一维非稳态导热反问题反演管道内壁面温度波动

Inverse Problem of One-Dimensional Unsteady Heat Conduction Deducing Temperature Fluctuation of Inner Wall of Pipe

以一维圆管壁厚为研究对象,基于有限差分法的瞬态导热正问题以及基于共轭梯度法的优化算法来构建一维瞬态导热反问题数学模型。采用C语言编写通用计算程序,以正问题所得到的外壁面温度波动值作为导热反问题的已知条件,并引入随机测量误差,探讨测量误差对反演结果精度的影响。将反演值与作为边界条件的内壁面温度理论值进行对比分析。对比结果显示,内壁面反演值与理论值吻合较好,表明该瞬态导热反问题模型能够较好地反演得到内壁面温度波动值。

A one-dimensional transient thermal conduction inverse problem mathematical model is constructed based on the finite difference method （FDM） and the optimization algorithm based on the conjugate gradient method （CGM）. The general calculation program is written in C language, and the temperature fluctuation value of the outer wall surface obtained by the direct heat conduction problem is used as the known condition of the inverse heat conduction problem. And the random measurement error is introduced to investigate the effect of measurement error on the accuracy of the inversion result. The inversion value is compared with the theoretical value of the inner wall surface as the boundary condition. The comparison results show that the inversion value of the internal wall surface is in good agreement with the theoretical value, indicating that the transient thermal conductivity anti-problem model can well inverse the temperature fluctuation value of the inner wall surface.