MATHEMATICAL MODEL FOR VORTEX-INDUCED OSCILLATIONS OF CONTINUOUS SYSTEMS WITH CIRCULAR CROSS SECTION

1984 ◽  
pp. 431-442
Author(s):  
Y. TAMURA ◽  
A. AMANO
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Circular Cross Section ◽  
Continuous Systems

scholarly journals A Refined Mathematical Model of Physical Processes in a Conductor at a High-Current Pulse Discharge

2021 ◽  
Vol 60 (3) ◽  
pp. 124-132
Author(s):  
Yevgen Bajda ◽  
Michael Pantelyat
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Current Density ◽  
Thermal Stresses ◽  
Pulse Discharge ◽  
Circular Cross Section ◽  
Nonuniform Heating ◽  
Physical Processes ◽  
Short Term ◽  
The Cross

A novel mathematical model describing physical processes during the flow of an aperiodic pulse current with amplitude of 100 kA along a conductor with a circular cross-section is proposed and investigated. It is shown how a short-term electric discharge of an aperiodic shape affects the distribution of the current density in the cross-section of the conductor, causing its nonuniform heating and the appearance of significant thermal forces as well as mechanical stresses and strains. Based on the developed mathematical model, the relation-ship between electromagnetic, thermal and mechanical phenomena is shown, allowing a deeper understanding of the multiphysics processes taking place. The maximum values of the current density are calculated, which on the surface of the conductor reach values of 47 kA/mm2, while the temperature rise of a copper conductor with a diameter of 2.44 mm is no more than 80ºC at high temperature gradients, which causes the appearance of thermal stresses that have value (40–50)% of the value of the short-term strength limit of electrical copper. Utilization of this model allows to more accurately determine the required conductor cross-section based on the characteristics of electromagnetic, thermal and mechanical pro-cesses. It is shown that the simplified model (the condition for the uniform distribution of the current over the cross-section) gives significantly underestimated values of temperatures and does not take into account temperature deformations.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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