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Theoretical Calculation on Shape of Fusion Boundary and Temperature Distribution around Moving Heat Source (Report I)

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Shape of steady state fusion boundary and temperature distribution around a point heat source moving a constant velocity on a thick plate are calculated theoretically by solving the free boundary problem of heat conduction where the emission and absorption of the latent heat at the boundary and the difference between the thermal diffusivity in solid phase and that in liquid phase are taken into account. The fusion boundary is determined so that the heat balance equation on the fusion boundary including the latent heat is satisfied by successive approximation. In a typical case, the fusion boundary is displaced forward and its length is 10% shorter, when the latent heat and the difference of the thermal diffusivity are ignored. Obtained results are compared with experimental data quoted from Christensen's work. The theoretical pool widths agree with the experimental ones, but the ripple lag and pool lengths obtained by experiments are longer than those obtained by the present theory.



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