Feature analysis aided design of lightweight heat sink from network structures

Summary

The advent of electronic devices has revolutionized engineering applications and fundamentally transformed society. However, their lifespan is significantly impacted by operational temperatures, as excess heat can elevate localized temperatures (hot spot) and damage components. Efficient heat dissipation through heat sinks is therefore crucial. In this research, we optimized intricate network structures for designing heat sink fins. These novel configurations provide thermal dissipation capabilities equivalent to conventional designs while substantially reducing weight. We utilized 3D printing to manufacture these designs and confirmed their effectiveness through experimental validation. The optimized network-based heat sink designs exhibit a weight reduction of approximately 50% while maintaining cooling efficiency comparable to commercially available models. Additionally, we introduced the “effective heat transfer coefficient h_eff” to assess heat dissipation effectiveness. This factor considers temperature fluctuations under thermal loads and the heat sink’s surface area. The refined heat sink designs were successfully implemented to cool light emitting diodes (LEDs） in practical applications.

Graphical abstract

Highlights

• •A novel network structure as an alternative to the bulk structure heat sinks
• •Introducing a quantitative approach to assess network heat dissipation efficiency
• •Significant reduction in heat sink weight, but same heat dissipation capacity
• •Introducing a coefficient to measure the improvement of heat dissipation performance

Heat transfer; Thermal engineering; Materials science; Computational materials science

Introduction

The modularization, integration, high frequency, and miniaturization of micro/nano electronic and optoelectronic devices leads to an increased heat flux density and temperature rise, significantly affecting the reliability and lifespan of these devices.^{1,2,3,4,5,6,7}

The design of heat sinks is a multifaceted task requiring efficient thermal transfer, minimal resistance, lightweight, compactness, and robustness. According to Newton’s law of cooling, increasing the contact area between the heat sink and the cooling medium is crucial for enhancing heat dissipation. To improve heat dissipation capacity, heat sinks often feature multiple arrays of fins to increase the surface area for thermal exchange with air. However, as LEDs deliver enhanced performance and generate more heat, additional fins are needed to reduce operating temperatures efficiently. This demand for improved heat dissipation typically leads to more fins, enlarged heat sink, and weight, because most sinks are primarily made from metals like aluminum or copper. This increase in size and weight poses challenges for transportation and installation, and of course the cost. Moreover, an excessive number of fins or overly dense arrangements can obstruct local airflow and impede effective heat dissipation.

Multiple studies have explored optimization techniques to design lightweight and compact heat sink.^8,9 However, the existing literature highlights two primary issues related to both the structure of heat sinks and the methods of optimization. First, simplistic fin structures such as rectangles, triangles, pins, or trapezoids offer limited design parameters, constraining the scope for further optimization.^10,11,12,13 Second, single-path optimization methods often lack comprehensive feature analysis and detailed examination of how structural variations impact cooling efficiency.^14,15,16

In recent years, numerous artificial structural materials, collectively known as metamaterials, have been extensively studied.^{17,18,19,20,21} These materials are designed to achieve complex requirements through the fabrication of specific structures.^22,23,24,25 Network structures are one of them. Amorphous networks, composed of multiple nodes and connecting edges, offer complex geometrical patterns that provide both a large design space and a larger specific surface area, making them suitable alternatives for heat sink fin structures.^26,27,28 Heat transport in complex networks has been extensively studied, particularly how edges and nodes affect the thermal conductivity of networks.^{29,30,31,32,33,34,35} These theories have been applied to scenarios such as the thermal conductivity of carbon nanotubes and metal nanowires.³⁶ Feature analysis, widely used in data science, statistics, and machine learning, involves extracting key attributes from raw data to understand patterns, trends, and structures, simplifying data complexity, enhancing predictive models, and revealing underlying information.^37,38,39,40

This study presents the optimization and practical implementation of a lightweight heat sink by employing amorphous network structures. Through feature analysis and quantitative calculations, we propose a lightweight approach that significantly reduces the heat sink’s weight while maintaining its cooling efficiency. Validation of the heat dissipation capabilities of different heat sink designs was conducted using a defined performance factor. The optimized network-based heat sinks demonstrated impressive heat dissipation capabilities for operational LEDs, reaffirming their potentials of practical applications. We anticipate that our innovative design strategy will find broad applications in addressing diverse challenges in heat sink design.

Results

Dataset creation

Due to their stochastic nature, amorphous networks offer a wide range of configurations, presenting a substantial design space for optimizing lightweight heat sinks. The construction of a network structure begins by randomly distributing a set number of nodes within a rectangular area. Subsequently, these nodes are symmetrically mirrored to the adjoining panel with respect to a vertical axis, forming a square region measuring $6\times 6c{m}^2$. Notably, each side of this square area consists of evenly distributed $N$ nodes. It is ensured that the total number of nodes in each network equals $N_{tot}=N\times N$. This process is visually outlined in Figure 1A.

Figure 1.

Optimization process for constructing network heat sinks

(A) The process of constructing a network-based heat sink. Initially, numerous nodes are placed randomly within a rectangular area on the left side of a square region. Subsequently, these nodes are symmetrically projected to the right side, filling the entire $6\times 6c{m}^2$ square region. Finally, the Delaunay triangulation is employed to connect these nodes, forming the network structure.

(B) Calculating the temperature rise at each node of the network fins under heating using an algorithm.

(C) Specifying the fin optimization strategy by analyzing the relationship between network structure characteristics and heat dissipation capability.

(D) Final optimization results of the fins.

Characterization of network heat dissipation capability

As the fin is oriented vertically during operation, heat flows from the bottom boundary throughout the entire network structure. We calculate the heat dissipation capacity of the network fins using a method based on Newton’s cooling law. This calculation method, invented by Kraus, can determine the temperature at any node in the network at equilibrium.⁴¹ Recognizing that a heat sink with superior heat dissipation exhibits lower temperatures, we have introduced the maximum excess temperature $T_{ET}$ of the nodes at the network’s steady state as a key parameter for quantifying the heat dissipation capacity of the system. The definition of $T_{ET}$ is shown in Equation 1.

$$T_{ET}=T_{\mathit{max},Network}-T_{amb}$$ (Equation 1)

• $T_{\mathit{max},Network}$-represents the highest temperature node in the network ($K$).

• $T_{amb}$-ambient temperature ($K$).

Approach to lightweighting network fins

In accordance with Newton’s law of cooling, objects with larger surface areas typically exhibit enhanced heat dissipation capacities. However, our investigation has revealed that the heat dissipation capacity of our network structure remains unaffected by its surface area. This finding is substantiated by the Pearson’s coefficient data provided in Figure 2B. The Pearson’s coefficient (Equation 2) indicates a positive (negative) correlation when approaching 1 (−1), while a value of 0 signifies no intercorrelation between the factors being compared.⁴² The heat maps displayed in Figure 2B showcase an example network featuring 20,22 and 24 boundary nodes. The heatmap illustrates the absence of any linear relationship between the heat dissipation capacity $T_{ET}$ and factors such as surface area, volume, total edge length, or average edge length in the networks under observation. Note that the range of normalized surface areas is measured solely from the originally generated network structures, with values extending from 1.19 to 1.31.

Figure 2.

Foundations for eliminating links with minimal contributions to heat dissipation

(A) A flowchart outlines the process of weight reduction for the network-based heat sink.

(B) The Pearson correlation coefficient is used to measure the relationship between excess temperature $T_{ET}$ and various geometrical parameters, including surface area ($S$), volume ($V$), total edge length ($L_{tot}$), and average edge length ($L_{ave}$).

(C) An analysis of the contribution of individual bonds to the heat dissipation capacity of a selected network heat sink. Some bonds have minimal impact on the overall heat dissipation, potentially allowing for their removal to reduce the weight of the heat sink.

Remarkably, the heat dissipation capacity $T_{ET}$ is independent of the network’s surface area and volume, as evidenced by the close-to-zero value of the Pearson’s coefficient. This finding suggests that in a network system, a larger surface area does not guarantee superior heat dissipation performance, and a smaller surface area does not necessarily imply poor heat dissipation. Notably, both the surface area and volume are determined by the total length of connections within the network, highlighting the presence of edges that contribute minimally to the overall heat dissipation. Therefore, it is possible to identify and eliminate these connections from the network, resulting in a lighter heat sink. Importantly, removing these minimally impact edges will not compromise the heat sink’s cooling performance.

$$r=\frac{{\sum }_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^2}\sqrt{{\sum }_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}$$ (Equation 2)

• $X_i,Y_i$-are the observed values.

• $\overline{X},\overline{Y}$-are their means.

• $n$-is the number of observations.

To assess the influence of individual connections on overall heat dissipation, we have introduced a quantity of “contribution”, which is represented by Equation 3. Furthermore, Figure 2C illustrates that each edge within the selected network exhibits significant variation in contribution values. Consequently, as depicted in Figure 2A, we selectively eliminate the less crucial edges, aiming to match the heat dissipation capability of the network with that of a bulk fin. This results in a fin structure that possesses comparable heat dissipation efficiency to a bulk fin yet remains as lightweight as possible.

$$Contributio{n}_i=\frac{T_{\mathit{max},i=1}-T_{\mathit{max},i}}{l_i}$$ (Equation 3)

• $T_{\mathit{max},i}$-$T_{ET}$ after removing the i-th edge ($K$).

• $l_i$-Length of the i-th edge removed ($m$).

Results of network fin optimization

We meticulously screened an extensive network dataset containing 50,000 potential candidates to isolate the most optimized networks with varying boundary nodes. The comparative results between the original and final optimized networks are depicted in Figure 3. Notably, the optimized network structures exhibited minimal temperature elevation under external heat loading, highlighting their exceptional heat dissipation efficiency. Our bond removal strategy, guided by the aforementioned optimization framework, systematically assessed the contribution of each edge within the three network types. We progressively eliminated edges until their collective heat dissipation capacity resembled that of a bulk fin.

Figure 3.

Structure of three networks optimized using lightweight strategy before and after optimization

Experimental verification of heat sink capacity

The heat dissipation capacities of the theoretically optimized networks were substantiated through experimental validation. An optimized planar network was replicated to generate eight instances, which were subsequently spaced evenly on a sheet. This arrangement transformed the initial two-dimensional network into three-dimensional heat sink entities, as shown in Figure 4A. To this end, four heat sinks were fabricated: three network fin heat sinks with boundary node counts of 20, 22, and 24 respectively, alongside a standard heat sink for comparative purposes. Specific parameters for each heat sink are outlined in Table 1. All heat sinks were uniformly 3D printed under identical conditions to ensure consistency across the experimental setup. The printing material used in this study is AlSi₁₀Mg (thermal conductivity is $155W/\left(m·K\right)$), chosen because its thermal properties are similar to those of common commercial heat sink materials such as 6061 aluminum alloy (thermal conductivity = $155W/\left(m·K\right)$) and ZL104 aluminum alloy (thermal conductivity = $147W/\left(m·K\right)$). Heat sinks made from aluminum-silicon-magnesium alloy can closely approximate the performance of commercial heat sinks.

Figure 4.

Preparation for experimental measurement of heat dissipation

(A) Three types of heat sink using network structure as fins and the corresponding bulk heat sink.

(B) Schematic diagram of experimental configuration of heat sink heat dissipation capacity.

(C) Use of polyimide heating sheets as heat sources.

(D) Use LED lamp beads as heat source.

Table 1.

Heat sink structure size detail

Name	Fin thickness(cm)	Fin distance(cm)	Normalized fin weight
20Network	0.1	0.3	0.5381
22Network	0.1	0.3	0.5486
24Network	0.1	0.3	0.5590
Bulk	0.1	0.3	1

The experimental setup is illustrated in Figure 4B. Heat loading is facilitated by the heating sheet, enabling the generation of varying heat flux densities. As the heating sheet possesses a consistent resistance, diverse heat flux densities are produced by applying distinct voltages. The polyimide heating sheet measures $1\times 1.5c{m}^2$, and when the heating power is between $2-4W$, the heat flux density generated by the heating sheet is approximately $1300-2600W/m^2$, effectively simulating various heating scenarios for LEDs. To comprehensively investigate the heat dissipation performance of the heat sinks, two heating modes were used. The first mode involves heating the center on the bottom boundary of the heat sink using a polyimide heating sheet (see Figure 4C). The efficacy of various heat sinks in dissipating heat is assessed by monitoring the temperature of the heating sheet at a stable state across varying heating powers.

The second mode involves placing the LED at the bottom of the heat sink and measuring the equilibrium temperature of the LED to evaluate the heat sink’s heat dissipation capability (see Figure 4D). As shown, the overall experimental setup is similar to the heating sheet method. The LED and heat sink are filled with the same thermal interface material and stored under constant pressure for 2 h. This is because the performance of thermal interface materials varies with pressure, so storing them under the same pressure for a period ensures the uniformity of the interfacial thermal resistance.⁴³

LEDs, known for their energy efficiency and high brightness, emit light by applying voltage to a semiconductor, prompting electron transitions. Due to their long lifespan, pure light color, and focused beam distribution, LEDs have become a popular lighting solution with profound impacts on human production and life.⁴⁴ However, the development of LEDs is constrained by overheating issues, as their operating temperature directly relates to their lifespan.⁴⁵ It is estimated that for every 10°C rise in temperature, the reliability of LEDs may decrease by about 10%.⁴⁶

As shown in Figure 5A, the fins optimized through structural design not only reduced weight but also maintained almost the same heat dissipation capability as the bulk fins. In fact, they even exhibited a lower $T_{ET}$ under low heating power, indicating better heat dissipation capability. This is consistent with the results of numerical simulations.

Figure 5.

Heat sink heat dissipation capacity results

(A) $T_{ET}$ of the heat source when heated at different powers using heating sheets. Error bars indicate the variance of $T_{ET}$.

(B) $h_{eff}$ values of four different heat sinks.

(C) $T_{ET}$ of LED lamp beads when using LED as heat source.

The heat generated by the heating sheet is transferred to the air through thermal convection and radiation. Assuming the heating power as $P$, the thermal transport process across the entire heat sink can be expressed by Equation 4, incorporating Newton’s cooling law and the Stefan-Boltzmann law.

$$P=\epsilon \sigma S\left(T_S^4-T_{amb}^4\right)+h\left(T_S-T_{amb}\right)S=\left[\epsilon \sigma S\left({T_S}^2+T_{amb}^2\right)\left(T_S+T_{amb}\right)+hS\right]\left(T_S-T_{amb}\right)$$ (Equation 4)

• $P$-Heating power (W)

• $T_S$-Temperature ($K$) of heating sheet when it reaches steady state.

• $h$-Heat transfer coefficient ($W/\left(m^2·K\right)$) of fluid working medium.

• $\epsilon$-The radiation coefficient of the blackbody.

• $\sigma$-The Stefan constant.

• $T_{amb}$-Ambient temperature ($K$).

• $S$-Contact area ($m^2$) between the heat sink and the working medium.

Note that $T_S-T_{amb}$ on the right-hand side of Equation 4 represents the excess temperature of the heat sink, defined as $T_{ET}=T_S-T_{amb}$. It is important to highlight that the standard unit value of $\sigma$ is approximately $5.670373\times {10}^{-8}W·m^{-2}·K^{-4}$. This suggests that $\left(T_S^2+T_{amb}^2\right)\left(T_S+T_{amb}\right)$ can be treated as a constant within a specific temperature range. Consequently, the heat flow is directly proportional to the excess temperature $T_{ET}$ of the heat sink. By differentiating $P$ with respect to $T_{ET}$ in Equation 4, we arrive at $dP/d{T}_{ET}=\epsilon \sigma S\left(T_S^2+T_{amb}^2\right)\left(T_S+T_{amb}\right)+hS$. Excluding the slight differences in surface area among different network heat sinks, we define the convective heat dissipation capacity coefficient $h_{eff}$ (with the same dimension of heat transfer coefficient) of the heat sink as shown in Equation 5.

$$h_{eff}=\frac{dP}{d{T}_{ET}S}=\epsilon \sigma \left(T_S^2+T_{amb}^2\right)\left(T_S+T_{amb}\right)+h$$ (Equation 5)

The $h_{eff}$ effectively characterizes the overall heat dissipation capability of the network. In practical situations, $T_S$ should represent the temperature at every point where the heat sink’s surface contacts the air. Within the heat sink, temperatures vary across different regions, making it impractical to measure the temperature at every local position on its surface. Therefore, it is essential to choose a representative temperature that reflects the overall excess temperature. As we focus on the electronic device cooled by the heat sink, we measure the temperature of the heating sheet, which we denote as $T_s$. Consequently, the excess temperature is calculated as $T_{ET}=T_s-T_{amb}$.

By fitting the data in Figure 5A, we obtained the $h_{eff}$ values for Bulk, 20Network, 22Network, and 24Network heat sinks, as shown in Figure 5B. It can be seen that the 22Network has the highest $h_{eff}$, followed by 24Network, and the 20Network has the lowest $h_{eff}$. This indicates that the 22Network structure has the strongest convective heat dissipation capability. Moreover, the $h_{eff}$ of all three networks are significantly higher than that of the bulk fin. This demonstrates that the convective heat dissipation capacity of network structures is better than that of the bulk fin.

The optimized network-based heat sinks were experimentally attached to LED beads to evaluate their heat dissipation performance in real-world scenarios. A $12V-12W$ cool white LED bead served as the experimental model. In our investigation, four distinct types of network heat sinks underwent five independent tests. The findings, presented in Figure 5C, demonstrate that network heat sinks effectively dissipate heat generated by the LED. Impressively, their heat dissipation ability matches or exceeds that of conventional bulk fin heat sinks, despite the network heat sinks weighing only half as much.

Discussion

Heat management is ubiquitous in both the natural world and human society. Notably, biological bodies like humans maintain a steady body temperature of approximately 36.5°C. This consistent body temperature is sustained by a widely distributed vascular network within the human body, which efficiently dissipates excess heat generated in our organs. Consequently, network structures possess inherent potential for heat dissipation, shedding light on the importance of network-based heat sinks. In conjunction with network architecture, we have achieved a 50% reduction in heat sink weight without compromising its heat dissipation capabilities. To comprehensively simulate LED heat dissipation scenarios, an LED light has been utilized as a heat source under open environment and natural convection conditions, demonstrating the superior heat dissipation capability of the network heat sink. The research revealed that the maintained heat dissipation capability is due to the network structure that helps increasing the surface area and thereby enhances convection.

Moreover, we have introduced a significant parameter, denoted as $h_{eff}$, to facilitate fair comparisons between heat sinks with different surface areas. This metric can be regarded as an effective heat transfer coefficient as it shares the same dimension as $h$. It is crucial in the context of cooling functional electronic devices, where heat dissipation tends to decrease with larger volumes and increased surface areas of the heat sink. Our experimental findings align with this notion, showing that the 24Network heat sink outperforms its 20Network and 22Network counterparts by effectively reducing temperature rises across all operational heating powers.

However, as the size of the heat sink increases, its weight also increases, making the selection process among multiple candidates more complex. The maintained heat dissipation capability is attributed to the network structure, which enhances the convective intensity of the heat sink. By utilizing the proposed $h_{eff}$ metric, we can quantitatively evaluate this characteristic across various heat sinks and identify the optimal choice based on the heat sink with the highest “$h_{eff}$” value. This approach allows for a more nuanced understanding of heat dissipation capabilities and facilitates the selection of the most effective heat sink for specific applications.

Limitations of the study

In future studies on network structure heat sinks, several directions are worth further exploration.

• (1)We expect to achieve an even higher cooling rate for the electronic device by integrating forced-air convection flow into our network-based heat sink. This is due to the increased surface area, which facilitates better heat dissipation. Furthermore, the network channels can be designed as hollow, allowing cooling mediums to flow through them, thereby greatly enhancing thermal convection efficiency.
• (2)The network structure used in this paper started from amorphous structures. Amorphous structures are very diverse and complicated. How to characterize different amorphous structures, in particular how to map its structure into functions, in particular the heat dissipation function is an ultimate goal.
• (3)In this study we focused only on the contribution of convection. As we know, heat radiation is also another important factor of heat transfer. Radiation cooling is a rapidly developing field and technique. How to incorporate the radiation cooling technique into the technique proposed in this paper to dissipate heat is also an interesting topic.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Guimei Zhu (zhugm@sustech.edu.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •Data reported in this paper will be shared by the lead contact upon request.
• •All original code has been listed in the key resources table and is publicly available at GitHub: https://github.com/luodarling123/Create-Delauney-network-fin-/releases/tag/network.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work was supported by the Guangdong Basic and Applied Basic Research Foundation (Project No. 2024A1515030139), National Natural Science Foundation of China (Grant Nos. 12205138; 52250191), Shenzhen Science and Technology Innovation Committee, Grant/Award Number: JCYJ20220530113206015, and China Postdoctoral Science Foundation (Certificate Number: 2024M761275).

Author contributions

Conceptualization, B.W.L.; Methodology, T.L.L. and C.L.Z.; Software, T.L.L. and C.L.Z.; Validation, T.L.L. and C.L.Z.; Writing – Original Draft, T.L.L. and C.L.Z.; Writing – Review and Editing, B.W.L., X.Y.S., and G.M.Z.; Supervision, B.W.L., X.Y.S., and G.M.Z.; Funding Acquisition, B.W.L.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
AISi10Mg	Ji Hua Laboratory	http://www.jihualab.com/
Software and algorithms
MATLAB 2023b	MathWorks	https://ww2.mathworks.cn/products/matlab.html
Code of network structure generation and temperature calculation	This paper	[GitHub]: [https://github.com/luodarling123/Create-Delauney-network-fin-/releases/tag/network]

Experimental model and study participant details

There are no experimental models (animals, human subjects, plants, microbe strains, cell lines, primary cell cultures) used in the study.

Method details

Experimental design and data collection

This project employed 3D printing technology to fabricate the network fin heat sinks and used the same material and process to prepare bulk heat sink control groups for experimental comparison. We constructed an experimental platform for testing the heat dissipation capacity of the heat sinks. The device heats the heat sink by deploying heating pads or LEDs at the bottom and records temperature changes using thermocouples, determining the steady-state temperature (when the temperature data changes are within ±0.5°C within 5 min, we consider the heating process to have reached steady state).

We placed four thermocouples in the heat source area to record changes in the heat source temperature $T_{bottom}$, and the average temperature was taken to obtain the heat source temperature change. We also used a thermocouple to record real-time changes in ambient temperature ($T_{amb}$). Each set of experiments subtracts the ambient temperature at the time as a measure of the heat sink’s heat dissipation capacity, i.e., the lower the excess temperature ($T_{ExcessTemperature},T_{ET}$), the stronger the heat dissipation capacity of the heat sink.

Experimental instruments and materials

• (1)Stabilized Power Supply: Provides constant electrical power using the UNI-T UTP1306S digital switching regulated model, featuring a maximum output voltage of 32.00 V and a maximum output current of 6.00 A.
• (2)Thermocouples: Employed for temperature detection using the OMEGA K-type model, with external dimensions of 0.4 × 0.7 mm² and a wire diameter of 0.08 mm. It has a temperature range of 0°C–1300°C and an accuracy of ±0.75%.
• (3)Heating Pads: Designed to provide constant current under constant electrical power. The model used is a polyimide heating pad with dimensions of 1 × 1.5 cm², a resistance of 3 Ω, and a maximum temperature resistance of 110°C.
• (4)Signal Acquisition Card: Utilized for collecting temperature signals from thermocouples, specifically the ART DAM-3038 model, which offers a maximum sampling frequency of 10 Hz and an accuracy of ±0.1%.
• (5)LED Light Beads: Used to simulate LED working conditions in experiments. The specific model is a 12 W LED cool white light bead, with chip dimensions of 0.762 × 0.762 mm² and device dimensions of 20 × 20 mm².
• (6)Aluminum Foil Tape: Used to secure thermocouples in designated positions. The specific model is produced by Shanghai DB Biotechnology Co., Ltd.

Quantification and statistical analysis

All the statistical analysis and the results are described in the main text (See results and discussion sections).

Additional resources

This work does not include any additional resources.

Published: December 18, 2024