Multi-phase modeling considering the nanofluid heterogeneity and slip velocity is not explored in simulating nanofluid flow and heat transfer at higher Reynolds numbers (Re). A comprehensive study of turbulent flow around hot circular cylinders is lacking. The flow patterns are not tackled, and the relationship between flow behaviors and force variations due to the influencing parameters is not established. The heat transfer enhancement and hydrodynamics with forced convection in a rectangular duct are investigated using Ansys FLUENT 15.0, applying a nodal spectral-element method based on the Eulerian-mixture model. The current investigation focuses on demonstrating the correlation between high Re values, size of the bluff body in relation to duct height, nanoparticle volume fraction, magnetic field strength, and heat transfer for magnetohydrodynamic flow. In general, the Nusselt number (Nu) increases with Re, cylinder diameter in relation to duct height, and nanoparticle volume fraction (ϕ) and decreases with the Hartmann number (Ha), except at Ha 0 ≤ 20. Nu increases with Ha from 0 to 20 with a drastic increase up to Ha = 10 and moderate from 10 to 20 with augment of Ha. The best heat transfer enhancement case is reported with the identification of ideal influencing parameters. The significant finding is that the control of flow over a circular cylinder for heat transfer enhancement using different parameters significantly changes vortical structures in the wake and reduces mean drag and lift fluctuations, destabilizes the shear layer and reattaches the flow on the surface before main separation, which delays main separation and decreases drag, and finally reduces the lift fluctuations.