The interaction between the magneto-hydrodynamic buoyant convection and the radiation in a partly heated hexagonal enclosed space filled with SWCNTs/water nanoliquid was inspected in the current work for the first time. The lowermost wall of the enclosed space was partially heated, while the other regions of this wall were presumed thermally insulated. The upper wall was considered insulated also. The four inclined walls of the enclosed space were maintained at a constant cold temperature. A magnetic field with magnitude, Bo is enforced on the enclosed space. The enclosed space was included inside it a concave hexagonal shaped body under three different conditions at its boundary namely (cold, adiabatic and heated). The outcomes of the present work are obtained for diverse Hartmann number, Rayleigh number varied as 104≤Ra≤106, heated region length varied as 0.1≤LT≤0.4, various conditions of the internal hexagonal body (cold, adiabatic and heated), solid volume fraction diverse as 0≤φ≤0.04 and radiation parameter varied as 0≤Rd≤1. In the present work, the standard Galerkin finite element method (SGFEM) is employed to model the fluid flow and heat transfer. It is established that the Nusselt number along the heated bottom wall of the hexagonal enclosed space (Nuout) rises as Rayleigh number rises. The same increasing is seen for the velocity distribution along vertically mean position. The stream function and Nuout decrease as the Hartmann number increases. The stream function, temperature and velocity have the maximum profiles at the heated condition followed by the adiabatic one, while the cold condition has the minimum profile.