In this work, a mathematical model of fractional-order in fluid will be analyzed numerically to describe and study the influence of thermal radiation on the magnetohydrodynamic flow of nanofluid thin film which moves due to the unsteady stretching surface with viscous dissipation. The set of nonlinear fractional differential equations in the form of velocity, temperature and concentration which describe our proposed problem are tackled through the spectral collocation method based on Chebyshev polynomials of the third-kind. This method reduces the presented model to a system of algebraic equations. The effect of the influence parameters which governs the process of flow and mass heat transfer is discussed. The numerical values of the dimensionless velocity, temperature and concentration are depicted graphically. Also, computations of the values of skin-friction, Nusselt number and Sherwood number have been carried out and presented in the same figures. Finally, our numerical analysis shows that both the magnetic and the unsteadiness parameters can enhance the free surface temperature and nanoparticle volume fraction.

中文翻译：

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使用光谱搭配切比雪夫近似的纳米流体薄膜流过具有分数导数的非定常拉伸片的数值研究

在这项工作中，将数值分析流体中分数阶的数学模型，以描述和研究热辐射对纳米流体薄膜的磁流体动力学流动的影响，该纳米流体薄膜由于具有粘性耗散的非定常拉伸表面而移动。描述我们提出的问题的速度、温度和浓度形式的非线性分数微分方程组是通过基于第三类切比雪夫多项式的谱配置方法来解决的。该方法将所提出的模型简化为代数方程组。讨论了控制流动和传热过程的影响参数的影响。以图形方式描绘了无量纲速度、温度和浓度的数值。还，对皮肤摩擦、努塞尔数和舍伍德数的值进行了计算，并在相同的图中显示。最后，我们的数值分析表明，磁性和非稳态参数都可以提高自由表面温度和纳米颗粒体积分数。