Thermal rhythms in composite ladle walls

Conclusions Analytical and numerical solutions have been obtained for the propagation of thermal rhythms in a composite ladle wall. In particular an analytical model simulating switch on-off thermal conditions at the inner ladle wall with Newton Cooling at the outer ladle wall is found to be in exact agreement with the full numerical solution for the composite wall. This analytical solution is seen to possess novel mathematical features.From a practical viewpoint, to obtain minimum heat loss from the ladle of molten steel it is clear that in early operations the insulating region is most effective if it were located close to the inner wall. As the thermal rhythms approach periodicity it is seen that minimum heat loss would be achieved if the insulating region were placed close to the outer ladle wall. Moreover in the later operational stages it was shown that the minimum heat loss is actually obtained if the insulating layer was omitted altogether. Since it is also shown that the time taken to achieve a periodic thermal rhythm is always least when the insulating region is located centrally in the composite ladle wall it can be argued that the evolution of the thermal rhythm is controlled by its inclusion. Inclusion of the insulating layer yields a marked reduction in the outside wall temperature and this could have considerable bearing on the life of the ladle in an integrated steel works.Preheating the ladle walls was found to reduce the ladle heat loss by more than 50 percent during the initial cycle.Finally it is hoped that the above theoretical results will be of considerable value in the understanding of thermal stratification in ladles of molten steel during standing and pouring.