On Adaptation of Third Kind Boundary Conditions for Grid Models of Nonstationary Heat Exchange

Abstract

The non-stationary heat exchange (heating) process is a typical kind of technological operation in metallurgy. The most common technological units for such operation are continuous heating furnaces, in which steel billets are heated in the course of their movement through the furnace. The billets have different inner chemical structures and physical characteristics, so different values of heating parameters are needed (heating time, setpoint temperature, etc.). Usually, to find such optimal values, a model of transient heat conduction is used. The general problem of such models is the necessity to adapt them to the thermophysical parameters of each certain steel grade being heated inside the furnace. Usually adaptation processes is to find the dependence between the final billet temperature and the steel density, thermal capacity, and thermal conductivity. But, in addition to these independent variables, considering the non-stationarity of the heating processes, not only should the inner structure of the billets be taken into account, but also the heating environment parameters too. Adaptation to them is the scope of this research and closely related to the third kind boundary condition of nonstationary heat exchange. Generally, it means to find the value of the heat transfer coefficient, which is also non-stationary and depends on the temperatures of the heated material and heating medium. The result of the study is an approach based on the Nusselt number and the criterion equation, which allows to reduce the average error of the billets temperature prediction by 9.7 degrees Celsius.