ABSTRACT

In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving inverse heat transfer problem of axisymmetric stagnation flow impinging on a cylinder with uniform transpiration and to estimate the time-dependent heat flux using temperature distribution at a point. $\overline{k}$ The effect of noisy data on the final result is studied. The maximum value of the sensitivity coefficient is related to estimation of exponential heat flux and its value is 0.1718 also the minimum value of the sensitivity coefficient is 7.50 × 10⁻⁶ which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.458 and 0.492, respectively the reason for the increase in error in estimating these functions is the existence of points where the first derivative of the function does not exist. This method also exhibits considerable stability for noisy input data. In most cases, surface blowing decreases the prediction accuracy by removing the boundary layers from the surface whereas suction acts vice versa.

摘要

本文首次提出了一种基于 Levenberg-Marquardt 方法的数值代码，用于求解轴对称滞流撞击具有均匀蒸腾作用的圆柱体的逆传热问题，并利用温度分布估计随时间变化的热通量。观点。 $\overline{克}$研究了噪声数据对最终结果的影响。灵敏度系数的最大值与指数热通量的估计有关，其值为 0.1718，灵敏度系数的最小值为 7.50 × 10 ^-6这与三角形热通量有关。结果表明，计算三角和梯形热通量的参数估计误差大于指数和正余弦热通量，这是因为这两种情况下得到的均方根误差最大值分别为0.458和0.492。因为估计这些函数时误差的增加是存在函数的一阶导数不存在的点。这种方法对于有噪声的输入数据也表现出相当大的稳定性。在大多数情况下，表面吹气通过从表面去除边界层而降低了预测精度，而吸力则相反。