二维圆管导热反问题内壁瞬态温度的快速识别

以二维圆管为研究对象，基于控制容积积分法的导热正问题以及基于共轭梯度法的优化算法来构建二维瞬态导热反问题数学模型，分别采用Gauss-Seidel点迭代法与托马斯算法（tridiagonal matrix algorithm，TDMA）线迭代法对导热正问题离散方程进行求解。为了探究Gauss-Seidel点迭代法与TDMA线迭代法两种模型的精确性与时效性，设定了3种内壁面温度变化规律，以正问题所得到的外壁面温度值作为导热反问题的输入条件，并引入标准正态随机测量误差，探讨测量误差对反演结果精度的影响。数值试验证明了两种方法反演的精确性和抗噪性，且对比结果表明TDMA线迭代法的求解速度要优于Gauss-Seidel点迭代法，能够较快地反演得到内壁面温度波动值。

Rapid estimation of the transient temperature of the inner wall in a two-dimensional pipe for the inverse heat conduction problem

Taking a two-dimensional circular tube as the research object, a mathematical model of the two-dimensional transient heat conduction inverse problem has been constructed based on the forward heat conduction problem of the control volume integral method and the optimization algorithm based on the conjugate gradient method. The Gauss-Seidel point iteration method and the tridiagonal matrix algorithm (TDMA) line iteration method were used to solve the discrete equation of the heat conduction problem. In order to study the accuracy and speed of the two models (the Gauss-Seidel point iteration method and the TDMA line iteration method) three kinds of internal wall temperature change laws were set. The external wall temperature value obtained from the positive problem was used as the input of the inverse heat conduction problem. Standard normal random measurement errors were introduced in order to discuss the impact of measurement errors on the accuracy of the inversion results. Numerical results confirm the accuracy and noise resistance of the two methods. The inner wall temperature fluctuation value can be rapidly inverted by means of the TDMA line iteration method which has a faster solution speed than the Gauss-Seidel point iteration method.