# A Quick Overview of Compact Air-Cooled Heat Sinks Applicable for Electronic Cooling—Recent Progress

## Abstract

**:**

## 1. Introduction

## 2. Problems of Heat Sink for Housing More Fin Surfaces

## 3. Heat Transfer Augmentation via Fin Configuration

_{o}surface efficiency, and ΔT is the mean temperature difference. Thus, heat transfer enhancement is primarily by increasing surface area, heat transfer coefficient or ΔT. Enhancement upon heat transfer coefficient through fin geometry can be made available through mechanisms such as boundary layer restarting or swirled flow. To enhance the performance of air-cooled heat sink, Yang et al. [29] proposed some highly interrupted fin surfaces in forms of louver or slit fin for their compact heat sink as shown in Figure 8. Apparently through the help of highly interrupted surfaces, the renewal of boundary layer augments the heat transfer performance appreciably. However, they found that the enhancements are effective only when the fin spacing is above 1.6 mm. In the meantime, severe pressure drop penalty accompanies with the interrupted surfaces. Moreover, for a smaller fin spacing like 0.8 mm, significant drop of heat transfer performance is observed especially when the low Reynolds number drops below 600. The significant decline in heat transfer performance is due to the presence of fully developed flow. The original concept of heat transfer enhancement via interrupted surface is with periodical renewal of boundary layer. Unfortunately, some researchers like Yang et al. [29] and Webb and Trauger [30] had pointed out that typical interrupted surfaces such as louver fin reveals detectable heat transfer degradation in the low velocity region. This is because the airflow may not be directed through the louver fin but mainly flows alongside the channel (so called “duct flow” phenomenon). Some similar results concerning the performance drop for the louver fin geometry in the low velocity region had been reported by Davenport [31] and Achaichia and Cowell [32]. The flow visualization experiment carried out by Webb and Trauger [30] also confirmed the phenomenon that some of the air streams bypass the louvers, representing the so-called “duct flow” between the fin channels, and lower its heat transfer coefficient accordingly. A schematic of the airflow pattern in association with fin direct flow and duct flow is shown in Figure 9. Though the low velocity operation in automotive heat exchanger may not be so common, however, low velocity operation with dense fin spacing is often encountered in many electronic cooling applications since space constraint and noise concerns need to be resolved in practice.

## 4. Augmentation via Temperature Difference

_{o}h)

_{trap 1/3}> (η

_{o}h)

_{step 1/3}> (η

_{o}h)

_{rstep 1/2}> (η

_{o}h)

_{trap 1/2}> (η

_{o}h)

_{plate}, while the effective conductance of trap 1/3 surpasses plate surface by approximately 38% at a fontal velocity of 5 m/s with the corresponding surface reduction of about 20.6%.

_{step 1/2}> R

_{step 1/3}> R

_{trap 1/2}> R

_{plate}> R

_{trap 1/3}. Notice that R represents the thermal resistance. The trapezoid design is normally superior to the step design. This is because a longer effective perimeter of entrance region is seen for the trapezoid design, although the perimeter is actually inclined to the airflow, it still offers some positive influence on the heat transfer performance. The resultant thermal resistance of trapezoid 1/3 reveals a 10% lower thermal resistance than the plate fin surface despite its surface is still 20.6% less than the reference plate design. Note that the partial bypass concept is also applicable for heat exchangers subject to dehumidification, see Wang et al. [49].

## 5. Augmentation via Material Saving

_{t}representing the tip to base thickness ratio. Their derivation greatly simplifies the calculation as compared to the equation derived from Kraus et al. [52]. By introducing the r

_{t}and fin length b, the taper angle for trapezoidal fin profile then can be defined as Equation (2).

_{t}, one can estimate a much lighter heat sink with only a very minor performance loss. This is very important in heat sink markets since a weight saving target is defined with little allowable performance loss. They also derived a closed form solution of the temperature distribution for the trapezoid fin:

_{t}= 1) and triangular fin (r

_{t}= 0). As the velocity is increased, it can be seen that the tip temperature variation for different r

_{t}is gradually becoming smaller. The temperature distributions merge almost together when r

_{t}> 0.6, suggesting that the performance loss for r

_{t}> 0.6 is negligible while retains a material saving of 20%. Note that the material saving relative to r

_{t}can be shown in the following Equation (4).

_{t}= 0, it has a maximum material saving of 50%, and this saving ratio declines with the rise of r

_{t}value, starting from r

_{t}= 0 of 50% saving down to r

_{t}= 1 where no saving at all. Notice that r

_{t}= 1.0 represents zero degree angle and it corresponds to the rectangular fin profile.

_{t}value is 0.5 for this modified design, and a theoretical estimation of material saving by Equation (4) is 25%. The actual measurement of the real weight between these two samples suggests that the actual material saving is 23%. The slight 2% deviation between the theoretical material saving and real weight saving is associated with the removal of four corner heat sink area subject to screw installation. The performance loss is termed as Q

_{trap}/Q

_{rec}vs. frontal velocity and is shown in Figure 16. As seen in the figure, a material saving of 25% can be achieved with a performance drop as small as 1% for this case when the flow rate is 10 CFM (cubic feet per minute) or 4 m/s air velocity, and with r

_{t}= 0.5. In addition, shown in the figure, the experimental results agree nicely with the theoretical calculation. The rectangular fin heat sink contains a thermal resistance of 0.297 °C/W at a frontal velocity of 4 m/s, while the trapezoidal fin is 0.301 °C/W. The theoretical prediction of the total heat transfer ratio Q

_{trap}/Q

_{rec}is 0.987 while it is 0.993 for actual test results. The difference amid prediction and measurement is only 0.88%. When the frontal velocity is increased to 12 m/s, the measured Q

_{trap}/Q

_{rec}is 0.967; while theoretical result is 0.986. The difference is 2.05%. The foregoing concept fulfills the possibility of significant material cost reduction with little performance loss.

_{h}(4A

_{c}/P

_{h}, A

_{c}is the cross sectional area, P

_{h}is the perimeter), the friction factor f subject to fully developed flow can be evaluated. This estimation is accurate for large scale cooling devices since the majority portion of flow path is fully developed. However, in PC or server applications, the small fin spacing will cause significant pressure loss in the entrance or exit of heat sink due to contraction and expansion. In coping with the entrance and exit losses for developing flow in parallel plate channels, Kays and London [25] and Webb [54] had proposed correlations for inlet K

_{i}and outlet K

_{o}loss coefficients for parallel plate channels. Notice that inclusion of the entrance and exit loss for accurate estimation of the flow impedance is essential since the size of the air-cooled heat sink is normally small.

## 6. Conclusions and Recommended Future Studies

- The drawbacks of adding surface may lead to significantly increase the pressure drop. As a result, the thermal resistance may be offset by more surface area due to the constraint of a prescribed fan subject to a specified P-Q curve.
- Though the metal foam may accommodate significant surface area, it is comparatively ineffective for air-cooling application due to its much lower fin efficiency. However, the metal foam can incorporate with solid fin to reduce the loss in fin efficiency. It is recommended that future studies should ingeniously integrate both solid fins and metal foam with varying porosity to achieve optimum design.
- The carbon foam features extreme high thermal conductivity that could appreciably improve drawback of metal foam. However, the major limitation of the carbon foam is difficult to shape and join them. Hence, it is recommended that future works should manage to resolve these issues.
- Heat sinks with periodic contraction and expansion profile may not be suitable for it introduces additional pressure drop penalty. The influence is especially pronounced when the size of heat sink is small.
- Highly interrupted surfaces like louver or slit fin are effective only when the fin spacing is sufficient large (e.g., >1.6 mm) and is operated at a considerable large frontal velocity (e.g., >1.5 m/s). A duct flow phenomenon may prevail when the velocity is low and the fin spacing is small which may jeopardize the heat transfer performance.
- Longitudinal vortex generator (LVG) is also effective when the fin spacing is large (e.g., >1.6 mm) and the number of LVG should be limited to small number to ensure the entrained swirled flow can flow alongside the heat sink.
- For highly dense fin spacing (e.g., <1.0 mm), cannelure or grooved surface may simultaneously increase the heat transfer performance and reduce the pressure drop moderately. Fin surface with concave configuration may be beneficial in reducing the flow impendence while still maintain (or slightly increase) the heat transfer. It is recommended that future works in association with fin design should be made in the concave morphology both numerically and experimentally.
- The partial bypass concept, which manipulates a larger temperature difference at poor heat transfer portion, can be implemented to significantly reduce the pressure drop at an expense of loss of heat transfer surface. Through certain niche operation, the thermal resistance of the partial bypass heat sink may be superior to the conventional heat sink. However, further future studies are recommended to quantify the effective region of partial bypass.
- The trapezoid fin surface featuring easier manufacturing is shown to have competitive performance against traditional rectangular fin geometry and it also reveals great potential in substantial material saving.
- The IPFM design combines two different geometrical fins where the fins with odd numbers are rectangular shape, and the even numbers are parallelogram shape, shows 8%–12% less surface than conventional design and still possesses a lower thermal resistance when the flow rate is less than 10 CFM; yet the thermal performance is slightly inferior to the conventional design when the flowrate is raised towards 25 CFM. Future studies are suggested on designing non-uniform fin pattern designs for specific targets.
- The cross-cut design offers appreciable improvements as compared to the conventional plate fin design especially in high velocity regime and the single cross-cut heat sinks are superior to multiple cross-cut heat sinks in the thermal performance. However, for electronic cooling, the fin thickness is usually small and the operational velocity is comparatively low. Hence, it is suggested that future works should focus on these issues during actual implementation.
- The asymmetry fin design, e.g., IPFM, had proved to be quite effective in heat transfer improvement, impedance reduction, and material saving. It is recommended that researchers should devote more efforts on this concept.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic of the configuration of typical air-cooled plate heat sink used in electronic cooling. Where W is width of heat sink, D: depth of heat sink, t: fin thickness, s: fin spacing, and H is fin height. The arrow indicates the inlet airflow.

**Figure 2.**Effect of bypass and fin number on the thermal performance of a heat sink [16] with permission from Electronics Cooling / ITEM Media. (

**a**) Schematic of airflow into a parallel plate fin heat sink with flow bypass; (

**b**) Effect of number of fins on heat sink thermal resistance with and without flow bypass; (

**c**) Heat sink pressure drop curves (with and without flow bypass) and fan curve with flow operating points. CFM is flow rate in English unit (cubic feet per minute).

**Figure 4.**Typical metal foam. Reprinted with permission from [19]. Copyright 2014 Elsevier. (

**a**) Sample is with 5 PPI (pore per inch) having a porosity of 95%; (

**b**) Sample is with 10 PPI (pore per inch) having a porosity of 95%.

**Figure 5.**Fin structure tested by Krishnan et al. Reprinted with permission from [24]. Copyright 2012 IEEE. (

**a**) Fin metal foam heat sink; (

**b**) slotted hexagon heat sink; (

**c**) Schwartz type heat sink.

**Figure 6.**Test results in terms of thermal resistance vs. operational conditions for parallel plate, slotted hexagon, fin-foam, and Schwartz structure. Reprinted with permission from [24]. Copyright 2012 IEEE. (

**a**) Thermal resistance vs. frontal velocity; (

**b**) Thermal resistance vs. pumping power.

**Figure 7.**(

**a**) Typical carbon foam; (

**b**) mesophase pitch-based carbon foam produced at ORNL. Reprinted with permission from [26]. Copyright 2003 Elsevier.

**Figure 8.**Schematic of heat sinks geometry, (

**a**) plate fin; (

**b**) louver fin; and (

**c**) slit fin. Reprinted with permission from [29]. Copyright 2007 Elsevier. Where L

_{p}is louver pitch, L

_{h}: louver height, t: fin thickness, S

_{h}: slit height, S

_{w}: slit width, L

_{l}: louver length, θ: louver angle, F

_{p}: fin pitch. (Unit: mm).

**Figure 9.**Special flow characteristics for slit and louver fin geometry. (

**a**) Effect of periodic entrance/exit loss of slit fin; (

**b**) duct flow vs. fin-directed flow for louver fin geometry at smaller and larger flow velocities. Reprinted with permission from [29]. Copyright 2007 Elsevier.

**Figure 10.**Schematic of heat sinks geometry, (

**a**) plain fin; (

**b**) Delta vortex generators; (

**c**) Delta vortex generators + plain; (

**d**) Semi-circular vortex generators fin. (Unit: mm). Where L

_{VG}is the pitch of LVG. Reprinted with permission from [35]. Copyright 2010 IEEE.

**Figure 11.**Schematic of the air model of flow across in an isolated rectangular pit. Where δ

_{h}is thickness of velocity boundary layer, u

_{∞}: free stream velocity. Reprinted with permission from [38]. Copyright 2011 Elsevier.

**Figure 12.**Simulation of the heat transfer coefficient distribution and actual module (reduced volume by 30% relative to original one) Reprinted with permission from [43]. Copyright 2015 American Society of Mechanical Engineers. (

**a**) Temperature distribution alongside the V-shape cannelure structure; (

**b**) photo of actual sample.

**Figure 13.**Cross-connected alternating converging–diverging heat sink proposed by Kanargi et al. Reprinted with permission from [44]. Copyright 2017 Elsevier. (

**a**) Isometric view of the cross-connected alternating converging/diverging fin; (

**b**) Top view; (

**c**) Vortices formation.

**Figure 14.**Thermal resistance vs. pumping power for all test samples. Reprinted with permission from [48]. Copyright 2014 Springer.

**Figure 15.**Schematic of the test samples for comparison. Reprinted with permission from [51]. Copyright 2016 Elsevier. (

**a**) Original design with rectangular profile; (

**b**) trapezoidal fin profile design. (Unit: mm)

**Figure 16.**Comparisons of the dimensionless heat transfer ratio subject to various frontal velocities between analytical predication and experimental measurements. Reprinted with permission from [51]. Copyright 2016 Elsevier.

**Figure 17.**Actual implementation of the heat sinks for the original and the proposed IPFM design. Reprinted with permission from [55]. Copyright 2017 Elsevier. (

**a**) Conventional module and IPFM module; (

**b**) Photo of mockup samples. (Unit: mm).

**Figure 18.**Thermal performance between the original design and IPFM design. Reprinted with permission from [55]. Copyright 2017 Elsevier. (

**a**) Thermal resistance vs. flowrate for analytical prediction and experimental data; (

**b**) Thermal resistance vs. pumping power.

**Figure 19.**Cross-cut deign and its thermal performance. Reprinted with permission from [59]. Copyright 2009 Elsevier. (

**a**) Single cross-cut; (

**b**) Multiple cross-cut; (

**c**) Thermal resistance ratio vs. pumping power.

**Figure 20.**Flow behavior of air inside the cross-cut heat sink. Reprinted with permission from [60]. Copyright 2016 Elsevier. The cross cut in this image is 1 mm and the arrow indicate the local airflow direction.

**Table 1.**Detailed geometry of the heat sink. (Unit: mm). Reprinted with permission from [35]. Copyright 2010 IEEE.

Fin Type | Fin Pitch (Fp) | Number of Fins (N) | LVG Pitch (L_{VG}) | Opening Angle |
---|---|---|---|---|

Plain | 1.00 | 50 | – | – |

Plain | 1.85 | 27 | – | – |

Plain | 2.63 | 19 | – | – |

Delta VG | 1.00 | 50 | 2 | 60° |

Delta VG | 1.85 | 27 | 2 | 60° |

Delta VG | 2.63 | 19 | 2 | 60° |

Delta VG | 1.00 | 50 | 4 | 60° |

Delta VG | 1.85 | 27 | 4 | 60° |

Delta VG | 2.63 | 19 | 4 | 60° |

Delta VG + plain | 1.00 | 50 | 2 | 60° |

Delta VG + plain | 1.85 | 27 | 2 | 60° |

Delta VG + plain | 2.63 | 19 | 2 | 60° |

Semi-circular VG | 1.00 | 50 | 2 | 60° |

Semi-circular VG | 1.85 | 27 | 2 | 60° |

Semi-circular VG | 2.63 | 19 | 2 | 60° |

Heat Sink | Side View | Photos of Test Sample |
---|---|---|

(a) Plate | ||

(b) Oblique dimple gap 4–12 fin | ||

(c) Oblique dimple gap 6–12 fin | ||

(d) Cannelure fin I | ||

(e) Cannelure fin II | ||

(f) Oblique dimple gap 4–12 cannelure fin | ||

(g) Oblique dimple gap 6–12 cannelure fin I | ||

(h) Oblique dimple gap 6–12 cannelure fin II |

© 2017 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Wang, C.-C.
A Quick Overview of Compact Air-Cooled Heat Sinks Applicable for Electronic Cooling—Recent Progress. *Inventions* **2017**, *2*, 5.
https://doi.org/10.3390/inventions2010005

**AMA Style**

Wang C-C.
A Quick Overview of Compact Air-Cooled Heat Sinks Applicable for Electronic Cooling—Recent Progress. *Inventions*. 2017; 2(1):5.
https://doi.org/10.3390/inventions2010005

**Chicago/Turabian Style**

Wang, Chi-Chuan.
2017. "A Quick Overview of Compact Air-Cooled Heat Sinks Applicable for Electronic Cooling—Recent Progress" *Inventions* 2, no. 1: 5.
https://doi.org/10.3390/inventions2010005