This paper is centered on a numerical solution of non-Newtonian Casson magneto-nanofluid flow underlying an axisymmetric surface through a non-Darcian porous medium with heat generation/absorption. Using similarity transformations, the system of PDEs with the corresponding boundary conditions are reduced to system of nonlinear ODEs. The Chebyshev pseudospectral (CPS) method is used to get a numerical solution for the formulated differential system. Comparisons of the present numerical results with previously published results are made, and fine agreements for some the considered values of parameters were noted. Two cases of nanofluid are considered. The first case is Newtonian nanofluid, water with suspended gold (Au) or alumina (Al2O3) nanoparticles, and representative results are obtained for β → ∞ and Pr = 6.785 (the Prandtl number of water). The second case is non-Newtonian bio-nanofluid, blood with suspended gold (Au) or alumina (Al2O3) nanoparticles, and representative results are obtained for β = 0.1 and Pr = 25 (the Prandtl number of blood). The variation of different physical parameters on non-dimensional velocity and temperature fields as well as the skin friction coefficient and the Nusselt number are discussed. It is demonstrated that the implication of a nanoparticle into bio-fluid can modify the stream design. Also, the nanoparticles with high thermal conductivity (gold) have better enhancement on heat transfer compared to alumina, i.e., the effectiveness of adding gold to the water and blood is higher than adding alumina. One of the most important applications of nanotechnology in the field of medicine is the use of nanoparticles (gold molecules) in chemotherapy to get rid of cancer cells.

中文翻译：

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含有金和氧化铝纳米颗粒的非牛顿磁流体通过非达西多孔介质流动

本文的中心是非牛顿卡森磁纳米流体流动的数值解，该流体在轴对称表面下方通过具有发热/吸收的非达西多孔介质。使用相似变换，具有相应边界条件的偏微分方程系统被简化为非线性常微分方程系统。Chebyshev 伪谱 (CPS) 方法用于获得公式化微分系统的数值解。将目前的数值结果与先前公布的结果进行比较，并注意到一些考虑的参数值的良好一致性。考虑了纳米流体的两种情况。第一种情况是牛顿纳米流体，含有悬浮金 (Au) 或氧化铝 (Al2O3) 纳米粒子的水，β → ∞ 和 Pr = 6.785（水的普朗特数）获得了代表性结果。第二种情况是非牛顿生物纳米流体，血液中含有悬浮的金 (Au) 或氧化铝 (Al2O3) 纳米颗粒，β = 0.1 和 Pr = 25（血液的普朗特数）获得了代表性结果。讨论了不同物理参数在无量纲速度场和温度场以及表面摩擦系数和努塞尔数上的变化。结果表明，纳米颗粒对生物流体的影响可以改变流设计。另外，高导热性的纳米颗粒（金）与氧化铝相比具有更好的传热增强作用，即在水和血液中加入金的效果比加入氧化铝要高。