Simulation of the liquid pool for VT3-1 titanium alloy during vacuum arc   remelting process
  This article describes a simple heat model of the vacuum arc remelting (VAR) process that includes solution of the nonlinear heat conductivity equation with the nonlinear boundary conditions which are typical for VAR process. The finite-difference analogue of the model equations was obtained through the finite volume method. To check the efficiency of the simplified model that does not include magnetohydrodynamic phenomena in the liquid metal pool, the comparison has been made of the numerical calculation of the metal pool depth when melting the Russian titanium alloy VT3-1 with the results of radiographical tests. It was established that the model adequately describes the test data for various melting modes (ingot diameter and current strength). 
E.N. Kondrashov, M.I. Musatov, A.Yu. Maksimov, A.E. Goncharov, and   L.V. Konovalov