Browse > Article
http://dx.doi.org/10.12989/scs.2017.24.3.297

Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories  

Ezzat, M.A. (Department of Mathematics, Faculty of Education, Alexandria University)
El-Bary, A.A. (Arab Academy for Science and Technology)
Publication Information
Steel and Composite Structures / v.24, no.3, 2017 , pp. 297-307 More about this Journal
Abstract
A unified mathematical model of phase-lag Green-Naghdi magneto-thermoelasticty theories based on fractional derivative heat transfer for perfectly conducting media in the presence of a constant magnetic field is given. The GN theories as well as the theories of coupled and of generalized magneto-thermoelasticity with thermal relaxation follow as limit cases. The resulting nondimensional coupled equations together with the Laplace transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of magneto-thermoelasticity with one relaxation time. The effects of Alfven velocity and the fractional order parameter on copper-like material are discussed in different types of GN theories.
Keywords
generalized magneto-thermoelasticity; caputo fractional derivatives; phase-lag Green-Naghdi theories; laplace transforms; numerical results;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
연도 인용수 순위
1 Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., Int. J., 20(5), 1103-1117   DOI
2 Alzahrani, F.S. and Abbas, I.A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., Int. J., 22(2), 369-386.   DOI
3 Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51, 705-730.   DOI
4 Chirita, S. and Ciarletta, M. (2010), "Reciprocal and variational principles in linear thermoelasticity without energy dissipation", Mech. Res. Commu., 37(3), 271-275.   DOI
5 Ciarletta, M. (2009), "A theory of micropolar thermoelasticity without energy dissipation", J. Therm. Stress., 22(6), 581-594.   DOI
6 El-Karamany, A.S. and Ezzat, M.A. (2016), "On the phase- lag Green-Naghdi thermoelasticity theories", Appl. Math. Model., 40(9), 5643-5659.   DOI
7 El-Karamany, A.S. and Ezzat, M.A. (2011), "On fractional thermoelasticity", Math. Mech. Solids, 16(3), 334-346.   DOI
8 El-Karamany, A.S. and Ezzat, M.A. (2014), "On the dual-phaselag thermoelasticity theory", Meccanica, 49(1), 79-89.   DOI
9 Ezzat, M.A. (2006), "The relaxation effects of the volume properties of electrically conducting viscoelastic material", Mater. Sci. Eng. B: Solid-State Mater. Adv. Technol., 130(1-3), 11-23.   DOI
10 Ezzat, M.A. (2001), "Free convection effects on perfectly conducting fluid", Int. J. Eng. Sci., 39(7), 799-819.   DOI
11 Ezzat, M.A. (2011), "Thermoelectric MHD with modified Fourier's law", Int. J. Therm. Sci., 50(4), 449-455.   DOI
12 Ezzat, M.A. (2012), "State space approach to thermoelectric fluid with fractional order heat transfer", Heat Mass Trans., 48(1), 71-82.   DOI
13 Biot, M. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253.   DOI
14 Ezzat, M.A. and Abd-Elaal, M.Z. (1997a), "Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium", J. Frank. Inst., 334(4), 685-706.   DOI
15 Ezzat, M.A., El-Karamany, A.S. and Fayik, M.A. (2012), "Fractional order theory in thermoelastic solid with three-phase lag heat transfer", Arch. Appli. Mech., 82(4), 557-572.   DOI
16 Ezzat, M.A. and El-Bary, A.A. (2016), "Modeling of fractional magneto-thermoelasticity for a perfect conducting materials", Smart Struct. Syst., Int. J., 18(4), 707-731.   DOI
17 Ezzat, M.A. and El-Karamany, A.S. (2011a), "Fractional order heat conduction law in magneto- thermoelasticity involving two temperatures", ZAMP, 62(5), 937- 952.   DOI
18 Ezzat, M.A. and El-Karamany, A.S. (2011b), "Theory of fractional order in electro-thermoelasticity", Eur. J. Mech. A/Solids, 30(4), 491-500.   DOI
19 Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 432(1885), 171-194.
20 Gorenflo, R. and Mainardi, F. (1997), "Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics", Springer, Wien, Austria.
21 Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264.   DOI
22 Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elas., 31(3), 189-208.   DOI
23 Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132.   DOI
24 Ezzat, M.A. and Abd-Elaal, M.Z. (1997b), "State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium", ZAMM, 77(3), 197-209.   DOI
25 Horgan, C.O. and Quintanilla, R. (2005), "Spatial behaviour of solutions of the dual-phase-lag heat equation", Math. Meth. Appl. Sci., 28(1), 43-57.   DOI
26 Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587.   DOI
27 Jou, D. and Criado-Sancho, M. (1998), "Thermodynamic stability and temperature overshooting in dual-phase-lag heat transfer", Phys. Lett. A, 248(2), 172-178.   DOI
28 Kumar, R. and Ailawalia, P. (2007), "Mechanical/thermal sources in a micropolar thermoelastic medium possessing cubic symmetry without energy dissipation", Int. J. Thermophys., 28(1), 342-367.   DOI
29 Kumar, R. and Ranil, L. (2008), "Thermoelastic interactions without energy dissipation due to inclined load", Tamk. J. Sci. Eng., 11(2), 109-118.
30 Kumar, R., Sharma, K.D. and Garg, S.K. (2014), "Effect of two temperatures on reflection coefficient in micropolar thermoelastic with and without energy dissipation media", Adv. Acoust. Vib., 846721.
31 Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309.   DOI
32 Mehditabar, A., Akbari Alashti, R. and Pashaei, M.H. (2014), "Magneto-thermo-elastic analysis of a functionally graded conical shell", Steel Compos. Struct., Int. J., 16(1), 79-98.
33 Othman, M.I., Ezzat, M.A., Zaki, S.A. and El-Karamany, A.S. (2002), "Generalized thermo-viscoelastic plane waves with two relaxation times", Int. J. Eng. Sci., 40(12), 1329-1347.   DOI
34 Parkus, H. (1970), Variational Principles in Thermo-and Magneto-Elasticity, International Centre for Mechanical Sciences, Springer, Vienna, Austria, pp. 1-47.
35 Roy Choudhuri, S.K. (2007), "On a thermoelastic three-phase-lag model", J. Therm. Stress., 30(3), 231-238.   DOI
36 Sharma, S. and Sharma, K. (2014), "Influence of heat sources and relaxation time on temperature distribution in tissues", Int. J. Appl. Mech. Eng., 19(2), 427-433.   DOI
37 Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22, 107-117.
38 Sharma, K., Sharma, S. and Bhargava, R. (2013a), "Propagation of waves in micropolar thermoelastic solid with two temperatures bordered with layers of half-space of inviscid liquid", Mater. Phys. Mech., 16, 66-81.
39 Sharma, S., Sharma, K. and Bhargava, R. (2013b), "Effect of viscosity on wave propagation in anistropic thermoelastic with Green-Naghdi theory type-II and type-III", Mater. Phys. Mech., 16(2), 144-158.
40 Sharma, S., Sharma, K. and Bhargava, R. (2014), "Plane waves and fundamental solution in an electro-microstretch elastic solids", Afrika Matematika, 25(2), 483-497.   DOI
41 Tzou, D.Y. (1995), "A unified filed approach for heat conduction from macro- to macro-scales", ASME J. Heat Trans., 117(1), 8-16.   DOI
42 Zenkour, A.M. (2014), "Torsional analysis of heterogeneous magnetic circular cylinder", Steel Compos. Struct., Int. J., 17(4), 535-548.   DOI