Solution of Moore–Gibson–Thompson Equation of an Unbounded Medium with a Cylindrical Hole

Ahmed E. Abouelregal; Hakan Ersoy; Ömer Civalek

doi:10.3390/math9131536

Solution of Moore–Gibson–Thompson Equation of an Unbounded Medium with a Cylindrical Hole

Mathematics ◽

10.3390/math9131536 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1536

Author(s):

Ahmed E. Abouelregal ◽

Hakan Ersoy ◽

Ömer Civalek

Keyword(s):

Diffusion Processes ◽

Relaxation Times ◽

Mass Diffusion ◽

Cylindrical Hole ◽

Cavity Surface ◽

Approximation Technique ◽

Diffusion Analysis ◽

Unbounded Medium ◽

Inversion Techniques ◽

And Diffusion

In the current article, in the presence of thermal and diffusion processes, the equations governing elastic materials through thermodiffusion are obtained. The Moore–Gibson–Thompson (MGT) equation modifies and defines the equations for thermal conduction and mass diffusion that occur in solids. This modification is based on adding heat and diffusion relaxation times in the Green–Naghdi Type III (GN-III) models. In an unbounded medium with a cylindrical hole, the built model has been applied to examine the influence of the coupling between temperature and mass diffusion and responses. At constant concentration as well as intermittent and decaying varying heat, the surrounding cavity surface is traction-free and is filled slowly. Laplace transform and Laplace inversion techniques are applied to obtain the solutions of the studied field variables. In order to explore thermal diffusion analysis and find closed solutions, a suitable numerical approximation technique has been used. Comparisons are made between the results obtained with the results of the corresponding previous models. Additionally, to explain and realize the presented model, tables and figures for various physical fields are presented.

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Meridional Circulation, Turbulence, and Diffusion Processes in Stars

International Astronomical Union Colloquium ◽

10.1017/s0252921100080477 ◽

1976 ◽

Vol 32 ◽

pp. 109-116 ◽

Cited By ~ 1

Author(s):

S. Vauclair

Keyword(s):

Convection Zone ◽

Diffusion Processes ◽

Meridional Circulation ◽

Diffusion Time ◽

Work In Progress ◽

First Results ◽

Stellar Envelopes ◽

And Diffusion ◽

Turbulence And Diffusion ◽

Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

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NMR-Study of Structure and Diffusion Processes in Li3N

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1980607 ◽

1980 ◽

Vol 41 (C6) ◽

pp. C6-28-C6-31 ◽

Cited By ~ 2

Author(s):

R. Messer ◽

H. Birli ◽

K. Differt

Keyword(s):

Diffusion Processes ◽

Nmr Study ◽

And Diffusion

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Effect of cluster-gradient architecture of nanostructured topocomposites on features of tribointeraction with heterophased material

10.36652/1813-1336-2020-16-3-130-135 ◽

2020 ◽

pp. 130-135

Author(s):

D.N. Korotaev ◽

K.N. Poleshchenko ◽

E.N. Eremin ◽

E.E. Tarasov

Keyword(s):

Wear Resistance ◽

Titanium Alloy ◽

Energy Dissipation ◽

Phase Structure ◽

Diffusion Processes ◽

Structural Phase ◽

High Wear Resistance ◽

Wear Characteristics ◽

And Diffusion

The wear resistance and wear characteristics of cluster-gradient architecture (CGA) nanostructured topocomposites are studied. The specifics of tribocontact interaction under microcutting conditions is considered. The reasons for retention of high wear resistance of this class of nanostructured topocomposites are studied. The mechanisms of energy dissipation from the tribocontact zone, due to the nanogeometry and the structural-phase structure of CGA topocomposites are analyzed. The role of triboactivated deformation and diffusion processes in providing increased wear resistance of carbide-based topocomposites is shown. They are tested under the conditions of blade processing of heat-resistant titanium alloy.

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Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Diffusional Change of Solid Particle Size

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19960536 ◽

1996 ◽

Vol 61 (4) ◽

pp. 536-563

Author(s):

Vladimír Kudrna ◽

Pavel Hasal

Keyword(s):

Particle Size ◽

Solid Particle ◽

Chemical Engineering ◽

Diffusion Processes ◽

Granular Systems ◽

Size Distributions ◽

Particle Size Distributions ◽

Diffusion Term ◽

Population Balances ◽

And Diffusion

To the description of changes of solid particle size in population, the application was proposed of stochastic differential equations and diffusion equations adequate to them making it possible to express the development of these populations in time. Particular relations were derived for some particle size distributions in flow and batch equipments. It was shown that it is expedient to complement the population balances often used for the description of granular systems by a "diffusion" term making it possible to express the effects of random influences in the growth process and/or particle diminution.

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NMR Relaxation Times of Benzene Adsorbed on Charcoal: Molecular Rotation and Diffusion

The Journal of Chemical Physics ◽

10.1063/1.1696574 ◽

1965 ◽

Vol 43 (11) ◽

pp. 3853-3865 ◽

Cited By ~ 31

Author(s):

J. K. Thompson ◽

J. J. Krebs ◽

H. A. Resing

Keyword(s):

Relaxation Times ◽

Nmr Relaxation ◽

Molecular Rotation ◽

Nmr Relaxation Times ◽

And Diffusion

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Influence of Geometry on Thin Layer and Diffusion Processes at Carbon Electrodes

Langmuir ◽

10.1021/acs.langmuir.0c03315 ◽

2021 ◽

Author(s):

Qun Cao ◽

Zijun Shao ◽

Dale K. Hensley ◽

Nickolay V. Lavrik ◽

B. Jill Venton

Keyword(s):

Thin Layer ◽

Diffusion Processes ◽

Carbon Electrodes ◽

And Diffusion

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Decoupling Electrochemical Reaction and Diffusion Processes in Ionically-Conductive Solids on the Nanometer Scale

ACS Nano ◽

10.1021/nn101502x ◽

2010 ◽

Vol 4 (12) ◽

pp. 7349-7357 ◽

Cited By ~ 77

Author(s):

Nina Balke ◽

Stephen Jesse ◽

Yoongu Kim ◽

Leslie Adamczyk ◽

Ilia N. Ivanov ◽

...

Keyword(s):

Diffusion Processes ◽

Electrochemical Reaction ◽

Nanometer Scale ◽

And Diffusion ◽

Reaction And Diffusion

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Rapid Thermal Annealing of Ni/Al/Si and Ni/Si Systems

MRS Proceedings ◽

10.1557/proc-74-647 ◽

1986 ◽

Vol 74 ◽

Cited By ~ 2

Author(s):

A. Katz ◽

Y. KOMEM

Keyword(s):

Thermal Annealing ◽

Rapid Thermal Annealing ◽

Thermal Processing ◽

Reference System ◽

Diffusion Processes ◽

Eutectic Temperature ◽

Melting Process ◽

Polycrystalline Layer ◽

Smooth Interface ◽

And Diffusion

AbstractThe effect of Rapid Thermal Annealing on phase formation and diffusion processes in the Ni(30 nm) /Al(10 nm)/Si system was studied and coxpared to a Ni(30 nm)/Si reference system. Heat treatments were carried out at temperatures between 400°C and 900°C for 2 seconds.The results obtained by means of TEM, AES and XRD indicated that the Ni/Al/Si system underwent a local melting in the intermediate Al layer at the Al/Si eutectic temperature (577°C). This reaction, due to the rapid melting process, resulted in formation of a unique layered-structure composed of a columnar polycrystalline layer (60 nm thick) of Ni2Si and NiSi adjacent to the Si substrate with relatively smooth interface and an outer layer of two separate polycrystalline films (both about 10 m thick) of Al3Ni (inside) and Ni(Al0.5Si0.5 ) (outside). Under the same rapid thermal processing conditions the Ni/Si reference system underwent a solid state reaction which resulted in the formation of a polycrystalline layer (60 nm thick) composed of Ni2Si and NiSi as well as NiSi2.

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