A steady MHD boundary layer flow of Powell–Eyring dusty nanofluid over a stretching surface with heat flux condition is studied numerically. It is assumed that the fluid is incompressible and the impacts of thermophoresis and Brownian motion are taken into regard. In addition, the Powell–Eyring terms are considered in the momentum boundary layer and thermal boundary layer. The dust particles are seen as to be having the same size and conform to the nanoparticles in a spherical shape. We obtain a system of ordinary differential equations that are suitable for analyzed numerically using the fourth-order Runge–Kutta method via software algebraic MATLAB by applying appropriate transformations to the system of the governing partial differential equations in our problem. There is perfect compatibility between the bygone and current results when comparing our numerical solutions with the available data for values of the selected parameters. This confirms the validity of the method used here and thus the validity of the results. The influence of some parameters on the boundary layer profiles (the velocity and temperature for the particle phase and fluid phase, and nanoparticle concentration) is discussed. The results of this study display that the profiles of the velocity for particle and fluid phases increase with increasing Powell–Eyring fluid parameter, but reduce with height in magnetic field values. Mass concentration of the dust particles decreases the temperature of both the particle and fluid phases. The results also indicate the concentration of nanoparticle contraction as Schmidt number increases.

中文翻译：

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MHD鲍威尔–带有热通量边界条件的拉伸表面导致的尘土飞扬的纳米流体流动

数值研究了带有热通量条件的拉伸表面上Powell-Eyring尘土纳米流体的稳定MHD边界层流动。假定流体是不可压缩的，并考虑了热泳和布朗运动的影响。另外，在动量边界层和热边界层中考虑了鲍威尔-艾林项。灰尘颗粒被认为具有相同的尺寸并且符合球形的纳米颗粒。通过对我们问题中控制偏微分方程组的系统进行适当的转换，我们获得了适合于使用四阶Runge–Kutta方法通过软件代数MATLAB进行数值分析的常微分方程组。将我们的数值解与所选参数值的可用数据进行比较时，过去的结果和当前的结果之间具有完美的兼容性。这证实了此处使用的方法的有效性，从而证实了结果的有效性。讨论了一些参数对边界层轮廓的影响（粒子相和液相的速度和温度，以及纳米粒子的浓度）。这项研究的结果表明，粒子和流体相的速度分布随Powell-Eyring流体参数的增加而增加，但随磁场值的高度而减小。灰尘颗粒的质量浓度降低了颗粒相和流体相的温度。结果还表明，随着施密特数的增加，纳米颗粒的收缩浓度增加。