A two-dimensional magneto-thermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative

References

• R. B. Hetnarski, and J. Ignaczak, “Generalized thermoelasticity,” J. Therm. Stresses., vol. 22, pp. 45–476, 1999.
   Web of Science ®Google Scholar
• H. W. Lord, and Y. Shulman, “The generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids., vol. 15, pp. 299–309, 1967. doi:10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• A. E. Green, and K. A. Lindsay, “Thermoelasticity,” J. Elasticity., vol. 2, pp. 1–7, 1972. doi:10.1007/BF00045689.
   Google Scholar
• R. S. Dhaliwal, and H. H. Sherief, “Generalized thermoelasticity for anisotropic media,” Q. Appl. Math., vol. 38, pp. 1–8, 1980. doi:10.1090/qam/575828.
   Web of Science ®Google Scholar
• D. S. Chandrasekharaiah, “Thermoelasticity with second sound – a review,” Appl. Mech. Rev., vol. 39, pp. 355–376, 1986. doi:10.1115/1.3143705.
   Google Scholar
• C. C. Ackerman, B. Bartman, H. A. Fairbank, and R. A. Guyer, “Second sound in helium,” Phys. Rev. Lett., vol. 16, pp. 789–791, 1966. doi:10.1103/PhysRevLett.16.789.
   Web of Science ®Google Scholar
• R. A. Guyer, and J. A. Krumhansal, “Thermal conductivity, second sound and phonon, hydrodynamic phenomenon in non-metallic crystals,” Phys. Rev., vol. 148, pp. 778–788, 1966. doi:10.1103/PhysRev.148.778.
   Web of Science ®Google Scholar
• C. C. Ackerman, and W. C. Overtone, “Second sound in helium-3,” Phys. Rev. Lett., vol. 22, pp. 764–766, 1969. doi:10.1103/PhysRevLett.22.764.
   Web of Science ®Google Scholar
• P. J. Chen, M. E. Gurtin, and W. O. Williams, “A note on non-simple heat conduction,” Zamp., vol. 19, pp. 969–970, 1968. doi:10.1007/BF01602278.
   Web of Science ®Google Scholar
• P. J. Chen, M. E. Gurtin, and W. O. Williams, “On the thermodynamics of nonsimple elastic materials with two temperatures,” Zamp., vol. 20, pp. 107–112, 1969. doi:10.1007/BF01591120.
   Web of Science ®Google Scholar
• J. K. Chen, J. E. Beraun, and C. L. Tham, “Ultrafast thermoelasticity for short-pulse laser heating,” Int. J. Eng. Sci., vol. 42, pp. 793–807, 2004. doi:10.1016/j.ijengsci.2003.11.001.
   Web of Science ®Google Scholar
• T. Q. Quintanilla, and C. L. Tien, “Heat transfer mechanism during short-pulse laser heating of metals,” ASME J. Heat Transfer., vol. 115, pp. 835–841, 1993. doi:10.1115/1.2911377.
   Web of Science ®Google Scholar
• H. M. Youssef, “Theory of two-temperature-generalized thermoelasticity,” IMA J. Appl. Math., vol. 71, pp. 383–390, 2006. doi:10.1093/imamat/hxh101.
   Web of Science ®Google Scholar
• H. M. Youssef, and E. A. Al-Lehaibi, “State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem,” Int. J. Solids Struct., vol. 44, pp. 1550–1562, 2007. doi:10.1016/j.ijsolstr.2006.06.035.
   Web of Science ®Google Scholar
• N. Sarkar, and A. Lahiri, “Eigenvalue approach to two-temperature magneto-thermoelasticity,” Vietnam J. Math. Math., vol. 40, pp. 13–30, 2012.
   Google Scholar
• Y. Povstenko, “Fractional radial heat conduction in an infinite medium with a cylindrical cavity and associated thermal stresses,” Mech. Res. Commun., vol. 37, pp. 436–440, 2010. doi:10.1016/j.mechrescom.2010.04.006.
   Web of Science ®Google Scholar
• A. S. El-Karamany, and M. A. Ezzat, “On fractional thermoelasticity,” Math. Mech. Solid., vol. 16, pp. 334–346, 2011. doi:10.1177/1081286510397228.
   Web of Science ®Google Scholar
• M. A. Ezzat, “Thermoelectric MHD non-Newtonian fluid with fractional derivative heat transfer,” Physica B., vol. 405, pp. 4188–4194, 2010. doi:10.1016/j.physb.2010.07.009.
   Web of Science ®Google Scholar
• M. A. Ezzat, and A. S. El-Karaman, “Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures,” Z. Angew. Math. Phys., vol. 62, pp. 937–952, 2011. doi:10.1007/s00033-011-0126-3.
   Web of Science ®Google Scholar
• M. A. Ezzat, and A. S. El-Karaman, “Fractional thermoelectric viscoelastic materials,” Appl. Polym. Sci., vol. 124, pp. 2187–2199, 2012. doi:10.1002/app.35243.
   Web of Science ®Google Scholar
• M. Bachher, N. Sarkar, and A. Lahiri, “Generalized thermoelastic ifinite medium with voids subjected to a instantaneous heat sources with fractional derivative heat transfer,” Int. J. Mech. Sci., vol. 89, pp. 84–91, 2014. doi:10.1016/j.ijmecsci.2014.08.029.
   Web of Science ®Google Scholar
• M. Bachher, N. Sarkar, and A. Lahiri, “Fractional order thermoelastic interactions in an infinite porous material due to distributed time-dependent heat sources,” Meccanica., vol. 50, pp. 2167–2178, 2015. doi:10.1007/s11012-015-0152-x.
   Web of Science ®Google Scholar
• J. Wang, and H. Li, “Surpassing the fractional derivative: Concept of the memory- dependent derivative,” Comput. Math. Appl., vol. 62, pp. 1562–1567, 2011. doi:10.1016/j.camwa.2011.04.028.
   Web of Science ®Google Scholar
• Y-J. Yu, W. Hu, and X.-G. Tian, “A novel generalized thermoelasticity model based on memory-dependent derivative,” Int. J. Eng. Sci., vol. 811, pp. 23–134, 2014.
   Google Scholar
• M. Ezzat, A. S. El-Karamany, and A. El-Bary, “Generalized thermoelasticity withmemory-dependent derivatives involving two temperatures,” Mech. Adv. Mater. Str., vol. 23, pp. 545–553, 2016. doi:10.1080/15376494.2015.1007189.
   Web of Science ®Google Scholar
• M. Ezzat, A. El-Karamany, and A. El-Bary, “Generalized thermo-viscoelasticity with memory-dependent derivatives,” Int. J. Mech. Sci., vol. 89, pp. 470–475, 2014. doi:10.1016/j.ijmecsci.2014.10.006.
   Web of Science ®Google Scholar
• M. Ezzat, A. El-Karamany, and A. El-Bary, “Modeling of memory-dependent derivatives in generalized thermoelasticity,” Eur. Phys. J. Plus., vol. 131, pp. 131–372, 2016. doi:10.1140/epjp/i2016-16372-3.
   Web of Science ®Google Scholar
• A. Al-Jamel, M. F. Al-Jamal, and A. El-Karamany, “A memory-dependent derivative model for damping in oscillatory systems,” J. Vibration Control., 2016. doi:10.1177/1077546316681907.
   PubMed Web of Science ®Google Scholar
• N. Sarkar, “A novel Pennes' bioheat transfer equation with memory-dependent derivative,” J. Math. Models Eng., vol. 2, pp. 151–157, 2016. doi:10.21595/mme.2016.18024.
   Google Scholar
• Kh. Lotfy, and N. Sarkar, “Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature,” Mech. Time-Depend. Mater., vol. 21, pp. 15–30, 2017.
   Web of Science ®Google Scholar
• R. Belman, R. E. Kalaba, and J. Lockett, Numerical Inversion of the Laplace Transform, American Elsevier, New York, 1966.
   Google Scholar