Chapters authored
Thermal Fields in Laser Cladding Processing: A “Fire Ball” Model. A Theoretical Computational Comparison, Laser Cladding versus Electron Beam Cladding
Laser cladding processing can be found in many industrial applications. A lot of different materials processing were studied in the last years. To improve the process, one may evaluate the phenomena behaviour from a theoretical and computational point of view. In our model, we consider that the phase transition to the melted pool is treated using an absorption coefficient which can underline liquid formation. In the present study, we propose a semi-analytical model. It supposes that melted pool is in first approximation a “sphere”, and in consequence, the heat equation is solved in spherical coordinates. Using the Laplace transform, we will solve the heat equation without the assumption that “time” parameter should be interpolated linearly. 3D thermal graphics of the Cu substrate are presented. Our model could be applied also for electron cladding of metals. We make as well a comparison of the cladding method using laser or electron beams. We study the process for different input powers and various beam velocities. The results proved to be in good agreement with data from literature.
Part of the book: Nonlinear Optics
A New Approach to Solve Non-Fourier Heat Equation via Empirical Methods Combined with the Integral Transform Technique in Finite Domains
This chapter deals with the validity/limits of the integral transform technique on finite domains. The integral transform technique based upon eigenvalues and eigenfunctions can serve as an appropriate tool for solving the Fourier heat equation, in the case of both laser and electron beam processing. The crux of the method consists in the fact that the solutions by mentioned technique demonstrate strong convergence after the 10 eigenvalues iterations, only. Nevertheless, the method meets with difficulties to extend to the case of non-Fourier equations. A solution is however possible, but it is bulky with a weak convergence and requires the use of extra-boundary conditions. To surpass this difficulty, a new mix approach is proposed with this chapter resorting to experimental data, in order to support a more appropriate solution. The proposed method opens in our opinion a beneficial prospective for either laser or electron beam processing.
Part of the book: Matrix Theory