scholarly journals MATHEMATICAL MODELING OF GRAIN DRYING

2003 ◽  
Vol 8 (2) ◽  
pp. 103-112 ◽  
Author(s):  
R. Čiegis ◽  
T. Leonavičiene ◽  
V. Skakauskas ◽  
O. Suboč
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Experiments ◽  
A Priori ◽  
Simplified Model ◽  
Discrete Solution ◽  
Drying Process ◽  
Grain Moisture ◽  
Grain Drying ◽  
The Mathematical Model

In this paper we consider the mathematical model which describes the grain drying process. The air and grain moisture and temperature are described by a system of PDE. A finite difference scheme is proposed for finding a numerical solution. The convergence of the discrete solution is proved for a simplified model, when the temperature is assumed to be given a priori. Results of numerical experiments are presented.

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

MODELLING THE OZONE PENETRATION IN A GRAIN LAYER / OZONO SKVERBTIES GRŪDŲ SLUOKSNYJE MODELIAVIMAS

2012 ◽  
Vol 20 (4) ◽  
pp. 292-300 ◽  
Author(s):  
Aušra Steponavičienė ◽  
Dainius Steponavičius ◽  
Algirdas Raila ◽  
Aurelija Kemzūraitė
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Initial Concentration ◽  
Real Process ◽  
Grain Moisture ◽  
Grain Drying ◽  
Ozonation Time ◽  
Grain Surface ◽  
The Mathematical Model ◽  
Ozonation Process

Studies of grain drying with ozone-air mixture were carried out to detect the ozone penetration patterns through the grain mound of various moisture content (14.6 ≤ w 0 ≤ 23.0%) at different ozone concentrations (500 ≤ C 0 ≤ 1250 ppb) in the supplied air. The ozone penetration through the grain layer depends on the initial ozone concentration in the supplied air, ozonation time, velocity of the supplied air, height of the grain mound, initial grain moisture content and mycobiotic contamination of grain surface. It was determined that in a 60 cm height of the grain layer ozone is first recorded after 12 h, and at 105 cm – only after 34 h at w 0 = 19.0%, C 0 = 500 ppb. If the initial concentration of ozone is higher, it is first recorded sooner. Ozone penetration through the grain layer with higher moisture level is slower, and ozone reaction with grain surface and microflora present on it is longer. Hypothesis about the adequacy of the model (how it reflects the real process) has been verified by calculating reproduction and adequacy variance. The mathematical model could be applied for prediction of the course of grain ozonation process. Santrauka Grūdų džiovinimo ozono ir oro mišiniu tyrimai atlikti siekiant išaiškinti ozono skverbties per skirtingo drėgnio grūdų sampilą dėsningumus (14,6 ≤ w 0 ≤ 23,0%), esant skirtingoms ozono koncentracijoms (500 ≤ C 0 ≤ 1250 ppb) tiekiamame ore. Ozono skverbtis grūdų sluoksnyje priklauso nuo pradinės ozono koncentracijos tiekiamame ore, ozonavimo trukmės, tiekiamo oro greičio, grūdų sampilo aukščio, pradinio grūdų drėgnio ir jų paviršiaus mikobiotinio užterštumo. 60 cm grūdų sluoksnio aukštyje ozonas pradėtas fiksuoti po 12 h, o 105 cm – tik po 34 h, kai w 0 = 19,0%, C 0 = 500 ppb. Padidinus pradinę ozono koncentraciją, ozonas pradedamas fiksuoti greičiau. Ozonuojant drėgnesnius grūdus, ozonas per jų sluoksnį skverbiasi lėčiau, vyksta ilgesnė jo reakcija su grūdų paviršiumi ir ant jų esančia mikroflora. Hipotezė apie modelio adekvatumą (kaip jis atspindi realų procesą) buvo patikrinta apskaičiavus reprodukcijos ir adekvatumo dispersijas. Sudarytas matematinis modelis gali būti taikomas grūdų ozonavimo procesui prognozuoti.

scholarly journals FORMALIZATION OF THE COTTON DRYING PROCESS BASED ON HEAT AND MASS TRANSFER EQUATIONS

2020 ◽  
Vol 21 (2) ◽  
pp. 256-265
Author(s):  
Sayyora Yunusnova, Toshkenboyevna ◽  
Davron Holmatov, Abdalimovich ◽  
Muhiddin Atajonov, Odiljonovich ◽  
Ulugjon Huzanazarov
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
A Priori ◽  
Management Theory ◽  
Drying Process ◽  
Transfer Equations ◽  
Cotton Seeds ◽  
The Mathematical Model ◽  
Transfer Properties ◽  
Heat Agent

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.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT

2015 ◽  
Vol 1 ◽  
pp. 249
Author(s):  
Edmunds Teirumnieks ◽  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Inductively Coupled Plasma ◽  
Optical Emission ◽  
Peat Bog ◽  
Inductively Coupled ◽  
Pollution Loading ◽  
The Mathematical Model ◽  
Optical Emission Spectrometer

Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are determined using inductively coupled plasma optical emission spectrometer. Mathematical model for calculation of concentrations of metal has been described in the paper. As an example, mathematical models for calculation of Pb concentrations have been analyzed.

scholarly journals Mathematical modeling and harmonic analysis of SISFCL

2017 ◽  
Vol 36 (1) ◽  
pp. 258-270
Author(s):  
Debraj Sarkar ◽  
Debabrata Roy ◽  
Amalendu Bikash Choudhury ◽  
Sotoshi Yamada
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Harmonic Analysis ◽  
Voltage Drop ◽  
Element Model ◽  
Iron Core ◽  
Content Type ◽  
Hysteresis Characteristic ◽  
The Core ◽  
The Mathematical Model

Purpose A saturated iron core superconducting fault current limiter (SISFCL) has an important role to play in the present-day power system, providing effective protection against electrical faults and thus ensuring an uninterrupted supply of electricity to the consumers. Previous mathematical models developed to describe the SISFCL use a simple flux density-magnetic field intensity curve representing the ferromagnetic core. As the magnetic state of the core affects the efficient working of the device, this paper aims to present a novel approach in the mathematical modeling of the device with the inclusion of hysteresis. Design/methodology/approach The Jiles–Atherton’s hysteresis model is utilized to develop the mathematical model of the limiter. The model is numerically solved using MATLAB. To support the validity of model, finite element model (FEM) with similar specifications was simulated. Findings Response of the limiter based on the developed mathematical model is in close agreement with the FEM simulations. To illustrate the effect of the hysteresis, the responses are compared by using three different hysteresis characteristics. Harmonic analysis is performed and comparison is carried out utilizing fast Fourier transform and continuous wavelet transform. It is observed that the core with narrower hysteresis characteristic not only produces a better current suppression but also creates a higher voltage drop across the DC source. It also injects more harmonics in the system under fault condition. Originality/value Inclusion of hysteresis in the mathematical model presents a more realistic approach in the transient analysis of the device. The paper provides an essential insight into the effect of the core hysteresis characteristic on the device performance.

scholarly journals A STABILIZING SUBGRID FOR CONVECTION–DIFFUSION PROBLEM

2006 ◽  
Vol 16 (02) ◽  
pp. 211-231 ◽  
Author(s):  
ALI I. NESLITURK
Keyword(s):  
Numerical Experiments ◽  
A Priori ◽  
Diffusion Problem ◽  
Triangular Element ◽  
Discrete Solution ◽  
Convergence Properties ◽  
Small Diffusion ◽  
Galerkin Finite Element ◽  
Convection Diffusion ◽  
Priori Error Estimates

A stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection–diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.

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