Simulation of magnetohydrodynamics (MHD) free convection and radiation in a cavity packed with CuO‐water nanofluid has been numerically performed. To gain the outputs, control volume‐based finite element method (CVFEM) has been used. The physical domain is considered porous space and new model has been involved for modeling. This review covers a broad range of Rayleigh number, Hartmann radiation parameter, nanoparticles' shape on nanoliquid behavior, and interface heat transport variable were validated. The obtained average Nusselt number is compared with that of Rudraiah et al. for higher estimations of Gr and Ha at Prandtl number 0.733 and found good analysis with them. Furthermore, the temperature distribution of the present work on the axial midline between the obtained outcomes and computational outcomes of Sharif et al. and Khanafer et al. subject to Gr = 104, ϕ = 0.1, and Pr = 6.2(Cu − Water). It is also noticed that the conduction phenomenon is more significant against rising Nhs, while heat transfer rate declines. The convective mode strongly depends on shape factor of various nanoparticles, that is, platelet, spherical, brick, and cylinder.