Cirkl, and Lubos Hes. "New approach for the prediction of compression pressure using the cut strip method." Textile Research Journal 90, no. 15-16 (January 10, 2020): 1689–703. http://dx.doi.org/10.1177/0040517519896757.

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The main objective of the current research is the development of a new mathematical model for the prediction of compression pressure based on the incorporation of some new parameters. These new parameters include deformed width (wf), true stress ([Formula: see text]), true/logarithm strain ([Formula: see text]), true modulus of elasticity ([Formula: see text]), along with measurement of engineering stress ([Formula: see text]), engineering strain ([Formula: see text]) and engineering modulus of elasticity ([Formula: see text]) at ankle position. Various brands of compression socks comprising similar fibrous combinations, as well as knit type, were purchased. Initially they were hand washed, put on the leg for marking, marked in a square, sliced, and cut into rectangular strips. The rectangular cut strips were evaluated for force–elongation characterization at different strain values considering the requisite practical elongation values (circumferential difference between leg and sock at ankle portion). For pressure measurement, a Salzmann MST MK IV pressure measuring device using a standard-sized wooden leg (circumference = 240 mm) was used. For tensile evaluation, a Testometric tensile tester was used. In this research we developed the two mathematical models based on true Young’s modulus and engineering Young’s modulus were compared with Hooke’s law and Laplace’s law. The developed models were also compared with previously existing models statistically.

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Head, R., D. Shepherd, G. Butt, and G. Buck. "OTTER mathematical process simulation of potable water treatment." Water Supply 2, no. 1 (January 1, 2002): 95–101. http://dx.doi.org/10.2166/ws.2002.0012.

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Process modelling has been used for many years in the chemical engineering field and more recently has become well established for as a tool for analysing and optimising the performance of wastewater treatment works. In the clean water area, models are routinely used for simulating distribution networks. In contrast, however, the use of modelling tools on potable water treatment works is relatively new and has yet to become well established. A range of tools have been suggested, including artificial neural networks, computational fluid dynamics and process simulation. WRc have developed a dynamic simulation package for predicting the performance of water treatment works, via models of individual processes. The software has a range of uses, including process and works optimisation, operational decision support, as a design aid and for training engineers and operators. The models are dynamic so that they predict the response of the treatment works to changes in flow, raw water quality and process operating conditions. The software has been used in a wide variety of applications, including optimising process plant operation to minimise cost and to investigate the reasons why a treatment works failed to meet its design criteria at the maximum design throughput.

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Lukic, Natasa, Svetlana Popovic, and Jelena Markovic. "Mathematical modelling of flux recovery during chemical cleaning of tubular membrane fouled with whey proteins." Acta Periodica Technologica, no. 40 (2009): 135–44. http://dx.doi.org/10.2298/apt0940135l.

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Membrane process efficiency in the dairy industry is impaired by the formation of deposits during filtration processes. This work describes cleaning procedures for ceramic tubular membrane (50 nm) fouled with whey proteins. Also, mathematical modelling was performed to obtain models which allow deeper insight into the mechanisms involved during cleaning procedures. The caustic solutions (0.2%w/w, 0.4%w/w and 1.0%w/w NaOH) and the mixture of two commercial detergents (0.8%w/w P3-ultrasil 69+0.5% w/w P3-ultrasil 67 and 1.2% P3-ultrasil 69+0.75 P3-ultrasil 67) were used as chemical cleaning agents. The results showed that the best flux recovery was achieved with 0.4%w/w NaOH solution. After analyzing the experimental data, five parameter and six parameter kinetic models were suggested for alkali and detergent cleaning, respectively. The changes of total and specific resistances, as well as the change of the effective pore diameter and deposit thickness during cleaning are estimated by applying these models.

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