Additionally, the OFAT method often requires a larger number of experiments to obtain the same level of information as an FFD, resulting in reduced efficiency [16]. In industrial settings, an FFD is utilized to systematically and simultaneously investigate the effects of multiple factors on a process or product. This comprehensive approach helps identify interactions between factors, which can optimize processes and improve product quality. For instance, a study on optimizing the leaching process for heavy metals from lead smelting slag using a 2\({}^{3}\) (two levels and three factors) FFD demonstrated significant improvements in process efficiency and environmental safety. This method allowed researchers to determine the optimal conditions for the leaching process, reducing waste and improving the recovery of valuable metals [18]. Another example is the optimization of gold recovery from industrial solutions, where an FFD was used to analyze the effects of parameters such as pH, temperature, and the initial concentration on the adsorption process. The study concluded that an FFD is an excellent tool for optimizing complex processes, helping to enhance resource utilization and reduce experimental costs [19]. From the perspective of heat exchangers, [PERSON] et al. [10] employed a full factorial design to optimize the thermal performance of a heat exchanger. The study examined the nanofluid concentration (0.2% to 1.5% Al\({}_{2}\)O\({}_{3}\)-TiO\({}_{2}\) in water), Reynolds number (3000 to 12,000), and the twist ratio (2 to 8). The results indicated that higher nanofluid concentrations significantly enhance thermal conductivity and heat transfer efficiency. Increased Reynolds numbers correlated with improved thermal performance due to greater turbulence, while an intermediate twist ratio optimized the balance between turbulence and pressure drop. These optimizations yielded significant improvements in thermal efficiency, lower operational costs, and enhanced sustainability through better energy efficiency [10]. [PERSON] et al. [12] used a multivariate approach to optimize the performance of a scraped surface heat exchanger, focusing on key factors such as rotor speed, the mass flow rate, and the outgoing heat flux. The findings indicated that a higher rotor speed improved the convection heat transfer coefficient, optimized the mass flow rate, and enhanced thermal efficiency, while effectively managing outgoing heat flux to maintain optimal performance. These optimizations led to improved heat transfer, energy efficiency, and operational cost reduction. Overall, the use of an FED in industrial applications not only aids in optimizing processes and improving product quality but also contributes to better resource management and cost efficiency. Recent advancements in the design and optimization of cooling systems for electronic devices [20] have led to significant progress in thermal management, encompassing innovations ranging from fluid inlet and outlet positioning to advanced microchannel geometries and two-phase systems [8; 21; 22; 23]. In exploring the effects of geometry and positioning on cooling performance, [PERSON] et al. [19] investigated the impact of nanofluid inlet and outlet placements on CPU cooling. They found that positioning these components at the top of the CPU reduced the maximum temperature by 9.0 \({}^{\circ}\)C compared to lateral placement, highlighting the importance of layout optimization for enhancing thermal performance and achieving a more uniform temperature distribution in CPUs. These insights provide valuable strategies for improving heat transfer efficiency in high-density electronic systems. Similarly, [PERSON] et al. [24] introduced a Z-MMC (Z-type Microchannel Cooling) design featuring trapezoidal collectors, which effectively dissipated ultra-high heat fluxes of up to 1842 W/cm\({}^{2}\) using single-phase water flow.