The main purpose of this study is to investigate the multislip effects on the magneto-hydrodynamic (MHD) mixed convection unsteady flow of micropolar nano-fluids over a stretching/shrinking sheet along with radiation in the presence of a heat source. The consequences of multislip and buoyancy conditions have been integrated. By using the suitable similarity variables are used to solve the governing non-linear partial differential equations into a system of coupled non-linear ordinary differential equations. The transformed equations are solved numerically by using Runge–Kutta fourth-order method with shooting technique. The impacts of the several parameters on the velocity, temperature, micro-rotation, and concentration profiles as well as on the skin friction coefficient, Sherwood number, and Nusselt number are discussed with the help of graphs and tables.

The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index $ϵ$, and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, $ϵ$, Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter $\Omega$, and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions.