Various engineering applications commonly involve the flow of nanofluids over a porous 45° inclined square cylinder. Therefore, the current study is to assess the impact of the Darcy parameter (Da), nanoparticle volume fraction (ϕ), and Reynolds number (Re) on the momentum transport characteristics over the 45° inclined porous square cylinder. The governing equations were solved numerically using the Darcy–Brinkman–Forchheimer model for different values of Da (), nanoparticle volume fraction ϕ (), and Reynolds number Re (). The results for each parameter were visualized using streamline plots, velocity profiles within the porous cylinder, and vorticity contours. Complex flow behaviors were observed between Da = 10⁻³–10⁻², flow separation detached and disappeared at the cylinder's downstream side at critical Darcy number. Drag and pressure coefficents are used to represent the global and local parameter of the flow fields. The pressure coefficient on the surface of the cylinder showed an inverse relationship with the nanoparticles volume fraction and Darcy number. The strength of the drag coefficient decreased with the addition of nanoparticles to the base fluid, with a decreasing trend observed for Da = 10⁻⁴–10⁻² and no change observed for Da = 10⁻⁶–10⁻⁴. At last, the comparative analysis has been conducted between a porous square cylinder at 0° inclined and another 45° inclined.

中文翻译：

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使用 Darcy-Brinkman-Forchheimer 模型对 45° 倾斜多孔方形圆柱体上的纳米流体流动进行流体动力学分析

各种工程应用通常涉及纳米流体在多孔 45° 倾斜方形圆柱体上的流动。因此，本研究旨在评估达西参数（Da）、纳米颗粒体积分数（phi）和雷诺数（Re）对 45° 倾斜多孔方圆柱体动量传输特性的影响。使用 Darcy-Brinkman-Forchheimer 模型对Da ( )、纳米颗粒体积分数phi ( ) 和雷诺数Re ( ) 的不同值对控制方程进行数值求解。使用流线图、多孔圆柱体内的速度剖面和涡度等值线将每个参数的结果可视化。在Da  = 10 ^-3 –10 ^-2之间观察到复杂的流动行为，在临界达西数处，流动分离在气缸下游侧分离并消失。阻力和压力系数用于表示流场的全局和局部参数。圆柱体表面压力系数与纳米颗粒体积分数和达西数呈反比关系。阻力系数的强度随着纳米颗粒添加到基液中而降低，当Da  = 10 ^-4 –10 ^{-2时观察到下降趋势，而当}Da  = 10 ^-6 –10 ^-4时没有观察到变化。最后对0°倾斜的多孔方柱体和45°倾斜的多孔方柱体进行了对比分析。