The current work is concerned with the two-dimensional boundary layer flow of a non-Newtonian fluid in the presence of nanoparticles. The heat and mass transfer mechanism for Carreau nanofluid flow due to a radially stretching/shrinking sheet is further investigated in this article. The governing physical situation is modelled in the form of partial differential equations and are simplified to a system of non-linear ordinary differential equations by employing dimensionless variables. Numerical simulations for non-dimensional velocity, temperature and concentration fields has been performed with the assistance of built-in Matlab solver bvp4c routine. One significant computational outcome of this study is the existence of multiple numerical solutions for the flow fields. The impacts of various developing parameters, for instance, Weissenberg number, power-law index, shrinking parameter, suction parameter, Prandtl number, Schmidt number, Brownian motion and thermophoresis parameter on the velocity, temperature and nanoparticles concentration are visualized through tables and graphical experiment. The numerical results demonstrate that the rates of heat and mass transfer are raised by higher Weissenberg number for first solution and an inverse is seen for second solution. Moreover, an increasing trend is seen in nanofluids temperature for both solutions with greater values of thermophoresis parameter. In addition, the numerical results obtained by the applied technique are validated with existing literature and found to be in an excellent agreement.