The paper studies an unsteady MHD squeezing flow in a rotating inclined channel filled with Cu–Fe \(_3\) O \(_4\) and Cu–Fe \(_3\) O \(_4\) –Au hybrid nanofluids. The carrier liquid is an ethylene glycol–methanol mixture. The model is formulated for situations where squeezing, rotation, magnetic damping, wall slip, and convective wall heating may occur simultaneously, as in compact cooling passages, rotating thermal units, and small-scale electromagnetic flow-control devices.The governing equations for momentum, heat, and concentration are written for a laminar incompressible suspension. Brownian diffusion, thermophoretic migration, mixed convection, thermal radiation in the wall heat-transfer rate, and a chemical reaction term are retained. Similarity variables reduce the original partial differential equations to a coupled nonlinear boundary-value problem. The resulting system is solved with the MATLAB bvp4c routine after conversion to first-order form. Accuracy is checked by comparison with limiting results available in the literature, and the computed profiles are further examined through mesh-independence and convergence tests.The calculations indicate that squeezing and rotation promote the flow, while the magnetic field reduces both the axial and transverse velocities through Lorentz force resistance. Wall slip reduces the near-wall shear and alters the momentum layer near the plates. Brownian motion and thermophoresis do not act in the same way: their relative strengths determine the shapes of the thermal and concentration fields. Adding Au to the Cu–Fe \(_3\) O \(_4\) suspension gives a measurable, but small, heat-transfer gain. For the selected baseline case, the lower-wall Nusselt number changes from 0.024260 to 0.024282. Thus, the ternary mixture should be viewed as a mildly improved formulation rather than as a strongly superior coolant. The model provides a useful quantitative description of coupled MHD squeezing transport in rotating, inclined, parallel-plate systems.
