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Comparative Analysis of Heat Transfer Performance of Heat Sinks with Lattice Geometry

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24 June 2024

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26 June 2024

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Abstract
This paper presents a comparative study of heat transfer performance of lattice structured heat sinks. 20 different unit cells were chosen and heat sinks were modelled in nTop with constant unit cell size. Al 6061 alloy was chosen for analysis due to its good thermal conductivity, low weight, low cost, and high strength. Steady state thermal analysis was performed using ANSYS with constant input parameters for all samples. Heat flux and temperature distribution within the heat sinks were analysed. The study aims to provide a comprehensive understanding of the thermal performance of lattice heat sink designs.
Keywords: 
Subject: Engineering  -   Mechanical Engineering

1. Introduction

Efficient heat transfer is crucial in various engineering applications, ranging from electronics cooling to HVAC systems, where enhancing heat dissipation capabilities can significantly improve system performance and reliability. Numerous studies have investigated the influence of fin geometry such as shape [1,2], size, arrangement [3] and spacing [4,5], on heat transfer performance. Advancements in manufacturing techniques have enabled the fabrication of intricate fin designs to further enhance heat transfer efficiency [6]. Lattice structures, drawing inspiration from the intricate patterns found in nature’s cellular formations [7], have been designed to overcome inherent limitations in fin shape and structure. Lattice structures, characterized by their periodic arrangement of unit cells, possess distinct advantages such as high surface area-to-volume ratio, high strength to weight ratio [8] and low relative density. These attributes make lattice heat sinks promising candidates for applications requiring efficient heat dissipation. However, comprehensive analyses evaluating the thermal performance of lattice heat sink designs remain limited.
This paper presents a systematic investigation into the heat transfer characteristics of heat sinks with lattice structure using numerical analysis.

2. Lattice Structures

Lattice structures (also known as architected cellular materials) are a type of cellular structures [9] with repeating unit cells. Certain physical properties of lattice structures can be tailored by controlling their geometrical parameters [10]. Some lattice structures (lattice metamaterials) exhibit unique characteristics such as negative Poisson ratio [11], negative compressibility, negative thermal expansion, phononic band gap, etc., which make them useful for a wide range of applications which include light weighting, energy absorption, bioscaffolds, wave (noise/vibration) insulation and thermal management [12]. Lattice structures have been found to break the parasitic performance tradeoffs [13] seen in bulk materials such as strength vs. toughness [14,15], stiffness vs. energy dissipation, flexibility vs. fast response, etc... High surface area to volume ratio of lattice structures makes them an ideal choice for high performance heat exchanger applications. Powered by the rapid development of additive manufacturing techniques, compact lattice heat sinks may soon replace traditional heat sink types.
Based on the type and arrangement of unit cells, lattice structures are grouped into many classes [16,17,18,19,20,21,22] as shown in Figure 1 and Figure 2.

3. Modelling and Analysis

3.1. Geometric Modelling

The fins were modelled using nTop, an implicit modelling software. Unlike explicit modelling techniques which represent a body as a set of polygons or parametric patches [23], implicit modelling technique distinguishes between points inside and outside a body by representing them as a function or scalar field [24]. This allows for the creation of complex shapes and features which are otherwise impossible to model with explicit modelling softwares. Implicit modeling is also ideal for designing additively manufactured parts. However, implicit models require significantly high computational resources and is not the ideal method to represent 3d models for subtractive manufacturing as calculating the boundary of the slice is a complicated process [25]. All fins taken for analysis possess similar basic dimensions (Figure 3). The unit cells selected for analysis are depicted in Figure 4, Figure 5 and Figure 6. Constant unit cell size was used throughout the analysis.
The unit cells chosen for analysis are shown in Figure 4, Figure 5 and Figure 6. All unit cells are of the following dimensions: 15 m m * 20 m m * 20 m m

3.2. Analysis

Steady state thermal analysis was carried out using ANSYS. In steady state analysis, the object under study is assumed to be in equilibrium. Ambient conditions are also assumed to be constant. Same material properties and boundary conditions were defined for all heat sink types. The material is assumed to be isotropic and homogeneous with constant thermal conductivity.

3.2.1. Material Properties

Usually Aluminium alloys are the most preferred choice for heat sinks due to their good thermal conductivity, low weight, low cost and high strength. Al 6000 series alloys are widely used as they can be extruded easily. Al 6061 alloy was taken for analysis. Some important properties of Al 6061 alloy are given below:
  • Material: Al 6061 T6
  • Density: 2713 k g / m 3
  • Poisson’s Ratio: 0.33
  • Young’s modulus: 6.904E+10 Pa
  • Bulk modulus: 6.7686E+10 Pa
  • Isotropic Thermal Conductivity: 155.3 W/mK
  • Ultimate Tensile strength: 3.131E+8 Pa
  • Specific Heat(constant Pressure): 915.7 J/kgK
  • Isotropic Secant Coefficient Of Thermal Expansion: 2.278E-5 /K
Compositon of Al 6061 alloy is shown in Table 1.

3.2.2. Boundary Conditions

In this study, a constant film coefficient was assumed for simplicity. In actual practice, the film coefficient of a heat sink depends on various factors like surface roughness, geometrical parameters, fluid properties (viscosity, density), flow rate, heat flux, temperature gradient, etc... [26] Additionally, obtaining an accurate value of heat transfer coefficient is difficult as it changes locally and temporally [27,28,29,30,31]. Heat transfer due to radiation was neglected. A constant heat input of 100W was given in the bottom face of the base plate.
The following boundary conditions were defined:
(1)
Film coefficient: 25 W/m2; K
(2)
Heat flow(base): 100 W
(3)
Ambient temperature: 300 C
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Figure 7. Boundary regions.
Figure 7. Boundary regions.
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Properties of the heat sinks used for analysis are tabulated below:
Table 2. Heat sink data.
Table 2. Heat sink data.
Unit cell type Thickness (mm) Nodes Elements Mass(g) Surface area (mm2;) Wt. %
Simple cubic 4 223143 138108 173.74 44571.33 22.87136012
Body centred cubic 3 279253 162839 191.86 55570.87 25.25670054
Face centred cubic 3 321148 187137 208.27 66091.82 27.41693434
Diamond 3 304447 181469 191.64 55724.85 25.22773946
Octet 3 526883 316205 291.18 98070.46 38.33131483
Kelvin cell 3 303670 177447 206.2 62850.66 27.14443684
Fluorite 3 438067 258296 260.78 82638.74 34.3294192
Isotruss 3 219156 136626 253.29 81405.53 33.34342583
Triangular honeycomb 3 343357 224716 494.2 96459.57 65.05713233
Hexagonal honeycomb 3 29284 122089 355 74245.7 46.73266284
Reentrant honeycomb 3 219977 135062 417.63 87043.11 54.9773577
Square honeycomb 3 123582 74924 289.2 60256.69 38.07066505
FCC plate 1 428251 253213 326.36 155390.4 42.9624559
BCC plate 1 477545 296874 370.86 180576.59 48.82049392
Gyroid 2 197347 103200 247.82 102846.45 32.6233479
Schwarz 2 207814 121741 350.62 79234.29 46.15607393
Diamond TPMS 2 226259 116393 275.64 120721.57 36.28560897
Lidinoid 2 281184 166176 360.86 157632.11 47.50408088
SplitP 2 609100 325740 295.65 152601.96 38.91975146
Neovinous 1 866475 597273 422.76 74812.35 55.65267758
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Figure 8. Mass vs Surface area plot
Figure 8. Mass vs Surface area plot
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4. Results and Discussion

From Table 3, it is evident that the temperature difference is the highest within the simple cubic heat sink. But, the maximum temperature produced in the simple cubic heat sink is the highest among all types taken for analysis. Maximum temperature reached in plate based heat sinks is lower when compared to other types.In most of the cases, the temperature difference increases with decreasing mass of the heat sink (with same film coefficient). Temperature distribution in the 2D lattice structured heat sinks is not uniform along the vertical axis and changes based on the unit cell orientation. A more uniform heat flux distribution is seen in 2D, honeycomb and TPMS lattices as compared to beam/truss based structures. The results are highly subject to the design parameters of unit cells and the heat transfer coefficient. It can be seen that for a given value of film coefficient, beam/truss based heat sinks outperform other types in terms of mass and temperature difference produced. Future works may study the heat transfer properties of heat sinks with film coefficient obtained using CFD analysis results.
The results of the analysis are tabulated below:
The following figures show the temperature distribution within the heat sinks.
The following figures show the heat flux distribution within the heat sinks.
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Figure 9. Temperature difference
Figure 9. Temperature difference
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Figure 10. Temperature distribution results (contd...)
Figure 10. Temperature distribution results (contd...)
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Figure 11. Temperature distribution results (contd...)
Figure 11. Temperature distribution results (contd...)
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Figure 12. Heat flux distribution (contd...)
Figure 12. Heat flux distribution (contd...)
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Figure 13. Heat flux distribution (contd...)
Figure 13. Heat flux distribution (contd...)
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Figure 14. Maximum and minimum temperatures plot
Figure 14. Maximum and minimum temperatures plot
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Figure 15. Minimum and maximum heat flux plot
Figure 15. Minimum and maximum heat flux plot
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Figure 16. Mass vs Temperature difference plot
Figure 16. Mass vs Temperature difference plot
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Figure 17. Temperature difference vs surface area plot
Figure 17. Temperature difference vs surface area plot
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Acknowledgments

The author expresses his sincere gratitude to nTop (formerly nTopology) for providing free access to their state-of-the-art software, which greatly facilitated his research endeavors. I would also like to thank Autodesk (Fusion) and ANSYS for their exceptional products.

Conflicts of Interest

The author hereby declares that he has no competing interests.

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Figure 1. Classification of lattice structures (based on unit cell).
Figure 1. Classification of lattice structures (based on unit cell).
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Figure 2. Classification of lattice structures (based on periodicity).
Figure 2. Classification of lattice structures (based on periodicity).
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Figure 3. Basic heat sink dimensions.
Figure 3. Basic heat sink dimensions.
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Figure 4. Beam/Truss based unit cells.
Figure 4. Beam/Truss based unit cells.
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Figure 5. 2D and plate based unit cells.
Figure 5. 2D and plate based unit cells.
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Figure 6. TPMS unit cells.
Figure 6. TPMS unit cells.
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Table 1. Material composition (Al 6061).
Table 1. Material composition (Al 6061).
Element Wt. %
Al 95.8- 98.6
Cr 0.04- 0.35
Cu 0.15- 0.4
Fe Max 0.7
Mg 0.8- 1.2
Mn Max 0.15
Si 0.4- 0.8
Ti Max 0.15
Zn Max 0.25
Table 3. Analysis results.
Table 3. Analysis results.
Unit cell type Min. temp. Max. temp. Temperature difference Min. heat flux Max. heat flux
Simple cubic 104.16 176.89 72.73 365.95 5.61E+05
Body centred cubic 89.87 144.43 54.56 99.05 4.82E+05
Face centred cubic 75.89 128.43 52.54 171.42 2.43E+05
Diamond 86.84 144.33 57.49 41.645 4.31E+05
Octet 64.18 90.85 26.67 41.633 1.34E+05
Kelvin cell 83.23 129.14 45.91 175.63 4.17E+05
Fluorite 71.93 101.24 29.31 56.76 3.00E+05
Isotruss 69.61 104.44 34.83 135.36 2.29E+05
Triangular honeycomb 72.54 80.04 7.5 572.32 50991
Hexagonal honeycomb 85.58 95.22 9.64 246.49 1.29E+05
Reentrant honeycomb 76.86 86.59 9.73 195.95 99972
Square honeycomb 104.63 109.75 5.12 654.98 69641
FCC plate 52.44 66.94 14.5 143.12 99131
BCC plate 49.34 61.32 11.98 53.9 1.00E+05
Gyroid 64.4 84.07 19.67 149.76 1.23E+05
Schwarz 80.96 93.69 12.73 219.91 1.44E+05
Diamond TPMS 58.67 74.94 16.27 107.53 1.57E+05
Lidinoid 66.23 76.42 10.19 135.47 64755
SplitP 51.46 66.83 15.37 67.57 1.82E+05
Neovinous 86.51 95.77 9.26 129.53 72583
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