In the present paper, unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically. The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated. The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations. In numerical simulations, four types of nanoparticles such as magnetite (Fe₃O₄), cobalt ferrite (CoFe₂O₄), Mn-Zn ferrite (Mn-ZnFe₂O₄), and silicon dioxide (SiO₂), and three types of base fluids such as water (H₂O), engine oil (EO) and kerosene (Ke) have been considered. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various model parameters such as thermal Rayleigh number, nanoparticles volume fraction and nanoparticles shape factor are studied. The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify. The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles. Kerosene-based nanofluids exhibit higher heat transfer rate. Mn-ZnFe₂O₄-kerosene nanofluid has a higher average Nusselt number than that of other 11 types of nanofluids which are studied in the present analysis.