In the present analysis, an unsteady MHD mixed convection flow is scrutinized for a non-Newtonian Casson hybrid nanofluid in the stagnation zone of a rotating sphere, resulting from the impulsive motion of the angular velocity of the sphere and the velocity of the free stream. A set of linearized equations is derived from the governing ones, and these differential equations are solved numerically using the hybrid linearization–differential quadrature method. The surface shear stresses in the $x$- and $y$-directions and the surface heat transfer rate are improved due to the Casson ${\beta }_o$, mixed convection $\alpha$, rotation $\gamma$ and magnetic field $M$ parameters. In addition, as nanoparticles, the solid volume fraction (parameter $\varphi$) increases, and the surface shear stresses and the rate of heat transfer are raised. A comparison between earlier published data and the present numerical computations is presented for the limiting cases, which are noted to be in very good agreement.

In this study, we investigate the convective flow of a micropolar hybrid nanofluid through a vertical radiating permeable plate in a saturated porous medium. The impact of the presence or absence of the internal heat generation (IHG) in the medium is examined as well as the impacts of the magnetic field and thermal radiation. We apply similarity transformations to the non-dimensionalized equations and render them as a system of non-linear ODEs (Ordinary Differential Equations) subject to appropriate boundary conditions. This system of non-linear ODEs is solved by an adaptive mesh transformation Chebyshev differential quadrature method. The influence of the governing parameters on the temperature, microrotation and velocity is examined. The skin friction coefficient and the Nusselt number are tabulated. We determine that the skin friction coefficient and heat transport rate increase with the increment in the magnetic field. Moreover, the increment in the micropolarity and nanoparticle volume fraction enhances the skin friction coefficient and the Nusselt number. We also conclude that the IHG term improved the flow of the hybrid nanofluid. Finally, our results indicate that employing a hybrid nanofluid increases the heat transfer compared with that in pure water and a nanofluid.