The irreversibility examination in steady flows of water based silver and copper nanofluids between two rotating disks is presented in this paper. The Darcy–Forchheimer relation is applied to the fluid flow. The two disks are kept at constant temperatures and are rotating with angular velocities. A magnetic field along radial and tangential directions is also applied. Moreover, viscous dissipation, heat generation, and Joule heating influences are taken in the nanofluid flows. The modeled problem is treated with the homotopy analysis method (HAM) and shooting techniques. The deviations in both nanofluids due to embedded factors are shown in graphs. The HAM and shooting techniques are compared and are shown with the help of figures and tables. The leading arguments of the current study are stated in the concluding section.