1.
Introduction
With the rapid development of electronic technology, heat flux per unit area increases dramatically as the components size shrinks. Therefore, heat dissipation becomes an important issue for electronics cooling. There are a number of methods in electronics cooling, such as jet impingement cooling, heat pipe, and heat sink[1]. Conventional electronics cooling normally used air cooling with heat sink such as LED heat sinks. Natural convective cooling heat sinks are one of the main cooling techniques to solve the LED heat dissipation problem due to their cheap unit price, simplicity and high reliability[2].
Radial heat sinks have been researched widely in recent years due to the special need on LED design. There are three kinds of radial heat sinks. One is an externally finned heat sink where the heat sources are located on the bottom surface of the heat sink base. Many researchers have studied this kind of heat sink[3–6]; in this case, the heat sink is composed of fins and base. Another is an externally finned heat sink where the heat sources are located on the inter surface of the heat sink[7, 8]. The other is an internally finned heat sink where the heat sources are located on the outer surface of the heat sink and the fins cannot be directly attached to the outside[9, 10].
The aforementioned internally finned heat sinks were studied subject to forced convection, while studies proposed for internally finned heat sinks in natural convection are limited. However, internally finned heat sinks have been proved to yield significant heat transfer enhancements in natural convection[11, 12]. Joo and Kim[13] optimized internally finned heat sinks in natural convection analytically and experimentally. They developed a correlation of the heat transfer coefficient, which is expressed in terms of fin thickness, fin height, and fin number. However, the optimum diameter and overall height were not studied in their work. In addition, they investigated thermal performances of internally finned heat sinks only based on the vertical direction, while the thermal performances of heat sinks on the horizontal direction were not considered.
In the present study, we investigate thermal performances of internally finned heat sinks in natural convection comparing with the thermal performance of externally finned heat sinks. Diameter analysis of internally finned heat sinks has been studied in order to find an optimal diameter ratio. Thermal performances of heat sinks which have different diameter and overall height are investigated. Flow characteristics and heat transfer coefficient with respect to the installation direction of heat sinks are analyzed. Finally, the weight comparison between a perforated cylinder heat sink and an imperforated heat sink is studied.
2.
Study method
2.1
Comparison of two types of heat sinks
The schematic diagrams of externally and internally finned radial heat sinks are shown in Fig. 1. Two kinds of radial heat sinks are composed of a cylinder and fins. The same fin geometry is used when comparing thermal performances of heat sinks, which means the size of fin height, fin length, and fin thickness are the same. The fin height, fin thickness, fin number and fin length are denoted as H, tf (2 mm), N (14) and L (10 mm), respectively; the overall diameter of the internally finned heat sink is denoted as Di; the overall diameter of the externally finned heat sink is calculated as: De + L; the overall height of the cylinder is H; the thickness of the cylinder is tc (5 mm). Heat sinks are made of 6061 T6 aluminum alloy of which the thermal conductivity is 167 W/(m·K). The fins were circumferentially arranged at constant intervals.
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Figure1.
(Color online) (a) Externally and (b) internally finned heat sinks.
2.2
Diameter analysis
To analyze the effect of cylinder diameter on the thermal performance of internally finned heat sinks, numerical study is performed by increasing the cylinder diameter from 40 to 100 mm; nevertheless, the external volume of heat sinks are constant regarding the heat sink (D = 60 mm, H = 60 mm) as a benchmark. This means that the cylinder height decreases as the cylinder diameter increases. The overall heights of other heat sinks are calculated as follows:
$$V = {V_{{ m typeD}}}, $$  | (1) |
$$pi {D^2}H = pi {D_{{ m typeD}}}^2{H_{{ m typeD}}}.$$  | (2) |
When the cylinder diameter of the heat sink ranges from 40 to 100 mm, the cylinder height is estimated as shown in Table 1, which keeps one decimal place by using the rounding-off method.
| Type | D (mm) | H (mm) | ε | ||
| A | 40 | 135 | 0.30 | ||
| B | 50 | 86.4 | 0.58 | ||
| C | 60 | 60 | 1.00 | ||
| D | 70 | 44.1 | 1.59 | ||
| E | 80 | 33.8 | 2.37 | ||
| F | 90 | 26.7 | 3.37 | ||
| G | 100 | 21.6 | 4.63 |
Table1.
Diameter and overall height of internally finned heat sinks.
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| Type | D (mm) | H (mm) | ε | ||
| A | 40 | 135 | 0.30 | ||
| B | 50 | 86.4 | 0.58 | ||
| C | 60 | 60 | 1.00 | ||
| D | 70 | 44.1 | 1.59 | ||
| E | 80 | 33.8 | 2.37 | ||
| F | 90 | 26.7 | 3.37 | ||
| G | 100 | 21.6 | 4.63 |
The relationship between the cylinder diameter and height of internally finned heat sinks can be non-dimensionalized as the parameter: diameter ratio factor (ε), which is defined as follows.
$$varepsilon = frac{D}{H}.$$  | (3) |
2.3
Perforated cylinder heat sink
In this study, a novel and efficient internally finned heat sink is proposed as shown as Fig. 2(a). The difference from the aforementioned internally finned heat sink is that circumferentially arranged channels are generated in the cylinder. Channels are arranged in two lines; the height of the channel is 20 mm; the width of the channel is 2 mm. The effect of installation direction with respect to gravity is studied. Three installation directions: vertical, incline (45 °C), and horizontal are considered as shown in Fig. 2(b).
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Figure2.
(Color online) Numerical models of perforated cylinder heat sinks. (a) A perforated cylinder heat sink (D = 60 mm, H = 60 mm). (b) Three installation directions of heat sinks.
2.4
Governing equation and boundary condition
The numerical study was conducted by ICEPAK in ANSYS based on the finite volume method (FVM). The governing equations for the present numerical study are given as follows:
Continuity equation:
$$nabla cdot ( ho { V}) = 0.$$  | (4) |
Momentum equation:
$$nabla cdot ( ho u { V} ) = - frac{{partial p}}{{partial x}} + mu {nabla ^2}u, $$  | (5) |
$$nabla cdot ( ho nu { V}) = - frac{{partial p}}{{partial x}} + mu {nabla ^2}nu, $$  | (6) |
$$nabla cdot ( ho wmathop { V}) = - frac{{partial p}}{{partial x}} + mu {nabla ^2}w - ho g. $$  | (7) |
Energy equation:
$$nabla cdot ( ho mathop { V}) = frac{k}{{{c_v}}}{nabla ^2}T + S, $$  | (8) |
where S is the source term for radiation heat transfer, which is calculated using the discrete ordinates method[14]. In the case of the internally finned heat sink, a constant heat flux was applied to the external surface of the cylinder; in the case of the externally finned heat sink, it was applied to the internal surface of the cylinder. The heat conduction obeys Fourier’s heat conduction law. The pressure of the computation domain are set to be the atmospheric pressure (= 1 atm) and the ambient temperature is set to be 20 °C. The bottom surface of the computational domain was set as a wall where no mass or heat transfer occurs to imitate the actual installation environment, while other surfaces were openings in order to take into account the natural convection through the domain boundaries. The assumptions for the numerical analysis are as follows: the flow is three-dimensional, steady, and laminar; the air is an ideal gas.
The computational domain is set to range six times larger than the heat sink volume to ensure that the effect of the computational domain size on the result is negligible. Grid independence was performed by increasing the number of grid points from 38421 to 256577. The estimated temperature solution shows that 130 181 is a large-enough grid number since the additional grid points produced a change of less than 0.5% in the maximum temperature of the heat sink, as shown in Fig. 3(a). The temperature field around the internally finned heat sink (D = 60 mm) for the selected numerical case is shown in Fig. 3(b) when the heat transfer rate is 15 W.
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Figure3.
(Color online) Numerical results for grid test. (a) Maximum temperature versus grid number. (b) Temperature field.
2.5
Experiment and validation
Experimental studies were carried out to validate the numerical results. The schematic diagram of the experimental apparatus is shown in Fig. 4. The experimental apparatus consists of the test section with an internally finned heat sink, DC power supply (Agilent N5767A), and data acquisition system (Agilent 34972A) as shown. The heat sink is mounted in cylindrical Bakelite for fixation and insulation. The DC power supply transfers thermal energy to a circular film heater which is located on the outer surface of the heat sink. Thermal grease is applied between the outer surface of the heat sink and the film to minimize the thermal contact resistance. The geometry and material of the heat sink are set to be the same as those of the numerical study. Four J-type thermocouples circuits are connected to the data acquisition system to measure the maximum temperature. As illustrated in Figure, three thermocouples are attached at one side of the outer surface of the heat sink, and one thermocouple is attached at the other side to estimate the average temperature. The ambient temperature is controlled to 20 °C. The heat loss through the Bakelite test section can be estimated by following the previous work[4].
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Figure4.
(Color online) Schematic diagram of the experimental setup.
3.
Results and discussion
3.1
Comparison result
Fig. 5 shows a comparative plot of the maximum temperature of the externally finned heat sink and internally finned heat sink when overall diameters of heat sinks are 60 mm at the vertical direction. The maximum temperatures of two kinds of heat sink both increase as the heat transfer rate increases. The internally finned heat sink has better thermal performance than the externally finned heat sink. The temperature difference between two heat sinks increases as the heat transfer rate increases. The calculation result indicates that the internally finned heat sink enhances the thermal performance by up to 20.25% compared with the externally finned heat sink. As shown in this figure, numerical predictions match well with the experimental results, within the maximum error of 5%. This implies that the present numerical model can predict the cylinder heat sink well.
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Figure5.
Comparison of the maximum temperature.
Cut plane plots of the velocity field of two kinds of heat sinks are shown in Fig. 6 subject to different heat transfer rates. Fig. 6(a) shows the velocity field of the externally finned heat sink; Fig. 6(b) shows the velocity field of the internally finned heat sink. The plots indicate that air flows quicker at the high heat transfer rate condition than that at the low heat transfer condition. In the case of the externally finned heat sink, the heat source is attached on the interface of the cylinder, leading to no air flowing in the center section; the air flows along the outer fins, velocity shows a high value near the top of the fins, while it has a lower value near the bottom of the fins. Conversely, in the case of the internally finned heat sink, the heat source is attached on the outer surface of the cylinder, leading to air flowing smoothly in the inner section. The natural convection flow quickly enters the bottom of the cylinder due to the “chimney effect”; the upward flow is slow thereafter. This is why the temperature at the heat sink’s upper part is higher than that at the lower part, as illustrated in Fig. 3(b).
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Figure6.
(Color online) Velocity magnitude comparison between heat sinks ((a) Externally finned heat sinks. (b) Internally finned heat sinks.).
3.2
Parametric analysis and result
A parametric study was conducted to examine the influence of cylinder diameter and height on the thermal performance in the case of the internally finned heat sink. The relationship between the cylinder diameter and height of internally finned heat sinks was non-dimensionalized as the diameter ratio factor parameter. Fig. 7 illustrates the influence of diameter ratio on the maximum temperature of heat sink. As shown in the figure, the maximum temperature varies markedly in ranges of 0.3 to 4.63 for the diameter ratio. Therefore, cylinder diameter and height have significant effects on the thermal performance of the internally finned heat sink. The maximum temperature decreases as the diameter ratio increases from 0.3 to 1.59; then, it increases as the diameter ratio increases thereafter. It can be concluded that internally finned heat sinks have an optimal diameter ratio. In this study, the internally finned heat sink has the best thermal performance when the diameter ratio is 1.59.
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Figure7.
Maximum temperature variation by diameter ratio factor.
Fig. 8(a) shows the numerically-estimated heat transfer coefficients of the perforated cylinder heat sink and the imperforated cylinder heat sink versus the heat transfer rate at the vertical installation direction. As shown in this figure, the heat transfer coefficient increases as the heat transfer rate increases. This is coincident with Newton’s law of cooling, and is due to the fact that the heat transfer coefficient is proportional to the heat transfer rate. The effect of channels in the cylinder on the thermal performance is illustrated as well. The heat sink with a perforated cylinder (in other words, the cylinder has channels) dissipates heat more efficiently comparing with the heat sink, which has an imperforated cylinder.
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Figure8.
(Color online) (a) Comparison of heat transfer coefficient between perforated and imperforated cylinder heat sinks. (b) Heat transfer coefficients comparison at different directions.
Heat transfer coefficients of heat sinks were investigated at different installation directions, and the numerically-estimated results are shown in Fig. 8(b). As shown, heat sinks with the perforated cylinder obviously have better thermal performance than those with the imperforated cylinder at any installation direction. This can be attributed to the unhindered natural convective flow through the cylinder. The heat transfer coefficient is relatively sensitive to the installation direction. A clear presentation for the installation direction effect on the heat transfer coefficient shown in this figure indicates that heat sinks at the vertical direction lead to the best thermal performance, while the incline direction is subsequent, and the horizontal direction is the worst. The result shows that the heat transfer coefficient of the perforated cylinder heat sink is higher than that of the imperforated cylinder heat sink by up to 34% at the horizontal direction when Q is 20 W.
The results obtained in Fig. 8 are demonstrated by illustrating the flow characteristics around heat sinks. Fig. 9 shows the natural convective flow characteristics of heat sinks at vertical and horizontal directions. In Fig. 9, (a) is the imperforated cylinder heat sink and (b) is the perforated cylinder heat sink. Natural convective flows of heat sinks at the vertical direction are quicker than those at the horizontal direction. Heat sinks with the perforated cylinder have the advantage that the air can easily flow through the channels, which then enters the cylinder inside by the buoyancy effect from any direction, leading to more efficient heat exchange. However, in the case of the imperforated cylinder heat sink, natural convective flow flows from the cylinder bottom to the top, which nevertheless is prevented at the middle part of the cylinder by the existence of the solid surface, especially at the horizontal direction.
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Figure9.
(Color online) Air flow characteristics comparison between (a) imperforated and (b) perforated heat sinks.
A mass reduction parameter, which was proposed in reference[15], is used to characterize the thermal performance of heat sinks in this work. The mass reduction is defined as follows:
$$theta = frac{{{M_{{ m{imperforated}}}} - {M_{{ m{perforated}}}}}}{{{M_{{ m{imperforated}}}}}}, $$  | (9) |
where θ is the mass reduction factor, and M is the total mass of heat sink, which is equal to the product of the density of aluminum and the total volume. The total mass of a perforated cylinder heat sink was shown to be less than that of an imperforated cylinder heat sink by up to 13%.
4.
Conclusion
In this study, numerical studies are performed on the natural convective heat transfer from internally and externally finned radial heat sinks. The present numerical model can predict the cylinder heat sink well, within the maximum error of 5%. The results indicate that internally finned heat sinks have better thermal performance than externally finned heat sinks. In the case of the internally finned heat sink, it has an optimum diameter ratio. The optimized internally finned heat sink enhances the thermal performance by up to 20% compared with the externally finned heat sinks, while reducing the mass of heat sink. In addition, it is important to note that the installation direction affects the thermal performance of the heat sink significantly. The results show that heat sinks at the vertical direction have the best thermal performance, while heat sinks at the horizontal direction have the worst thermal performance. This study provides an effective reference for heat sink design and application.
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Nomenclature
