This paper investigates the non-linear convective flow due to non-coaxial rotation of vertical planar plate by utilizing three different liquids namely H2O (water), Al2O3-H2O (nanofluid) and Cu-Al2O3-H2O (hybrid nanofluid). The impacts of Rosseland's radiative heat and internal heat generation are also included in this study. The non-coaxial rotation of the plate crafts sine or cosine oscillations in its plane and the liquid at infinity. The density-temperature relation is studied which is nonlinear and causes a nonlinear convective heat transfer. The dynamic viscosity, thermal conductivity, density and specific heat of hybrid-nanofluids are assumed to vary with the volume fraction. These thermophysical properties of hybrid and nanofluids are determined by phenomenological laws and mixture theory. The simulation of the flow was carried out using the appropriate values of the empirical shape factor for five different particle shapes (i.e., sphere, hexahedron, tetrahedron, column and lamina). The LTM (Laplace Transform Technique) is employed to find the exact solutions. The flow, skin friction and thermal features are scrutinized with the discrepancy of governing parameters. The effective fluid properties and the Nusselt number are also calculated for sixteen different hybrid-nano-liquids.