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

Li Zhengdao; Ren Huahua; Zhang Zhuo; Guo Haobo; Tao Wenquan

doi:10.12465/issn.0253-4339.20260427001

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

更新时间：2026-06-29

- Multi-Objective Optimization of Air Heat Transfer and Pressure Drop Characteristics in Parallel Channels Composed of Dimpled Plate with Reverse-Side Protrusion
- Journal of Refrigeration Pages: 1-11(2026)
- 作者机构：
  
  1.西安交通大学能源与动力工程学院热流科学与工程教育部重点实验室西安 710049
  2. 阿里云计算有限公司杭州 311121
- 作者简介：
  
  Tao Wenquan， male， professor， School of Energy and Power Engineering， Xi'an Jiaotong University， Tel： 029-82669106， E-mail： wqtao@mail.xjtu.edu.cn. Research fields： Performance enhancement technologies for hydrogen fuel cells； Energy saving and low-carbon technologies for data centers （including cooling technologies for high heat flux density chips）； Molten salt energy storage and solid-liquid phase change energy storage technologies； Application of AI in CFD/NHT.
- 基金信息：
- DOI：10.12465/issn.0253-4339.20260427001
  CLC： TK124;TK172
- Received：27 April 2026，
  
  Revised：2026-05-18，
  
  Accepted：23 May 2026，
  
  Online First：29 June 2026，
- 稿件说明：
移动端阅览
李政道，任华华，张卓，等. 带反向凸起凹坑的平板通道空气传热与压降特性的多目标优化［J］. 制冷学报，XXXX，XX（XX）：1-11.

Li Zhengdao，Ren Huahua，Zhang Zhuo，et al. Multi-Objective Optimization of Air Heat Transfer and Pressure Drop Characteristics in Parallel Channels Composed of Dimpled Plate with Reverse-Side Protrusion［J］. Journal of Refrigeration，XXXX，XX（XX）：1-11.
李政道，任华华，张卓，等. 带反向凸起凹坑的平板通道空气传热与压降特性的多目标优化［J］. 制冷学报，XXXX，XX（XX）：1-11. DOI： 10.12465/issn.0253-4339.20260427001.

Li Zhengdao，Ren Huahua，Zhang Zhuo，et al. Multi-Objective Optimization of Air Heat Transfer and Pressure Drop Characteristics in Parallel Channels Composed of Dimpled Plate with Reverse-Side Protrusion［J］. Journal of Refrigeration，XXXX，XX（XX）：1-11. DOI： 10.12465/issn.0253-4339.20260427001.

摘要

电池和芯片在运行过程中会产生大量热量，若不能及时散热将显著降低其运行安全性、寿命和性能。低效散热将导致更高的冷却能耗，降低整体能效。因此，传热表面的结构优化对电池和芯片的热管理至关重要。本文提出一种新型带反向凸起的凹坑板，研究了影响其传热性能的关键参数。结果表明，与凹坑深度相关的2个参数（

和

）及凹坑倾角（

）对其流动传热性能影响显著。为进一步优化性能，采用XGBoost算法和NSGA-Ⅱ多目标遗传算法，以努塞尔数（

）和压降（Δ

）为优化目标，通过基于熵权法的TOPSIS算法确定当前三变量设计空间内的最优折中解。采用等泵功下的性能评价准则（PEC）作为传热性能评估指标，数值模拟结果表明，在所研究的雷诺数（

）范围内，PEC约为1.55，表明强化传热效果显著。

Abstract

Objective

Air-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.

Methods

A 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 （

=2.5-4.0 mm）， the depth of the small dimple （

=0.5-2.0 mm）， and the dimple inclination angle （

=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

and Δ

. 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 Discussions

Univariate analysis reveals that

，

， and

all have significant influences on the thermal-hydraulic performance. Increasing

intensifies the flow separation and reattachment and enlarges the recirculation zone. Consequently， the heat transfer performance （

） increases rapidly. However， once

exceeds a certain level， the increase in

becomes much smaller than the increase in frictional resistance （

）， resulting in a turning point in the comprehensive performance. Both

and

increase rapidly with an increase in

； beyond a certain threshold， further increases in

， cause the trends of

and the performance evaluation criteria （PEC） gradually flatten out. Additionally，

and

show a tendency to increase and then decreasing with the increase of

. The XGBoost surrogate model reproduces the CFD results with high accuracy. The maximum deviations are only 0.44% for

and 3.31% for Δ

， while the coefficients of determination （

²） 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

=2.8 mm，

=0.6 mm， and

=47°. Further CFD simulations over

=5 000-10 000 confirm that the optimized structure had superior overall heat transfer performance.

Conclusions

The 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

range， indicating substantial comprehensive performance improvements， promising application potential in battery thermal management， chip cooling， and other compact forced-air cooling devices.

关键词

Keywords

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