Cube-shaped cavities explore many noteworthy applications in practice. Cans or storage tanks are the possible application of large cavities, while thermosyphons are the classic example of small cavities. Cubic cavities are used in space satellite systems, optical designing, electronic devices, transformer cores, nuclear reactors, combustion engines, heat pipes, liquid-based solar heating systems, heat exchangers, engine cooling, etc. Also, experimentally it is assured that hydrothermal variations triggered by fitted obstacles and their thermal modes within the closed enclosure affect the flow evolutions and most importantly heat transference. Nanofluids are acknowledged as the most gifted heat transport medium compared to conventional coolants. Additionally, hybrid nanofluids reveal comparatively promising and efficient heat transfer features than common mono nanofluids owing to their dual metallic tiny nanoparticles’ existence within the base medium. With such an objective, the current investigation deals with the computational investigation of a magnetized Ag-MgO water hybrid nanofluidic stream inside a cube-shaped enclosure with an inner circular cylinder fitted inside the cube. Several thermal modes namely, heated, adiabatic, and cold are fixed to the inner cylinder and corresponding hydrothermal consequences are noted. The right and left vertical faces are kept as cold and heated respectively, while the remaining surfaces are made thermally insulated. The Galerkin weighted residual finite element strategy is clutched to deal with the foremost dimensionless equations. Experimental verifications, numeric comparisons, and grid independence are completed to reveal the model’s precision. Several isotherms, velocities, and Nusselt number diagrams for Rayleigh numbersRa, solid particles’ concentrationsϕ, and Hartmann numbers Ha are offered to frame the requisite fallouts. The investigation reflects that the Rayleigh number strengthens the energy transport, while the magnetic factor reduces it. The cylinder’s heated mode explores high-velocity magnitudes inside the cube, while the cold mode reveals high heat transference. Finally, multiple linear regression is developed statistically to inspect the parametric impression on the average Nusselt number.