Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface

•Magnetohydrodynamic flow of Carreau nanofluid is modeled.•Flow is induced by a porous nonlinear stretching surface.•Brownian motion and thermophoresis effects are considered.•Numerical solutions are obtained by Runge-Kutta-Fehlberg method. The impact of magnetic field and nanoparticles on the two-phase flow of a generalized non-Newtonian Carreau fluid over permeable non-linearly stretching surface has been analyzed in the existence of all suction/injection and thermal radiation. The governing PDEs with congruous boundary condition are transformed into a system of non-linear ODEs with appropriate boundary conditions by using similarity transformation. It solved numerically by using 4th–5th order Runge-Kutta-Fehlberg method based on shooting technique. The impacts of non-dimensional controlling parameters on velocity, temperature, and nanoparticles volume concentration profiles are scrutinized with aid of graphs. The Nusselt and the Sherwood numbers are studied at the different situations of the governing parameters. The numerical computations are in excellent consent with previously reported studies. It is found that the heat transfer rate is reduced with an increment of thermal radiation parameter and on contrary of the rising of magnetic field. The opposite trend happens in the mass transfer rate.