Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

The magnetohydrodynamic (MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al₂O₃ nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter. Meanwhile, the assisting flow and the rise of the thermal radiation reduce these quantities. Two solutions are found, and the boundary layer separation is dependent on the mixed convection parameter.