Calculated estimation of influence of convection rate of molten working and heating medium during hardening of restored parts

Abstract

The paper presents a computational and mathematical assessment of the convection rate of the molten working and heating medium during the strengthening of the restored parts. The calculated estimate is based on the theory of multidimensional heat and mass transfer processes occurring in the electrode furnace during the strengthening of the restored parts. Computational modeling is carried out based on the choice of initial data and characteristics. The calculation results made it possible to establish the effect of the convection rate of the molten working and heating medium on the hardening of the restored parts. The theoretical description of the conditions for the onset of convective motion of a molten continuous medium is based on the Rayleigh–Bénard, Navier–Stokes, and Lorenz equations for the flow of a viscous continuous medium using the Oberbeck-Boussinesq approximation. The description of the internal space of the tank furnace is carried out by a system of differential equations of the balances of elementary volumes into which it is divided. Transformations into a system of differential equations are carried out on the basis of the Galerkin method. The use of this transition method leads to the fact that the sought functions are represented in a variable-separated form that exactly satisfies the boundary conditions. The introduction of assumptions and boundary conditions made it possible to obtain the equations of motion of mass forces and a viscous medium in a polar coordinate system. A formula describing the configuration of the temperature field is obtained.