The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge–Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.

中文翻译：

---

垂直表面上非定常自由对流边界层流的李对称群

使用李对称群变换方法研究偏微分方程，该偏微分方程模拟了自然对流非定常流经过非等温垂直平面的运动。连续两次应用一参数李群变换，将运动控制方程式转换为常微分方程组。使用Lobatto IIIA公式（隐式Runge-Kutta方法）对获得的常微分方程组进行了数值求解。图形显示了普朗特数对温度和速度分布的影响。