Significance of quadratic thermal radiation and quadratic convection on boundary layer two-phase flow of a dusty nanoliquid past a vertical plate

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.