Thermoelastic interaction in a magneto-thermoelastic rod with memory-dependent derivative due to the presence of moving heat source

Abstract

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory effects which is defined in the form of convolution-type integrals involving kernels as power functions. Due to the shortcomings of power law distributions, some other forms of derivatives with few other kernel functions have been proposed. This present survey deals with a novel mathematical model of generalized thermoelasticity which investigates the transient phenomena due to the influence of an induced magnetic field and the presence of moving heat source in a thermoelastic rod in the context of Lord–Shulman (LS) theory of generalized thermoelasticity. Both ends of the rod are fixed and are thermally insulated. Employing the Laplace transform, the problem has been transformed to the space-domain have been solved analytically. Finally, solutions in the real-time domain are obtained on applying the numerical inversion of Laplace transform, which has been carried out employing the Riemann-sum approximation method. Numerical computations for stress, displacement and temperature within the rod is carried out and have been demonstrated graphically. The results also demonstrate how the speed of the moving heat source influences the thermophysical quantities. It is observed that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field and memory effect also.