scholarly journals Determination of Temperature of Components of Cotton-Raw Material in a Drum Dryer with a Constant

2021 ◽  
Vol 939 (1) ◽  
pp. 012052
Author(s):  
A Z Mamatov ◽  
A K Usmankulov ◽  
I Z Abbazov ◽  
U A Norboyev ◽  
E T Mukhametshina
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Comparative Analysis ◽  
Boundary Value Problem ◽  
Parabolic Type ◽  
Raw Material ◽  
Drying Process ◽  
Moisture State ◽  
Type Boundary

Abstract This article solves one parabolic-type boundary value problem for determining the heat-moisture state of raw cotton in drum dryers at a constant air temperature. Numerical results are obtained by the Bubnov – Galerkin method of the problem under consideration, a comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

scholarly journals Mathematical model for calculating the temperature field of a direct-flow drying drum

2021 ◽  
Vol 2131 (5) ◽  
pp. 052067
Author(s):  
A Mamatov ◽  
A Parpiev ◽  
M Shorakhmedova
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Parabolic Type ◽  
Drying Process ◽  
Air Velocity ◽  
Direct Flow ◽  
Proposed Model ◽  
Cotton Seeds ◽  
The Finite Difference Method ◽  
Type Boundary

Abstract In this paper, one parabolic-type boundary value problem is solved for determining the temperature field of the raw cotton and air components in drum dryers. In the proposed model, convective heat transfer is used according to Newton’s law, the terms describing the evaporation of moisture from the components of raw cotton (seeds, fiber) and the influence of air velocity are taken into account. The resulting system of Galerkin’s differential equations is solved by the finite-difference method in time. It is shown that the approximate solution is estimated according to Galerkin in Sobolev space.The numerical results of the considered problem are obtained by the Bubnov–Galerkin method. A comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

scholarly journals Mathematical modeling and determination of thermodynamic properties of jabuticaba peel during the drying process

2016 ◽  
Vol 20 (6) ◽  
pp. 576-580 ◽  
Author(s):  
Cristian F. Costa ◽  
Paulo C. Corrêa ◽  
Jaime D. B. Vanegas ◽  
Fernanda M. Baptestini ◽  
Renata C. Campos ◽  
...  
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Drying Process ◽  
Drying Temperature ◽  
Air Temperatures ◽  
Nutritional Qualities ◽  
Forced Air ◽  
Air Circulation ◽  
Best Fit

ABSTRACT Jabuticaba is a fruit native of Brazil and, besides containing many nutritional qualities, it also has a good field for use in products such as flour for cakes and biscuits, juice, liqueur, jelly and others. This study aimed to model the drying kinetics and determine the thermodynamic properties of jabuticaba peel at different drying air temperatures. Ripe fruits of jabuticaba (Myrciaria jaboticaba) were collected and pulped manually. Drying was carried out in a forced-air circulation oven with a flow of 5.6 m s-1 at temperatures of 40, 50, 60 and 70 °C. Six mathematical models commonly used to represent the drying process of agricultural products were fitted to the experimental data. The Arrhenius model was used to represent the drying constant as a function of temperature. The Midilli model showed the best fit to the experimental data of drying. The drying constant increased with the increment in drying temperature and promoted an activation energy of 37.29 kJ mol-1. Enthalpy and Gibbs free energy decreased with the increase in drying temperature, while entropy decreased and was negative.

scholarly journals MATHEMATICAL MODELING OF LEACHING PROCESS OF RED MUD IN ORDER TO OBTAIN THE KINETICS PARAMETERS

2015 ◽  
Vol 14 (2) ◽  
pp. 90 ◽  
Author(s):  
K. L. M. Dos Passos ◽  
B. M. Viegas ◽  
E. N. Macêdo ◽  
J. A. S. Souza ◽  
E. M. Magalhães
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Red Mud ◽  
Mineralogical Composition ◽  
Raw Material ◽  
Data Conversion ◽  
Kinetics Parameters ◽  
Leaching Process ◽  
Iron Leaching ◽  
The Mathematical Model

The use of the waste of the Bayer process, red mud, is due to its chemical and mineralogical composition that shows a material rich in oxides of iron, titanium and aluminum. Some studies conducted show that this waste can be applied as a source of alternative raw material for concentration and subsequent recovery of titanium compounds from an iron leaching process, which is present in higher amounts, about 30% by weight. To obtain a greater understanding about the leaching kinetics, the information of the kinetic data of this process is very important. In this context, the main objective of this work is the development of a mathematical model that is able to fit the experimental data (conversion / extraction iron, titanium and aluminum) of the leaching process by which is possible to obtain the main kinetic parameters such as the activation energy and the velocity of chemical reactions as well as the controlling step of the process. The development of the mathematical model was based on the model of core decreasing. The obtained model system of ordinary differential equations was able to fit the experimental data obtained from the leaching process, enabling the determination of the controlling step, the rate constants and the activation energies of the leaching process.

scholarly journals Interpolation of Boundary Condition at Time-Interval of Unknown Lenghth for the Problem of Convective Diffusion in a Three-Layered Water Filter

2019 ◽  
pp. 25-28
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Convective Diffusion ◽  
Lower Boundary ◽  
Time Interval ◽  
Water Filter ◽  
The Right

On the basis of mathematical model of convectivediffusion in a three-layered filter it is formulated a contactinitial-boundary value problem for description of mass transferof pollution accompanying the sorption processes. It is proposedthe algorithm for establishing the estimation of values of soughtfunction (concentration of pollution) at the lower boundary of thefilter on the basis of the interpolation of experimental data. It istaken into account that the right end of the interpolation segmentis unknown. It is determined the exact solutions of contact-initialboundaryvalue problems of mass transfer with provision forboth diffusive and convective mechanisms of transfer as well assorption processes, which is based on integral transformationsover space variables in the contacting regions. Is it designedsoftware and established regularities of convective diffusionprocess in the three-layered filter.

scholarly journals Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

2003 ◽  
Vol 10 (1) ◽  
pp. 37-50 ◽  
Author(s):  
L.F.P. Franca ◽  
M.A. Savi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Random Noise ◽  
Noise Sensitivity ◽  
Correct Identification ◽  
Chaotic Motions ◽  
Nonlinear Pendulum

This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

scholarly journals Determination of technological parameters of soil compacting process

2020 ◽  
pp. 3-15
Author(s):  
V. A. Basarab
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Differential Equations ◽  
Fourier Analysis ◽  
Soil Properties ◽  
Soil Compaction ◽  
Technological Parameters ◽  
Compaction Process ◽  
Properties Of Soil

The article is devoted to determine the technological parameters of soil compaction by rollers according to soil properties in construction. The compaction of the soil occurs due to certain force loads on the soil. Nowadays, there are enough methods to determine the technological parameters of soil compaction process, however, there are few research methods that consider the system of soil-machine-technological parameters. The urgency of the soil compaction process, which ultimately determines the quality of construction products, was emphasized. The basic physical and mechanical properties of soil and technological parameters of the compaction process were given. Analysis of discrete mathematical model of interaction between roller and soil was carried out in order to determine the technological parameters of soil compaction process in the field of construction technologies. A rheological model to describe the soil properties was used. The differential equations of the interaction between roller and soil have been made. A numerical calculation method to solve the differential equations has been proposed. The basic technological parameters of soil compaction process by rollers have been determined - the thickness of soil layer to be compacted, the number of the roller passes, and the speed of the roller movement. The methodology of theoretical and experimental researches of interaction between roller and soil has been proposed in order to clarify the mathematical model and to find the technological parameters of the compaction process. Experimental research methods are based on the determination of the stress-strain state of soil and on the Fourier analysis of the experimental data. Fourier analysis of the experimental data makes it possible to analyze the qualitative energy spectrum of the interaction between roller and soil to determine the rational amplitude-frequency characteristics of the compaction process. Experimental studies allow obtaining such rheological properties of soil as elasticity, viscosity, coefficient of elastic resistance, etc. The main recommendations for the choice of compaction method depending on the type of soil have been proposed.

scholarly journals MOISTURE DYNAMICS MODELLING IN HYSSOPI HERBA DRYING PROCESS BY ACTIVE VENTILATION/DRĖGNIO KITIMO MODELIAVIMAS HYSSOPI HERBA DŽIOVINANT AKTYVIOSIOS VENTILIACIJOS BŪDU/МОДЕЛИРОВАНИЕ ИЗМЕНЕНИЯ ВЛАЖНОСТИ HYSSOPI HERBA В ПРОЦЕССЕ СУШКИ С АКТИВНОЙ ВЕНТИЛЯЦИEЙ

2009 ◽  
Vol 17 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Aurelija Kemzūraitė ◽  
Algirdas Raila ◽  
Kristina Bimbiraitė ◽  
Olga Kornyšova ◽  
Audrius Maruška
Keyword(s):  
Mathematical Model ◽  
Medicinal Herbs ◽  
Raw Material ◽  
Drying Process ◽  
Drying Time ◽  
Dynamics Modelling ◽  
Experimental Values ◽  
Moisture Dynamics ◽  
Hyssopus Officinalis

Medicinal herbs after their harvesting participate in heat exchange with the environmental, as does each organic and hygroscopic material. Drying helps to conserve the medicinal raw material with the maximal preservation of its quality. The present investigation deals with the influence of the surrounding air factors (temperature and relative humidity) on drying intensity. The study object was aboveground part of hyssop (Hyssopus officinalis L.), i.e. Hyssopi herba was used as medicinal raw material. The aim of the study was to offer a mathematical model of time‐related medicinal herbs moisture dynamics and to show its qualitative agreement with the physical model of diffusion as well as to determine the optimum ventilation intensity of medicinal herbs. Drying of Hyssopi herba using active ventilation was investigated. Ventilation intensity and the parameters of the drying agent influenced the processes of moisture dynamics, the total drying time and the quality of Hyssopi herba. The basic prerequisites of the drying process have been analysed. A mathematical model of moisture dynamics has been proposed and used to show the dependence of theoretical moisture dynamics on ventilation velocity. The obtained experimental values of moisture content dynamics during the drying of Hyssopi herba have been shown to agree with theoretical dependences. Santrauka Vaistiniai augalai, kaip ir kiekviena organinė higroskopinė medžiaga, dalyvauja šilumos mainų procese su aplinka. Džiovinant siekiama konservuoti vaistinius augalus iki reikiamo drėgnio, kiek įmanoma išsaugant jų kokybę. Nagrinėta aplinkos oro veiksnių (temperatūros ir santykinio oro drėgnio) įtaka džiovinimo intensyvumui. Tyrimams naudota antžeminė vaistinio isopo (Hyssopus officinalis L.) dalis, t. y. vaistinė augalinė žaliava – isopų žolė (Hyssopi herba). Tyrimų tikslas – sudaryti drėgmės kitimo per tam tikrą laiką matematinį modelį, taikant gautą difuzijos sprendinį, bei nustatyti optimalų ventiliavimo intensyvumą. Tirtas Hyssopi herba džiovinimo taikant aktyviąją ventiliaciją procesas. Išanalizavus pagrindines džiovinimo sąlygas, sudarytas drėgmės kitimo priklausomybės nuo ventiliavimo intensyvumo, matematinis modelis. Ventiliavimo intensyvumas ir džiovinimo agento parametrai turėjo įtakos drėgmės mainų procesams, džiovinimo trukmei ir vaistinės augalinės žaliavos kokybei. Gauti drėgnio kitimo džiovinant Hyssopi herba rezultatai patvirtino, kad teorinės priklausomybės kokybiškai atitinka tiriamąjį procesą. Резюме Лекарственные растения, как и всякий органический гигроскопический материал, участвуют в процессе теплообмена с окружающей средой. С помощью сушки требуется консервировать лекарственные растения до нужной влажности, максимально сохраняя их качествo. Исследовалось влияние температуры и относительной влажности окружающего воздуха на интенсивность сушки. Объект исследования – наземная часть лекарственного иссопа (Hyssopus officinalis L.), т.е. лекарственное сырьё Hyssopi herba. Целью исследования было создать математическую модель изменения влажности с течением времени, применяя полученное решение диффузии, и определить оптимальную интенсивность вентиляции. Процесс сушки Hyssopi herba исследовался способом активной вентиляции. Различные параметры интенсивности вентиляции и сушильной среды влияли на процесс влагообмена, продолжительность сушки и качество лекарственного сырья. Произведен качественный анализ основных предпосылок процесса сушки. Предложена математическая модель изменения влажности, и на ее основе получена теоретическая зависимость изменения влажности от интенсивности вентиляции. Полученные результаты подтвердили соответствие между теоретической моделью и экспериментальными данными.

scholarly journals Calculation of erosion scour of cohesive soil

2021 ◽  
pp. 187-195
Author(s):  
А.Ю. Виноградов ◽  
О.В. Зубова ◽  
Е.А. Парфенов
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Shear Stress ◽  
Cohesive Soil ◽  
Cohesive Soils ◽  
Large Specific Surface Area ◽  
Empirical Relationships ◽  
Clay Particles ◽  
Angle Of Internal Friction

Проведен анализ существующих способов оценки размыва грунтов в гидротехнических и водопропускных сооружениях, показывающий, что определение глубины и скорости размыва проводится без учета физических свойств связных грунтов. Таким образом, данные параметры оцениваются по эмпирическим зависимостям и с существенными погрешностями. Опытные данные по размыву связных грунтов доказывают, что большая удельная поверхность и гидрофильность глинистых частиц приводят к разуплотнению и выносу микроагрегатов грунта в поток. Предложена математическая модель расчета глубины размыва связных грунтов в зависимости от касательного напряжения в грунте. Учет показателей сцепления и угла внутреннего трения в данной модели позволит избежать погрешностей в расчетах. The analysis of existing methods for assessing soil erosion in hydraulic engineering and culverts, showing that the determination of the depth and rate of erosion is carried out without taking into account the physical properties of cohesive soils. Thus, these parameters are estimated using empirical relationships and with significant errors. Experimental data on erosion of cohesive soils prove that the large specific surface area and hydrophilicity of clay particles lead to decompaction and the removal of soil microaggregates into the flow. A mathematical model is proposed for calculating the depth of erosion of cohesive soils depending on the shear stress in the soil. Taking into account the adhesion indicators and the angle of internal friction in this model will avoid errors in the calculations.

scholarly journals Comparative Analysis of Methods for Mathematical Modeling of Specific Electrical Conductivity of Plasma in the Channel of an Electric Discharge in Water

2021 ◽  
Vol 57 (4) ◽  
pp. 24-34
Author(s):  
V.M. Kosenkov ◽  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Electrical Conductivity ◽  
Comparative Analysis ◽  
Electric Discharge ◽  
Specific Electrical Conductivity ◽  
Empirical Function ◽  
Electric Discharge In Water

In the present work, a comparative analysis of three methods for determining the specific electrical conductivity of the plasma formed in the channel of an electric discharge in water is carried out for its mathematical modeling. The parameters of the empirical function are determined, at which the results of mathematical modeling are consistent with the experimental data. The necessity of using empirical functions in calculating the specific electrical conductivity of plasma has been substantiated. The obtained ratios made it possible to significantly increase the adequacy of the previously developed mathematical model of the physical discharge processes in water and to expand the range of parameters in which it can be used.

Determination of the intensity of polychromatic radiation in the reaction compartment as a function of wavenumber

1991 ◽  
Vol 56 (6) ◽  
pp. 1173-1179 ◽  
Author(s):  
Radim Hrdina ◽  
Igor Čepčiansky ◽  
Hana Bittová
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
High Pressure ◽  
Emission Spectrum ◽  
Photochemical Reactions ◽  
Tabular Form ◽  
Mercury Lamp ◽  
Kinetics Of ◽  
Polychromatic Radiation

A procedure is suggested for studying the kinetics of photochemical reactions using excitation with polychromatic radiation, where the wavenumber dependence of the intensity of the polychromatic radiation entering the reaction compartment must be known. The observed relative intensities of the polychromatic source are calibrated by ferrioxalate actinometry, selected parts of the emission spectrum being eliminated by insertion of filters. The relative intensities of an HBO 200 high-pressure mercury lamp were measured. For the sake of brevity, the experimental data were fitted by a mathematical model (a polynominal), and only the parameters of the polynomial are presented in a tabular form.

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