References
- Berman R. The thermal conductivity of dielectric solids at low temperatures. Adv Phys. 1953;2:103–140. doi: https://doi.org/10.1080/00018735300101192
- Sherief HH, Hamza FA. Modeling of variable thermal conductivity in a generalized thermoelastic infinitely long hollow cylinder. Meccanica. 2016;51:551–558. doi: https://doi.org/10.1007/s11012-015-0219-8
- Zenkour AM, Abouelregal AE. Effects of phase-lags in a thermoviscoelastic orthotropic continuum with a cylindrical hole and variable thermal conductivity. Arch Mech. 2015;67:457–475.
- Mondal S, Mallik SH, Kanoria M. Fractional order two-temperature dual-phase-lag thermoelasticity with variable thermal conductivity. Int Sch Res Notices. 2014: 13, Article ID 646049.
- Sur A, Kanoria M. Fractional order generalized thermoelastic functionally graded solid with variable material properties. J Solid Mech. 2014;6:54–69.
- Youssef HM, El-Bary AA. Mathematical model for thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity. Comput Methods Sci Tech. 2006;12:165–171. doi: https://doi.org/10.12921/cmst.2006.12.02.165-171
- Ezzat MA, El-Bary AA. Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder. Int J Thermal Sci. 2016;108:62–69. doi: https://doi.org/10.1016/j.ijthermalsci.2016.04.020
- Abbas IA, Abo-Dahab SM. On the numerical solution of thermal shock problem for generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity. J Comput Theor Nano. 2014;11:607–618. doi: https://doi.org/10.1166/jctn.2014.3402
- Xiong C, Ying G. Electromagneto-thermoelastic diffusive plane waves in a half-space with variable material properties under fractional order thermoelastic diffusion. Inter J Appl Electromagnet Mech. 2017;53:251–269. doi: https://doi.org/10.3233/JAE-160038
- Abbas IA, El-Amin MF, Amgad S. Effect of thermal dispersion on free convection in a fluid saturated porous medium. Int J Heat and Fluid Flow. 2009;30:229–236. doi: https://doi.org/10.1016/j.ijheatfluidflow.2009.01.004
- Bahar LY, Hetnarski RB. State space approach to thermoelasticity. J Therm Stress. 1978;1:135–145. doi: https://doi.org/10.1080/01495737808926936
- Singh R, Kumar V. Eigen value approach to two dimensional problem in generalized magneto-micropolar thermoelastic medium with rotation effect. Int J of Appl Mech Eng. 2016;21:205–219. doi: https://doi.org/10.1515/ijame-2016-0013
- Abbas IA. Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source. J Magnet Magnet Mater. 2014;377:452–459. doi: https://doi.org/10.1016/j.jmmm.2014.10.159
- Das NC, Lahiri A, Giri RR. Eigenvalue approach to generalized thermoelasticity. Indian J Pure Appl Math. 1997;28:1573–1594.
- Lahiri A, Kar TK. Eigenvalue approach to generalized thermoviscoelasticity with one relaxation time parameter. Tamsui Oxford J Mathemat Sci. 2007;23:185–218.
- Bayones FS, Abd-Alla AM. Eigenvalue approach to coupled thermoelasticity in a rotating isotropic medium. Res Phys. 2018;8:7–15.
- Abbas IA. Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory. J Mech Sci Tech. 2014;28:4193–4198. doi: https://doi.org/10.1007/s12206-014-0932-6
- Abbas IA. The effects of relaxation times and a moving heat source on a two temperature generalized thermoelastic thin slim strip. Canad J Phys. 2014;93:585–590. doi: https://doi.org/10.1139/cjp-2014-0387
- Nowinski JL. Theory of thermoelasticity with applications. Sijthoff & Noordhoff International Publishers, Alphen Aan Den Rijn. 1978.
- Kaliski S, Nowacki W. Combined elastic and electro-magnetic waves produced by thermal shock in the case of a medium of finite electric conductivity. IntJ Eng Sci. 1963;1:163–175. doi: https://doi.org/10.1016/0020-7225(63)90031-4
- Massalas C, Dalamangas A. Coupled magneto-thermoelastic problem in elastic half-space having finite conductivity. Int J Eng Sci. 1983;21:991–999. doi: https://doi.org/10.1016/0020-7225(83)90076-9
- Paria G. On magneto-thermoelastic plane waves. Math Proc Camb Philos Soc. 1962;58:527–531. doi: https://doi.org/10.1017/S030500410003680X
- Paria G. Magneto-elasticity and magneto-thermoelasticity. Adv Appl Mech. 1967;10:73–112. doi: https://doi.org/10.1016/S0065-2156(08)70394-6
- Zakaria M. Effect of Hall current on generalized magneto-thermoelasticity micropolar solid subjeted to ramp-type heating. Amer J Mater Sci. 2011;1:26–39.
- Abo-Dahab SM, Biswas S. Effect of rotation on Rayleigh waves in magneto-thermoelastic transversely isotropic medium with thermal relaxation times. J Electromag Waves Appl. 2017;31:1485–1507. doi: https://doi.org/10.1080/09205071.2017.1351403
- Said SM. Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model. J Com Appl Math. 2016;291:142–157. doi: https://doi.org/10.1016/j.cam.2014.12.016
- Othman MIA, Hasona WM, Abd-Elaziz EM. Effect of rotation on micropolar generalized thermoelasticity with two-temperatures using a dual-phase-lag model. Canad J Phys. 2014;92:149–158. doi: https://doi.org/10.1139/cjp-2013-0398
- Othman MIA, Edeeb ERM. Effect of initial stress on generalized magnetothermoelasticity medium with voids: A comparison of different theories. Int J Eng Math Com Sci. 2016;4:15–26.
- Othman MIA, Eraki EEM. Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model. Mech Based Design Struct Machines. 2017;45:145–159. doi: https://doi.org/10.1080/15397734.2016.1152193
- Abbas IA, Youssef HM. A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method. Int J Thermophys. 2012;33:1302–1313. doi: https://doi.org/10.1007/s10765-012-1272-3
- Abbas IA, Youssef HM. Finite element analysis of two-temperature generalized magneto-thermoelasticity. Arch Appl Mech. 2009;79:917–925. doi: https://doi.org/10.1007/s00419-008-0259-9
- Mohamed RA, Abbas IA, Abo-Dahab SM. Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction. Comm Nonlinear Sci Numer Simul. 2009;14:1385–1395. doi: https://doi.org/10.1016/j.cnsns.2008.04.006
- Zenkour AM, Abbas IA. A generalized thermoelasticity problem of an annular cylinder with temperature-dependent density and material properties. Int J Mech Sci. 2014;84:54–60. doi: https://doi.org/10.1016/j.ijmecsci.2014.03.016
- Hetnarski RB, Eslami MR. Thermal stresses –advanced theory and applications. B.V. Springer Science Business Maedia. 2009.
- Montanaro A. On singular surface in isotropic linear thermoelasticity with initial stress. J Acoust Soc. 1999;A106:1586–1588. doi: https://doi.org/10.1121/1.427154
- Shaw S, Mukhopadhyay B. Moving heat source response in micropolar half–space with two-temperature theory. Continum Mech Thermody. 2013;25:523–535. doi: https://doi.org/10.1007/s00161-012-0284-3
- Schoenberg M, Censor DC. Elastic waves in rotating media. Q Appl Math. 1973;31:115–125. doi: https://doi.org/10.1090/qam/99708
- Noda N. Thermal Stresses in Materials with temperature-dependent properties. In: RB Hetnarski, Thermal Stresses I. Amsterdam. 1986.
- Sarkar N, Lahiri A. Eigenvalue approach to two-temperature magneto-thermoelasticity. Vietnam J Math. 2012;40:1–18.
- Das NC, Bhakata PC. Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics. Mech Res Cumm. 1985;12:19–29. doi: https://doi.org/10.1016/0093-6413(85)90030-8