The study focuses on the in-depth analysis of flow and heat transfer phenomena within a heat sink. This research relies on a numerical methodology using the finite element method and primarily aims to assess the impact of using a nanofluid to enhance heat dissipation of the heat sink. Specifically, this investigation explores various influential parameters. Initially, the Hartmann number is systematically varied from 0 to 50 to examine the influence of magnetic fields on the heat sink's performance. Additionally, kinematics is examined by modifying the Reynolds number over a range from 5 to 60. Moreover, the purpose of the study is to determine the effect of heat sink geometry on heat transfer. The results from this comprehensive numerical approach are presented in the form of velocity and Temperature contours, graphically illustrating flow patterns, as well as Nusselt plots, quantifying heat transfer. These visual and numerical data provide substantial contributions to understanding heat sink cooling mechanisms, particularly concerning the application of nanofluids under various operational conditions.