A stable finite difference scheme for solving a hyperbolic two-step model in a 3D micro sphere exposed to ultrashort-pulsed lasers

Purpose - To develop a numerical method for solving hyperbolic two-step micro heat transport equations, which have attracted attention in thermal analysis of thin metal films exposed to ultrashort-pulsed lasers. Design/methodology/approach - An energy estimation for the hyperbolic two-step model in a three-dimensional (M) micro sphere irradiated by ultrashort-pulsed lasers is first derived, and then a finite difference scheme for solving the hyperbolic two-step model based on the energy estimation is developed. The scheme is shown to be unconditionally stable and satisfies a discrete analogue of the energy estimation. The method is illustrated by investigating the heat transfer in a micro gold sphere exposed to ultrashort-pulsed lasers. Findings - Provides information on normalized electron temperature change with time on the surface of the sphere, and shows the changes in electron and lattice temperatures. Research limitations/implications - The hyperbolic two-step model is considered under the assumption of constant thermal properties. Practical implications - A useful tool to investigate the temperature change in a micro sphere irradiated by ultrashort-pulsed lasers. Originality/value - Provides a new unconditionally stable finite difference scheme for solving the hyperbolic two-step model in a 3D micro sphere irradiated by ultrashort-pulsed lasers.