Summary: In this paper, free, forced and Marangoni convective flows within an open enclosure partially filled with a porous medium under impacts of an inclined magnetic field are investigated. The forced convection is due to the movement of the side walls, the free convection induces from the heated part in the bottom wall and the Marangoni convection is a responsible on the thermal interaction at the free surface (top wall). The flow domain is partially heated from below and partially filled by a porous medium. The local thermal non-equilibrium model (LTNEM) is used to represent the thermal field in the porous layer (bottom layer) while the two-phase model is used to simulated the micropolar nanofluid behavior. Two cases based on the direction of the movement of the side walls are considered, namely, assisting flow (downward lid motion) and opposing flow (upward lid motion). Numerical analysis based on the finite volume method is conducted and the obtained are presented in terms of the streamlines, isotherms, angular velocity, and the cup-mixing temperature \(\theta_{cup}\), the bulk-averaged temperature \(\theta_{ave}\) and the average Nusselt numbers. The controlling parameters, in this situation, are the Darcy number Da, the Marangoni number Ma, the Nield number H, the vortex viscosity \(\Delta\), the Biot number Bi and the Hartmann number \(Ha\). The results revealed that the increase in the Nield number enhances the cup-mixing temperature \(\theta_{cup}\) and bulk-averaged temperature \(\theta_{ave}\) regardless the direction of the side walls motion. Also, the average Nusselt number is boosted as the Marangoni number is grown.