Cross fluid is one of the important kinds of non-Newtonian fluid, which is most beneficial for the transport of heat and mass. The current model is to investigate the deformation in nanofluid at very high/low shear rate and has the capacity to characterize the properties of nanofluid in shear thinning/thickening region. The impacts of homogeneous-heterogeneous chemical process (HHCP) and Lorentz forces (LFs) on 3-D radiative magnetized Cross nanofluid using two stretching rotatory disks are also presented. HHCP is launched to depict the viscous dissipation, mass transport, joule heating, thermal radiation and heat transport. The nanofluid velocity is investigated in the inclined magnetic field based on the LFs. For the heat's transportation of time and space based on the non-uniform heat sink/source with convective boundary conditions is also indicated. The governed partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) and numerically treated with the reputed bvp4c and Keller–Box schemes. Moreover, it is also observed that the increment in the rotation rate of disk, the enhancement in velocities of Cross nanofluid, the greater magnetic parameter drops sharply and escalation in temperature for strong LFs.