scholarly journals Mathematical modeling of chilling process of polymer tube billets

2020 ◽  
Vol 8 (2) ◽  
pp. 24-33
Author(s):  
I. Kuzyayev ◽  
◽  
O. Mitrokhin ◽  
I. Kazimirov ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Integral Transform ◽  
Extrusion Process ◽  
Polymer Processing ◽  
Heating Process ◽  
Transform Method ◽  
Polymer Tube ◽  
Main Components ◽  
The Mathematical Model

There are many works about producing of polymer tubes. But less attention is paid to the process of chilling of polymer products. The chilling of polymer tube billets, as most polymer processing processes, is a non-isothermal process. This means that it is necessary to solve the heat problem. Accurate calculation of the heat balance is one of the main components for the final result of the extrusion process. The mathematical model had been created for process of chilling of polymer tube billets after extrusion in this work. Several mathematical models of heating process for heat and power equipment have been created. Different calculation schemes, methods and equations for its solution are suggested. The mathematical model for process of chilling of polymer tube billets after it extrusion can be considered an expansion of research. The mathematical model is based on cylindrical coordinate system with assumption of axisymmetric along angular coordinate. The initial problem statement considered non-stationary process. A transition was made to the differential equation in partial derivatives along two linear coordinates. Solution of this equation was found using the operation method (Laplace integral transform method). The final solution of the problem (after direct and reverse Laplace transform) was obtained from the Bessel function. It was calculated in MathCAD with the help of built-in functions and computing modules. The mathematical model was created for modeling and optimization of process of chilling of polymer tube billets. The results of calculation were presented as graphs that make it possible to characterize the adequacy of the materials. Keywords: mathematical model, balance equation, Laplace transform, program block.

The Calculation of Ship Wave in Shallow Water by Finite Difference Method

2013 ◽  
Vol 409-410 ◽  
pp. 1461-1464
Author(s):  
Deng Hui ◽  
Zhi Hong Zhang ◽  
Jian Nong Gu
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Shallow Water ◽  
Difference Method ◽  
Integral Transform ◽  
Fourier Integral ◽  
Transform Method ◽  
The Mathematical Model ◽  
Supercritical Speed

Based on the shallow water wave potential flow theory and slender ship assumption, the mathematical model is established for calculating wave caused by ship moving at supercritical speed. The wave pattern caused by ship moving at supercritical speed in shallow water was calculated by using the finite difference method. The effects of channel wall were analyzed. The computed results were compared with the ones calculated by Fourier integral transform method and experiment. A good agreement exists between the calculated with experimental results. The mathematical model and the calculation method were validated.

scholarly journals Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

2020 ◽  
Author(s):  
A. John Christopher ◽  
N. Magesh ◽  
G. Tamil Preethi
Keyword(s):  
Mathematical Model ◽  
Preventive Measures ◽  
Control Strategies ◽  
Transformation Method ◽  
Dynamical Analysis ◽  
Transform Method ◽  
Potential Control ◽  
Corona Virus ◽  
Differential Transform ◽  
The Mathematical Model

Abstract The aim of this paper is applying the Differential Transformation Method (DTM) to analyze and find the solution for the mathematical model described by the system of nonlinear ordinary differential equations which describe the epidemiology of the most threatening virus called Corona-virus later labelled as COVID-19. The behaviour of the outcomes is presented in terms of plots. Finally, the present study may help you to examine the wild class of real world models and also aid to predict their behaviour with respect to parameters considered in the model. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

Mathematical Model and Analytical Solution for the Vibration of Inclined Fluid-Transporting Submarine Pipelines

2019 ◽  
Vol 161 (A4) ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Integral Transform ◽  
Internal Flow ◽  
Equation System ◽  
Theoretical Understanding ◽  
Wake Oscillator ◽  
Lock In ◽  
Irregular Topography ◽  
The Mathematical Model

Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free-spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.

Effect of Continuous Heating on Grain Growth in Fe-40Ni-Ti Alloy

2014 ◽  
Vol 988 ◽  
pp. 151-155
Author(s):  
Shao Qiang Yuan ◽  
Yue Hui Yang ◽  
Zhen Liang Wang
Keyword(s):  
Mathematical Model ◽  
Grain Size ◽  
Grain Growth ◽  
Experimental Results ◽  
Continuous Heating ◽  
Heating Process ◽  
Ti Alloy ◽  
Size Growth ◽  
Metallographic Observation ◽  
The Mathematical Model

The grain growth of Fe-40Ni-Ti alloy was investigated by means of metallographic observation during continuous heating. The experimental results indicate that: the microstructures consist of multi-polygon austenite. No transformation happens of tested alloy during heating only the grain size increases gradually. The size of grain grows steadily below 1160°C until 1200°C, the grain size growth unusually. The process of grain growth has relations with the dissolving of TiN particles. Finally, the mathematical model of grain growth in continuous heating process was obtained for the tested alloy.

scholarly journals The Effect of Functionally Graded Materials on Temperature during Frictional Heating: Under Uniform Sliding

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4285
Author(s):  
Aleksander Yevtushenko ◽  
Katarzyna Topczewska ◽  
Przemysław Zamojski
Keyword(s):  
Mathematical Model ◽  
Functionally Graded Materials ◽  
Frictional Heating ◽  
Ceramic Materials ◽  
Functionally Graded ◽  
Heating Process ◽  
Spatial Distributions ◽  
Graded Materials ◽  
Exponential Change ◽  
The Mathematical Model

The mathematical model of heating process for a friction system made of functionally graded materials (FGMs) was proposed. For this purpose, the boundary-value problem of heat conduction was formulated for two semi-spaces under uniform sliding taking into consideration heating due to friction. Assuming an exponential change in thermal conductivities of the materials, the exact, as well as asymptotic (for small values of time), solutions to this problem were obtained. A numerical analysis was performed for two elements made of ZrO2–Ti-6Al-4V and Al3O2–TiC composites. The influence of the gradient parameters of both materials on the evolution and spatial distributions of the temperature were investigated. The temperatures of the elements made of FGMs were compared with the temperatures found for the homogeneous ceramic materials.

scholarly journals Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1112
Author(s):  
María-Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Laplace Transform ◽  
Integral Transform ◽  
Gaussian Quadrature ◽  
Finite Degree ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform ◽  
Non Gaussian ◽  
Laplace Transform Inversion ◽  
Integral Transform Method

In this paper, we propose an integral transform method for the numerical solution of random mean square parabolic models, that makes manageable the computational complexity due to the storage of intermediate information when one applies iterative methods. By applying the random Laplace transform method combined with the use of Monte Carlo and numerical integration of the Laplace transform inversion, an easy expression of the approximating stochastic process allows the manageable computation of the statistical moments of the approximation.

scholarly journals Solution of One-dimensional Partial Differential Equation with Higher-Order Derivative by Double Laplace Transform Method

2021 ◽  
Vol 4 (3) ◽  
pp. 1-11
Author(s):  
Anongo D.O. ◽  
Awari Y.S.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Integral Transform ◽  
Higher Order ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Double Laplace Transform ◽  
Engineering Sciences

Many problems in natural and engineering sciences such as heat transfer, elasticity, quantum mechanics, water flow, and others are modelled mathematically by partial differential equations. Some of these problems may be linear, nonlinear, homogeneous, non-homogeneous, and order greater or equal one. Finding the theoretical solution to these problems with less cumbersome techniques is an active area of research in the aforementioned field. In this research paper, we have developed a new application of the double Laplace transform method to solve homogeneous and non-homogeneous linear partial differential equations (pdes) with higher-order derivatives (i.e order n where n≥2) in science and engineering. We discussed a brief theory of double Laplace transforms that helped in its application. The main advantage of our method is the reduction of computational effort in finding solution to pdes. Another major benefit of our method is solving problems in the form of (21) directly by transforming to an algebraic equation where the inverse double Laplace transform is implemented for analytical solution, unlike other integral transform methods that would first transform to a system of ODEs before they are solved, is it also very effective in solving linear high-order partial differential equations and yield fast convergence. We present a well-simplified solution for easier comprehension by upcoming researchers.

scholarly journals Solusi Model Perubahan Garis Pantai dengan Metode Transformasi Elzaki

2021 ◽  
Vol 4 (2) ◽  
pp. 66
Author(s):  
Maya Sari Wahyuni ◽  
S. Sukarna ◽  
Muh. Irham Rosadi
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Human Activities ◽  
Integral Transform ◽  
Research Result ◽  
Shoreline Change ◽  
Fourier Integral ◽  
Change Model ◽  
Transform Method

. Pantai merupakan kawasan yang sering dimanfaatkan untuk berbagai kegiatan manusia, namun seringkali upaya pemanfaatan tersebut menyebabkan permasalahan pantai sehingga garis pantai berubah. Salah satu cara yang dapat digunakan untuk mengetahui perubahan garis pantai yaitu dengan membuat model matematika. Model perubahan garis pantai berbentuk persamaan diferensial parsial dapat diselesaikan secara analitik dengan menggunakan metode transformasi Elazki. Metode transformasi Elzaki merupakan salah satu bentuk transformasi integral yang diperoleh dari integral Fourier sehingga didapatkan transformasi Elzaki dan sifat-sifat dasarnya. Perubahan garis pantai pada penelitian ini dipengaruhi oleh adanya groin. Penyelesaian model perubahan garis pantai dengan metode transformasi Elzaki dilakukan dengan menerapkan transformasi Elzaki pada model perubahan garis pantai untuk memperoleh model perubahan garis pantai yang baru, kemudian menerapkan syarat batas, kemudian menerapkan invers transformasi Elzaki sehingga diperoleh solusi model perubahan garis pantai. Berdasarkan hasil penelitian, diperoleh bahwa terdapat kesamaan antara pola grafik yang dihasilkan dari solusi model perubahan garis pantai dengan metode transformasi Elzaki dan solusi model perubahan garis pantai dengan metode numerik.Kata Kunci: Perubahan garis pantai, Groin, Analitik, Transformasi Elzaki.The beach is a region that is often used for various human activities, however often these utilization efforts cause beach problems so that the shoreline changes. One way that can be used to determine changes in shoreline is to make a mathematical model. The shoreline change model shaped of partial differential equation can be solved analytically by using the Elzaki transform method. The Elzaki transform method is a form of integral transform obtained from the Fourier integral so that the Elzaki transform and its basic properties are obtained. Shoreline change in this research were affected by groyne. Solution of shoreline change model using Elzaki transform method is carried by applying the Elzaki transform to the shoreline change model to obtain a new shoreline change model, then applying the boundary value, then applying the inverse of Elzaki transform so obtained a solution shoreline change model. Based on the research result, it was found that there was a similiarity between the graphic patterns generated from the solution of shoreline change model using Elzaki transform method and the solution of shoreline change model using numerical method.Keywords: Shoreline change, Groyne, Analitic, Elzaki transform

Simulation and Test of Seperated and Manually Adjustable Shock Absorber

2013 ◽  
Vol 803 ◽  
pp. 467-470
Author(s):  
Zhen Ping Zhou ◽  
Jing Tong ◽  
Zhi Yuan Gu ◽  
Gong Ke Yang ◽  
Da Feng Song
Keyword(s):  
Mathematical Model ◽  
Shock Absorber ◽  
Test Bench ◽  
Needle Valve ◽  
Depth Study ◽  
Absorber Structure ◽  
Working Principle ◽  
Time Test ◽  
Main Components ◽  
The Mathematical Model

A mathematical model was established on the bases of the analysis of an air-charged split-type adjustable damping shock absorber structure and its working principle, using Matlab to simulate the shock absorber model, at the same time test the shock absorber on the test bench, verified the validity of the mathematical model. On this basis, the main components of the vice-tube such as the nitrogen chamber, the diameter of the needle valve and the spring valve have been simulated to analysis the affection to the shock absorber, so as to lay the foundation for later in-depth study.

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