Table of contents
- Natural convection heat transfer in a cross-fin heat sink
- Natural convection heat transfer in a straight-fin heat sink
- Temperature diffusion of heat sink
- Effect of heating power on heat transfer coefficient
- Natural convection heat transfer in a radial heat sink
- Flow characteristics
- Effect on radial heat sink
(a) overall heat transfer coefficient considering both convection and radiation; (b) convective heat transfer coefficient .
Heat sink are a kind of heat exchanger used as a cooling system for electronic devices due to simplicity, low cost and reliable manufacturing process. The heat sink can be divided into plate fin, pin fin, cross fin, a combination of plate fin and pin fin, perforated plate fin and pin fin and radial heat sink. In the past decades, several published articles have focused on the thermal performance with forced convection. However, only a few publications have focussed on the thermal performance with natural convection. This study initiates with brief and comprehensive discussion regarding importance of heat sinks, its methodology; it’s suitability for present day heat dissipation issues, statistical data of various heat sink designs and a rich discussion of the work so far. The purpose of this article is to summarize the publications with respect to experimental research on the natural convection heat transfer in various geometry of heat sinks as well as offering guidelines for future research.
Heat sinks are typically divided into forced convection and natural convection heat sinks based on the operating conditions. Forced convection heat sinks dissipate a larger amount of heat due to mainly such flow inducing devices as fans, but their reliability is lower than that of natural convection heat sinks because of these additional devices. Therefore, natural convection heat sinks are widely used in application for which high reliability is required, and low performance may be tolerated. Two common types of natural convection heat sinks are plate-fin heat sinks and pin-fin heat sinks. Plate fin heat sinks are easy to design and fabricate, so they are widely used in application for which cost reduction is a main issue. Pin fin heat sinks have omnidirectional performance because of their geometric characteristics, so they are widely used in application for which heat sinks are used in various orientations [1-9]. Iyenger and bar-Cohen compared plate-fin heat sinks and pin-fin heat sinks that had been optimized using the least material method. In this method, the optimum fin thickness (or fin diameter for heat sinks) is determined when the fin height is given. Then, the optimum spacing between the adjacent fins is obtained by maximizing the amount of heat dissipated from the array for various value of the spacing. From their analytical results, they found that the optimized pin-fin heat sinks dissipate a larger amount of heat than to the optimized plate-fin heat sinks. However, there are some inherent limitation in the least-material method. This method is effective at reducing the mass of a single fin. But may not provide a mass-minimizing optimum design for the whole array of the heat sink. therefore, some different approaches are needed to compare the thermal performance per unit mass of both types of heat sink.
Heat dissipation is very important in the modern electronic industry, according to the statistical data, high temperature causes more than 55% failure of electronics. The heat sink is also used in other areas, for example, heat dissipation of DSC ( Dye-Sensitized Solar Cell) . The heat sink has different structures, and can be classified into active and passive types. Active cooling is usually realized by forcing the coolant to pass through an electronic component to take away the exhaust heat, whereas passive cooling utilizes natural convection and radiation heat transfer to dissipate the exhaust heat to ambient. Although active cooling yields a higher heat transfer rate, it require an additional pump or fan to drive the coolant flow, causing extra energy consumption and noise. In contrast, passive cooling is devoid of these issues and more reliable since no moving parts are involved. Compared to the active Heat sink, the passive heat sink dissipates thermal energy through the natural convection and usually it is made of aluminium finned radiator, so it has high reliability and low cost characters. The driving force in the passive heat sink is buoyancy force generated by temperature difference. The natural convection of heat sink can be divided into limited and infinite space convection according to the external space. Most of the passive heat sinks have simple structure and low cost character because of their straight fins. Elenbaas carried out the earliest investigation on natural convection heat transfer for a parallel fin heat sink, Bodoia and Osterle deduced a theoretical solution of the natural convection heat dissipation for the parallel vertical fin heat sink on the basis of theoretical analysis. Other researchers studied and optimised the geometrical dimensions of parallel fin heat sink, and gave out some formulas for calculating geometrical dimensions [14-20]. Heat dissipation performance of the parallel straight fin heat sink can be improved by increasing air turbulence between the fins, such as arranging staggered cylinders , drilling holes on base plate , opening slots  or drilling holes on the fins .
Light-emitting diode (LED) lights have recently attracted the attention of the illumination industry, due to their lower power consumption, longer life, and smaller, more durable structure compared to other light sources. However, their use presents a thermal problem, since about 70% of their total energy consumption is emitted as heat. An efficient heat sink design is essential to solve this lights, considering their overall advantages. However, natural convection heat sinks commonly have rectangular bases whereas LED lights are generally circular. It is therefore desirable to investigate natural convection heat transfer via a heat sink with a circular base. Starner and Mcmanus  experimentally investigated natural convection heat from four heat sinks of different dimensions, with the heat sinks oriented vertically, at a 45 degree angle , and horizontally Welling and Woolbridge  conducted an experimental study of vertically oriented rectangular fins of constant length attached to a vertical base. They found that there exists an optimal fin height, corresponding to a maximum rate of natural convection heat transfer, for any given fin spacing. However, most of these studies were concerned with heat sinks with rectangular bases, which might be inefficient for cooling circular LED lights.
Many techniques have been introduced in the past years to improve the efficiency of heat sink systems through natural convection heat transfer. Over the past recent years, a wide variety of designs have evolved to meet the rising heat dissipation demand. A number of studies concerning rectangular fins have been done from both applied and theoretical point of view, recently. Feng et al.  designed a new heat sink that is consisted of a number of long fins and a number of short fins arranged perpendicular, which aimed at maximizing free convection. Their outcomes showed 15% convective heat transfer enhancement, in comparison with plate-fin heat sink, without any overall volume/material usage augmentation, or extra exenses. Usually, the transfer of the generated heat to the heat sinks occurs through heat conduction, and dissipation of such heat to the environment is done through convection . To achieve a better heat sink design, different parameters as shape , size , material , inclination angle , flow regime (laminar, transitional, turbulence) [33-36], type of heat transfer (phase change, natural, forced or mixed convection) [37-39], and heat transfer rate  should be considered.
Natural convection heat transfer in a cross-fin heat sink
The design principle of the cross-fin heat sink was based on overcoming internal thermal fluid-flow defects in a conventional plate-fin heat sink. The thermal performance of the proposed heat sink was compared with a reference plate-fin heat sink in horizontal orientation. The study was initiated from an industrial project aiming to design a heat sink for thermal management of indoor small cells for communication. In this scenario, the device was hung from a ceiling and there was a gap of 20mm between the fin tip and the ceiling as shown in fig. 1.
Fig. 1. Schematic of a heat sink placed beneath the ceiling with a gap between the heat sink and ceiling. 
The objective was to reduce the temperature rise on the substrate of heat sink by 3-5 degree Celsius on top of a reference plate-fin heat sink for a given heat dissipation rate of 40 W. The dimensions of the reference plate-fin heat sink are shown in Fig. 2 (a). Overall dimensions of the heat sinks were 200 x 200 x 21 mm3 (length x width x height), with a height of 3 mm for the substrate and 18 mm for the fins. The thickness of each fin was 2 mm. The number of the plate-fins were claimed to be optimized in engineering conditions by the manufacturer, yielding an inter fin spacing of 10.38 mm. Fig. 2(b) shows geometrical notations of the proposed cross-fin heat sink, which included a series of parallel long fins as well as short fins perpendicularly arranged with respect to the long fins. The long fins in the cross-fin heat sink had the same length as the reference plate-fin heat sink (200 mm), while the length of the short fins in the cross-fin heat sink was 50 mm .
Fig. 2. Schematic of (a) conventional plate-fin heat sink and (b) proposed cross-fin heat sink.
Natural convection and radiation heat transfer of cross-fin heat sink and its counterpart plate-fin heat sink was simulated with varying heat inputs from 20 to 60 W. A heat input over 60W resulted in the chip temperature higher than 100 degree Celsius for the heat sinks investigated in the study, which was not practical and should be avoided. Thermal fluid-flow distributions in the two heat sinks were analyzed to explore the merits of the cross-fin heat sink. The velocity and temperature distributions in the long channel of cross-fin heat sink are similar to those in plate-fin heat sink. However, surprisingly, for the short fins the fresh air is able to invade the entire fin channel, thereby yielding a higher average heat transfer rate on the short fins than on the long fins. The flow entering the short fin channel eventually impinges toward the endwall of the channel, i.e., the long fin that intersects with the short fins. The impingement flow should cause a higher local heat transfer rate than parallel flow, thus providing another advantage of the cross-fin heat sink for heat transfer enhancement.
Fig. 3. Thermal performance comparison between plate- and cross-fin heat sinks:
(a) overall heat transfer coefficient considering both convection and radiation; (b) convective heat transfer coefficient .
Fig. 3 (a) and (b) compare the overall and convective heat transfer coefficients of the proposed cross-fin heat sink with those of the conventional plate-fin heat sink, respectively. Radiation heat transfer in the two heat sinks is similar, and hence heat transfer enhancement due to cross-fins is contributed mainly by improved thermal fluid-flow within the heat sink. For plate-fin heat sink, the results showed that cold air only can penetrate a limited distance into the fin channel from heat sink entrance, thus causing inferior thermal efficiency at heat sink centre. For cross-fin heat sink, the cold air was able to reach to the entire short fin channel and formed an impinging-like flow towards channel endwall, which was beneficial for heat transfer enhancement. Compared to plate-fin heat sink, the overall and convective heat transfer coefficients of cross-fin heat sink were increased by 11% and 15%, respectively. Such performance enhancement was mainly attributed to improved thermo-fluidic flow pattern in the cross-fin heat sink, as radiation contributions of the two heat sinks were similar. The concept of cross-fin opens a door to improve natural convective heat transfer in limited space without increasing material consumption and too much extra manufacture cost. 
Natural convection heat transfer in a straight-fin heat sink
Most of the studies are all conducted with the horizontal or vertical heat sink, nevertheless, the influence of the heat sink mounting angle on heat dissipation is rarely mentioned. Based on Mehrtash's research results, Tari et al.  developed a nusselt number formula, and found that the fin spacing is an important parameter affecting heat sink thermal performance. Shen et al.  investigated heat dissipation properties of the heat sinks placed in 8 different directions, and discovered that the denser the fin arrangement , the more sensitivity the directionality. There are two main factors limiting the sink natural convection heat dissipation, one is that the heat transfer does not match with natural convection flow, and the other one is that the convection between the fins is blocked. The influence of heat sink mounting angle on its heat dissipation is investigated. A test rig is studied heat dissipation performance of a heat sink at different mounting angles. A special support is designed to ensure the heat sink could rotate 360 degree freely, as shown in Fig. 4. The heat sink and heating plate are fastened by bolts to reduce the contact thermal resistance and prevent the relative displacement between them.
Fig. 4. Schematic of support.
Heat sink has a length of 150mm, width of 76mm, base thickness of 5mm, fin height of 50mm, fin thickness of 3 mm, fins pitch of 9.17mm and number of fins is 7. Coating thermal grease evenly on the heat sink bottom before fixing it to the heating substrate with screws. Adjusting the mounting angle of the heat sink to a certain angle, and then checking the output voltage of DC power supply to insure the constant heating power. The data of each measuring point are to be collected after the heat sink begin to be heated. The equilibrium between heating and dissipation is reached as the maximum temperature fluctuate on the bottom surface of the heat sink substrate is less than 0.5 degree Celsius within 20 min.
Temperature diffusion of heat sink
The fin bottom temperatures are almost same, but the surface temperatures are different. The surface temperature at the heat sink centre is obviously higher than those near the heatsink edge. As shown in Fig. 5, the temperature distributions of the heat sink fin and bottom are not uniform whether the mounting angle is 0 degree or 45 degree. At the mounting angle of 0 degree, the highest temperature appears at the heat sink centre while the lowest temperature happens at the fin corner. The fin temperature in the middle of the heatsink is always higher than the others. Compared with the mounting angle of 0 degree, the highest temperature zone moves to the fin end edge at the mounting angle of 45 degree.
Fig. 7. Temperature contours of fin and bottom of heat sink with mounting angles 0 degree and 45 degree. 
Effect of heating power on heat transfer coefficient
It is studied that the variation of simulation data is similar to that of experiment results. The maximum error between them is about 10.5% which is acceptable. Heat transfer coefficient increases rapidly with the heating power when the heating power is below 50 W as shown in fig. 8, but it increases moderately when the heating power is over 50 W. The heat transfer driving force in the heat sink is the air flow, the air will get more heat from the heat sink as the heating power increases, and its flow velocity will increases as well, so the heat transfer coefficient becomes higher. The air flow resistance, however, will increase with the velocity, therefore the increase rate of heat transfer coefficient will decrease synchronously.
Fig. 8. Experimental and simulation results of heat transfer coefficient.
The location of red zone is just at the corner of the fin when the mounting angle is 30 degree, so cutting this corner would decrease thermal resistance, this will confirm the inference that the heat transfer stagnation zone is the main aspect to affect the heat sink performance. Another reason for cutting this corner is that there is less influence on original air flow. Due to the cutting of the corner thermal resistance reduces about 2.64–3.77% at heating power of 50W and 6.00–10.13% at heating power of 80 W. The heat transfer coefficient increases about 7.30–10.77% at heating power of 50W and 11.46–17.07% at heating power of 80 W. The variations of thermal resistance at the mounting angles of 0 degree, 15 degree and 30 degree are smaller than those under other mounting angles. The heat sink performance is the worst at the mounting angle of 15 degree, and the best performance happens at the angle of 90 degree. The heat transfer stagnation zone is identified where the temperature difference is less than 2 degree Celsius in this study. The heat transfer stagnation zone area reaches the maximum when the mounting angle is 15 degree, that leads to the lowest performance because the effective heat dissipation area of the heatsink is the smallest. This is verified by cutting the corner portion of the heat sink where is the heat transfer stagnation zone. The heat transfer could be enhanced by cutting appropriate corner of the heat sink, the thermal resistance reduces 2.64–3.77% at heating power of 50W and 6.00–10.13% at heating power of 80 W, and heat transfer coefficient increases 7.30–10.77% at heating power of 50W and 11.46–17.07% at heating power of 80 W .
Natural convection heat transfer in a radial heat sink
An abrupt increase in the temperature of the LED chip results in a sharply reduced lifetime and considerably lower light emission efficiency. Studies have shown that 60% of the input power to the LED is converted into thermal energy, as evidenced by the high heat flux. Therefore, it is necessary to cool the LED system sufficiently for stable light emission. Fig. 9 shows a radial heat sink consisting of a circular base and rectangular fins. The fins were arranged radially at regular intervals. The heat sink base was oriented horizontally. The heat sink was made of aluminium. The effects of the number of fins, fin length, fin height, and heat flux on the thermal resistance and the heat transfer coefficient. Fig, 9 : n = 20, outer radius = 75 mm, L = 55 mm, H = 21.3 mm, t = 2 mm, and q = 700W/m2.
Fig. 9. Radial heat sink with a circular base and rectangular fins .
There are two flows, i.e., vertical and horizontal flows, around the radial heat sink. The vertical flow is in the upward direction, since air is heated by the heat sink (which is maintained at a higher temperature) and becomes lighter than the surrounding air. The horizontal flow is created by air entering from outside the heat sink to make up for the vertical flow in the inner region. Therefore, the overall flow pattern is chimney-like. The temperature of heat sink maintains almost uniformly high because of high conductivity of aluminium. The heat transfer rate in the outer region of the heat sink was higher than in the inner region. This was because the temperature difference between the air and the heat sink decreased as the cool air proceeded towards the inner region of the heat sink .
Effect on radial heat sink
The effect of the number of fins : The average heat transfer coefficient decreased as the number of fins increased, since the flow rate of the cooler air entering the spaces between the fins decreased and the air was heated more quickly on account of the reduced space between fins. However, when the number of fins was less than 36, the thermal resistance of the heat sink decreased with increasing n, since the effect of the increased heat transfer surface area was larger than the effect of the decreased heat transfer coefficient. When the number of fins was greater than 36, the thermal resistance of the heat sink increased with increasing n, since the heat transfer coefficient was very small. Consequently, there exists optimum number of fins that gives the minimum thermal resistance.
The effect of the fin length : As the fin length increased, the thermal resistance and average heat transfer coefficient decreased. The thermal resistance leveled off and reached a steady value when the fin was longer than 55 mm. This was because the air temperature in the inner region was almost the same as the heat sink temperature, and hence any additional fin length beyond 55 mm did not contribute to the heat transfer rate.
The effect of the fin height : A lower thermal resistance resulted from the increased heat transfer surface area created by the incremented fin height. However, the change in the heat transfer coefficient was relatively small, since the velocity of the air entering from outside increased very little with increasing fin height.
The effect of the heat flux applied to the heat sink base. The decrease in thermal resistance due to increasing heat flux resulted in a greater rising air velocity, which in turn increased the flow rate of the cooler air entering from outside. Accordingly, the average heat transfer coefficient increased almost linearly, thanks to the enhanced effect of natural convection.