In this work, a mathematical model of the fractional-order in non-Newtonian Powell–Eyring fluid flow (PEFF) and heat transfer is presented and solved numerically. The set of nonlinear differential equations in terms of velocity, temperature which describes our proposed problem is tackled through the spectral collocation method based on Chebyshev polynomials of the third kind. This method reduces the presented model to a nonlinear system of algebraic equations. This system is constructed as a constrained optimization problem and optimized to get the unknown coefficients of the series solution. The effects of the thermal radiation, Powell–Eyring parameters; suction parameter and Prandtl number on the PEFF are discussed. The numerical values of the dimensionless velocity and temperature are depicted graphically. The results show that the given procedure is an easy and efficient tool to investigate the solution of such models. Some of findings of this important work help to govern the velocity and the rate of heat transportation through the boundary layer. At the same time, this study highlights many applications in fields of engineering and industry, where the quality of the desired product depends on the rate of heat transfer, thermal radiation phenomenon, and the composition of the material used, and manufacturing processes.

中文翻译：

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热辐射存在下用分数导数研究 Powell-Eyring 流体流动的切比雪夫配置优化方法

在这项工作中，提出了非牛顿 Powell-Eyring 流体流动 (PEFF) 和传热的分数阶数学模型，并对其进行了数值求解。描述我们提出的问题的关于速度、温度的非线性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的非线性系统。该系统被构造为一个有约束的优化问题，并进行优化以获得级数解的未知系数。热辐射的影响，Powell-Eyring 参数；讨论了PEFF上的吸力参数和普朗特数。无量纲速度和温度的数值以图形方式描述。结果表明，给定的程序是研究此类模型的解决方案的一种简单有效的工具。这项重要工作的一些发现有助于控制通过边界层的热传输速度和速率。同时，这项研究强调了工程和工业领域的许多应用，其中所需产品的质量取决于传热速率、热辐射现象、所用材料的成分和制造工艺。