## 1 Introduction  
Medium and large-scale heat sinks are essential for managing thermal loads in high-performance systems such as data centers, high-performance servers, and industrial machinery. Their primary function is to transfer the heat generated by active components to a fluid medium, usually air or liquid coolant, to prevent overheating and ensure reliable system operation. Large-scale heat sinks come in various shapes and sizes, designed to meet specific thermal management requirements. Passive heat sinks, which do not require moving parts, rely on natural convection to dissipate heat, making them highly reliable and virtually silent. They are ideal for applications like consumer electronics and certain industrial settings where energy efficiency and noise reduction are critical. Active heat sinks, on the other hand, incorporate fans or pumps to enhance the movement of air or liquid, greatly improving heat dissipation efficiency. These systems are suited for high-power cooling needs but come with the trade-off of higher energy consumption and potential noise generation, even though they provide superior cooling in high-heat environments. Finned heat sinks, with extended surfaces or fins, increase the surface area for heat transfer. This enhanced surface area improves heat distribution and cooling performance, making them well-suited for applications with high power densities, such as power electronics and high-performance computing. Large-scale heat sinks encounter significant thermal challenges in their critical role of thermal management. Overheating is a significant concern, as insufficient heat dissipation can lead to excessive temperature rise, impairing component longevity and reliability. Thermal failure or degradation may compromise overall system performance if cooling is inadequate. Another issue is the formation of hot spots due to uneven heat distribution. These localized regions of high temperature can lead to inefficiencies, accelerate wear on specific components, and ultimately jeopardize system reliability and efficiency. Additionally, space and design limitations can hinder the effectiveness of heat sinks, requiring the development of more compact solutions that optimize heat dissipation without compromising system performance or utility. Over the past decade, extensive research has been conducted on heat sink performance using both experimental and numerical approaches. [PERSON] et al. [1] and [PERSON] et al. [2] explored natural convection and phase-change materials to enhance thermal behavior. Other researchers, such as [PERSON] et al. [3] and [PERSON] et al. [4], focused on complex convective and cavitation flows, while [PERSON] et al. [5] examined the effects of rotating components in mixed convection cavities. The Lattice Boltzmann Method (LBM) has also gained traction as an effective numerical tool for thermal flow simulations. [PERSON] et al. [6], [PERSON] et al. [7], and [PERSON] et al. [8] used LBM to study mixed convection, nanofluids, and turbulent boiling flows, respectively. Several studies [9; 10; 11] investigated complex geometries and hybrid cooling systems. [PERSON] et al. [12; 13; 14] and [PERSON] et al. [15] explored how mixed convection develops in vented cavities under different Rayleigh and Reynolds numbers. Their study shows that the interaction between buoyancy and forced flow significantly shapes heat transfer behavior, offering useful insights for improving the thermal management of complex systems.\", [PERSON] [16; 17] examined high-Rayleigh-number flows along non-uniformly heated walls. In a different context, [PERSON] et al. [18] studied the heat transfer performance of slush nitrogen in a horizontal circular pipe, demonstrating how flow velocity and particle concentration can influence thermal behavior in cryogenic systems. In the context of improving cooling performance for compact and high-power systems, several recent studies have proposed innovative configurations and modeling approaches. For instance, [PERSON] et al.