scholarly journals SIMPLIFIED MATHEMATICAL MODEL OF A MAGNETIC SYSTEM WITH A CIRCULAR MAGNETIC CONDUCTOR

2021 ◽  
Author(s):  
Yuriy Kreselyuk ◽  
Anastasiya Ivzhenko ◽  
Mihail Kirsa
Keyword(s):  
Mathematical Model ◽  
Magnetic Flux ◽  
Coordinate System ◽  
Magnetic System ◽  
Magnetic Core ◽  
Cylindrical Coordinate System ◽  
Magnetic Conductor ◽  
Rectangular Coordinate System ◽  
Cylindrical Coordinate ◽  
Simplified Mathematical Model

A simplified design of a magnetic system with a circular magnetic core is presented and its mathematical model is developed to determine the magnetic flux. Transition from a cylindrical coordinate system to a rectangular coordinate system.

scholarly journals Efficient Computation of Heat Distribution of Processed Materials under Laser Irradiation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1368
Author(s):  
Jianxin Zhu ◽  
Wencheng Lin
Keyword(s):  
Coordinate System ◽  
Boundary Value ◽  
Euler Method ◽  
Cylindrical Coordinate System ◽  
Heat Distribution ◽  
Efficient Computation ◽  
Rectangular Coordinate System ◽  
Boundary Value Condition ◽  
Backward Euler ◽  
Cylindrical Coordinate

In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient.

scholarly journals FIRST PROJECTION OF THE EQUATION OF MOTION IN THE CYLINDRICAL COORDINATE SYSTEM

2016 ◽  
pp. 90-92
Author(s):  
A. G. Obukhov ◽  
R. E. Volkov
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Equation Of Motion ◽  
Cylindrical Coordinate System ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Cylindrical Coordinate

It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.

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