根据热传导理论，推导出了激光烧结陶瓷过程中的热传导方程;并采用数值模拟的方法，编写了基于有限差分法的计算机程序。在此基础上，分别模拟计算了在各种不同的烧结工艺条件下，CO2激光辐照Al2O3陶瓷的温度场,结果表明,采用激光辐照的办法烧结陶瓷可以使陶瓷在短时间内达到很高的温度。此外，还计算了烧结过程中材料的温度随空间的变化曲线,结果表明,平行于激光辐照方向的温度梯度大小不随烧结时间变化而只与激光功率有关，激光功率越大温度梯度越大。研究还发现：垂直激光辐照方向的温度梯度的大小取决于激光束的功率密度分布和光斑大小。

A numerical simulation was studied on field of temperature in ceramics by using FDM (Finite Differential Method) during the laser sintering. At first, the heat conduction equations were given, then the boundary condition was given, Finally, the mathematical model of the laser sintering on ceramics was given and the equations were solved by FDM. The simulation program was given by above method, and then the change of field of temperature in ceramics was described by simulation program. The effect of technological conditions on field of temperature in ceramics was analyzed. It shows that the lengthways temperature gradient in ceramics is only relevant to the laser power, and the transverse temperature gradient in ceramics is relevant to the laser speckle radius and the transverse intensity distribution of laser.