Finite element method for solution of the three-dimensional time-dependent heat-conduction equation with application for heating of steels in reheating furnaces

摘要

A three-dimensional mathematical model is presented that is tailor made for calculation of the nonstationary temperature field in rectangular stocks of steel heated in a reheating furnace. Discretization of the governing equation is done by means of a finite element method where the time integration is performed by an exponential transformation of the heat equation combined with an alternating-direction-implicit method. The boundary conditions are assumed time dependent. The temperature uniformity of the heated stock is of great importance for the subsequent rolling. Nonuniformity of the stock discharge temperature may cause unacceptable thickness variations during the rolling and thus influences the quality of the final product. The proposed model is validated with respect to an analytical solution, to a numerical solution, as well as to full-scale experimental data. It is concluded that the three-dimensional finite element code is capable of taking into account nonuniform heating of the stocks caused by radiation shadowing of the skid pipes, the contact between the wearer bars and the stocks, baffles in the furnace, and end effects in the stocks.