Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet

•Axisymmetric flow of nanofluid due to radially stretching sheet.•General power-law surface velocity distribution is considered.•Brownian motion and thermophoresis effects are addressed.•Revised model of passively controlled wall nanoparticle volume fraction is considered.•Analytic and numerical solutions are computed and found in very good agreement.

This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet.