a thermo-elastic model with a single relaxation time of an unbounded medium heated by a heat supply and moving vertically

The current paper presents a thermoelastic model with a single relaxation time to examine the thermoelastic interaction in an isotropic infinite medium. the unbounded medium is exposed to a thermal shock with varying temperatures due to a vertically moving heat source in a planar region. the basic partial differential equations were solved using the laplace transform method. physical fields are studied and compared in terms of how the speed of the heat source, the relaxation time parameter, and the time parameters affect their behavior. graphical presentations are used to analyze physical field variables like temperature changes, thermal stress and deformation.