Effect of Hall Current in Thermoelastic Materials with Double Porosity Structure
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Department of Mathematics, Kurukshetra University Kurukshetra, Haryana, INDIA
of Mathematics and Statistics H.P. University, Shimla, HP, INDIA
Online publication date: 2017-06-09
Publication date: 2017-05-24
International Journal of Applied Mechanics and Engineering 2017;22(2):303-319
The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity structure in the presence of Hall currents subjected to thermomechanical sources. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. A numerical simulation is prepared for these quantities. The effect of the Hartmann number is depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.
Boer R.DE. and Ehlers W. (1988): A historical review of the foundation of porous media theories. - Acta Mech., vol.74, pp.1-8.
Boer R.DE. (2000): Theory of Porous Media. - New York: Springer-Verleg.
Wilson R.K. and Aifantis E.C. (1982): On the theory of consolidation with double porosity. - Int. J. Engg. Sci., vol.20, pp.1009-1035.
Khaled M.Y., Beskos D.E. and Aifantis E.C. (1984a): On the theory of consolidation with double porosity-III. - Int. J. Numer. Analy. Meth. Geomech., vol.8, pp.101-123.
Wilson R.K. and Aifantis E.C. (1984b): A double porosity model for acoustic wave propagation in fractured porous rock. - Int. J. Engg. Sci., vol.22, pp.8-10, 1209-1227.
Beskos D.E. and Aifantis E.C. (1986): On the theory of consolidation with double porosity-II. - Int. J. Engg. Sci., vol.24, pp.1697-1716.
Khalili N. and Valliappan S. (1996): Unified theory of flow and deformation in double porous media. - Eur. J. Mech. A, Solids, vol.15, pp.321-336.
Aifantis E.C. (1977): Introducing a multi -porous medium. - Developments in Mechanics, vol.8, pp.209-211.
Aifantis E.C. (1979): On the response of fissured rocks. - Developments in Mechanics, vol.10, pp.249-253.
Aifantis E.C. (1980a): On the problem of diffusion in solids. - Acta Mechanica, vol.37, pp.265-296.
Aifantis E.C. (1980b): The Mechanics of Diffusion in Solids. - T.A.M. Report No.440, Dept. of Theor. Appl. Mech., University of Illinois, Urbana, Illinois.
Aifantis E.C. (1980c): On the problem of diffusion in solids. - Acta Mechanica, vol.37, pp.265-296.
Khalili N. and Selvadurai A.P.S. (2003): A Fully Coupled Constitutive Model for Thermo-hydro -mechanical Analysis in Elastic Media with Double Porosity. - Geophys. Res. Lett., vol.30, No.2268.
Straughan B. (2013): Stability and uniqueness in double porosity elasticity. - Int. J. Eng. Sci., vol.65, pp.1-8.
Svanadze M. (2005): Fundamental solution in the theory of consolidation with double porosity. - J. Mech. Behav. Mater., vol.16, pp.123-130.
Svanadze M. (2010): Dynamical problems on the theory of elasticity for solids with double porosity. - Proc. Appl. Math. Mech., vol.10, pp.209-310.
Svanadze M. (2012): Plane waves and boundary value problems in the theory of elasticity for solids with double porosity. - Acta Appl. Math., vol.122, pp.461-471.
Svanadze M. (2014a): On the theory of viscoelasticity for materials with double porosity. - Disc. and Cont. Dynam. Syst. Ser. B, vol.19, pp.2335-2352.
Svanadze M. (2014b): Uniqueness theorems in the theory of thermoelasticity for solids with double porosity. - Meccanica, vol.49, pp.2099-2108.
Scarpetta E., Svanadze M. and Zampoli V. (2014c): Fundamental solutions in the theory of thermoelasticity for solids with double porosity. - J. Therm. Stresses, vol.37, pp.727-748.
Scarpetta E. and Svanadze M. (): Uniqueness Theorems in the Quasi-Static Theory of Thermo Elasticity for Solids with Double Porosity. - J. Elas., DOI 10.1007/s10659-014-9505-2.
Bahar L.Y. and Hetnarski R.B. (1977a): Transfer matrix approach thermoelasticity. - Proceedings of the Fifteenth Midwestern Mechanics Conference, Chicago, pp.161-163.
Bahar L.Y. and Hetnarski R.B. (1977b): Coupled thermoelasticity of layered medium. - Proceedings of the Fourteenth Annual Meeting of the Society of Engineering Science, Lehigh University, Bethlehem, PA, pp.813-816.
Bahar L.Y. and Hetnarski R.B. (1978): State space approach to thermoelasticity. - J. Therm. Stresses, vol.1, No.1, pp.135-145.
Bahar L.Y. and Hetnarski R.B. (1979): Connection between the thermoelastic potential and the state space formulation of thermoelasticity. - J. Therm. Stresses, vol.2, pp.283-290.
Bahar L.Y. and Hetnarski R.B. (1980): Coupled thermoelasticity of a layered medium. - J. Therm. Stresses, vol.3, pp.141-152.
Ezzat M.A., Othman M.A. and El-Karamany A.S. (2002): State space approach to generalized thermoviscoelasticity with two relaxation times. - Int. J. Engg. Sci., vol.40, pp.283-302.
El-Maghraby N.M., El-Bary A.A. and Youssef H.M. (2006): State space approach to thermoelastic problem with vibrational stress. - Computational Mathematics and Modelling, vol.17, pp.243-253.
Youssef H.M. and Al-Lehaibi E.A. (2007): State space approach of two-temperature generalized thermoelasticity of one-dimensional problem. - Int. J. Solid. Struct., vol.44, pp.1550-1562.
Othman M.I.A. (2011a): State space approach to the generalized thermoelastic problem with temperature dependent elastic moduli and internal heat sources. - J. Appl. Mech. Tech. Phys., vol.52, pp.644-656.
Elisbai K.A. and Youseff H.M. (2011b): State space approach to vibration of gold nano-beam induced by ramp type heating without heating energy dissipation in femtoseconds scale. - J. Therm. Stresses, vol.34, pp.244-263.
Sherief H.H. and El-Sayed A.M. (2014): State space approach to two-dimensional generalized micropolar thermoelasticity. - Z. Angew. Math. Phys., DOI 10.1007/s00033-014-0442.
Knopoff L. (2005): The interaction between elastic wave motion and a magnetic field in a perfectly conducting medium. - Int. J. Solids and Structures, vol.42, pp.6319-6334.
Chadwick P. (1957): Ninth Int. Congr. Appl. Mech., vol.7, pp.143.
Kaliski S. and Petykiewicz J. (1959): Equation of motion coupled with the field of temperature in magnetic field involving mechanical and electrical relaxation for anisotropic bodies. - Proc. Vibr. Probl., vol.4.
Sarkar N. and Lahiri A. (2012): Temperature rate dependent generalized thermoelasticity with modified Ohm’s law. - International Journal of Computational Materials Science and Engineering, vol.1, No.4, pp.1-23.
Salem A.M. (2007): Hall- Current effects on MHD flow of a Power-Law fluid over a rotating disk. - Journal of the Korean Physical Society, vol.50, pp.28-33.
Zakaria M. (2011): Effect of Hall current on generalized magneto-thermoelasticity micropolar solid subjeted to ramp-type heating. - American Journal of Materials Science, vol.1, pp.26-39.
Zakaria M. (2012): Effects of Hall current and rotation on magneto-micropolar generalized thermoelasticity due to ramp-type heating. - International Journal of Electromagnetics and Applications, vol.2, No.3, pp.24-32.
Zakaria M. (2014): Effect of Hall current on magneto-thermoelasticity micropolar solid subjected to ramp-type heating. - International Applied Mechanics, vol.50, No.1, pp.92-104.
Attia H.A. (2011): A two dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation. - Sadhana, Indian Academy of Sciences, vol.36, pp.411-423.
Iesan D. and Quintanilla R. (2014): On a theory of thermoelastic materials with a double porosity structure. - J. Therm. Stresses, vol.37, pp.1017-1036.
Sherief H. and Saleh H. (2005): A half space problem in the theory of generalized thermoelastic diffusion. - Int. J. Solid and Structures, vol.42, pp.4484-93.
Khalili N. (2003): Coupling effects in double porosity media with deformable matrix. - Geophys. Res. Lett., vol.30, No.22, 2153, DOI 10.1029/2003GL018544.
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