Dynamic response of a half-space with time-fractional heat conduction and nonlocal strain theory

In this work, a heat conduction model is generalized by employing the time-fractional heat conduction and nonlocal strain theory. In order to conduct a qualitative analysis of the problem, a half-space subjected to thermal shock is studied. For the convenience of obtaining numerical results, Laplace transform is used and analytical solutions in the Laplace domain are obtained. Solutions in the time domain are then obtained by Laplace inverse transform. Numerical results show that fractional order parameters have a relatively small influence on displacement but a larger influence on other quantities; nonlocal coefficients have a significant influence on all quantities; as time increases, the response of each quantity becomes more obvious; the strain relaxation coefficient has a small influence on temperature but a larger influence on other quantities. It is therefore necessary to consider the fractional theory generalized in this work in practical engineering problems and in the design of materials with heat conduction.