Generalized mathematical model of thermal diffusion in powder metallurgy

Lyashenko, Viktor; Hryhorova, Tetiana

doi:10.1063/1.4902262

Cited by 5 publications

(2 citation statements)

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“…After finishing the averaging the backward process of temperature distributions determination in the inner layers starts 0 1 , r r r 1 2 1 , N N r r r r r r . If it is possible to neglect the temperature distribution along the radius in the second layer of the cylinder, too, then, after averaging by analogy with (8) we get the boundary condition at the interface of the first and second cylinders 2 2 2 2 2 0 2 2 1 2 0 3 3 2 0 2 2 2 2 2 2 2 2 3 0 3 0 3 0 3 3 3 0 2 4 4 2 2 2 2 2 2 2 2 2 2 0 3 3 0 0 ( , …”

Section: T R T T T R L T Tmentioning

confidence: 99%

“…Determination of three-dimensional temperature distributions generated by electromagnetic field activity in electrical machines is an extremely complicated problem of mathematical modeling and mathematical physics [3,4,5,6,7,8]. Electromagnetic fields are described by models containing Maxwell equations system, equation of charge continuity and Ohm's law [9,10,11,12 H E J -magnetic fieldstrength, electric field strength, electric current density, electric charge density, electrical conductivity.…”

Section: Introductionmentioning

confidence: 99%

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The generalized mathematical model of heat conduction in a complex multi-layered area

Zaika

Hrytsiuk

Kobilskaya

et al. 2017

AIP Conference Proceedings

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Abstract.A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area -a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.

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Section: T R T T T R L T Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The generalized mathematical model of heat conduction in a complex multi-layered area

Zaika

Hrytsiuk

Kobilskaya

et al. 2017

AIP Conference Proceedings

Self Cite

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Contact of boundary-value problems and nonlocal problems in mathematical models of heat transfer

Lyashenko

Kobilskaya

2015

AIP Conference Proceedings

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Transient Dynamic Response of a Semi-infinite Elastic Permeable Solid with Cylindrical Hole Subject to Laser Pulse Heating Under Different Theories of Generalized Thermoelasticity

Paul

Mukhopadhyay

2021

TECM

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Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole. The temporal scheme of laser beam is considered as non-Gaussian and is acted on the surface of the cylindrical hole. The problem is solved with the help of Laplace transform domain and finally illustrated graphically. Note: This article will be very useful in material science specially, in powder metallurgy during sintering, hot pressing, wire and rods annealing are examined from a unified physical point of view, in different branches of engineering physics like plasma physics, nuclear physics, geophysics and related topics and also in oil industry (Lyashenko and Hryhorova (2014), Long and Heng-Wei (2018), Fryxell and Aitken (1969), Nowinski (1978), Legros et al. (1998), Galliero et al. (2019) etc.).

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Generalized mathematical model of thermal diffusion in powder metallurgy

Cited by 5 publications

References 1 publication

The generalized mathematical model of heat conduction in a complex multi-layered area

The generalized mathematical model of heat conduction in a complex multi-layered area

Contact of boundary-value problems and nonlocal problems in mathematical models of heat transfer

Transient Dynamic Response of a Semi-infinite Elastic Permeable Solid with Cylindrical Hole Subject to Laser Pulse Heating Under Different Theories of Generalized Thermoelasticity

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