Effect of fractional parameter on plane waves of generalized magneto-thermoelastic diffusion with reference temperature-dependent elastic medium

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic reference temperature-dependent elastic medium with fractional order generalized thermoelastic diffusion. The formulation is applied to the generalized thermoelasticity based on the fractional time derivatives under the effect of diffusion. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using the normal mode analysis technique. These expressions are calculated numerically for a copper-like material and depicted graphically. Effect of fractional parameter and presence of diffusion is analyzed theoretically and numerically. Comparisons are made with the results predicted by the fractional and without fractional order in the presence and absence of diffusion.

[1]  E. A. Aitken,et al.  High temperature studies of Urania in a thermal gradient , 1965 .

[2]  R. A. Oriani.  Thermomigration in solid metals , 1968 .

[3]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[4]  Hamdy M. Youssef,et al.  Fractional order generalized thermoelastic half-space subjected to ramp-type heating , 2010 .

[5]  Magdy A. Ezzat,et al.  Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer , 2011 .

[6]  M. Caputo.  Vibrations of an infinite viscoelastic layer with a dissipative memory , 1974 .

[7]  M. Caputo,et al.  A new dissipation model based on memory mechanism , 1971 .

[8]  Hamdy M. Youssef,et al.  Theory of Fractional Order Generalized Thermoelasticity , 2010 .

[9]  Y. Povstenko.  Fractional Cattaneo-Type Equations and Generalized Thermoelasticity , 2011 .

[10]  M. Fayik,et al.  Fractional Order Theory of Thermoelastic Diffusion , 2011 .

[11]  Rainer Kimmich,et al.  Strange kinetics, porous media, and NMR , 2002 .

[12]  Martin Ostoja-Starzewski,et al.  Thermoelasticity with Finite Wave Speeds , 2009 .

[13]  Y. Povstenko.  FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS , 2004 .

[14]  F. Hamza,et al.  The theory of generalized thermoelastic diffusion , 2004 .

[15]  H. Sherief,et al.  A half-space problem in the theory of generalized thermoelastic diffusion , 2005 .

[16]  F. Incropera,et al.  Fundamentals of Heat Transfer , 1981 .

[17]  M. Othman,et al.  The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green–Naghdi theory , 2009 .

[18]  M. Othman.  Effect of rotation and relaxation time on a thermal shock problem for a half-space in generalized thermo-viscoelasticity , 2005 .

[19]  A. Lahiri,et al.  A three-dimensional thermoelastic problem for a half-space without energy dissipation , 2012 .

[20]  Francesco Mainardi,et al.  Linear models of dissipation in anelastic solids , 1971 .

[21]  Baljeet Singh,et al.  Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion , 2005 .

[22]  M. Othman,et al.  Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times , 2008 .