Thermal wave propagation in a two-dimensional problem under gravitational field due to time-dependent thermal loading and memory effect

Abstract

This paper presents a comprehensive study on developing a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite thermoelastic half-space under the action of ramp-type thermal loading and due to the influence of a gravitational field. The bounding plane of the half-space is subjected to rough and rigid foundation so that the rough surface prevents the vertical displacement. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. The present analysis deals with the heat transport which involves the memory-dependent derivative (MDD) on a slipping interval in the context of Lord–Shulman model to describe the physical phenomena which is defined in the form of convolution with the kernels in the form of power functions. Employing the Laplace and the Fourier transform techniques as tools, the analytical expressions for different physical fields have been obtained on the transformed domain. The numerical inversion of the Fourier transforms have been performed analytically, whereas numerical inversion of the Laplace transform is carried out using the Riemann-sum approximation method. Excellent predictive capability is demonstrated due to the presence of MDD, delay time and gravitational field also.