Abstract
The use of fractional derivatives has been very useful in recent decades for modeling many problems of engineering sciences. The literature includes several different concepts of a fractional derivative. In this regard, most fundamental models are based on the Riemann- Liouville and Caputo concepts that include singular kernels. Based on the Caputo-Fabrizio fractional derivative, the current investigation deals with providing a new mathematical heat conduction model involving a non-singular kernel. Also, Eringen's nonlocal elasticity theory has been applied to study the size dependent effect. The suggested model is then used to analyze the transient reactions of a finite thermoelastic rod when exposed to a heat resource that moves to the right axial direction. The rod is posed in a constant primary magnetic field and its ends are assumed to be thermally insulated and fixed. In solving the governing equations, the Laplace transform technique has been applied and the inversions have been calculated numerically using an appropriate numerical procedure. The effect of the coefficient of nonlocality, fractional order parameter and the velocity of the moving heat supply has been studied in separate cases. The findings indicate that these factors significantly affect the scale of the studied physical variables.