Numerical simulation of the unsteady non-linear heat transfer problems. Application on nanosecond laser annealing of Si

The aim of the present work is the numerical simulation of the unsteady non-linear heat transfer problems. A nanosecond Gaussian in time and space pulse is considered as the heat source acting on a Si substrate. Four different scenarios are considered in order to examine the influence of the laser parameters on the Si surface temperature, namely variation of the fluence of the laser beam, the radius of the laser beam at the Si surface, the duration of the pulse and finally the number of laser pulses. A meshfree point collocation method (MPC) has been employed for the solution of the problem. More precisely, the moving least squares (MLS) approximation is incorporated for the construction of the shape functions, in conjunction with the general framework of the point collocation method. The accuracy and stability of the proposed scheme are demonstrated through three representative benchmark problems in 1D, 2D and 3D. Numerical results are found to be in very good agreement with analytical, numerical and experimental results presented in the literature.