[en] Highlights: • CVFEM utilized for simulation of nanofluid flow in porous cavity. • Thermal radiation is considered in energy equation. • Effect of magnetic field on hydrothermal behavior is considered. • Nu reduces with increase of Ha. • Nu enhances with increase of radiation parameter and Darcy number. Influence of uniform magnetic field on nanofluid hydrothermal treatment in a porous enclosure is analyzed numerically using Control volume based finite element method. Influence of thermal radiation is considered in energy equation. Non-Darcy and KKL models have been utilized for porous media and nanofluid properties, respectively. Numerical approach is presented for various values of Radiation parameter, Darcy number, Hartmann number, volume fraction of nanofluid and Rayleigh number. Results indicated that heat transfer rate enhances with rise of Radiation parameter while it reduces with rise of Hartmann number. Also it can be concluded that Nusselt number has direct relationship with Darcy and Rayleigh numbers.