Equilibrium and energy equations have been developed in describing the solid-fluid transition zone during the melting and solidification of the binary alloys. Due to the existence of the transition region exhibiting both solid and fluid phases at the same material point from continuum point of view, mixture theory was utilized to analyze the region. Unlike the Stefan problem, the latent heat due to the phase change appears as a source term in the heat equation. The molten fluid is treated as a thermoviscous and incompressible fluid, whereas the solid is thermoviscoplastic described by the Bodner-Partom/Walker type of constitutive equations. Thermal mechanical behaviors of the solid and the fluid phases are determined separately because of insignificant mechanical interactions between them. Volume fractions of the phases are obtained according to the equilibrium phase diagram. The simulation process of the transition zone and the welding process was carried out by FEM. The molten fluid motion, the sizes, and the contours of the transition zone were presented.

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