This study aims to thoroughly investigate the flow behaviour of a Reiner–Philippoff nanofluid over a nonlinearly stretching sheet, with a particular focus on the effects of viscous dissipation. The research delves into the complex interactions within the nanofluid, assessing how viscous dissipation influences heat and mass transfer rates. To model the nanofluid flow, the Darcy–Forchheimer model was employed alongside slip velocity effects. Thermal radiation was incorporated to control heat transfer, while activation energy was considered for mass transfer regulation. The Buongiorno hypothesis was used to account for thermophoresis and Brownian motion in the governing equations. Following appropriate transformations, the nonlinear ordinary differential equations were formulated and solved using the shooting method. Key parameters such as skin friction, Nusselt number, and Sherwood number were analysed in tabular form, while graphical representations highlighted the impact of variables like concentration, velocity, and temperature. The study found that considering slip velocity in combination with the Darcy–Forchheimer model significantly enhances mass transfer. A comparison with existing data demonstrated the consistency of the results. This research holds relevance for applications in acid rain, pollution migration, groundwater treatment, and related environmental processes. It has been noted that raising the porosity parameter and the Forchheimer number causes the temperature and concentration levels to drop while boosting the fluid’s velocity.

中文翻译：

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采用 Darcy-Forchheimer 模型的 Reiner-Philippoff 纳米流体中耗散传热活化能引起的物理特性


本研究旨在彻底研究 Reiner-Philippoff 纳米流体在非线性拉伸片上的流动行为，特别关注粘性耗散的影响。该研究深入研究了纳米流体内复杂的相互作用，评估了粘性耗散如何影响热量和质量传递速率。为了模拟纳米流体流动，采用了 Darcy-Forchheimer 模型以及滑移速度效应。热辐射被用来控制传热，而活化能则被考虑用于传质调节。 Buongiorno 假设用于解释控制方程中的热泳和布朗运动。经过适当的变换，非线性常微分方程被建立并使用打靶法求解。以表格形式分析了皮肤摩擦、努塞尔数和舍伍德数等关键参数，而图形表示则强调了浓度、速度和温度等变量的影响。研究发现，考虑滑移速度与达西-福希海默模型的结合可以显着增强传质。与现有数据的比较证明了结果的一致性。这项研究对于酸雨、污染物迁移、地下水处理和相关环境过程的应用具有相关性。人们注意到，提高孔隙率参数和福希海默数会导致温度和浓度水平下降，同时提高流体速度。