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The purpose of this paper is the study of the electro-vortex flow (EVF) as well as heating and melting processes for mini industrial direct current electric arc furnace (DC EAF).

A mini DC EAF was designed, manufactured and installed to study the industrial processes of heating and melting a small amount of melt, being 4.6 kg of steel in the case under study. Numerical modelling of metal melting was performed using the enthalpy and porosity approach at equal values and non-equal values of the solidus and liquidus temperatures of the metal. The EVF of the liquid phase of metal was computed using the large eddy simulation model of turbulence. Melt temperature measurements were made using an infrared camera and a probe with a thermocouple sensor. The melt speed was estimated by observing the movement of particles at the top surface of melt.

The thermal flux for metal heating and melting, which is supplied through an arc spot at the top surface of metal, is estimated using the thermal balance of the furnace at melting point. The melting time was estimated using numerical modelling of heating and melting of metal. The process started at room temperature and finished once whole volume of metal was molten. The evolution of the solid/melt phase boundary as well as evolution of EVF patterns of the melt was studied.

Numerical studies of heating and melting processes in metal were performed in the case of intensive liquid phase turbulent circulation due to the Lorentz force in the melt, which results from the interaction of electrical current with a self-magnetic field.

The purpose of this paper is to the study the multiphase bubbles flow motion in a vertical channel with an electroconducting liquid without and under the influence of a magnetic field.

For numerical calculations, the lattice Boltzmann method (LBM) is used, which is based on the kinetic theory for solving fluid mechanics and other physical problems. The phase-field lattice Boltzmann model is developed to simulate the behaviour of multiphase bubble–bubble interaction while rising in the fluid with high density ratios.

The behaviour of the rising bubble flow in a rectangular column of two phases is investigated with the two-dimensional LBM.

The multiphase flow in electroconducting liquids with high ratio of density is studied using the LBM.