This paper aims to examine the transient thermo-diffusion responses for a half-space with changing thermal conductivity and diffusivity within the framework of extended thermo-diffusion theory. The surface of the half-bounding space is tractionless and subject to a time-varying thermal shock, but it is assumed that the chemical potential is a known function of time. Due to the complexity of the nonlinear equations, the finite element method is used to solve them. The results are produced numerically and visually. Through the use of parameter studies, the effects of changing thermal conductivity and diffusivity on the response are investigated. Researchers seek to gain a better understanding of how thermo-mechanical fields interact in actual materials using the findings of this study. In order to verify the accuracy of the suggested method, the behaviour of physical quantities for numerical solutions is examined and compared with numerical results and analytical cases where the new parameter is ignored.
