由激光辐照固体表面引起的非Fourier三维传热问题的解析解

针对激光束瞬间加热物体表面时，材料表面附近温度场变化的问题，建立了基于非傅里叶热传导理论的三维热传导数学模型. 考虑了激光束的聚焦特征，即热量或高温主要集中在光束中心附近的局部区域，且沿材料表面切向呈非均匀分布. 利用积分变换技巧，得到了问题Laplace逆变换的解析形式，从而给出了新的温度场解析解，并据此分析了传热过程中固体内部的温度场演化规律及特征. 数值计算结果显示，该问题的温度场呈现出明显的非傅里叶传热特征，与经典的热传导的扩散形式不同，它是以波的形式进行传热的. 

Non-Fourier Effect in Three-Dimensional Heating Conduction by Laser Irradiation on Surface

To the heat conduction problem rising as laser beam irradiating on the metallic surfaces, a three dimensional mathematical model was established based on non-Fourier heat conduction theory for thermal distribution near the surface of material. The focusing property of laser beam was considered, that the high temperature mainly focus in a local area around the center of the laser beam and distributes non-uniform in direction along the surface. Based the techniques of integral transform, the analytic solution of the problem in form of inverse Laplace transform was derived and the patterns and characters of the thermal field were analyzed based on the two dimensional analytic solution. The numerical solutions show that the thermal field has clear property of non-Fourier heat conduction. Being different from the classical thermal conduction, the heat travels with waveform in the material.