×

An analytical solution for effect of magnetic field and initial stress on an infinite generalized thermoelastic rotating nonhomogeneous diffusion medium. (English) Zbl 1291.76358

Summary: The problem of generalized magneto-thermoelastic diffusion in an infinite rotating nonhomogeneity medium subjected to certain boundary conditions is studied. The chemical potential is also assumed to be a known function of time at the boundary of the cavity. The analytical expressions for the displacements, stresses, temperature, concentration, and chemical potential are obtained. Comparison was made between the results obtained in the presence and absence of diffusion. The results indicate that the effect of nonhomogeneity, rotation, magnetic field, relaxation time, and diffusion is very pronounced.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Motreanu, D.; Sofonea, M., Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials, Abstract and Applied Analysis, 4, 4, 255-279 (1999) · Zbl 0974.58019
[2] Atanacković, T. M.; Konjik, S.; Oparnica, L.; Zorica, D., Thermodynamical restrictions and wave propagation for a class of fractional order viscoelastic rods, Abstract and Applied Analysis, 2011 (2011) · Zbl 1217.74064 · doi:10.1155/2011/975694
[3] Fares, R.; Panasenko, G. P.; Stavre, R., A viscous fluid flow through a thin channel with mixed rigid-elastic boundary: variational and asymptotic analysis, Abstract and Applied Analysis, 2012 (2012) · Zbl 1246.76022 · doi:10.1155/2012/152743
[4] Marin, M.; Agarwal, R. P.; Mahmoud, S. R., Modeling a microstretch thermoelastic body with two temperatures, Abstract and Applied Analysis, 2013 (2013) · Zbl 1291.74062 · doi:10.1155/2013/583464
[5] Allam, M. N. M.; Zenkour, A. M.; Elazab, E. R., The rotating inhomogeneous elastic cylinders of variable-thickness and density, Applied Mathematics & Information Sciences, 2, 3, 237-257 (2008) · Zbl 1288.74035
[6] Abd-Alla, A. M.; Mahmoud, S. R.; Al-Shehri, N. A., Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material, Applied Mathematics and Computation, 217, 22, 8914-8922 (2011) · Zbl 1387.74062 · doi:10.1016/j.amc.2011.03.077
[7] Abd-Alla, A. M.; Mahmoud, S. R.; Abo-Dahab, S. M., On problem of transient coupled thermoelasticity of an annular fin, Meccanica, 47, 5, 1295-1306 (2012) · Zbl 1293.74066 · doi:10.1007/s11012-011-9513-2
[8] Abd-Alla, A. M.; Mahmoud, S. R.; El-Naggar, A. M., Analytical solution of electro-mechanical wave propagation in long bones, Applied Mathematics and Computation, 119, 1, 77-98 (2001) · Zbl 1052.74513 · doi:10.1016/S0096-3003(99)00231-3
[9] Lord, H. W.; Shulman, Y., A generalized dynamical theory of thermo-elasticity, Journal of the Mechanics and Physics of Solids, 7, 71-75 (1967)
[10] Dhaliwal, R. S.; Sherief, H. H., Generalized thermoelasticity for anisotropic media, Quarterly of Applied Mathematics, 33, 1, 1-8 (1980) · Zbl 0432.73013
[11] Abd-Alla, A. M.; Mahmoud, S. R., Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model, Meccanica, 45, 4, 451-462 (2010) · Zbl 1258.74055 · doi:10.1007/s11012-009-9261-8
[12] Mahmoud, S. R., Wave propagation in cylindrical poroelastic dry bones, Applied Mathematics & Information Sciences, 4, 2, 209-226 (2010) · Zbl 1423.74625
[13] Kumar, R.; Devi, S., Deformation in porous thermoelastic material with temperature dependent properties, Applied Mathematics & Information Sciences, 5, 1, 132-147 (2011) · Zbl 1221.74020
[14] Othman, M. I. A., Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermoelasticity, Journal of Thermal Stresses, 25, 11, 1027-1045 (2009) · doi:10.1080/01495730290074621
[15] Kumar, R.; Gupta, R. R., Deformation due to inclined load in an orthotropic micropolar thermoelastic medium with two relaxation times, Applied Mathematics & Information Sciences, 4, 3, 413-428 (2010)
[16] Green, A. E.; Lindsay, K. A., Thermoelasticity, Journal of Elasticity, 2, 1, 1-7 (1972) · Zbl 0775.73063 · doi:10.1007/BF00045689
[17] Abd-Alla, A. M.; Yahya, G. A.; Mahmoud, S. R., Radial vibrations in a non-homogeneous orthotropic elastic hollow sphere subjected to rotation, Journal of Computational and Theoretical Nanoscience, 10, 2, 455-463 (2013)
[18] Abd-Alla, A. M.; Abo-Dahab, S. M.; Mahmoud, S. R.; Al-Thamalia, T. A., Influence of the rotation and gravity field on stonely waves in a non-homogeneous orthotropic elastic medium, Journal of Computational and Theoretical Nanoscience, 10, 2, 297-305 (2013)
[19] Sherief, H. H.; Hamza, F. A.; Saleh, H. A., The theory of generalized thermoelastic diffusion, International Journal of Engineering Science, 42, 5-6, 591-608 (2004) · Zbl 1211.74080 · doi:10.1016/j.ijengsci.2003.05.001
[20] Sherief, H. H.; Saleh, H. A., A half-space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures, 42, 15, 4484-4493 (2005) · Zbl 1119.74366 · doi:10.1016/j.ijsolstr.2005.01.001
[21] Singh, B., Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration, 291, 3-5, 764-778 (2006) · Zbl 1243.74025 · doi:10.1016/j.jsv.2005.06.035
[22] Kumar, R.; Kansal, T., Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate, International Journal of Solids and Structures, 45, 22-23, 5890-5913 (2008) · Zbl 1362.74020 · doi:10.1016/j.ijsolstr.2008.07.005
[23] Ram, P.; Sharma, N.; Kumar, R., Thermomechanical response of generalized thermoelastic diffusion with one relaxation time due to time harmonic sources, International Journal of Thermal Sciences, 47, 3, 315-323 (2008) · doi:10.1016/j.ijthermalsci.2007.02.005
[24] Aouadi, M., A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures, 44, 17, 5711-5722 (2007) · Zbl 1126.74013 · doi:10.1016/j.ijsolstr.2007.01.019
[25] Abd-Alla, A. M.; Mahmoud, S. R., Analytical solution of wave propagation in a non-homogeneous orthotropic rotating elastic media, Journal of Mechanical Science and Technology, 26, 3, 917-926 (2012) · doi:10.1007/s12206-011-1241-y
[26] Othman, M. I. A.; Atwa, S. Y.; Farouk, R. M., The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green-Naghdi theory, International Communications in Heat and Mass Transfer, 36, 8, 857-864 (2009) · doi:10.1016/j.icheatmasstransfer.2009.04.014
[27] Xia, R.-H.; Tian, X.-G.; Shen, Y.-P., The influence of diffusion on generalized thermoelastic problems of infinite body with a cylindrical cavity, International Journal of Engineering Science, 47, 5-6, 669-679 (2009) · Zbl 1213.74108 · doi:10.1016/j.ijengsci.2009.01.003
[28] Deswal, S.; Kalkal, K., A two-dimensional generalized electro-magneto-thermoviscoelastic problem for a half-space with diffusion, International Journal of Thermal Sciences, 50, 5, 749-759 (2011) · doi:10.1016/j.ijthermalsci.2010.11.016
[29] Abd-Alla, A. M.; Abo-Dahab, S. M., Time-harmonic sources in a generalized magneto-thermo-viscoelastic continuum with and without energy dissipation, Applied Mathematical Modelling, 33, 5, 2388-2402 (2009) · Zbl 1185.74015 · doi:10.1016/j.apm.2008.07.008
[30] Mahmoud, S. R., Influence of rotation and generalized magneto-thermoelastic on rayleigh waves in a granular medium under effect of initial stress and gravity field, Meccanica, 47, 7, 1561-1579 (2012) · Zbl 1293.74243 · doi:10.1007/s11012-011-9535-9
[31] Abd-Alla, A. M.; Abo-Dahab, S. M.; Hammad, H. A.; Mahmoud, S. R., On generalized magneto-thermoelastic rayleigh waves in a granular medium under the influence of a gravity field and initial stress, Journal of Vibration and Control, 17, 1, 115-128 (2011) · Zbl 1271.74239 · doi:10.1177/1077546309341145
[32] Abd-Alla, A. M.; Mahmoud, S. R., On problem of radial vibrations in non-homogeneity isotropic cylinder under influence of initial stress and magnetic field, Journal of Vibration and Control, 19, 9, 1283-1293 (2013)
[33] Kraus, J. D., Electromagnetics (1984), New York, NY, USA: Mc Graw-Hill, New York, NY, USA
[34] Sokolnikoff, I. S., Mathematical Theory of Elasticity (1946), New York, NY, USA: Dover, New York, NY, USA · Zbl 0070.41104
[35] Thomas, L., Fundamentals of Heat Transfer (1980), Englewood Cliffs, NJ, USA: Prentice-Hall, Englewood Cliffs, NJ, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.