Dual prediction model-based optimization of Cantor fractal microchannel structures under high heat flux

Abstract

With the continuous increase in chip integration and computational load, the exponential growth of local heat flux density poses a formidable challenge to microelectronic cooling technologies. Traditional microchannel heat sinks (MCHS) encounter difficulties in achieving coordinated thermal-hydraulic optimization under high heat flux (q_w) conditions, where heat transfer enhancement tends to reach a state of saturation, while the pressure drop (ΔP) exhibits a nonlinear growth with increasing Reynolds number (Re). This study proposes a phased modeling and optimization strategy for Cantor fractal microchannel structures under low Re conditions, aiming to balance thermal resistance (R_t) and ΔP performance. Initially, a single-variable analysis was conducted to evaluate how critical geometric parameters influence the flow and thermal performance of the CF-MCHS. A response surface model (RSM) is then constructed to decouple the local influence and interaction trends of structural parameters. Subsequently, Sobol sensitivity analysis is introduced to quantify the global parameter contributions and uncover higher-order interaction effects. To address the shortcomings of traditional surrogate models in highly nonlinear regimes, this research develops a LightGBM model and an MLP neural network to independently predict ΔP and R_t. A genetic algorithm (GA) is introduced based on a normalized weighted objective function to search for the optimal structural parameters. The optimal parameter set is determined to be b/a = 0.1, f_y = 1.375, and f_x = 1.69. Numerical simulations conducted on the optimized structure confirm that the relative error between predicted and simulated values remains below 5 %. It is evident that, relative to the baseline structure, the optimized design achieves a maximum ΔP reduction of 28.84 % while maintaining controllable variations in R_t. This research offers theoretical foundations and engineering guidance for the design of fractal-based thermal management strategies for electronic systems operating under high q_w.