Abstract
This paper addresses a modified constitutive equation by incorporating the size effect of nanostructured materials and a new formulation of Fourier's law including Caputo-Fabrizio fractional heat conduction equation with a non-singular kernel. The Kelvin-Voigt model is used to characterize the viscoelastic behavior of the material. In the absence of mechanical relaxation and nonlocal effects, the results of different generalized theories of thermoelasticity can be achieved as specific cases. The presented model is then applied to analyze the magneto-thermoelastic interactions in a viscoelastic rotating rod subject to a moving heat source. The analytical solutions are obtained through Laplace transform method and its reversal followed by residue calculations. Several illustrations are presented to evaluate the effects of system parameters, fractional order, nonlocal and vicsocity parameters, magnetic field and the velocity of heat source on the features of physical variables.