This paper presents a numerical exploration on the unsteady three-dimensional hydromagnetic flow of Carreau nanofluid over a slendering stretchable sheet in the presence of thermal radiation and chemical reaction. Furthermore, the effects of velocity slip, thermal slip, solutal slip, Soret and Dufour are taken into account. The prevailing time-dependent partial differential equations are metamorphosed into a system of coupled nonlinear ordinary differential equations by using the appropriate similarity transformations. The resultant nonlinear coupled differential equations are solved numerically by using the Runge–Kutta fourth-order method along with shooting scheme. The sway of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient has been premeditated, and numerical results are presented graphically and in tabular form. Comparison amid the previously published results, and the current numerical results are made for the limiting cases, which are found to be in a virtuous agreement. © 2019 Authors.