Abstract Boundary layer two-phase flow of particulate Al2O3-H2O nanoliquid over a vertical flat plate is studied numerically subjected to the aspects of quadratic thermal convection and quadratic thermal radiation. The Khanafer-Vafai-Lightstone monophasic nanofluid model (KVL model) and Saffman's dusty fluid model are used for the equations governing the flow of dusty nanoliquids. The quadratic Boussinesq approximation is used together with the Prandtl's boundary layer approximation. The non-linear problem is treated with the finite difference method. Surface plots and streamlines are presented to visualize the results. A comparison of linear thermal radiation, quadratic thermal radiation, and nonlinear thermal radiation is performed. Among the three types of radiation, the greatest heat transfer is observed in nonlinear thermal radiation followed by quadratic thermal radiation and linear thermal radiation. Also, in the presence of quadratic convection, the heat transport, and velocity field get enhanced. It is found that the presence of Al2O3 nanoparticles of 3% volume concentration in particulate water effectively advances the heat transport of the system. However, heat transport gets reduced by increasing the mass fraction of dust particles. Furthermore, in the presence of a transverse magnetic field, the velocity of the dusty nanoliquid gets reduced.

中文翻译：

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二次热辐射和二次对流对粉尘纳米液体通过垂直板边界层两相流的意义

摘要 在二次热对流和二次热辐射作用下，数值研究了颗粒状Al2O3-H2O纳米液体在垂直平板上的边界层两相流。Khanafer-Vafai-Lightstone 单相纳米流体模型（KVL 模型）和 Saffman 的尘埃流体模型用于控制尘埃纳米液体流动的方程。二次 Boussinesq 近似与 Prandtl 边界层近似一起使用。非线性问题用有限差分法处理。呈现表面图和流线以可视化结果。进行了线性热辐射、二次热辐射和非线性热辐射的比较。在三种辐射中，在非线性热辐射中观察到最大的热传递，其次是二次热辐射和线性热辐射。此外，在二次对流的存在下，热传输和速度场得到增强。结果表明，颗粒水中 3% 体积浓度的 Al2O3 纳米颗粒的存在有效地促进了系统的热传输。然而，通过增加灰尘颗粒的质量分数会减少热传输。此外，在横向磁场的存在下，尘土飞扬的纳米液体的速度会降低。结果表明，颗粒水中 3% 体积浓度的 Al2O3 纳米颗粒的存在有效地促进了系统的热传输。然而，通过增加灰尘颗粒的质量分数会减少热传输。此外，在横向磁场的存在下，尘土飞扬的纳米液体的速度会降低。结果表明，颗粒水中 3% 体积浓度的 Al2O3 纳米颗粒的存在有效地促进了系统的热传输。然而，通过增加灰尘颗粒的质量分数会减少热传输。此外，在横向磁场的存在下，尘土飞扬的纳米液体的速度会降低。