Magnetohydrodynamic natural convection of second-grade hybrid nanofluid on variable heat flux surface

The natural convection flow of a second-grade hybrid nanofluid along vertical plate is investigated. effects variable heat flux and magnetic field are considered. governing equations for the momentum energy transport reduced to dimensionless equations. finite difference method used solve obtained by stream-function formulation. A comparison between present results relevant published gives good agreement. For higher volume fraction copper magnetite nanoparticles, index parameter flux, Deborah number, coefficient skin friction decreases; however, transfer increases. converse observed increasing Eckert number. velocity temperature increase larger number decrease parameter. Moreover, parameter, augment thicknesses thermal boundary layers.