Nonlinear hydro-magnetic convection at a permeable cylinder in a porous medium

We consider the longitudinal steady nonlinear hydromagnetic convection flow over a permeable vertical cylinder in a porous medium. We assume that both the mainstream velocity at the outer edge of the boundary layer and the surface temperature of the cylinder vary linearly with axial distance from the leading edge, and extend the existing literature by including the nonlinear density temperature variation, magnetic field, and heat source/sink.