Numerical Solution to Heat Conduction Problem in Shaping Castings without Friction

A process of shaping castings without friction in a crystallizer is considered in which the forced rejection of the melt from a wall is provided by the gas blown in the region where a casting is shaped. In the melted metal region of the casting being shaped the gas pressure is determined on condition that pressures in a gap and liquid metal column neighboring upon it are the same. The heat conduction problem is solved for the casting crystallization region. At each iteration, while solving the equation, the temperature distribution in metal, position of the phase transition surface and also the temperature distribution in the gap and porous wall are found by the finite element method according to the obtained velocity distribution in the gap. The solution results allow the continuous casting to be provided taking into account all factors determining the forming of the near-wall gas layer and heat conduction.