Mathematical modeling of slab heating in a furnace with walking beams due to their curvature

Abstract

Slab heating before hot rolling process 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 places 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. Previously, the authors developed and programmatically implemented a mathematical model of slab heating in a furnace with walking beams, based on the numerical solution by finite difference method of the three-dimensional heat conduction problem with piecewise defined boundary conditions on the slab bottom surface. In this model, for the open zones of the slab bottom surface, boundary conditions were similar to those on the top surface, and for the zones of contact with the beams were set effective boundary conditions assuming duration of this contact. In this paper, the model was modified to take into account the curvature of the beams and to recalculate the configuration of zones with different boundary conditions on the slab bottom surface for each position of the slab along the furnace. By variant calculations at different values of heat transfer intensity from the slab bottom surfaces to the beams it was determined that curvature of a single beam can significantly change the characteristic of the corresponding “cold” spot, but it practically does not affect the general characteristic of the slab heating non-uniformity. If all fixed beams are subjected to curvature, the final drop across the slab is significantly reduced due to an increase in its minimum temperature. It was found that the influence of beam curvature on the temperature field at the end of heating process is higher the more intensive the heat transfer to the beams is.