A semi-analytical approach for thermoelastic wave propagation in infinite solids subject to linear heat supply using two-phase lag theory

Abstract

This study examines how heat travels as thermoelastic waves in a uniform, isotropic, and infinitely large solid material due to a constant line heat source. We leverage the theory of thermoelasticity with two phase lags to account for the time difference between temperature changes and the material’s stress response. By employing a potential function approach alongside Laplace and Hankel transforms, we can convert the governing equations into more manageable domains. This enables us to derive mathematical formulas for temperature, displacement, and stress distributions within the solid. Through a complex inversion process of the Laplace transforms, we obtain analytical formulas for these field distributions. These formulas, however, are only valid for short time periods and are most applicable in the initial stages of wave propagation. We then use these analytical formulas to visualize how temperature, displacement, and stress are distributed, revealing the influence of the heat source and phase lag parameters on these fields. This approach provides valuable insights into the characteristics of wave propagation, the heat source’s impact, and the time-dependent nature of the thermoelastic response. Furthermore, to demonstrate the method’s versatility and ability to connect with established theories, we incorporate specific examples from other thermoelasticity theories. This broadens our understanding of thermoelastic behavior under various conditions.