A fractal geometry enhanced topology optimization design for high-performance liquid cooling plates

The density-based bi-objective topology optimization (TO) has been widely adopted in liquid cooling plate design, where the design domain is treated as porous media with porosity as the design variable. However, conventional TO method struggles to directly optimize the convective heat transfer due to its incapabilities of explicitly depicting the heat transfer area in objective function, which limits the optimization of thermal performance. In this study, a fractal geometry topology optimization (FGTO) method is proposed, which incorporates fractal dimension as an additional design freedom into the density-based TO framework. Different from the conventional TO methods, the FGTO explicitly describes the heat transfer area, and achieves a direct optimization of convective heat transfer through the objective function. Compared to the conventional TO, the FGTO achieves a more complex structural topology in the optimized liquid cooling plate with a 46% improvement in heat transfer area. The fractal dimension is manipulated by varying the input parameter s, and increasing s can improve thermal performance of the FGTO results at the cost of larger pressure drop. Superior thermal-hydraulic performance can be achieved by varying s, with the average and maximum temperatures of the FGTO results reduced by 15.6 K and 16.9 K, respectively, compared with those of the conventional TO results. The integration of fractal geometry into the TO intensifies the difference in objective function sensitivity between solid and liquid phases, which is conducive to facilitating solid-liquid separation and contributes to escape from local optimal solutions.