Browse > Article
http://dx.doi.org/10.12989/sem.2016.57.1.091

Effects of Hall current in a transversely isotropic magnetothermoelastic with and without energy dissipation due to normal force  

Kumar, Rajneesh (Department of Mathematics, Kurukshetra University)
Sharma, Nidhi (Department of Mathematics, MM University)
Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University)
Publication Information
Structural Engineering and Mechanics / v.57, no.1, 2016 , pp. 91-103 More about this Journal
Abstract
This investigation is concerned with the disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperature, in the presence of the combined effects of Hall currents and magnetic field due to normal force of ramp type. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. Laplace and Fourier transform technique is applied to solve the problem. The analytical expressions of displacements, stress components, temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically to show the effects of Hall current and anisotropy on the resulting quantities. Some special cases are also deduced from the present investigation.
Keywords
transversely isotropic; thermoelastic; laplace transform; fourier transform; normal force; hall current;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Sharma, K. and Kumar, P. (2013), "Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids", J. Therm. Stress., 36, 94-111.   DOI
2 Sharma, N. and Kumar, R. (2012), "Elastodynamics of an axi-symmetric problem in generalised thermoelastic diffusion", Int. J. Adv. Sci. Tech. Res., 2(3), 478-492.
3 Sharma, N., Kumar, R. and Ram, P. (2012), "Interactions of generalised thermoelastic diffusion due to inclined load", Int. J. Emer. Trend. Eng. Develop., 5(2), 583-600.
4 Sharma, S., Sharma, K. and Bhargava, R.R. (2013), "Effect of viscousity on wave propagation in anisotropic thermoelastic with Green-Naghdi theory Type-II and Type-III", Mater. Phys. Mech., 16, 144-158.
5 Slaughter, W.S. (2002), The Linearised Theory of Elasticity, Birkhausar.
6 Warren, W.E. and Chen, P.J. (1973), "Wave propagation in the two temperature theory of thermoelasticity", Acta Mechanica, 16, 21-33.   DOI
7 Youssef, H.M. (2006), "Theory of two temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390.   DOI
8 Youssef, H.M. and AI-Lehaibi, E.A. (2007), "State space approach of two temperature generalized thermoelasticity of one dimensional problem", Int. J. Solid. Struct., 44, 1550- 1562.   DOI
9 Youssef, H.M. and AI-Harby, A.H. (2007), "State space approach of two temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading", J. Arch. Appl. Mech., 77(9), 675-687.   DOI
10 Youssef, H.M. (2011), "Theory of two - temperature thermoelasticity without energy dissipation", J. Therm. Stress., 34, 138-146.   DOI
11 Youssef, H.M. (2013), "Variational principle of two-temperature thermoelasticity without energy dissipation", J. Thermoelast., 1(1), 42-44.
12 Zakaria, M. (2012), "Effects of hall current and rotation on magneto-micropolar generalized thermoelasticity due to ramp-type heating", Int. J. Electrom. Appl., 2(3), 24-32.   DOI
13 Zakaria, M. (2014), "Effect of hall current on generalized magneto-thermoelasticity micropolar solid subjected to ramp-type heating", Int. Appl. Mech., 50(1), 92-104.   DOI
14 Abbas, I.A., Kumar, R. and Reen, L.S. (2014), "Response of thermal sources in transversely isotropic thermoelastic materials without energy dissipation and with two temperatures", Can. J. Phys., 92(11), 1305-11.   DOI
15 Boley, B.A. and Tolins, I.S. (1962), "Transient coupled thermoelastic boundary value problem in the half space", J. Appl. Mech., 29, 637-646.   DOI
16 Abbas, I.A. (2011), "A two dimensional problem for a fibre- reinforced anisotropic thermoelastic halfspace with energy dissipation", Sadhana, 36(3), 411-423.   DOI
17 Attia, H.A. (2009), "Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties and uniform suction and injection", Comput. Appl. Math., 28(2), 195-212.
18 Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized ThermoMicrostretch Elastic Solid", Int. J. Thermophys., 35, 175-193.   DOI
19 Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity: a review of recent literature", Appl. Mech. Rev., 51, 705-729.   DOI
20 Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two parameters", Zeitschrift fur angewandte Mathematik und Physik (ZAMP), 19, 614-627.   DOI
21 Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on simple heat conduction", J. Appl. Math. Phys. (ZAMP), 19, 969-70.   DOI
22 Chen, P.J., Gurtin, M.E. and Williams,W.O. (1969), "On the thermodynamics of non simple elastic materials with two temperatures", ZAMP, 20, 107-112.   DOI
23 Das, P. and Kanoria, M. (2014), "Study of finite thermal waves in a magnetothermoelastic rotating medium", J. Therm. Stress., 37(4), 405-428   DOI
24 Dhaliwal, R.S. and Singh, A. (1980), Dynamic coupled thermoelasticity, Hindustance Publisher corp, New Delhi, India.
25 Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31, 189-208.   DOI
26 Ezzat, M.A. and Awad, E.S. (2010), "Constitutive relations, uniqueness of solutionand thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures", J. Therm. Stress., 33(3), 225-250.
27 Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. Roy. Soc. London Ser. A, 432, 171-194.   DOI
28 Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15, 253-264.   DOI
29 Honig, G. and Hirdes, U. (1984), "A method for the inversion of Laplace Transform", J. Comput. Appl. Math., 10, 113-132.   DOI
30 Kaushal, S., Kumar, R. and Miglani, A. (2011), "Wave propagation in temperature rate dependent thermoelasticity with two temperatures", Math. Sci., 5, 125-146.
31 Kaushal, S., Sharma, N. and Kumar, R. (2010), "Propagation of waves in generalized thermoelastic continua with two temperature", Int. J. Appl. Mech. Eng., 15, 1111- 1127.
32 Kumar, R. and Devi, S. (2010), "Magnetothermoelastic (Type-II AND III) Half-Space in contact with Vacuum", Appl. Math. Sci., 69(4), 3413-3424.
33 Kumar, R. and Kansal, T. (2010), "Effect of rotation on Rayleigh Lamb waves in an isotropic generalized thermoelastic diffusive plate", J. Appl. Mech. Tech. Phy, 51(5), 751-56.   DOI
34 Kumar, R. and Mukhopdhyay, S. (2010), "Effects of thermal relaxation times on plane wave propagation under two temperature thermoelasticity", Int. J. Eng. Sci., 48(2), 128-139.   DOI
35 Press, W.H., Teukolshy, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge.
36 Kumar, R. (2009), "Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources", Chaos Solit. Fract., 41, 1619-1633.   DOI
37 Kumar, R., Sharma, K.D. and Garg, S.K. (2014), "Effect of two temperature on reflection coefficient in micropolar thermoelastic media with and without energy dissipation", Adv. Acoust. Vib., ID 846721, 11.
38 Mahmoud, S.R. (2013), "An analytical solution for effect of magnetic field and initial stress on an infinite generalized thermoelastic rotating non homogeneous diffusion medium", Abs. Appl. Anal., ID 284646,11.
39 Quintanilla, R. (2002), "Thermoelasticity without energy dissipation of materials with microstructure", J. Appl. Math. Model., 26, 1125-1137.   DOI
40 Salem, A.M. (2007), "Hall current effects on MHD flow of a Power-Law Fluid over a rotating disk", J. Korean Phys. Soc., 50(1), 28-33.   DOI
41 Sarkar, N. and Lahiri, A. (2012), "Temperature rate dependent generalized thermoelasticity with modified Ohm's law", Int. J. Comput. Mater. Sci. Eng., 1(4), 23.
42 Sharma, K. and Bhargava, R.R. (2014), "Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermolastic solid", Afika Mathematika, 25, 81-102.
43 Sharma, K. and Marin, M. (2013), "Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space", U.P.B. Sci. Bull Series, 75(2), 121-132.