No 2, Vol. 18, 2013, pages 108-126


Magdy A. Ezzat, Ahmed S. El-Karamany, A.A. El-Bary, Mohsen A. Fayik


In this work, a new mathematical model of two-step heat conduction for an isotropic generalized thermoelasticity is derived using the methodology of fractional calculus. Some theorems of generalized thermoelasticity follow as limiting cases. An ultrafast fractional thermoelasticity model utilizing the modified fractional parabolic two-step heat conduction model and the generalized fractional thermoelastic theory was formulated to describe the thermoelastic behavior of a thin metal irradiated by a femtosecond laser pulse. The temporal profile of the ultrafast laser was regarded as being non-Gaussian. An analytical. numerical technique based on the Laplace transform was used to solve the governing equations and the time histories of the electron temperature, lattice temperature, displacement and stress in gold were analyzed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameter on all the studied fields. The effect of α where (0<α<1), on all the fields is very much prominent, as the calculation results show that an ultrafast laser pulse at α=1, induces a stronger stress wave and stronger stress attenuation compared with fractional α. In addition, the peak values of the electron, lattice temperatures and the displacement are larger in a modified fractional model as compared with the original model (α=1). Thus, we can draw the conclusion that an ultrafast laser pulse induces a stronger thermo-mechanical response in a modified fractional model.

Keywords: thermoelasticity; fractional calculus; femtosecond laser; modified two-step heat conduction; Laplace transforms; numerical results

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