A multi-criteria optimization for a radial heat sink with semicircular fins based on the design of experiments approach

Radial fins play a crucial role in enhancing energy efficiency and supporting sustainable industrial practices by optimizing heat transfer, aligning with the Sustainable Development Goals (SDGs). Addressing the need for high-efficiency systems to reduce greenhouse gas emissions, this study highlights the importance of optimizing factors in a General Factorial Design (GFD). Factors were coded and scaled within the range of +1 to −1, accounting for variations in the units of independent variables. This study utilized the Nusselt number and thermal resistance, along with an effective regression analysis, to develop a novel predictive model. Key performance indicators included R 2 , adjusted R 2 , predicted R 2 , coefficient of variation (CV), and parameter separation from the best-fit results. The proposed model demonstrated remarkable accuracy in predicting the Nusselt number, with values of R 2 , predicted R 2 , adjusted R 2 , and CV at 98.15 %, 97.08 %, 94.87 %, and 2.44 %, respectively. For thermal resistance, the corresponding values were 97.91 % for predicted R 2 , 96.70 % for adjusted R 2 , 94.21 % for CV, and 3.33 % for parameter separation. Therefore, it is evident that the proposed model is highly accurate in predicting semicircular radial heat sink performance, offering a robust tool for future heat sink designs and sustainable thermal management systems. • Nu number rises with Ra number; R th decreases as Ra number increases. • Optimal transfer function for Nu : R 2 = 98.15 %, Adj-R 2 = 97.08 %, C.V. = 2.44 %. • Model predictions show <1.52 % error for Nu ; <5.38 % for thermal resistance. • DOE reveals heat transfer power needs and offers a clear, simple solution.