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

Abstract

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