Application of fractional order theory of thermoelasticity to 3D time-dependent thermal shock problem for a half-space

ABSTRACT

A three-dimensional model of thermoelasticity with fractional order heat transfer is established. The resulting nondimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverses of Fourier transforms and Laplace transforms are obtained numerically. Numerical results for the temperature, the stress, the strain, and the displacement distributions are represented graphically. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity.

KEYWORDS:

• fractional calculus
• generalized thermoelasticity
• three-dimensional modeling
• Laplace