一类带Stenfen-Boltzmann 边界条件的热输运反问题的单调算法

在钢体铸造过程中, 当钢铁在钢包中被加热并且融化后, 如何探测接近高温铁水的钢包内壁是否出现了腐蚀现象是一个重要的问题. 我们尝试通过钢包外表面的温度知道内部腐蚀的情况. 本文得到了表面温度关于内部腐蚀区域的“拟单调” 性质, 并由此提出解决边界反演问题的数值算法. 数值例子表明本文算法是有效的.

The monotone reconstruction algorithms for one kind of heat transfer problem with Stenfen-Boltzmann conditions

In the procedure of the steel-making,the steel is heated and melted in one container.It is very important to detect whether the corrosion appears inside the inner-surface of the container near the steel fluid before the container is broken.We try to use the thermal image of the out-surface of the container surrounded by air to reconstruct the erosion area.In this paper,the ＂quasi-monotone＂ properties of the temperature which is dependent on the inner corrosion domain are obtained.And the numerical algorithms based on the properties are proposed to reconstruct the corrosive inner-boundary.The numerical results show that the reconstruction algorithms are effective.