Thermal plasma cutting. Part I: Modified mathematical model - Dashkovskiy, Sergey; Narimanyan, Arsen (Mathematical Modelling and Analysis, 2007)
The moving‐boundary methodology with Stefan‐ and Signorini‐type boundary conditions is used for the modelling of the thermal cutting of metals by a plasma beam. We model the problem as a coupled system of equations, the heat conduction equation with Signorini‐type boundary conditions for calculating the temperature distribution in the workpiece, Stefan‐type boundary condition for computing the unknown domain geometry and ODEs which account for the solid‐solid phase transformations occurring due to the heat treatment of the material. For latter purpose a general model describing the kinetics of phase transformation is used. Finally, a model for computing the heat flux density absorbed by the cutting interface is derived using the data of emitted heat and radius of the plasma beam. First Published Online: 14 Oct 2010