Scaling of non-linear effects in heat transfer of a continuously fed melting wire

This paper performs a comprehensive scaling analysis of heat transfer in a wire melting under conditions typical of Gas Metal Arc Welding and similar processes. This formulation includes the typical conduction and Joule heating effects, but also considers heat losses by convection and radiation and non-linearities in the thermal and electrical properties of the wire. Different regions in the wire are identified, expressions for the heat flux through the wire are developed, and the typical regime of operation is identified. Scaling laws are obtained and verified against a numerical model.