Abstract Transient natural convection of an alumina-water nanofluid saturated in non-Darcy porous media is investigated in this paper. The domain of the nanofluid is an annulus composed from a square cavity confining a solid conductive body. The nanoparticles are assumed to be slipping in the base fluid according to Buongiorno model. The Brinkman-Forchheimer-extended Darcy formulation has been adopted for the porous medium. The dimensionless governing equations are solved by implementing the finite difference method. In this study, a special focus is given on the following model parameters; porosity of the porous medium, Darcy number and the nanoparticles average volume fraction. The results show that the nanoparticles possess high uniformity in the base fluid and the Nusselt number augments with increasing values of the Darcy number. The porosity increases the average Nusselt number at a higher Darcy number while its influence remains negligible at a low Darcy number. For the given porosity, there is a critical value of the nanoparticles volume fraction when the average Nusselt number is maximal.

中文翻译：

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非均匀纳米流体模型对包含内部固体的非达西多孔腔中瞬态自然对流的影响

摘要 本文研究了在非达西多孔介质中饱和的氧化铝-水纳米流体的瞬态自然对流。纳米流体的域是由限制固体导电体的方形腔组成的环。根据 Buongiorno 模型，假设纳米颗粒在基液中滑动。多孔介质采用 Brinkman-Forchheimer-extended Darcy 公式。通过实施有限差分法求解无量纲控制方程。在本研究中，特别关注以下模型参数：多孔介质的孔隙率、达西数和纳米颗粒的平均体积分数。结果表明，纳米颗粒在基液中具有高均匀性，并且努塞尔数随着达西数的增加而增加。孔隙率在较高达西数时增加了平均努塞尔数，而在低达西数时其影响仍然可以忽略不计。对于给定的孔隙率，当平均努塞尔数最大时，纳米颗粒的体积分数存在一个临界值。