Entropy production is scrutinized within a 2-D rectangular cavity housing a cylindrical heat exchanger featuring rectangular fins with sharp and smoothed edges. This study examines the influence of fin geometry on entropy production in pursuit of a strategic design for minimizing irreversibility and enhancing system efficiency. Numerical simulations are implemented to examine fluid dynamics and thermal exchange within the enclosure considering fins with both sharp and rounded edges. The results indicate that while both fin types yield minimal disparity in total entropy production at lower heat fluxes, significant differences emerge as heat generation escalates, stabilizing at around 5 percent beyond 60 kW. These findings offer valuable insights into optimal system design strategies aimed at minimizing irreversibility and enhancing overall efficiency.