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首页> 外文期刊>International Journal of Heat and Mass Transfer >Lie group analysis of flow and heat transfer over a stretching rotating disk
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Lie group analysis of flow and heat transfer over a stretching rotating disk

机译：拉伸旋转圆盘上的流动和传热的李群分析

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The present paper discusses steady three dimensional flow and heat transfer of viscous fluid on a rotating disk stretching in radial direction. Using Lie group theory symmetries of the governing equations are calculated. Imposing restrictions from the boundary conditions it is shown that the similarity in the problem can be achieved for two types of radially stretching velocities namely; linear and power-law. Linear stretching has already been discussed in the literature; however power-law stretching is discussed here for the first time. Using new similarity transformations, the governing partial differential are transformed into a system of ordinary differential equations which are later treated both analytically and numerically. Exact analytical solutions are found for the case of pure stretching and the large stretching parameter case, for power-law stretching index n ＝ 3. Numerical solutions are obtained for combined effects of stretching and rotation for all values of n using Keller box method. Comparison of numerical solution with the corresponding analytical solution (for n = 3) shows an excellent agreement. The quantities of physical interest, such as azimuthal and radial skin friction and also Nusselt number are presented and discussed physically.
机译：本文讨论了粘性流体在径向拉伸的旋转圆盘上的稳定三维流动和热传递。使用李群理论，计算了控制方程的对称性。从边界条件施加限制表明，对于两种类型的径向拉伸速度，可以实现该问题的相似性。线性和幂律。线性拉伸已经在文献中讨论过了。但是，这里首次讨论了幂律拉伸。使用新的相似性变换，将控制的偏微分转换为一个常微分方程组，然后对其进行解析和数值处理。对于纯拉伸情况和大拉伸参数情况，对于幂律拉伸指数n ＝ 3，找到了精确的解析解。使用凯勒盒方法，对于所有n值，都获得了拉伸和旋转联合效应的数值解。数值解与相应的解析解（对于n = 3）的比较显示出极好的一致性。物理上感兴趣的量（例如方位角和径向皮肤摩擦以及Nusselt数）将在物理上显示和讨论。

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