The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in engineering, industrial and technological processes. In this report, the outcome of a comparative analysis between the dynamics of blood carrying Cu nanoparticles and blood carrying single-walled carbon nanotubes (SWCNTs) due to the stretching and rotation of two disks at various levels of rotation, stretching, power-law index and heat source/sink is presented. By using appropriate similarity variables, the leading partial differential equations (PDEs)are altered into one-dimensional equations (ODEs). The resulting ODEs are handled using the shooting method. The impact of governing parameters on the boundary layer profiles is analysed graphically. Fluid velocity gets enhanced in three dimensions during the rotation of the disk, but they predict different behaviours for the stretching parameters of the upper and lower disks. The temperature decays for power-law index, rotation and stretching parameters. Also,the rates of heat transfer are more extensive for shear-thinning. Finally, the effects of the Cu–blood(blood) nanofluid are dominant over the base fluid (blood) and SWCNTs–blood nanofluid.