## 4 Results and Discussion
### Heat Transfer  
To thoroughly investigate the heat transfer performance within the cavity, the study follows a structured three-step analysis based on the global Nusselt number \(Nu_{g}\). In the first stage, the instantaneous evolution of \(Nu_{g}\) is computed on all surfaces of the heat sinks for both Rayleigh numbers values (\(Ra=5\times 10^{7}\) and \(Ra=5\times 10^{8}\)). This step provides insight into the temporal behavior of heat exchange between the solid blocks and the surrounding fluid, particularly under unsteady and transitional regimes. It helps to identify the onset of flow stabilization and the influence of the Reynolds number on the thermal response over time. In the second stage, averaged global Nusselt number \(Nu_{g}^{m}\), it enables precise quantification of the net heat transfer rate in the fully developed regime. The average Nusselt number serves as a reliable metric for assessing the impact of forced convection intensity on overall thermal performance. Finally, the third stage focuses on deriving empirical correlations that relate to the Reynolds number, separately for each Rayleigh number. These correlations provide practical predictive tools for estimating thermal efficiency under similar operating conditions, and they reflect the nonlinear interplay between buoyancy-driven and forced convective effects in transitional regimes. Importantly, this Nusselt-based thermal analysis complements the physical interpretation of the flow and temperature fields previously obtained from isotherm contours and streamlines. While visualizations offer qualitative insights into flow structures and thermal pathways, the Nusselt number offers a quantitative synthesis, helping to bridge local flow phenomena with global heat transfer performance. For \(Ra=5\times 10^{7}\) when analyzing the overall variations in the global Nusselt number alongside the fluid dynamics inside the cavity (see Figure 9), a more physical and intuitive understanding of the heat transfer emerges. At the beginning of the simulation, for all Reynolds numbers considered, a transient phase is observed, characterized by strong fluctuations in the global Nusselt number. This period corresponds to the gradual establishment of flow and temperature structures within the cavity, with heat exchanges still unstable. Then, for low Reynolds values (up to about \(1.5\times 10^{3}\)), the global Nusselt number tends to stabilize around an average value, exhibiting only slight oscillations. This reflects a regime still dominated by natural convection, where the air circulates in relatively regular recirculation cells. These structures allow fresh air to reach the bottom of the cavity, locally enhancing cooling. In the thermal field, this is manifested by well-organized isotherms concentrated along the vertical walls near the openings, indicating sustained heat transfer on these surfaces. However, for \(Re\geq 1.5\times 10^{3}\), a regime change takes place. The forced air jet becomes strong enough to disrupt the natural flow. More pronounced oscillations appear in the global Nusselt curves, becoming nearly periodic with marked peaks, especially for \(Re=1.5\times 10^{3}\) and \(Re=2.5\times 10^{3}\). These oscillations are not simply numerical instabilities; they reflect the real competition between two heat transfer mechanisms: the natural convection trying to organize the flow, and the forced convection imposing a dynamic, often unstable jet. The fluid alternates between phases of recirculation and phases dominated by the blown jet, causing the rises and falls in \(Nu\). Physically, this instability results in the emergence of secondary recirculation zones, notably above the heat sink. These flow structures enable effective cooling of the right block but disrupt the airflow toward the left block, creating an asymmetry in thermal efficiency. These zones, clearly visible in the streamlines, directly influence heat exchange at the walls.