2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model

Mohamed I. A. Othman; Nehal T. Mansour

doi:doi:10.11648/j.nano.20160404.11

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2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model

Mohamed I. A. Othman, Nehal T. Mansour

Published in American Journal of Nano Research and Applications (Volume 4, Issue 4)

Received: 8 December 2016 Accepted: 20 December 2016 Published: 14 January 2017

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Abstract

Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermo-elastic solid half-space under hydrostatic initial stress, rotation, magnetic field and gravity with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by the three-phase-lag model, Green-Naghdi III and Lord-Shulman theories.

Published in	American Journal of Nano Research and Applications (Volume 4, Issue 4)
DOI	10.11648/j.nano.20160404.11
Page(s)	33-42
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Initial Stress, Three-Phase-Lag, Gravity, Rotation, Magnetic Field, Two-Temperature

References

[1]	Hetnarski, R.-B. and Ignaczak, J., (1999) “Generalized thermoelasticity”, Journal of Thermal Stress, 22, 451-476.
[2]	Lord, H. and Shulman, Y.-A., (1967) “Generalized dynamical theory of thermoelasticity”, Journal of the Mechanics and Physics of Solids, 15, 299–309.
[3]	Green, A.-E. and Lindsay, K.-A., (1972) “Thermoelasticity”, Journal of Elasticity, 2, 1-7.
[4]	Hetnarski, R.-B. and Ignaczak, J., (1996) “Soliton-like waves in a low temperature non-linear thermoelastic solid”, International Journal of Engineering Science, 34, 1767-1787.
[5]	Tzou, D.-Y., (1995) “A unified field approaches for heat conduction from macro to micro scales”, The ASME Journal of Heat Transfer, 117, 8-16.
[6]	Chandrasekharaiah, D.-S., (1998) “Hyperbolic thermo-elasticity: A review of recent literature”, Applied Mechanics Reviews, 51, 705-729.
[7]	Ailawalia, P. and Singla, A. (2015) "Disturbance due to internal heat source in thermoelastic solid using dual phase lag model", Structural Engineering and Mechanics, An Int'l Journal, 56, 341-354.
[8]	Quintanilla, R. and Racke, R. (2008) "A note on stability in three-phase-lag heat conduction", International Journal of Heat and Mass Transfer, 51, 24-29.
[9]	Kumar, R. and Partap, G. (2011) "Vibration analysis of wave motion in micropolar thermo-visco-elastic plate", Structural Engineering and Mechanics, An Int'l Journal 39, 861-875.
[10]	Abo-Dahab, S. M., Abd-Alla, A. M. and Khan, A. (2016) "Rotational effect on Rayleigh, Love an Stoneley waves in non-homogeneous fibre-reinforced anisotropic general visco-elastic media of higher order," Structural Engineering and Mechanics, An Int'l Journal, 58, 181-197.
[11]	Abd–Alla, A. M., Abo–Dahab, S. M. and Bayones, F. S. (2015) “Wave propagation in fibre-reinforced anisotropic thermo-elastic medium subjected to gravity field,” Structural Engineering and Mechanics, An Int'l Journal, 53, 277–296.
[12]	Kakar, R. and Kakar, S. (2014) "Electro-magneto-thermo-elastic surface waves in non-homogeneous orthotropic granular half space", Geomechanics and Engineering, An Int'l Journal, 7, 1-36.
[13]	Chen, P. J. and Gurtin, M. E. (1968) "On a theory of heat conduction involving two-temperature", Zeitschrift für Angewandte Mathematik und Physik, 19, 614-627.
[14]	Ieşan, D. (1970) "On the linear coupled thermoelasticity with two-temperature", Zeitschrift für Angewandte Mathematik und Physik, 21, 583-591.
[15]	Abbas, I. A. and Othman, M. I. A. (2012) "Generalized thermo-elastic interaction in a fibre-reinforced anisotropic half-space under hydrostatic initial stress", Journal of Vibration and Control, 18, 175-182.
[16]	Othman, M. I. A. and Ahmed, E. A. A. (2015) "The effect of rotation on piezo-thermoelastic medium using different theories", Structural Engineering and Mechanics, An Int'l Journal, 56, 649-665.
[17]	Othman, M. I. A. and Said, S. M. (2016) "Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model", Structural Engineering and Mechanics, An Int'l Journal, 57, 201-220.
[18]	Gupta, R. R. and Gupta, R. R. (2013) "Analysis of wave motion in an anisotropic initially stressed fiber-reinforced thermo-elastic medium", Earthquakes and Structures, An Int'l Journal, 4, 1-10.
[19]	Othman, M. I. A. Elmaklizi, Y. D. and Said, S. M. (2013) "Generalized thermoelastic medium with temperature-dependent properties for different theories under the effect of gravity field", International of Journal Thermophysics, 34, 521–537.
[20]	De, S. N. and Sengurta, P. R. (1976) "Surface waves under the influence of gravity", Gerlands Beitr Geophys (Leipzig), 85, 311-318.

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APA Style

Mohamed I. A. Othman, Nehal T. Mansour. (2017). 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. American Journal of Nano Research and Applications, 4(4), 33-42. https://doi.org/10.11648/j.nano.20160404.11

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ACS Style

Mohamed I. A. Othman; Nehal T. Mansour. 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. Am. J. Nano Res. Appl. 2017, 4(4), 33-42. doi: 10.11648/j.nano.20160404.11

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AMA Style

Mohamed I. A. Othman, Nehal T. Mansour. 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. Am J Nano Res Appl. 2017;4(4):33-42. doi: 10.11648/j.nano.20160404.11

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@article{10.11648/j.nano.20160404.11,
  author = {Mohamed I. A. Othman and Nehal T. Mansour},
  title = {2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model},
  journal = {American Journal of Nano Research and Applications},
  volume = {4},
  number = {4},
  pages = {33-42},
  doi = {10.11648/j.nano.20160404.11},
  url = {https://doi.org/10.11648/j.nano.20160404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.nano.20160404.11},
  abstract = {Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermo-elastic solid half-space under hydrostatic initial stress, rotation, magnetic field and gravity with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by the three-phase-lag model, Green-Naghdi III and Lord-Shulman theories.},
 year = {2017}
}

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TY  - JOUR
T1  - 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model
AU  - Mohamed I. A. Othman
AU  - Nehal T. Mansour
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T2  - American Journal of Nano Research and Applications
JF  - American Journal of Nano Research and Applications
JO  - American Journal of Nano Research and Applications
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AB  - Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermo-elastic solid half-space under hydrostatic initial stress, rotation, magnetic field and gravity with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by the three-phase-lag model, Green-Naghdi III and Lord-Shulman theories.
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Author Information

Mohamed I. A. Othman

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
Nehal T. Mansour

Department of Mathematics, Faculty of Science, Taif University, Ta'if, Saudi Arabia

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APA Style

Mohamed I. A. Othman, Nehal T. Mansour. (2017). 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. American Journal of Nano Research and Applications, 4(4), 33-42. https://doi.org/10.11648/j.nano.20160404.11

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ACS Style

Mohamed I. A. Othman; Nehal T. Mansour. 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. Am. J. Nano Res. Appl. 2017, 4(4), 33-42. doi: 10.11648/j.nano.20160404.11

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AMA Style

Mohamed I. A. Othman, Nehal T. Mansour. 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model. Am J Nano Res Appl. 2017;4(4):33-42. doi: 10.11648/j.nano.20160404.11

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@article{10.11648/j.nano.20160404.11,
  author = {Mohamed I. A. Othman and Nehal T. Mansour},
  title = {2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model},
  journal = {American Journal of Nano Research and Applications},
  volume = {4},
  number = {4},
  pages = {33-42},
  doi = {10.11648/j.nano.20160404.11},
  url = {https://doi.org/10.11648/j.nano.20160404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.nano.20160404.11},
  abstract = {Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermo-elastic solid half-space under hydrostatic initial stress, rotation, magnetic field and gravity with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by the three-phase-lag model, Green-Naghdi III and Lord-Shulman theories.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - 2-D Problem of Magneto-Thermoelastic Medium Under the Effect of Different Fields with Two-Temperature and 3PHL Model
AU  - Mohamed I. A. Othman
AU  - Nehal T. Mansour
Y1  - 2017/01/14
PY  - 2017
N1  - https://doi.org/10.11648/j.nano.20160404.11
DO  - 10.11648/j.nano.20160404.11
T2  - American Journal of Nano Research and Applications
JF  - American Journal of Nano Research and Applications
JO  - American Journal of Nano Research and Applications
SP  - 33
EP  - 42
PB  - Science Publishing Group
SN  - 2575-3738
UR  - https://doi.org/10.11648/j.nano.20160404.11
AB  - Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermo-elastic solid half-space under hydrostatic initial stress, rotation, magnetic field and gravity with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by the three-phase-lag model, Green-Naghdi III and Lord-Shulman theories.
VL  - 4
IS  - 4
ER  -

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