Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer

Abstract

The model of equations of thermo-viscoelasticity with fractional order heat transfer is constructed. Some fundamental theorems on the linear coupled and generalized theories of thermo-viscoelasticity can be easily obtained as special cases. The medium is assumed initially quiescent. Laplace and Fourier integral transforms are utilized. The method of the matrix exponential which constitutes the basis of the state–space approach of modern control theory is applied to the system of two-dimensional equations. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using numerical method based on Fourier series expansions. Numerical results are given and illustrated graphically for the problem considered. Comparisons are made with the results predicted by the coupled theory and generalized theory. The effect of the fractional order parameter on all the considered fields is examined.