The influence of thermal radiation, multiple slip boundary conditions, and binary chemical reaction on the three‐dimensional circulation of unsteady magnetohydrodynamic (MHD) natural convection Carreau hybrid nanofluid () across a stretching sheet comprised of heat source/sink (H‐SS) and variable thermal conductivity are investigated. Runge‐Kutta‐Fehlberg 4th‐5th order (RKF‐45), in conjunction with the shooting approach, is utilized for numerical computation. Computed solutions indicate that the volume fraction of silicon dioxide and velocity slip parameters tends to retard the velocity profile. It is inferred from the graphs that temperature profile upsurges with enhancing the magnitude of thermal Grashof number, H‐SS parameter, mass Grashof number, variable conductivity parameter, and radiative parameter, whereas converse effects for thermal slip parameter. The chemical reaction parameter and solutal slip constraint tend to decrease the concentration profile. Furthermore, the heat transfer phenomenon uplifts with the consideration of radiative effects, while the mass transfer rate diminishes with enhancing the magnitude of magnetic parameters and activation energy.