Modeling of a thermal arc bent by cross flow and magnetostatic fields

Theoretical models of noncylindrical thermal arcs are derived. The introduction of a suitable choice of toroidal coordinates shows the three dimensional energy transfer equation relevant to the convected and the non-convected thermal arcs to be separable and analytical solutions are made possible by the introduction of proper mathematical transformations. These solutions are shown to be consistent and reducible to the solutions pertaining to the straight cylindrical arc in the limiting case where the curvature of the bent arc tends to infinity. The models can explain the asymmetry of the temperature distribution which characterizes the non-cylindrical arc. An approximate expression for the ratio of the cross-section of the column to its radius of curvature is derived analytically.