Research article

The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region

  • Received: 11 April 2020 Accepted: 09 June 2020 Published: 23 June 2020
  • This paper is dealing the modified Ohm’s law, including the temperature gradient and charge thickness impacts, and the generalized Fourier’s law, including the current density impact, the conditions of generalized thermo-viscoelasticity for a thermally, isotropic and electrically leading unbounded body with a spherical cavity is given. The detailing is applied to the generalized thermo elasticity dependent on Green–Naghdi (G-N II) and (G-N III) theory, where there is an underlying magnetic field corresponding to the plane limit, because of the utilization of the magnetic field, it results an incited magnetic and electric fields in the medium. The state space investigation is applied to acquire the temperature, displacement, stresses, induced electric field, instigated magnetic field and current density. Application is utilized to our concern to get the arrangement in the total structure. The considered variables are introduced graphically and discussions are made.

    Citation: Alaa. K. Khamis, Allal Bakali, A. A. El-Bary, Haitham. M. Atef. The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region[J]. AIMS Materials Science, 2020, 7(4): 381-398. doi: 10.3934/matersci.2020.4.381

    Related Papers:

  • This paper is dealing the modified Ohm’s law, including the temperature gradient and charge thickness impacts, and the generalized Fourier’s law, including the current density impact, the conditions of generalized thermo-viscoelasticity for a thermally, isotropic and electrically leading unbounded body with a spherical cavity is given. The detailing is applied to the generalized thermo elasticity dependent on Green–Naghdi (G-N II) and (G-N III) theory, where there is an underlying magnetic field corresponding to the plane limit, because of the utilization of the magnetic field, it results an incited magnetic and electric fields in the medium. The state space investigation is applied to acquire the temperature, displacement, stresses, induced electric field, instigated magnetic field and current density. Application is utilized to our concern to get the arrangement in the total structure. The considered variables are introduced graphically and discussions are made.


    加载中


    [1] Biot MA (1956) Thermo elasticity and irreversible thermo-dynamics. J Appl Phys 27: 240-253. doi: 10.1063/1.1722351
    [2] Lord HW, Shulman Y (1976) A generalized dynamical theory of thermo elasticity. J Mech Phys Solid 15: 299-309.
    [3] Müller MM, Kaiser E, Bauer P, et al. (1976) Lipid composition of the rat kidney. Nephron 17: 41-50. doi: 10.1159/000180709
    [4] Green AE, Laws N (1972) On the entropy production inequality. Arch Ration Mech An 45: 47-53. doi: 10.1007/BF00253395
    [5] Green AE, Lindsay KA (1972) Thermo elasticity. J Elasticity 2: 1-7. doi: 10.1007/BF00045689
    [6] Shuhubi E (1957) Thermo elastic solid, In: Eringen AC, Continuum Physics, New York: Academic Press.
    [7] Green AE, Naghdi PM (1991) A re-examination of the basic postulate of thermo-mechanics. P Roy Soc A-Math Phy 432: 171-194.
    [8] Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elasticity 31: 189-208. doi: 10.1007/BF00044969
    [9] Green AE, Naghdi PM (1992) An unbounded heat wave in an elastic solid. J Therm Stresses 15: 253-264. doi: 10.1080/01495739208946136
    [10] Illyushin AA, Pobedria BE (1970) Fundamentals of the mathematical theory of thermal viscoelasticity.
    [11] Biot MA (1954) Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J Appl Phys 25: 1385-1391. doi: 10.1063/1.1721573
    [12] Biot MA (1955) Variational principles in irreversible thermodynamics with application to viscoelasticity. Phys Rev 97: 1463-1469. doi: 10.1103/PhysRev.97.1463
    [13] Morland LW, Lee EH (1960) Stress analysis for linear viscoelastic materials with temperature variation. J Rheol 4: 233-263.
    [14] Tanner RI (1988) Engineering Rheology, Oxford: Oxford University Press.
    [15] Drozdov AD (1996) A constitutive model in thermoviscoelasticity. Mech Res Commun 23: 543-548. doi: 10.1016/0093-6413(96)00055-9
    [16] Bland DR (1960) The Theory of Linear Viscoelasticity, Oxford: Pergamon Press.
    [17] Lion A (1997) On the large deformation behavior of reinforced rubber at different temperatures. J Mech Phys Solids 45: 1805-1834. doi: 10.1016/S0022-5096(97)00028-8
    [18] Liao Z, Hossain M, Yao X, et al. (2020) Thermo-viscoelastic experimental characterization and numerical modelling of VHB polymer. Int J Nonlin Mech 118: 103263. doi: 10.1016/j.ijnonlinmec.2019.103263
    [19] Niyonzima I, Jiao Y, Fish J (2019) Modeling and simulation of nonlinear electro-thermo-mechanical continua with application to shape memory polymeric medical devices. Comput Method Appl M 350: 511-534. doi: 10.1016/j.cma.2019.03.003
    [20] Mehnert M, Hossain M, Steinmann P (2017) Towards a thermo-magneto-mechanical coupling framework for magneto-rheological elastomers. Int J Solids Struct 128: 117-132. doi: 10.1016/j.ijsolstr.2017.08.022
    [21] Mehnert M, Hossain M, Steinmann P (2016) On nonlinear thermo-electro-elasticity. P Roy Soc A-Math Phys 472: 20160170. doi: 10.1098/rspa.2016.0170
    [22] Youssef HM, El-Bary AA, Elsibai KA (2014) Vibration of gold nano beam in context of two-temperature generalized thermoelasticity subjected to laser pulse. Lat Am J Solids Stru 11: 2460-2482. doi: 10.1590/S1679-78252014001300008
    [23] Ezzat MA, El-Bary AA (2014) Two-temperature theory of magneto-thermo-viscoelasticity with fractional derivative and integral orders heat transfer. J Electromagnet Wave 28: 1985-2004. doi: 10.1080/09205071.2014.953639
    [24] Ezzat MA, El-Bary AA (2015) State space approach to two-dimensional magneto-thermoelasticity with fractional order heat transfer in a medium of perfect conductivity. Int J Appl Electrom 49: 607-625.
    [25] Ismail MAH, Khamis AK, El-Bary AA, et al. (2017) Effect of rotation of generalized thermoelastic layer subjected to harmonic heat: state-space approach. Microsyst Technol 23: 3381-3388. doi: 10.1007/s00542-016-3137-3
    [26] Khamis AK, Ismail AH, Youssef HM, et al. (2017) Thermal shock problem of two-temperature generalized thermoelasticity without energy dissipation with rotation. Microsyst Technol 23: 4831-4839. doi: 10.1007/s00542-017-3279-y
    [27] Youssef HM, Elsibai KA, El-Bary AA (2017) Effect of the speed, the rotation and the magnetic field on the Q-factor of an axially clamped gold micro-beam. Meccanica 52: 1685-1694. doi: 10.1007/s11012-016-0498-8
    [28] Ezzat MA, El-Karamany AS, El-Bary AA (2017) Thermoelectric viscoelastic materials with memory-dependent derivative. Smart Struct Sys 19: 539-551. doi: 10.12989/sss.2017.19.5.539
    [29] El-Karamany AS, Ezzat MA, El-Bary AA (2018) Thermodiffusion with two time delays and Kernel functions. Math Mech Solids 23: 195-208. doi: 10.1177/1081286516676870
    [30] Ezzat MA, El-Bary AA (2018) Thermoelectric spherical shell with fractional order heat transfer. Microsyst Technol 24: 891-899. doi: 10.1007/s00542-017-3400-2
    [31] El-Bary AA, Atef H (2016) On effect of viscous fractional parameter on infinite thermo Viscoelastic medium with a spherical cavity. Journal of computational and theoretical. Nanoscience 13: 1-5. doi: 10.1166/jctn.2016.4099
    [32] El-Bary AA, Atef M (2016) Modified approach for stress strain equation in the linear Kelvin-Voigt solid based on fractional order. J Comput Theor Nanos 13: 1027-1036. doi: 10.1166/jctn.2016.4332
    [33] Amin MM, El-Bary A, Atef H (2018) Effect of viscous fractional parameter on generalized magneto thermo-viscoelastic thin slim strip exposed to moving heat source. Mater Focus 7: 814-823. doi: 10.1166/mat.2018.1591
    [34] Amin MM, El-Bary AA, Atef HM (2018) Modification of Kelvin-Voigt model in fractional order for thermoviscoelastic isotropic material. Mater Focus 7: 824-832. doi: 10.1166/mat.2018.1592
    [35] Sharma K, Kumar P (2013) Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids. J Therm Stresses 36: 94-111. doi: 10.1080/01495739.2012.720545
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2612) PDF downloads(235) Cited by(1)

Article outline

Figures and Tables

Figures(9)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog