TITLE:
Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials
AUTHORS:
Essam Bassiouny, Refaat Sabry
KEYWORDS:
Fractional Order; Two Temperature; Generalized Thermoelectricity; Weak Diffusion; Thermal Loading; Piezoelectric Materials; Ceramics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.5,
November
12,
2013
ABSTRACT: A new mathematical model of time fractional order heat
equation and fractional order boundary condition have been constructed
in the context of the generalized theory of thermo piezoelasticity. The governing
equations have been applied to a semi infinite piezoelectric slab. The Laplace
transform technique is used to remove the time-dependent terms in the governing
differential equations and the boundary condition. The solution of the problem
is first obtained in the Laplace transform domain. Furthermore, a complex
inversion formula of the transform based on a Fourier expansion is used to get
the numerical solutions of the field equations which are represented
graphically.