Reflection of thermoelastic waves from the isothermal boundary of a solid half-space under memory-dependent heat transfer

References

• Mainardi F. Fractional calculus and waves in linear viscoelasticity. London: Imperial College Press; 2010.
   Google Scholar
• Gorenflo R, Mainardi F. Fractional calculus: Integral and differential equations of fractional orders. Wien: Springer; 1997. Fractals and Fractional Calculus in Continuum Mechanics.
   Google Scholar
• Atanacković TM, Pilipović S, Stanković B, Zorica D. Fractional calculus with application in mechanics. London: Wiley; 2014.
   Google Scholar
• Diethelm K. Analysis of fractional differential equation: an application oriented exposition using differential operators of Caputo type. Berlin: Springer; 2010.
   Google Scholar
• Wang J-L, Li H-F. Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput Math Appl. 2011;62:1562–1567. doi: 10.1016/j.camwa.2011.04.028
   Web of Science ®Google Scholar
• Cattaneo C. Sur une forme de l'equation de la chaleur eliminant le paradoxe d'ure propagation instantaneee [On a form of the heat equation eliminating the paradox of the instantaneous spread] [In French]. Comptes Rendus Acad Sci. 1958;2:431–433.
   Google Scholar
• Green AE, Naghdi PM. A re-examination of the basic postulates of thermomechanics. Proc Roy Soc London Ser A. 1991;432:171–194. doi: 10.1098/rspa.1991.0012
   Web of Science ®Google Scholar
• Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15:299–309. doi: 10.1016/0022-5096(67)90024-5
   Web of Science ®Google Scholar
• Green AE, Lindsay KA. Thermoelasticity. J Elast. 1972;2:1–7. doi: 10.1007/BF00045689
   Google Scholar
• Green AE, Naghdi PM. On undamped heat waves in an elastic solid. J Therm Stresses. 1992;15:253–264. doi: 10.1080/01495739208946136
   Web of Science ®Google Scholar
• Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208. doi: 10.1007/BF00044969
   Web of Science ®Google Scholar
• Sherief HH, El-Sayed A, El-Latief A. Fractional order theory of thermoelasticity. Int J Solids Struct. 2010;47:269–275. doi: 10.1016/j.ijsolstr.2009.09.034
   Web of Science ®Google Scholar
• Youssef H. Theory of fractional order generalized thermoelasticity. J Heat Transfer. 2010;132:061301. doi:10.1115/1.4000705
   Web of Science ®Google Scholar
• Ezzat MA, Fayik MA. Fractional order theory of thermoelastic diffusion. J Therm Stresses. 2011;34:851–872. doi: 10.1080/01495739.2011.586274
   Web of Science ®Google Scholar
• Yu Y-J, Hu W, Tian X-G. A novel generalized thermoelasticity model based on memory-dependent derivative. Int J Eng Sci. 2014;81:123–134. doi: 10.1016/j.ijengsci.2014.04.014
   Web of Science ®Google Scholar
• Ezzat MA, El-Karamany AS, El-Bary AA. Generalized thermo-viscoelasticity with memory-dependent derivatives. Int J Mech Sci. 2014;89:470–475. doi: 10.1016/j.ijmecsci.2014.10.006
   Web of Science ®Google Scholar
• Ezzat MA, El-Karamany AS, El-Bary AA. A novel magneto-thermoelasticity theory with memory-dependent derivative. J Electromagn Waves Appl. 2015;29:1018–1031. doi: 10.1080/09205071.2015.1027795
   Web of Science ®Google Scholar
• Ezzat MA, El-Karamany AS, El-Bary AA. Modeling of memory-dependent derivatives in generalized thermoelasticity. Eur Phys J Plus. 2016;131:131–372. doi: 10.1140/epjp/i2016-16372-3
   Web of Science ®Google Scholar
• Lotfy Kh, Sarkar N. Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature. Mech Time-Depend Mater. 2017;21:15–30. doi: 10.1007/s11043-017-9340-5
   Web of Science ®Google Scholar
• Sarkar N, Ghosh D, Lahiri A. A two-dimensional magneto-thermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative. Mech Adv Mater Struct. 2018. DOI:10.1080/15376494.2018.1432784
   Google Scholar
• Sharma JN, Kumar V, Chand D. Reflection of generalized thermoelastic waves from the boundary of a half space. J Therm Stresses. 2003;26:925–942. doi: 10.1080/01495730306342
   Web of Science ®Google Scholar
• Das NC, Lahiri A, Sarkar S, Basu S. Reflection of generalized thermoelastic waves from isothermal and insulated boundaries of a half space. Comput Math Appl. 2008;56:2795–2805. doi: 10.1016/j.camwa.2008.05.042
   Web of Science ®Google Scholar
• Othman MIA, Song Y. Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli. Appl Math Model. 2008;32:483–500. doi: 10.1016/j.apm.2007.01.001
   Web of Science ®Google Scholar
• Sharma JN, Grover D, Kaur D. Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids. Appl Math Model. 2011;35:3396–3407. doi: 10.1016/j.apm.2011.01.014
   Web of Science ®Google Scholar
• Allam MNM, Rida SZ, Abo-Dahab SM, Mohamed RA, Kilany AA. GL model on reflection of P and SV-waves from the free surface of thermoelastic diffusion solid under influence of the electromagnetic field and initial stress. J Therm Stresses. 2014;37:471–487. doi: 10.1080/01495739.2013.870861
   Web of Science ®Google Scholar
• Biswas S, Sarkar N. Fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model. Mech Mater. 2018;126:140–147. doi: 10.1016/j.mechmat.2018.08.008
   Web of Science ®Google Scholar
• Li Y, Wang W, Wei P, Wang C. Reflection and transmission of elastic waves at an interface with consideration of couple stress and thermal wave effects. Meccanica. 2018;53:2921–2938. doi: 10.1007/s11012-018-0842-2
   Web of Science ®Google Scholar
• Sarkar N, Tomar SK. Plane waves in nonlocal thermoelasticsolid with voids. J Therm Stresses. 2019;42:580–606. doi: 10.1080/01495739.2018.1554395
   Web of Science ®Google Scholar
• Mondal S, Sarkar N. Waves in dual-phase-lag thermoelastic materials with voids based on Eringen's nonlocal elasticity. J Therm Stresses. 2019. DOI: 10.1080/01495739.2019.1591249
   Google Scholar
• Das N, Sarkar N, Lahiri A. Reflection of plane waves from the stress-free isothermal and insulated boundaries of a nonlocal thermoelastic solid. Appl Math Model. 2019;73:526–544. doi: 10.1016/j.apm.2019.04.028
   Web of Science ®Google Scholar
• Sarkar N, De S, Sarkar N. Memory response in plane wave reflection in generalized magneto-thermoelasticity. J Electromagn Waves Appl. 2019;33:1354–1374. doi: 10.1080/09205071.2019.1608318
   Web of Science ®Google Scholar
• Biot M. Thermoelasticity and irreversible thermodynamics. J Appl Phys. 1956;27:240–53. doi: 10.1063/1.1722351
   Web of Science ®Google Scholar
• Achenbach JD. Wave propagation in elastic solids. New York (NY): North-Holland; 1976.
   Google Scholar
• Nayfeh AH, Nemat-Nasser S. Electromagneto-thermoelastic plane waves in solids with thermal relaxation. J Appl Mech. 1972;39:108–113. doi: 10.1115/1.3422596
   Web of Science ®Google Scholar
• Roychoudhuri SK. Effects of rotation and relaxation times on plane waves in generalized thermoelasticity. J Elast. 1985;15:59–68. doi: 10.1007/BF00041305
   Web of Science ®Google Scholar
• Chadwick P, Sneddon IN. Plane waves in an elastic solid conducting heat. J Mech Phys Solids. 1958;6:223–230. doi: 10.1016/0022-5096(58)90027-9
   Web of Science ®Google Scholar