Abstract In the present work, the influences of exponentially temperature-dependent viscosity on free convection in a porous cavity with a circular cylinder under local thermal non-equilibrium (LTNE) condition are investigated numerically via lattice Boltzmann (LB) method. To incorporate the LTNE effects, the temperature evolution equations are constructed by adding some unified source terms, which also preserve the parallel computation feature of the standard LB method. The effects of several physical parameters, including viscosity variation index (n), Rayleigh number ( R a ), Darcy number ( D a ), ratio of fluid-to-solid thermal conductivity (λ) and inter-phase heat transfer coefficient (H) on flow and heat transfer characteristics are numerically studied. The numerical results show that as the LTNE parameters increase (i.e., H and λ), the solid heat transfer rate increases dramatically, while few changes are found for the heat transfer rate of fluid. Additionally, we find that for most given parameters, both the heat transfer rate of fluid and solid are generally decreased with the increase of n, while for relatively small values of H and λ, the heat transfer coefficient of solid phase depends little on the value of n. Further, the impacts of the porosity (e) as well as the aspect ratio ( Γ ) are also considered.

中文翻译：

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局部热非平衡条件下温度相关粘度对圆柱体多孔空腔自然对流的影响

摘要 在目前的工作中，通过格子玻尔兹曼 (LB) 方法数值研究了在局部热非平衡 (LTNE) 条件下，指数温度相关粘度对圆柱多孔腔中自由对流的影响。为了结合LTNE效应，通过添加一些统一的源项来构建温度演化方程，这也保留了标准LB方法的并行计算特征。几个物理参数的影响，包括粘度变化指数（n）、瑞利数（R a ）、达西数（ D a ）、流固比热导率（λ）和相间传热系数（H ) 对流动和传热特性进行了数值研究。数值结果表明，随着 LTNE 参数（即 H 和 λ）的增加，固体传热速率显着增加，而流体传热速率几乎没有变化。此外，我们发现对于大多数给定的参数，流体和固体的传热速率一般都随着 n 的增加而降低，而对于相对较小的 H 和 λ 值，固相的传热系数几乎不依赖于该值的 此外，还考虑了孔隙率 (e) 和纵横比 (Γ) 的影响。固相传热系数与 n 值的关系不大。此外，还考虑了孔隙率 (e) 和纵横比 (Γ) 的影响。固相传热系数与 n 值的关系不大。此外，还考虑了孔隙率 (e) 和纵横比 (Γ) 的影响。