Numerical solution of non-Fourier heat transfer during laser irradiation on tooth layers

Abstract

This study reports on the simulation of temperature distribution of human tooth under a laser beam based on non-Fourier models. The temperature in the tooth depth that directly results from the conduction heat transfer process is caused by the lengthy thermal relaxation time in the tooth layers. A detailed tooth composed of enamel, dentin, and pulp with unstructured shape, uneven boundaries, and realistic thicknesses was considered. A finite difference scheme was separately adopted to solve time-dependent equations in solid layers and soft tissue of the tooth. In this study, a dual-phase-lag non-Fourier heat conduction model was applied to evaluate temperature distribution induced by laser irradiation. Results show that for the laser-irradiated tooth, the phase lag time of heat flux (τq) greatly affects the temperature of the early stage, whereas the phase lag time of the temperature gradient (τT) significantly influences the temperature of the later stage. Prediction of temperature profile in the tooth based on this investigation is more real using the non-Fourier model (i.e., τq = 16 and τT = 2 millisecond) compared with experimental studies. Meanwhile, the Fourier model (τq = τT) or classical Fourier form (τq = τT = 0) and the thermal wave model (τq = 16 and τT = 0) led to unreal heated point on the enamel. The effects of laser parameters, such as laser exposure time and laser intensity on the pulp, were also investigated. Increasing the laser duration and simulation time after laser irradiation was a logical approach to pulp ablation compared with increasing the laser intensity.