The local thermal non-equilibrium model (LTNEM) in case of a sinusoidal heating is applied to investigate the unsteady nanofluid flow and thermal fields inside an inclined enclosure filled with a thermally and hydrodynamically anisotropic porous medium. The Galerkin finite element method (GFEM) together with the Characteristic-based Split (CBS) Scheme is used to solve the dimensionless governing equations. Impacts of the controlling parameters are studied in two cases, namely, non-Darcy Regime in which values of the Darcy number and the Rayleigh number are, respectively, $Da={10}^{-2},Ra={10}^5$ and the Darcy regime where $Da={10}^{-6},Ra={10}^9$. Parametric studies are performed for wide ranges of the permeability ratio $0.1\le K^{\ast }\le 10$, the Nield number $0\le H\le 1000$, the inclination angle $0\le \gamma \le \frac{\pi }{2}$, the nanoparticles volume fraction $0\le \varphi \le 4\%$, the inclination of the principal axes $0\le \vartheta \le \frac{\pi }{2}$, the amplitude ratio $0\le a\le 1$ and the phase deviation $0\le \mathrm{\Phi }\le \frac{\pi }{2}$. The main outcomes revealed that the sinusoidal heating results in multicellular flow components inside the geometry. Also, the increase in the Nield number causes that the system converts from the LTNE state to local thermal equilibrium (LTE) state. For the non-Darcy regime, the convective process and the rate of the heat transfer are augmented as the inclination of the principal axes is increased.

中文翻译：

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纳米流体在充满流体动力学和热各向异性多孔介质的外壳内流动的有限元处理：正弦加热的影响

应用正弦加热情况下的局部热非平衡模型 (LTNEM) 来研究充满热和流体动力学各向异性多孔介质的倾斜外壳内的不稳定纳米流体流动和热场。Galerkin 有限元方法 (GFEM) 与基于特征的拆分 (CBS) 方案一起用于求解无量纲控制方程。在两种情况下研究控制参数的影响，即非达西制度，其中达西数和瑞利数的值分别为，$D\mathrm{一种}={10}^{-2},\mathrm{电阻}\mathrm{一种}={10}^5$ 和达西政权 $D\mathrm{一种}={10}^{-6},\mathrm{电阻}\mathrm{一种}={10}^9$. 对大范围的渗透率进行参数研究$0.1\le {钾}^{＊}\le 10$，尼尔数 $0\le H\le 1000$，倾角 $0\le \gamma \le \frac{\pi }{2}$, 纳米颗粒体积分数 $0\le \phi \le 4\%$, 主轴的倾角 $0\le ⑨\le \frac{\pi }{2}$，振幅比 $0\le \mathrm{一种}\le 1$ 和相位偏差 $0\le \mathrm{\Phi }\le \frac{\pi }{2}$. 主要结果表明，正弦加热导致几何内部的多细胞流动分量。此外，Nield 数的增加导致系统从 LTNE 状态转换为局部热平衡 (LTE) 状态。对于非达西状态，对流过程和传热速率随着主轴倾角的增加而增加。