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 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 Simulation of thermal processes on the electrode of a miniature protective spark gap

2021 ◽  
Vol 12 (32) ◽  
pp. 127-138
Author(s):  
Igor A. Murog ◽  
Valery F. Gnido ◽  
Elena V. Tinina ◽  
Igor A. Ilchuk ◽  
Tatiana A. Asayeva
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Temperature Field ◽  
Cathode Spot ◽  
Balance Of Power ◽  
Nonlinear Heat Equation ◽  
Thermal Processes ◽  
Melting Points ◽  
Spark Gap ◽  
The Finite Difference Method

The article discusses the issues that arise when determining the temperature in the region of the cathode spot in miniature protective spark gaps. The modeling principle is used to study the temperature field on the spark gap electrode. A mathematical model of the process is compiled on the basis of the balance of power entering the cathode spot and its removal inside the cathode due to thermal conductivity. A numerical solution of the obtained nonlinear heat equation with inhomogeneous boundary conditions by the finite-difference method is presented. The authors compared the found temperatures in the cathode spot for metals of the fourth and fifth groups of the Mendeleev's Periodic Table with the corresponding melting points of the selected metals. A complete correlation was obtained between these temperatures. Simulation of thermal processes in the region of the cathode spot on the electrode made of 42NA-VI alloy has been carried out. The results are presented in the form of diagrams.

Modeling of work of plate water evaporation coolers of indirect operation principle

10.12737/2199 ◽  
2014 ◽  
Vol 3 (4) ◽  
pp. 160-166
Author(s):  
Шацкий ◽  
Vladimir Shatskiy ◽  
Гулевский ◽  
Vyacheslav Gulevskiy
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Boundary Conditions ◽  
Cross Section ◽  
Parabolic Type ◽  
Water Evaporation ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Proposed Model ◽  
Complex Mathematical Model

More complex mathematical model is proposed which is a system of partial differential equations of elliptic and parabolic type with the corresponding initial and boundary conditions, which are not involved in the heat transfer coefficients, the deter-mination of the numerical values of which is very difficult. For its implementation diffe-rence analogue of the proposed model was built with Nx steps along the length of the channel, Ny steps along the section of channels, Ny / 2 +1 steps of the cross section of the plate. The presented model and the method of its implementation makes it possible to determine the temperature of the air flows along the length of coolers that offers a choice of the geometric parameters.

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. 

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1843
Author(s):  
Jelena Vlaović ◽  
Snježana Rimac-Drlje ◽  
Drago Žagar
Keyword(s):  
Mathematical Model ◽  
Spatial Information ◽  
Relevant Literature ◽  
Video Quality ◽  
Similarity Index ◽  
Video Encoding ◽  
Adaptation Algorithm ◽  
Subjective Testing ◽  
Proposed Model ◽  
The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

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