A novel mathematical model is envisaged to scrutinize the Darcy Forchheimer 3D Powell Eyring nanofluid flow in a porous medium. Flow is taken under the influence of zero mass flux and convective boundary conditions at the surface and a chemical reaction in the mass equation. The heat transfer flow is scrutinized with non-linear thermal radiation. Entropy generation analysis of the envisioned model is also conducted. The Homotopy Analysis method to yield the series solutions for the envisioned model. The graphs are plotted to witness the characteristics of several parameters versus velocity, heat, and mass distributions and are well cogitated accordingly. The findings show that the velocity is decreasing the function of Darcy-Forchheimer number. Further, the Biot number large values boost the fluid temperature. The outcomes obtained in the analysis are substantiated when compared with a published result in the literature. An outstanding matching is achieved in this regard.

设想了一种新颖的数学模型来检查多孔介质中Darcy Forchheimer 3D Powell Eyring纳米流体的流动。在零质量通量和表面对流边界条件以及质量方程式中的化学反应的影响下进行流动。用非线性热辐射仔细检查传热流。还对设想的模型进行了熵生成分析。产生同构模型的级数解的同伦分析法。绘制这些图以证明几个参数相对于速度，热量和质量分布的特性，并进行了充分的搅拌。研究结果表明，速度正在降低达西-福希海默数的函数。此外，比奥数大的值会提高流体温度。与文献中发表的结果相比，分析中得到的结果得到证实。在这方面实现了出色的匹配。