Boundary layer analysis of an incessant moving needle in MHD radiative nanofluid with joule heating

The steady, two dimensional MHD Newtonian nanofluid flow under the stagnation region of tinny needle is considered. Figure shows the cylindrical coordinate (x, r)such that the x-axis is axial direction and ris normal to the x-axis and termed as radial direction and c is the magnitude of the needle. We examined the flow with the assistance of thermal stratification. We assume that the temperature of the cylindrical surface is much greater than the ambient fluid. Also, U0 = uw + u∞ be composite velocity along x-axis, where uwis the velocity of a needle and u∞is opposite of mainstream velocity. 165