Multi-Objective Optimization of Air Heat Transfer and Pressure Drop Characteristics in Parallel Channels Composed of Dimpled Plate with Reverse-Side Protrusion

ObjectiveAir-cooled， parallel-plate channels used in battery packs， electronic chips， and compact heat exchangers are commonly limited by the trade-off between heat transfer and pressure drop. Although dimpled surfaces can intensify near-wall mixing at a relatively low manufacturing cost， their overall thermal-hydraulic performance is highly sensitive to the geometric configuration. To address this issue， this study investigates a novel parallel-plate channel equipped with a dimpled plate featuring reverse-side protrusions. This study aims to clarify the effects of major geometric parameters on the coupled flow and heat transfer characteristics， and to identify an optimal compromise design that enhances heat transfer while suppressing the pressure drop.MethodsA three-dimensional， periodic unit of a plate channel was established and solved using steady-state computational fluid dynamics. Air was treated as an incompressible fluid with constant thermophysical properties. Periodic boundary conditions were adopted for the inlet and outlet of the computational domain. Grid independence was achieved at approximately 5.68 million cells. The numerical method was validated against published pillow plate experimental data. Three geometric parameters were selected as decision variables， namely the depth of the large dimple （R1=2.5-4.0 mm）， the depth of the small dimple （R2=0.5-2.0 mm）， and the dimple inclination angle （α=30°-60°）. A total of 64 design cases were used to construct the sample database. Based on these CFD data， Extreme Gradient Boosting （XGBoost） surrogate models were trained for Nu and Δp. The trained models were then coupled with the Non-dominated Sorting Genetic Algorithm II （NSGAII） to perform multi-objective optimization， and the entropy-weighted technique for order preference by similarity to ideal solution （TOPSIS） was employed to determine the best compromise solution.Results and DiscussionsUnivariate analysis reveals that R1， R2， and α all have significant influences on the thermal-hydraulic performance. Increasing R1 intensifies the flow separation and reattachment and enlarges the recirculation zone. Consequently， the heat transfer performance （h） increases rapidly. However， once R1 exceeds a certain level， the increase in h becomes much smaller than the increase in frictional resistance （f）， resulting in a turning point in the comprehensive performance. Both h and f increase rapidly with an increase in R2； beyond a certain threshold， further increases in R2， cause the trends of h and the performance evaluation criteria （PEC） gradually flatten out. Additionally， h and f show a tendency to increase and then decreasing with the increase of α. The XGBoost surrogate model reproduces the CFD results with high accuracy. The maximum deviations are only 0.44% for Nu and 3.31% for Δp， while the coefficients of determination （R²） reach 0.999 6 and0.998 2， with root mean square errors of 2.94 and 6.42， respectively. Fourteen nondominated solutions were obtained on the Pareto front. The highest ranked compromise solution selected by entropy-weighted TOPSIS corresponds to R1=2.8 mm， R2=0.6 mm， and α=47°. Further CFD simulations over Re=5 000-10 000 confirm that the optimized structure had superior overall heat transfer performance.ConclusionsThe dimpled plate with reverse-side protrusions provides an effective passive strategy for enhancing air-side heat transfer in parallel-plate channels. However， maximizing thermal-hydraulic performance requires a rational combination of large dimple depth， small dimple depth， and inclination angle， rather than merely increasing geometric disturbances. The XGBoost， NSGAII， and TOPSIS frameworks provides a reliable and efficient approach for the multi-objective design of enhanced heat transfer surfaces. For the present channel， the optimized geometry achieves a PEC of approximately 1.55 under equal pumping power over the entire investigated Re range， indicating substantial comprehensive performance improvements， promising application potential in battery thermal management， chip cooling， and other compact forced-air cooling devices.