热轧钢板层流冷却过程导热反问题的非迭代法

Non-Iterative Method for IHCP of Laminar Cooling Process of Hot Rolled Steel Plate

为了解决共轭梯度法求解导热反问题过程中计算时间冗长、反演过程剧烈震荡等问题,基于有限元法建立了非迭代求解模型,并采用Fortran语言编制了相应的计算代码。将建立的数值模型应用于求解热轧钢板层流冷却过程的导热反问题,结果表明,非迭代方法能够获得较高精度的反演结果,计算时间较共轭梯度法减少了76%,且反演过程更加稳定。保留了矩阵的高度稀疏性,比已有的非迭代法更加简洁。此外,可同时反演出相应的热流密度和边界温度值,为热轧钢板层流冷却过程中热边界条件的实时输出提供了参考依据。

In order to solve the problems of time-consuming and intense vibration during the calculation process of inverse heat conducting problem （IHCP） with conjugate gradient method （CGM）, a non-iterative model was de- veloped based on finite element method （FEM） and related program code was compiled with Fortran. This non-it- erative method was then applied to IHCP of laminar cooling process of hot rolled steel plate to calculate the con- vective heat transfer coefficient in the boundary. Through comparison of the convective heat transfer coefficient ob- tained by both CGM and the non-iterative method, the results were shown to be consistent with each method. Fur- thermore, the computing result of the non-iterative method were more stable, and had an obviously faster speed, which eventually cut down the whole computing by 76%. The new method could retain high sparsity of the ma- trix, which is more concise than the exiting non-iterative method. Besides, the new non-iterative method could also be an efficient way to calculate the heat flux and wall temperature at the same time, which made it possible for re- al-time output of boundary conditions during laminar cooling process of hot rolled steel plate.