中文摘要：

基于顺序函数法（sequential function specification method, SFSM），通过求解二维非稳态导热反问题，建立了预测加热炉内钢坯表面热流分布的热模型。采用有限容积法获得整个加热过程的钢坯温度分布。利用仿真试验验证了本文所提出的热模型，并讨论了测量误差对反演结果的影响。结果表明，本文方法可以准确预测钢坯上表面和侧面随时间变化的热流分布。当温度测量误差较大时，可通过应用残差原理确定SFSM中未来时间步的最优值Topt，以抑制反问题的不适定性，改善反演效果。

英文摘要：

A thermal model for estimating the heat flux of a steel slab in the heating furnace is proposed in this paper by solving a 2-D transient inverse heat conduction problem based on the sequential function specification method （SFSM）. Finite Volume Method is applied to obtain the temperature distribution of the heated steel slab. Numerical simulations are carried out to validate the proposed thermal model and evaluate the effect of measurement errors on inversion results. The results demonstrate the capability of the proposed method to precisely estimate the time-dependent heat flux distribution on the upper and side surfaces of the slab. When the temperature measurement errors are large, it is required to determine the optimal time step ropt in the algorithm of SFSM by using residual principle, thus to restrain the ill-posed nature of inverse problem and further improve the inversion results.