Journal
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
Volume 75, Issue -, Pages 726-735Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijheatmasstransfer.2014.04.015
Keywords
Isotherm migration method; Stefan problem; Finite differences; Isotherm tracking; Laser material processing
Categories
Funding
- Agency for Innovation by Science and Technology in Flanders (IWT) within the SBO [110070]
- Research Council (OZR) of the Vrije Universiteit Brussel
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An isotherm migration method is presented to track the isotherms at the surface of a semi-infinite work-piece that is being heated by a point source with a linear motion. The governing heat conduction equation is first transformed into a one-dimensional isotherm migration equation in spherical coordinates, which expresses the isotherm velocities as a function of the isotherm positions and their temperature derivatives. A finite difference formulation of this equation is then derived together with the corresponding boundary conditions. It is shown through a number of simulations that this system converges to the analytical solution when the temperature mesh is refined. The additional presence of a phase change results in a Stefan problem that can be solved approximately with some minor modifications to the method. The resulting system of equations can be used as a simple but accurate thermal model for some laser-material interaction processes such as laser heat treatments and laser cladding. (C) 2014 Elsevier Ltd. All rights reserved.
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