The current study generally aims to improve heat transfer in heat sinks by presenting a numerical analysis of natural convection of an enclosure with hot right and cool left walls, and thermally insulated top and bottom walls. The cold wall included configurations (half circle/half square) in various sizes (S = 0.1, 0.2, and 0.3), numbers (N = 1, 2, 3, and 4), and locations (C = 0.35, and 0.65). A heat sink is constructed of Aluminum attached to the hot wall, and composed of five fins with protrusions. Fins of the heat sink will be examined in a solid and porous structure. The enclosure is filled with a hybrid nanofluid of Nanoparticles (MWCNT and Fe₃O₄) and water. The current study utilized COMSOL Multiphysics software due to its efficacy in addressing scientific and technical challenges involving partial differential equations. The solving of the governing equations is achieved using the finite element method with various parameters: Rayleigh number (Ra = 10³–10⁶), Darcy number (Da = 10⁻², 10⁻³), solid volume fraction ( $\mathrm{\phi }$ = 0–0.06) to determine stream function, isotherms lines, and average Nusselt number (Nu). The results of numerical simulations show that heat sink with solid fins have a 97% higher stream function when Ra is raised from 10³ to 10⁵. Whilst with porous fin heat sink, a stream function 96% for Da = 10⁻³ and 94% for Da = 10⁻². Changing solid fins to porous increases stream functions by 9% at Da = 10⁻³ and 20% at Da = 10⁻². It has been found that Ra increases Nu by 44% for solid fins and 50% for porous fins. Making solid fins porous increases Nu by 54% at Ra = 10⁶. The high increase in the percentage of (Nu) indicates the importance of the improvement in heat transfer, and this distinguishes the results of the current study from previous studies. Nu values were found highest for (half square) compared to (half circle), with 2% increases for numbers, 11.6% for sizes, and 11% for location. Solid volume fractions for all Ra at a solid-finned heat sink increased Nu by 23%.