scholarly journals ANALYSIS OF THE MATHEMATICAL MODEL OF THE WASTE OIL PURIFICATION IN A DIESEL LOCOMOTIVE ENGINE

2020 ◽  
Vol 61 (3) ◽  
pp. 108-113
Author(s):  
Olga M. Gorbacheva ◽  
◽  
Aleksandr S. Borovskii ◽  
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Impurity Particle ◽  
Waste Oil ◽  
Diesel Locomotive ◽  
Locomotive Engine ◽  
Oil Purification ◽  
Particle Velocities ◽  
The Mathematical Model ◽  
Concentration Of Impurities

The article analyses a mathematical model of the waste oil purification in the oil system of a diesel locomotive engine. Waste oil purification takes place directly in the engine during its operation, which enables to reduce considerably the time taken to purify, and to decrease the concentration of impurities in the oil. In the proposed system for automatic control of waste oil purification, the main monitored parameters are pressure and temperature of the oil being purified. During analyzing the analytical solution of the system, the authors studied an increase in the concentration of impurity particles, the behavior of particle velocities in the centrifuge, and determined assumptions, within the framework of which the velocity of impurity particles was simulated. The influence of the impurity particle shape in the oil was taken into account in making these assumptions.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Torus-Like Balloons

2020 ◽  
Vol 56 ◽  
pp. 59-65
Author(s):  
Ivïalo M. Mladenov ◽  
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Elliptic Integrals ◽  
Deployable Structures ◽  
The Future ◽  
The Mathematical Model

The concepts for inflatable deployable structures have been under development and evaluation for many years. Strangely enough only the Mylar balloon up to now has been described adequately. Here we provide the mathematical model and its analytical solution for the torus-like balloons. Their characteristics and shapes are described explicitly in terms of elliptic integrals. The obtained results are commented shortly and the possible directions for the related studies in the future are outlined.

scholarly journals On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Luisa Consiglieri ◽  
Ana Rute Domingos
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Analytical Solution ◽  
Parabolic Equations ◽  
Three Dimensional ◽  
Sodium Concentration ◽  
Dynamical Boundary Condition ◽  
Sodium Diffusion ◽  
The Mathematical Model ◽  
Concentration Diffusion

We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration. The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple. Our first novelty comes from this general dynamical boundary condition. The second one is the three-dimensional behaviour of the extracellular stimulus. An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.

scholarly journals Analysis of the non-stationary mathematical model of a simple hydraulic network with a centrifugal pump

Vestnik IGEU ◽  
2020 ◽  
pp. 64-70
Author(s):  
V.A. Naumov
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Centrifugal Pump ◽  
Similarity Criteria ◽  
Dimensionless Form ◽  
Maximum Volume ◽  
Stationary Flows ◽  
Variable Level ◽  
Hydraulic Network ◽  
The Mathematical Model

Simple hydraulic networks with a centrifugal pump are not only part of complex networks, but are also widely used in Autonomous water supply and Sewerage systems. The mathematical model of simple networks taking into account the variable level of liquid in reservoirs includes the well-known Bernoulli equation for non-stationary flows. Published works on this problem do not take into account the non-stationary nature of the flow due to the variable liquid level. The conditions for using the quasi-stationary model are not discussed. Similarity criteria for the issue were not found. The purpose of the study is to analyze the non-stationary mathematical model of the object, including the definition of criteria for similarity of the problem and their impact on the solution. The well-known equations of fluid quantity balance and Bernoulli for non-stationary flows with smoothly changing characteristics were used as a mathematical model of a simple hydraulic network. The pressure characteristic of a centrifugal pump is approximated by a well-established dependence in the form of a square three-member. The system of differential equations was reduced to a dimensionless form. Analytical and numerical methods were used to solve the problem. The analysis of the mathematical model of pumping liquid by a centrifugal pump in a hydraulic network with a variable level was carried out. The dimensionless form of the system of equations allowed us to determine three similarity criteria for the problem, including the analog of the Struhal number Str. The analytical solution to the Cauchy problem is found in the quasi-stationary formulation (Str = 0). The solution of the problem in the full statement is obtained by the numerical method. The results of the study of the influence of similarity criteria on the solution are presented. The dimensionless flow rate of the liquid decreases with increasing Str values. In this case, the maximum volume of liquid and the time to reach it increases. Increasing the values of the other two criteria leads to an increase in both the flow rate and the maximum volume of the liquid. The analytical solution in the quasi-rational formulation can be used only for Str < 0,1. The results obtained can be used in the design of Autonomous Water supply and Sewerage systems. Further research for the non-self-similar area of hydraulic resistance and for variable fluid viscosity is promising.

scholarly journals Growth of N-dimensional spherical bubble within viscous, superheated liquid: Analytical solution

2019 ◽  
pp. 380-380
Author(s):  
Gamiel Shalaby ◽  
Ali Abu-Bakr
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Variable Viscosity ◽  
Superheated Liquid ◽  
Spherical Bubble ◽  
The Mathematical Model

In this paper, we present the study of the bevaiour of spherical bubble in N-dimensions fluid. The fluid is a mixture of vapour and superheated liquid. The mathematical model is formulated in N-dimensions fluid on the basis of continuity and momentum equations, and solved its analytically. The variable viscosity is taken in an account problem. The obtained results show that the radius of bubble increases with the decreasing of the value of N-dimensions.

AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

2021 ◽  
pp. 2150033
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha sohail ◽  
Andleeb Zafar ◽  
Rana Talha ◽  
Sadiq M. Sait
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Ethylene Oxide ◽  
Ethylene Glycol ◽  
Exothermic Reaction ◽  
Plug Flow ◽  
Material Balance ◽  
Chemical Species ◽  
Future Research ◽  
The Mathematical Model

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198[Formula: see text]C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129[Formula: see text]C and freezes at [Formula: see text]C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

scholarly journals COMPUTER SIMULATION AND ANALYTICAL SOLUTION OF FOUR BAR MECHANISM

2020 ◽  
pp. 120-128
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Computer Model ◽  
Analytical Methods ◽  
Kinematic Analysis ◽  
Linkage Mechanism ◽  
The Creation ◽  
Four Bar Linkage ◽  
The Mathematical Model

Urgency of the research. The use of computers in technical practice leads to the extension of the possibility of solving mathematical models. This makes it possible to gradually automate complex calculations of equations of mathematical models. It is necessary to input the relevant inputs of the mathematical model, to build a simulation computer model and to monitor and evaluate the output results using a computer's output device. Target setting. The possibilities of modeling a four-bar linkage mechanism by classical analytical methods and methodsusing computer modeling are presented in this paper.The problem is to describe the creation of a computer model and to show the mathematical model and its solution in the classical ways. Actual scientific researches and issues analysis. The inspiration for the creation of the article was the study of the mechanisms in the work [1-3] and the study of other resources available in library and journal materials, as well as prepared study materials for students of Technical university Kosice. Uninvestigated parts of general matters defining. The question of building a real mechanism model. The possibilities to building a real model, based on the result of simulation. The research objective. The aim of this paper is to develop a functional model of the mechanism in ADAMS/View and Matlab and its complete kinematic analysis.The statement of basic materials.The task was to create a computer model in MSC Adams and Matlab and to perform a four-bar linkage mechanism kinematic analysis. At the same time the classical procedure of analytical methods of kinematic analysis was described. Kinematic сharacteristics of driven members and their selected points were determined. The movement of the parts of the mechanism in its significant points was analyzed. The results of the solution were shown in both programs in graphical form. Kinematic analysis was performed by both vector and graphical methods. Finally, the results with a graphical representation of parameters such as angular displacement, angular velocity and angular acceleration of mechanism members are presented in this work. The results of these solutions are created in the form of graphs. To ensure that the results do not differ from the model real, a good computer model gradually was created by its verification and modification, which is one of the advantages of MSC Adams. The practical applicability of the mathematical model was limited by the existence of an analytical solution. Conclusions. The development of computer technology has expanded the limit of solvability of mathematical models and made it possible to gradually automate the calculation of equations of mathematical models. In a computer model the auto-mated calculation can be treated as a real object sample. In various variations of calculation, we can monitor and measure the behavior of an object under different conditions, under the influence of different inputs. Graphical and vector methods were used for classical analytical methods. MSC Adams and Matlab were used for the automated calculations.

scholarly journals Mathematical model of heat transfer in opening electrical contacts with tunnel effect

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1003-1008
Author(s):  
Merey Sarsengeldin ◽  
Stanislav Kharin ◽  
Zhangir Rayev ◽  
Yermek Khairullin
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Moving Boundary ◽  
Thermal Contact ◽  
Electrical Contacts ◽  
Tunnel Effect ◽  
Heat Equations ◽  
Integral Error ◽  
The Mathematical Model

The mathematical model describing the dynamics of heating in opening electrical contacts is presented. It takes into account the imperfect thermal contact between anode and cathode due to tunnel effect. The model is based on the system of spherical heat equations in a domain with moving boundary. The analytical solution is found in the form of series containing the integral error functions.

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