Mathematical model of slab heating in a furnace with walking beams

Abstract

Slab heating before hot rolling is necessary for obtaining required metal ductility. The most effective for this purpose are furnaces with walking beams that provide heat supply to all sides of the slab. However, the areas of slabs lower surfaces, contacting with water-cooled beams, are shielded from the radiation of the furnace lower heating zones and take the heat from the beams.To study the inhomogeneity of the slab temperature field and its dependence on the peculiarities of their transport system design, a mathematical model of slab heating in a furnace with walking beams was developed and programmatically implemented, based on numerical solution of a three-dimensional heat conduction problem with piecewise defined boundary conditions on the lower surface. For the open areas of the slab bottom surface, the same boundary conditions were set as on the top surface; and for the areas of contact with the beams, modified boundary conditions were set, taking into account the duration of this contact. For the numerical solution of the system of difference equations, the line-by-line method was applied, which allows us to obtain a system with a three-diagonal matrix of coefficients. The calculations carried out in the approximation of adiabaticity of the contact areas of the slab with the beams during the contact period allowed us to obtain temperature fields for different slab sections. As a result, a significant irregularity of temperature field of the slab lower surface was revealed, affecting the irregularity of temperature field of the entire slab. The developed program for calculating and visualizing the results can be used to study the temperature field of the slab under various heating modes if there is experimental information that allows one to clarify the tuning parameters of the model.