The contemporary study demonstrates the combined convective nanofluid flow with variable permeability and nanoparticle shape effects over a non-Darcy porous medium. The nanoparticles in the present investigation include Co, and Fe₃O₄ with water as the base fluid, and the nanoparticle shapes are disc and sphere. The resultant governing equations are then numerically solved using a shooting technique. The current findings and those described in the literature have symmetrical outcomes. In the presence of variable permeability, the impacts on velocity, temperature, heat transfer, and the nanoparticle volume fraction for Darcy and non-Darcy flows of various shapes of nanoparticles are graphically depicted. The results reveal that for various mixed convection parameters, the temperature profile is better for Co discshaped particles than Fe₃O₄ nanoparticles in both assisting and opposing flows. The velocity drops as the nanoparticle volume fraction increases, whereas the temperature rises in the opposite direction. Temperature increases with increasing Biot number values for both nanoparticles. There is a substantial increase in heat transfer rates for the Darcy flow compared to the non-Darcy flow. In both uniform permeability and variable permeability, Fe₃O₄ sphere-shaped particles offer significantly greater heat transfer rates than Co nanoparticles. Fe₃O₄ nanoparticles have better heat transfer rates than Co nanoparticles in the presence of variable permeability, for different mixed convection parameters.

中文翻译：

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具有可变渗透率的纳米颗粒形状对非达西多孔介质的影响

当代研究证明了在非达西多孔介质上具有可变渗透率和纳米颗粒形状效应的组合对流纳米流体流动。本研究中的纳米颗粒包括 Co 和 Fe ₃ O ₄以水为基液，纳米颗粒形状为圆盘和球体。然后使用射击技术对得到的控制方程进行数值求解。目前的研究结果和文献中描述的结果是对称的。在存在可变渗透率的情况下，以图形方式描绘了各种形状纳米粒子的达西流和非达西流对速度、温度、传热和纳米粒子体积分数的影响。结果表明，对于各种混合对流参数，Co圆盘状颗粒的温度分布优于Fe ₃ O ₄纳米粒子在辅助和反向流动。速度随着纳米颗粒体积分数的增加而下降，而温度则以相反的方向上升。温度随着两种纳米粒子的 Biot 数值的增加而增加。与非达西流相比，达西流的传热率显着增加。在均匀渗透率和可变渗透率方面，Fe ₃ O ₄球形颗粒提供比Co纳米颗粒显着更高的传热速率。对于不同的混合对流参数，在可变渗透率存在下， Fe ₃ O ₄纳米颗粒比Co纳米颗粒具有更好的传热率。