This paper develops a finite element code based on the hyperbolic heat conduction equation including the non-Fourier effect in heat conduction. The finite element space discretization is used to obtain a system of differential equations for time. The time-related responses are obtained by solving the system of differential equations via finite difference technique. A relationship for the time step length and the element size was obtained to ensure that numerical oscillation in temperature be suppressed. Temperature-dependent material properties are taken into account in the proposed analysis model. In addition to the temperature field, the thermal stresses are also obtained from the developed method. The thermal stresses associated with the non-classical heat conduction are found to be considerably difference from those associated with classical heat conduction.
Wang, B., Han, J., & Sun, Y. (2012). A finite element/finite difference scheme for the non-classical heat conduction and associated thermal stresses. Finite Elements in Analysis and Design, 50, 201-206. https://doi.org/10.1016/j.finel.2011.09.010