Abstract The fractional partial differential equations governing a mixed convective flow within an inclined wavy enclosure filled by a porous medium using hybrid nanofluids are presented. The forced flow is due to an inlet part in the bottom wavy wall as well as a vent is located at the top wavy surface. The Caputo definition is used to evaluate the time fractional derivatives and the Darcy model is applied for the porous medium. Cases of the mixed aiding and the mixed opposing flows are analyzed. The analysis is starting by mapping the complex geometry to a rectangular domain and the finite difference method is used to solve the transformed system. The present investigation is carried out for various values of order of the fractional derivatives (0.8 ≤ α ≤ 0.95), the amplitude of the wavy wall (0.85 ≤ A ≤ 0.95), the inclination angle 0 ≤ Φ ≤ π 2 , the Peclet number (1 ≤ Pe ≤ 20) and the Rayleigh number (10 ≤ Ra ≤ 103). The outcomes revealed that an increase in order of the fractional derivatives causes a reduction in the local and average Nusselt numbers. Also, the mixed convection as well as the Nusselt numbers are augmented as the amplitude of the wavy wall is grown.

中文翻译：

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使用 Al2O3-Cu 混合纳米流体填充多孔介质的倾斜波浪形通风腔中的 Caputo 分数对流流动

摘要 提出了用混合纳米流体填充多孔介质的倾斜波状外壳内控制混合对流的分数偏微分方程。强制流动是由于底部波浪形壁的入口部分以及位于顶部波浪形表面的排气口。Caputo 定义用于计算时间分数阶导数，Darcy 模型用于多孔介质。分析了混合助推和混合反向流动的情况。分析首先将复杂几何图形映射到矩形域，并使用有限差分方法来求解变换后的系统。本研究针对分数阶导数 (0.8 ≤ α ≤ 0.95)、波浪壁的振幅 (0.85 ≤ A ≤ 0.95)、倾角 0 ≤ Φ ≤ π 2 、派克莱特数 (1 ≤ Pe ≤ 20) 和瑞利数 (10 ≤ Ra ≤ 103)。结果表明，分数阶导数的增加会导致局部和平均 Nusselt 数的减少。此外，混合对流以及 Nusselt 数随着波浪壁振幅的增加而增加。