Lie-group similarity solution and analysis for fractional viscoelastic MHD fluid over a stretching sheet

Lie-group is introduced for studying boundary layer flow and heat transfer of fractional viscoelastic MHD fluid over a stretching sheet. Fractional boundary layer equations, based on Riemann-Liouville operators, are reduced and solved numerically by Grünwald scheme approximation. Results show that the skin friction and thermal conductivity are strongly affected by magnetic field parameter, fractional derivative and wall stretching exponent. The bigger of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. Skin friction increases with increase of magnetic field parameter M, while the heat transfer decreases. For wall stretching exponent parameter β=1.0, the velocity profile decreases with the increase of similarity variable η. However, for β=−1.5, the velocity profile increases initially and then decreases afterwards with the biggest velocity at the interior of boundary layer.