Thermoelastic response of fiber-reinforced epoxy composite under continuous line heat source

Abstract

This present study deals with a novel mathematical model of generalized thermoelasticity in a fiber-reinforced, isotropic unbounded thermoelastic solid due to the presence of a continuous line heat source under the influence of magnetic field. The derivative is defined in an integral form of a common derivative on a slipping interval by incorporating memory-dependent heat transfer. Employing both Laplace and Hankel transforms as tools, analytical results for distributions of different fields have been derived with the help of potential function approach. The inversion of Hankel transform is performed analytically, whereas the numerical inversion of Laplace transform is carried out employing Zakian method and the method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory to exhibit the significance of the kernel functions and the time-delay parameter is constructed. The significant differences of the two different numerical schemes have also explained. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of reinforcement and magnetic field. Also, significant differences due to the choice of linear and nonlinear kernels in the heat equation is elaborated.