Initial Stress and Modified Ohm’s Law in Magneto-thermoelastic Problem Under Three Theories with Microtemperatures and Voids

Year 2022, Volume: 25 Issue: 1, 54 - 63, 01.03.2022

Latika Bawankar , G. D. Kedar

https://doi.org/10.5541/ijot.934363

Cited By: 2

Abstract

This paper studies the generalized magneto-thermoelastic problem with microtemperatures, voids taking into account initial stress and modified Ohm’s law under three theories. The analytical solution is obtained by normal modes and expressions for micro temperature, temperature distribution, displacement, components of heat flux, change in the volume fraction field as well as stress components are calculated. The effect of initial stress and thermal shock is observed on desired field variables. The results are established graphically for all physical quantities and variation is done for three theories due to the effect of modified Ohm’s law coefficient.

Keywords

Magneto-thermoelasticity, Voids, Initial stress, Modified Ohm, Microtemperatures, Modified Ohm's Law

References

• M. A. Biot, “Non-linear theory of elasticity and the linearized case for a body under initial stress,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 27(183), 468–489, 1939.
• H. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” Journal of the Mechanics and Physics of Solids, 15(5), 299–309, 1967.
• E. Green and K. A. Lindsay, “Thermoelasticity,” Journal of Elasticity, 1972.
• V. K. Agarwal, “On electromagneto-thermoelastic plane waves,” Acta Mechanica, 34(3), 181–191, 1979.
• G. Paria, “Magneto-elasticity and magneto- thermoelasticity,” In Advances in Applied Mechanics. Elsevier, 73–112, 1966.
• H. Youssef, “Generalized magneto-thermoelasticity in a conducting medium with variable material properties,” Applied Mathematics and Computation, 173(2), 822–833, 2006.
• R. A. Grot, “Thermodynamics of a continuum with microstructure,” International Journal of Engineering Science, 7(8), 801–814, 1969.
• P. Riha, “On the microcontinuum model of heat conduction in materials with inner structure,” International Journal of Engineering Science, 14(6), 529–535, 1976.
• P. S. Casas and R. Quintanilla, “Exponential stability in thermoelasticity with microtemperatures,” International Journal of Engineering Science, 43(1), 33–47, 2005.
• R. Quintanilla and D. Iesan, “On the theory of thermoelasticity with microtemperatures,” Journal of Thermal Stresses, 23(3), 199–215, 2000.
• D. Iesan, “On a theory of micromorphic elastic solids with microtemperatures,” Journal of Thermal Stresses, 24(8), 737–752, 2001.
• M. Svanadze, “Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures,” Journal of Thermal Stresses, 27(2), 151–170, 2004.
• M. I. Othman and E. M. Abd-Elaziz, “Influence of gravity and microtemperatures on the thermoelastic porous medium under three theories,” International Journal of Numerical Methods for Heat & Fluid Flow, 29(9), 3242–3262, 2019.
• R. Quintanilla, “Uniqueness in thermoelasticity of porous media with microtemperatures,” Archives of Mechanics, 61(5), 371–382, 2009.
• C. Eringen, “Microcontinuum field theories: I. Foundations and solids,” Springer Science & Business Media, 2012.
• C. Eringen and E. S. Suhubi, “Nonlinear theory of simple microelastic solids,” International Journal of Engineering Science, 2(2), 189–203, 1964.
• K. K. Kalkal, R. Goyal, and S. Deswal, “Thermomechanical interactions in a magneto Thermoelastic solid with microtemperatures and diffusion,” Microsystem Technologies, 25(10), 3747–3763, 2018.
• S. C. Cowin and J. W. Nunziato, “Linear elastic materials with voids,” Journal of Elasticity, 13(2), 125–147, 1983.
• J. W. Nunziato and S. C. Cowin, “A nonlinear theory of elastic materials with voids,” Archive for Rational Mechanics and Analysis, 72 (2), 175–201, 1979.
• D. Iesan, “A theory of thermoelastic materials with voids,” Acta Mechanica, 60(1), 67–89, 1986.
• Pompei and A. Scalia, “On the asymptotic spatial behavior in linear thermoelasticity of materials with voids,” Journal of Thermal Stresses, 25(2), 183–193, 2002.
• S. Chirita and A. Scalia, “On the spatial and temporal behavior in linear thermoelasticity of materials with voids,” Journal of Thermal Stresses, 24(5), 433–455, 2001.
• M. I. A. Othman, M. E. Zidan, and M. I. Hilal, “Effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation,” Canadian Journal of Physics, 1359–1371, 2014.
• D. Iesan, “A theory of initially stressed thermoelastic material with voids,” An. Stiint. Univ. Ai. I. Cuza Lasi Sect. I a Mat, 33, 167–184, 1987.
• M. A. Goodman and S. C. Cowin, “A continuum Theory for granular materials,” Archive for Rational Mechanics and Analysis, 44(4), 249–266, 1972.
• J. Jaric, “Theory of thermoelasticity of granular materials,” Rev. Roum. Sci. Techn., Méc. Appl 24, 793–805, 1979.
• M. I. A. Othman, R. S. Tantawi, and E. M. Abd-Elaziz, “Effect of initial stress on a thermoelastic medium with voids and microtemperatures,” Journal of Porous Media, 19(2), 155–172, 2016.
• K. K. Kalkal, R. Kumar, A. Gunghas, and S. Deswal, “Wave propagation in an initially stressed magneto-thermoelastic medium with voids and microtemperatures,” Journal of Thermal Stresses, 43(8), 962–980, 2020.
• M. I. A. Othman and E. M. Abd-Elaziz, “Effect of initial stress and hall current on a magneto-thermoelastic porous medium with microtemperatures,” Indian Journal of Physics, 93(4), 475–485, 2018.
• M. I. A. Othman and E. M. Abd-Elaziz, “Plane waves in A magneto-thermoelastic solids with voids and microtemperatures due to hall current and rotation,” Results in Physics, 7, 4253–4263, 2017.
• K. Ames and B. Straughan, “Continuous dependence results for initially prestressed thermoelastic bodies,” International Journal of Engineering Science, 30(1), 7–13, 1992.
• Montanaro, “On singular surfaces in isotropic linear thermoelasticity with initial stress,” The Journal of the Acoustical Society of America, 106(3), 1586–1588, 1999.
• Abbas and M. I. A. Othman, “Generalized thermoelastic interaction in a fiber-reinforced anisotropic half space under hydrostatic initial stress,” Journal of Vibration and Control, 18(2), 175–182, 2011.
• M. A. Ezzat and M. Z. A. Elall, “Generalized magneto thermoelasticity with modified ohm’s law,” Mechanics of Advanced Materials and Structures, 17(1), 74–84, 2009.
• N. Sarkar, “Generalized magneto¬ thermoelasticity with modified ohm’s law under three theories,” Computational Mathematics and Modeling, 25(4), 544–564, 2014.