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Chin. Phys. B, 2013, Vol. 22(7): 074601    DOI: 10.1088/1674-1056/22/7/074601

Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

Rajneesh Kumar, Vandana Gupta
Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana, India
Abstract  In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.
Keywords:  thermoelastic diffusion      fractional calculus      uniqueness theorem      reciprocity theorem  
Received:  13 December 2012      Revised:  18 January 2013      Accepted manuscript online: 
PACS:  46.70.-p (Application of continuum mechanics to structures)  
  46.15.-x (Computational methods in continuum mechanics)  
  46.05.+b (General theory of continuum mechanics of solids)  
Fund: Project supported by the Council of Scientific and Industrial Research (CSIR), India.
Corresponding Authors:  Rajneesh Kumar     E-mail:

Cite this article: 

Rajneesh Kumar, Vandana Gupta Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative 2013 Chin. Phys. B 22 074601

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