Combined convection and radiation heat transfer of

International Journal of Heat and Mass Transfer 80 (2015) 411–423

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Combined convection and radiation heat transfer of the radially finned heat sink with a built-in motor fan and multiple vertical passages Tzer-Ming Jeng ⇑ Department of Mechanical Engineering, Chienkuo Technology University, 500 Changhua, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 29 May 2014 Received in revised form 19 September 2014 Accepted 19 September 2014

Keywords: Finned heat sink Motor fan Vertical passages Heat transfer Experiment

a b s t r a c t This work proposed a novel finned heat sink with the air-driving device and vertical flow passages for LED lamp. The heat sink, made of aluminum alloy, was a cup-shaped cylinder with multiple externally radial fins. Various motor fans were mounted in the hollow chamber of the heat sink. Coupling with the multiple vertical passages in the ring wall of the heat sink and the separation board in the chamber of the heat sink, the air flow was driven through the internal of the heat sink. The measured air velocity within the vertical passages and the smoke flow visualization demonstrated that the present air-driving device did work. The heat-transfer experiments for the systems with the built-in motor fan and compressed air flow were performed, respectively. The overall heat transfer mechanism of the present cooling device was the combination of the internally forced convection and the externally natural convection coupling with radiation heat transfer. The overall Nusselt number of the heat sink with the built-in motor fan was 28–102% higher than that without motor fan. In general, bigger motor fan drove more air flow to enhance heat transfer. Finally, a theoretically empirical formula was proposed to predict the Nusselt numbers of the present combined convection and radiation heat transfer. The applied range was Grashof number Gr = 2.37 105–5.92 105 and Reynolds number Re 5 343. The maximum deviation of the total Nusselt number between the predictions and the experimental data of the system with compressed air flow was ±11%. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction About 85% consumption of electric power of the light-emitting diodes (LEDs) is converted to waste heat. If the waste heat is not effectively dissipated, high temperatures will cause the LED light failure and shorten the lifetime of use. The waste heat of LEDs is generally transferred from the LED substrate to the fined heat sink via thermal conduction, and then carried away from the fins by the air-flow thermal convection. Two cooling mechanisms of thermal convection are often used. One is using the temperature difference between the high-temperature fins and the ambient to generate the passive cooling of natural convection whose advantages are no additional power element required, high reliability and energy saving; the other is employing the air-driven device to lead the active cooling of forced convection, which is especially suitable for high power LEDs. In the assembly of the current LED heat sink, to facilitate the process, LED is welded to the printed circuit board (PCB) of the glass substrate (FR4), which is attached to a metal

⇑ Tel.: +886 4 7111111x3130; fax: +886 4 7357193. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.043 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

plate. The metal of high thermal conductivity such as aluminum or copper can help in dissipate heat. This is the Metal Core PCB (MCPCB) of high thermal conductivity. The main purpose of MCPCB is to uniformly spread the highly concentrated heat generated from LEDs, to increase the contact area with the air, so that the junction temperature of LEDs can drop quickly. However, for LEDs of growing power, MCPCB alone is unable to meet cooling requirements because the local ultrahigh heat flux generated from high power LED cannot be uniformly dispersed by the conventional thermal conductive plate, in addition to the insufficient spreader heat dispersing area. Therefore, as shown in Fig. 1, highly efficient spreader and heat sink are installed on MCPCB to uniformly disperse the heat and significantly increase the contact area of per unit volume with air, so that heat conduction and heat convection will be more sophisticated to get better heat dissipation. Many studies have adopted the heat pipes, such as loop heat pipes and vapor chamber plates, to be the highly efficient spreaders of LEDs. Shen et al. [1] developed a high-intensity LED headlight to replace the traditional high-pressure mercury headlight as autonomous underwater vehicle lighting. Their study presented a self-adjusting micro vapor chamber to reduce the high

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Nomenclature A d Cp D Din F^ Gr GrDin h H1 Hf I k n Nu Q Qflow Re ReDin T T 0 T⁄⁄ 0 T⁄⁄⁄ 0 V

surface area (m2) diameter of vertical passages (m) specific heat (W/kg/°C) diameter of film heater (m) inner diameter of cylindrical chamber of heat sink (m) effective radiation view factor of all exposed surface of heat sink Grashof number, Eq. (1) Grashof number, Eq. (10d) heat transfer coefficient (W/m2/°C) length of vertical passages (m) vertical length of fins or height of heat sink (m) input current (A) thermal conductivity (W/m/°C) umber of vertical passages average Nusselt number, Eq. (3) heat (W) volumetric air flow rate (m3/s) Reynolds number, Eq. (2) jet Reynolds number of the region b, Eq. (10d) temperature (°C) the bulk mean temperature of air through the region a the bulk mean temperature of air through the region b the bulk mean temperature of air through the region c input voltage (V) or air velocity in the vertical passage (m/s)

consumption of heat by 100 W/cm2, the use of composite moisturizing structures to improve the moisturizing efficiency of the micro-device inside the vapor chamber. Therefore, vapor chamber is able to maintain the original heat transfer capability and its gravitational effects can be reduced. Lu et al. [2] used the flat heat pipe to improve the cooling of high-power LED and conducted a series of experiments to investigate the heat transfer characteristics. That study pointed out that the performance of flat heat pipe is affected by the placement angle of inclination. Wang [3] experimentally and theoretically explored the heat transfer performances of three LED substrates. He found that the heat-transfer capacity of the vapor chamber plate is better than that of the copper or aluminum substrate when the input power is higher than 5 W. Xiang et al. [4] developed a new phase-change heat sink for high-power LED lamps. Its three-dimensional structure consists of the circumambient spiral micro grooves and the radial micro grooves. It can help to the phase-change refrigerant to evaporate by heat while circulating refrigerant is powered by the siphon force provided by the sintered copper-beads wick on the inners surface of the heat sink. Lin et al. [5] experimentally investigated the heat transfer characteristics of aluminum flat heat pipe, using acetone

Finned heat sink

High-performance spreader

Aluminum base plate MCPCB Printed circuit board (PCB) Heat source (LEDs)

Fig. 1. Schematic diagram of cooling-device model for LEDs.

Greek symbols r Stefan-Boltzmann constant [W/m2/K4] g fin efficiency Subscripts 0 the ambient environment 1 the first path (internal cooling path) 2 the second path (external cooling path) a region a (the vertical inlet passages of heat sink) b region b (the cylindrical chamber of heat sink) c region c (the vertical outlet passages of heat sink) ext external surface of heat sink fc forced convection heat heating surface Loss heat loss nc natural convection plate horizontal plate rd radiation s solid part of the heat sink t total vp vertical plate w heating wall

as the working fluid in the heat pipe. The heat pipes are arranged on the plane in a zigzag way to form a serially connected structure of a number of sharp 180-degree turns. At both sides of the plane, it is connected with the condenser and evaporator. That study indicated that an increase in the cross-sectional area and the number of turns of the internal passage can improve the heat transfer capability. Hsieh et al. [6] designed a flat heat pipe of mixed siphon structure of wick and copper mesh layer as the cooling device for the LED lamp. They found that this flat heat pipe can reduce the LED junction temperature by 28%, and make the LED substrate temperature uniform. Dehuai et al. [7] used the phase-change heat sink to improve the cooling of high power LED by developing 3D integral-fin boiling structures. Inside the micro grooves, there are two different fin structures. The cooling characteristics of using them in high power LED were analyzed. Wang [8] explored the possibility of integrating high power LED with thermoelectric generator for waste heat recovery. That study combined the vapor chamber plate with LED PCB substrate to increase the heat transfer. The result suggested that the combination could help heat transfer performance, illumination and thermoelectric conversion. Lin et al. [9] experimentally discussed the performance of applying the loop heat pipe of dual parallel condensers in high power LED. The loop heat pipe, under the operating conditions of natural convection, can get the thermal resistance from 1.0 to 0.4 °C/W with thermal load ranging from 30 W to 300 W. The heat transfer studies of LED heat sink can be divided into natural convection [10–20] and forced convection [21–27] by heat convection mechanism. LED cooling is the coupled heat transfer of heat conduction and heat convection. For natural convection, heat sink type, material and the direction of placement have a significant impact on the overall heat transfer performance. Yung et al. [10] analyzed the effect of placement angle on the natural convection heat transfer of high power LED packaged on PCB, and found that it is an important factor affecting heat transfer. Shyu et al.


[11,12] studied the natural convection heat transfer characteristics of aluminum finned heat sink with outer shell for different input power and placement angles, and found that the spacing between the outer shell and heat sink in the range of 5 mm to 10 mm can have a significant heat transfer impact. The increase in placement angle can reduce the heat transfer capabilities and make the outer shell spacing effect more significant. Jang et al. [13] numerically tested the heat transfer characteristics of the radially arranged pin–fin heat sinks with consideration of the natural convection and radiation heat transfer. According to the simulation results, the number and length of the pin fins have the significant impact on the overall heat transfer capability. Ji and Moon [14] observed the impact of input current on the equivalent thermal resistance of LED in natural convection, and found that they are positively correlated. However, the impact on the increase in equivalent thermal resistance is quite limited when the input current is above 100 mA. Yang et al. [15] discussed the impact of LED heat sink on thermal resistance by using different finned heat sinks including metal fins, metal-foam fins, carbon-foam fins. The results showed that the heat sink of carbon-foam fin embedded in the metal plate has the minimum thermal resistance, followed by pure carbon finned heat sink and the metal-foam finned heat sink. Yang et al. [16] manufactured the LED graphite heat sink with microsized graphite powders, metal powders and resins mixed in specific ratios by using the vacuum casting, vacuum pressure casting and rapid die technology. They also investigated the heat transfer characteristics of such heat sink by CFD numerical simulation and experimental measurement. Their results showed that the heat dissipation of LED device could be removed by natural convection within acceptable range. It suggested the low-cost and light-weight advantages of the LED graphite heat sinks as compared with the aluminum-alloy heat sinks. Jeng et al. [17] experimentally investigated the free convection heat transfer of the annular metal-foam heat sinks used for LED lamps. Their results showed that the heat transfer coefficient increased firstly and then decreased as the thickness of metal foams increased. Li et al. [18] experimentally explored the material effect of heat sinks of LED lamps on the heat transfer and illumination characteristics under the free convection condition. They indicated that the heat-transfer capacity of the pure aluminum-alloy heat sink was better than those of the composite-graphite heat sinks. However, the cost and weight of the composite-graphite heat sinks were reduced much more by comparing with those of the pure aluminum-alloy heat sink. Besides, the illuminations of their test heat sinks were similar after 2000-h lighting continuously. Jang et al. [19,20] numerically discussed the use of radially arranged pin–fin heat sink for cooling of the LED lamp in natural convection and radiation heat transfer. According to the findings of the study, if the number and length of the radially arranged pin fins of the heat sink are changed, the impact of the heat sink placement direction will have a more significant impact on thermal and fluid flow characteristics. The fin width is not a sensitive factor to the placement direction. In addition, the fin-height profiles of pin–fin array form a specific three-dimensional chimney flow, and the impact factors include the height difference of the fin array of the outer ring and the number of fins. In case of the forced convection heat transfer, besides the type and material of heat sink, different cooling fluids and methods such as water cooling, air cooling and ion wind have a significant impact on cooling performance. Wan et al. [21] numerically explored the forced convection heat transfer mechanism of the porous medium heat sink used in LED cooling. Their porous medium heat sink used the micro pump to drive sufficient water flow to cool the high power LED. Cheng et al. [22] used the finite element method to simulate the cooling of the finned heat sink coupled with fan on LED’s MCPCB for the reference in relevant cooling designs. Jeong

413

et al. [23] experimentally observed the performance of a liquidcooling heat-removed device. The device includes a hot plate, a cold plate, a chamber of working fluid and an activator. The study installed the device in between LED substrate and heat sink to understand the feasibility of the actual application. Bladimir et al. [24] numerically explored the possibility of applying the active liquid cooling device with micro passages in the thermal management of high power LED array. That study indicated that the proposed micro-passage liquid cooling device can be more effective than the micro-spray cooling device in dispersing the waste energy of the high power LED. Chen et al. [25] adopted the ion wind to strengthen the heat transfer of LED on substrate. In the range of their test voltage, it can maximally reduce thermal resistance by half. The study argued that the vertical and horizontal distances between the needle electrode and the grounding electrode as well as the type of the grounding electrode have an impact on ion wind. Maaspuro and Tuominen [26] used the finite element method software to simulate the 3D temperature field of 15 W LED. The cooling types include external natural convection and forced convection. Tzeng and Jeng [27] proposed a cooling device made of fan, rectangular channel and pin–fin array for LED lamp. They measured the end-wall heat transfer coefficient of in-line arranged square pin–fin array in such device, and indicated that the average Nusselt number with square pin fins was 1.46–2.58 times of that without any square pin fin. Besides, the pin–fin array with the medium longitudinal spacing had the maximum heat transfer enhancement. Faranda et al. [28] experimentally observed the impact of a refrigerating liquid prototype on LED cooling and illumination and suggested that increase of the refrigerating liquid can reduce LED junction temperature. This study proposed the design and production of ‘‘the novel finned heat sink with air-driven device and air-flow passages for LED lamp’’. The concept is to develop an active cooling device suitable for high power LED lamp by using a small motor fan coupled with the vertical flow passages and separation board of the aluminum-alloy radially finned heat sink. Under the same volume specification, the proposed design should be able to meet the cooling demand of higher-power LED lamp to achieve longer service life. In the case of the same power consumption, the overall size of the LED lamp will be more condensed. To the best knowledge of the author, the thermal characteristics of such LED lamp cooling device have not been discussed in detail. The cooling device is divided into heat sink and cooling wind generator. The heat sink, made of aluminum alloy, is a cup-shaped base externally with many radial fins. Multiple vertical passages are made along the ring wall of the heat sink. Inside the heat sink, it is separated by the dividing plate. A small motor fan is used as the cooling wind generator to drive the air flow. Half of the vertical passages of the heat sink are for inlet and the others are for outlet of the wind. This study experimentally investigated the fluid flow pattern and heat transfer characteristics of such novel LED lamp cooling device with various-size motor fans. This study measured the air flow rate of entering and leaving the vertical passages. The smoke flow visualization technology was used to observe the relevant flow patterns. The capacities of total heat transfer, internal forced convection heat transfer and external natural convection heat transfer coupling with radiation heat transfer are measured and analyzed. The relevant experimental results can be the basis for the design of the active LED lamp cooling device.

2. Experimental method This study constructed the appropriate flow-velocity measuring system and the smoke flow visualization system. As shown in Fig. 2(a), by taking the sensor head of the non-oriented hot-wire

414


1. 2. 3. 4. 5.

Test section Laser generator Incense Hot-wire anemometer Camera

1. DC Power supply 2. IR Camera 3. Acrylic box 4. Data recorder 5. Test section 6. Computer

(a) For fluid-flow investigation

(b) For heat-transfer measurement (I)

(c) For heat-transfer measurement (II) Fig. 2. Experimental setup.

anemometer into the opening above each vertical passage of the heat sink, this study measured the corresponding velocity of air flow driven by the built-in motor fan of the heat sink. The smoke flow visualization system used the incense below the heat sink. When the generated smoke flow rose to the upper opening of the vertical passage, it would change course due to the impact of blowing or suction flow driven by the fan. The laser generator would project the plate light cross the smoke flow traces that can be captured by the camera. This study also constructed the heat transfer measurement system as shown in Fig. 2(b) and (c). As shown in Fig. 2(b), the built-in motor fan is used as the airflow driving device. This study conducted the heat transfer experiments of various heat sinks. The system can be mainly divided into four parts including the heating system, the test section, infrared thermal imaging acquisition

Plastic cover 1. 2. 3. 4. 5. 6. 7.

Heat sink Thermal grease Film heater Thermal grease Copper piece Thermocouple Bakelite cylinder

Film heater

Unit: mm

Bakelite cylinder

Fig. 3. Configuration of test section and heating system.

system and data acquisition system. The heating system consists of the stainless steel film heater of diameter at 84 mm attached to the low-thermal conductivity Bakelite base at the same diameter and the height of 60 mm. The heating system used herein and its position are illustrated as Fig. 3. The DC power supply provides the film heater with electric heat to replace the waste energy generated by LED lamps. The configuration and dimensions of the radially finned heat sink are as shown in Fig. 4. Similar with the passive heat sink of PHILIPS MASTER LED PAR38 MV lamp, the present aluminum-alloy heat sink consists of a cup-shaped base with 24 radially arranged fins. However, on the ring wall of the cup-shaped base of the present heat sink, there are 24 vertical flow passages of diameter at 4 mm. Each passage is connected to the hollow chamber of the heat sink. Besides, a motor fan is installed in this chamber. Inside the chamber, it is separated by the dividing plate and the motor fan. The combinations of the heat sink and different motor fans can be divided into the following models (as shown in Fig. 5): (1) Model A – without motor fan and vertical flow passage, (2) Model B – without motor fan but with vertical flow passages, (3) Model C1 (no separation) – with 3 cm 3 cm motor fan and vertical flow passages, (4) Model C2 (complete separation) – with 3 cm 3 cm motor fan and vertical flow passages, (5) Model D (complete separation) – with 4 cm 4 cm motor fan and vertical flow passages; and (6) Model E (complete separation) – with 5 cm 5 cm motor fan and vertical flow passages. Table 1 illustrates the specifications of the motor fans. The infrared thermal imaging acquisition system was to use the infrared imager to capture the detailed temperature distribution of the heat sink surface. To reduce measuring error of the infrared thermal image, the surface of heat sink was coated with a thin film of black paint. The data acquisition system adopted five TT-T-30SLE T-type high precision thermocouples installed at the back of the film heater after passing through the Bakelite cylinder base (as shown in Fig. 3). Two other thermocouples were used to measure the ambient temperature and another two thermocouples

415


H2 =

=

H1 =

(a) With motor fan

(b) Without motor fan Fig. 4. Configuration and dimensions of the present radially finned heat sink (Unit: mm).

Table 1 Specifications of motor fans used in the present study. Photos (for Model C1 & C2) (for Model D)

Manufacturer Model Dimensions Power consumption Maximum air flow rate

ADDA ADD312 MB-D50 30 30 15 mm 0.96 W 3.5 CFM

were attached to the outer surface of the heat sink as the calibration benchmark for the surface temperature measurement by the infrared thermal imager. All the thermocouples were connected to the data recorder to convert the micro voltage signals into temperature values. To prevent the interference of the ambient in the heat transfer experiment, all the tests were conducted in the closed 40 40 30 cm box isolated by 10 mm thick acrylic board. The steady-state temperature is that the temperature changes over 15 min are within 0.2 °C; finally, the data are transferred to the computer for software monitoring and storage for subsequent parameter analysis and data reduction. As shown in Fig. 2(c), the 5HP air compressor is a gas source instead of the built-in motor fan. There was no motor fan in the

NONOI F4010M12B-RS 40 40 10 mm 0.48 W 5.3 CFM

(for Model E)

ELINA FAN HDF5216L-12 MB-6 50 50 15 mm 0.96 W 17.16 CFM

heat sink. Instead, 12 inlet pipes and 12 outlet pipes are separately connected the vertical-passage openings of the heat sink. Before the compressed air enters into the heat sink, it should enter an 800 L air tank to reduce the air flow pulse and then pass through the dryer and the filter to exclude contaminants and moisture. The air flow rate is controlled by the flow controller. The other heating and temperature measuring device are the same with the experimental system as shown in Figs. 2(b) and 3. Dependent on the air flow rate, the static pressure of the present compressed air through the heat sink is about 0.2–1.3 kpa higher than the Atmospheric pressure. The air flow velocity measured at the upper opening of each vertical passage (V) and temperature are measured in the

416


Model A

Model C2

Model B

Model D

Model C1

Model E

Fig. 5. Photos of various fan-heat sink assemblies.

experiment, and the Grashof number (Gr), Reynolds number (Re) and average Nusselt number (Nu) are calculated by the following equations:

b g ðT w T 0 Þ H3f

Gr ¼

ðl=qf Þ2

ð1Þ

Re ¼

qf V d l

ð2Þ

Nu ¼

ðQ t Q Loss Þ D Aheat ðT w T 0 Þ kf

ð3Þ 3. Results and discussion

where, Tw is the average heating wall temperature, T0 is ambient temperature, Hf (=0.055 m) is the vertical length of fins, d (=0.004 m) is the diameter of the vertical passage, D (=0.084 m) is the diameter of the film heater, Aheat is the heating surface area, Qt is the total input power, and QLoss is the heat loss. The heat loss (QLoss) can be estimated by the natural convection heat transfer experiment of the horizontal flat plate. In the heat loss experiment, the radiation heat loss dissipated from the exposed bare and smooth surface of the heated aluminum plate is negligible due to the very small radiation emissivity. Therefore, the total input power (Qt) can be dispersed by two parts: (1) the heat (Qnc) dissipated from the upper surface of the horizontal heated flat plate via natural convection and (2) the heat loss (QLoss) of the Bakelite base below the film heater.

Q Loss ¼ hLoss Aheat ðT w T 0 Þ ¼ Q t Q nc ¼ ðI VÞ hplate Aheat ðT w T 0 Þ

ð4Þ

where, V is the input voltage, I is the input current, Aheat is heating surface area, hplate is the heat transfer coefficient of the vertically upward natural convection of the plane. The empirical equation of hplate reported by Ellison [29] was cited as below in this study:

0:25 Tw T0 hplate ¼ 1:361 D=4

Equation (3) can obtain the corresponding heat transfer coefficients of heat loss (hLoss), so that the average Nusselt number (Nu) is obtained to analyze the heat transfer performance of different heat sinks. The uncertainty of the experiment was analyzed according to the uncertainty method of a single test as proposed by Moffat [30]. The uncertainty of instruments is based on the information provided by manufacturers. The uncertainties of Grashof number (Gr), Reynolds number (Re) and average Nusselt number (Nu) in this experiment are ±4.4%, ±3.5% and ±6.4%, respectively.

ð5Þ

In the heat loss experiments under natural convection, the different total input heat (Qt) will result in various differences (DT) between heating wall temperature and ambient temperature.

As shown in Fig. 6, with Model E as the typical case, the smoke flow visualizations of the heat sink are represented under the unheated/heated state with built-in motor fan being on or off. When the built-in motor fan was not actuated and the heat sink was not heated, as shown in Fig. 6(a), the incense trajectory was upward free. Fig. 6(b) displays the stably upward incense trajectory at the condition of the built-in motor fan being not actuated but the heat sink being heated. It demonstrates that the spacing between fins of the heated heat sink did form the chimney effect, providing the driving force of free convection to air. When the fan was activated, Fig. 6(c) (the heat sink was not heated) and Fig. 6(d) (the heat sink was heated) depict that the incense was absorbed into the upper suction openings of vertical passages evidently; the incense continuously and stably moves upwards at the blowing side of vertical passages. It confirms that the heat sink with built-in motor fan actually generates the forced convection. Fig. 7 illustrates the Reynolds number of driven air flow measured at the upper opening of each vertical passage in the case of the heat sink with built-in motor fan. The positive and negative Reynolds numbers represent the velocity data to be measured at blow and suction sides, respectively. This study conducted twice tests for the heat sinks of different models, and found that the root-meansquare values of Reynolds numbers (ReRMS) at the upper openings of the 24 vertical passages were Model E (ReRMS = 260) ; Model D (ReRMS = 263) > Model C2 (ReRMS = 87) > Model C1 (ReRMS = 18). This suggests that the forced convection generated by Model D with


(a) The built-in fan was not actuated and Qt=0W

(b) The built-in fan was not actuated and Qt=15.48W

(c) The built-in fan was actuating and Qt=0W

(d) The built-in fan was actuating and Qt=15.48W

417

Fig. 6. Smoke flow visualization for Model E test section.

4 cm 4 cm motor fan was not less than that generated by Model E with 5 cm 5 cm motor fan. This should be the integration result of the motor fan and the current vertical passages. Model C2 with 3 cm 3 cm motor fan had a complete separation in the chamber of the heat sink. As a result, although the driven air flow velocity was less than that of Model E and Model D, there was actually significant inflow and outflow. However, in the case of Model C1 with the same 3 cm 3 cm motor fan, almost no inflow and outflow velocities could be measured as there was no separation in the chamber of the heat sink. The reason is that incomplete separation in the chamber of Model C1 heat sink will lead the driven air flow to circulate inside the hollow chamber of the heat sink and thus it cannot result in effective forced convection through vertical passages. Fig. 8 shows the air flow schematic diagrams of the airflow inside and outside the heat sink based on measurement results and theoretical inference as shown in Figs. 6 and 7. The diagrams can be for the verification of the subsequent heat transfer measurement results. Fig. 9 illustrates the infrared thermal images of external surfaces of various heat sinks when the input power is 15.48 W. The radiation emissivity for taking the infrared thermal images was calibrated according to the thermocouple measurements of temperature, and was around 0.5 herein. The results suggest that the surface temperatures of Model A, Model B and Model C1 were apparently higher (about 60–65 °C), followed by Model C2, Model

D and Model E (about 50 °C), suggesting that the heat of Model A, Model B and Model C1 could not be effectively dispersed. The heat of Model C2, Model D and Model E could be transferred to the environment more easily. Fig. 10(a) shows the relationship between the Nusselt number Nu and Grashof number Gr for various heat sinks without and with the motor fan. According to the results, the Nu values of Model A, Model B and Model C1 were similar and apparently low, being lower than that of Model C2 by 22– 29%, being lower than Model D and Model E by 41–50%. That is, the heat sink with the motor fan could enhance the overall heat transfer by 28–102%; the wide range of heat transfer enhancement for Model C2, Model D and Model E can be attributed to the very different air flow rates through these heat sinks by various motor fans as shown in Fig. 7. Nevertheless, the Nusselt numbers of these three heat sinks still increased with the Grashof number, suggesting that there was the external natural convection in addition to the internal forced convection. In other words, the heat transfer mechanism of Model C2, Model D and Model E is the combined convection heat transfer coupling with the radiation heat transfer by the exposed surface of the heat sink. As both of Model A and Model B have no airflow driving device in the heat sink, there is only the external natural convection heat transfer coupling with the radiation heat transfer. As a result, the Nusselt number will be lower. Regarding Model C1, although it has 3 cm 3 cm motor fan and vertical passages; there is no separation above motor fan

418


(a) Model C1

(b) Model C2

(c) Model D

(d) Model E

Fig. 7. Reynolds numbers of driven air flows at the open ends of vertical passages.

and side. Therefore, the most of the airflow driven by the fan may only cycle inside the chamber of the heat sink (as shown in Fig. 8(c)). It cannot form the effective internal forced convection in vertical passages and the hollow chamber of heat sink. In order to understand further the heat transfer happening in the present heat sink, a heat-transfer experiment with air flow supplied by the compressor was conducted (see Fig. 2(c)). Fig. 10(b) displays the relationship between the Nusselt number Nu and Grashof number Gr for the cases with different-velocity compressed air blown in heat sink, instead of air flow driven by the motor fan. The results demonstrate that the air flow of larger Reynolds number (Re) through the vertical passage made bigger Nusselt number; it also made the trend of the Nusselt number increasing with Grashof number more obvious at smaller Re since that the heat-transfer dominance mainly is the natural convection. Besides, comparing the Nusselt numbers shown in Fig. 10(a) and (b), it is found that, at the similar Reynolds number and Grashof number, there were similar Nu values for the built-in motor-fan system and the compressed-air-blown system. Of course, owing to the swirling air flow driven by the built-in motor fan, the Nu of the motor-fan system was somewhat higher than that of the compressed-air system. Fig. 11 illustrates the thermal network schematic diagram of the present active heat sink. The input heat dissipated by the heat sink is divided into two coupled heat transfer paths to the ambient environment. The first path is the internal cooling path, which is to

transfer heat from the film heater to the vertical inlet passages (region a), the cylindrical chamber (region b) and the vertical outlet passages (region c) of the heat sink via heat conduction firstly, and then to the air flow through those internal regions via heat convection; the second path is the external cooling path, which is to transfer heat from the film heater to the fins of the heat sink via heat conduction firstly, and then to the ambient environment through the chimney duct between neighboring fins via natural convection and radiation. According to Fig. 11, the heats through various paths can be expressed as follows: "

Q 1a ¼ A1a h1a;fc ðT s1 T 0 Þ ¼ A1a

Q 1a h1a;fc T s1 T 0 þ 2qf C p Q flow

Q 1b ¼ A1b h1b;fc ðT s1 T 0 Þ "

¼ A1b h1b;fc T s1 T 0 þ Q 1c ¼ A1c h1c;fc ðT s1 T 0 Þ " ¼ A1c h1c;fc T s1 T 0 þ

Q 1a Q 1b þ qf C p Q flow 2qf C p Q flow

ð6aÞ

!#

Q 1a Q 1b Q 1c þ þ qf C p Q flow qf C p Q flow 2qf C p Q flow

Q 2 ¼ Aext hv p;nc ðT s2 T 0 Þ þ Aext F^ r ðT 4s2 T 40 Þ

!#

ð6bÞ !# ð6cÞ ð6dÞ

where Q1a, Q1b, Q1c and Q2 are separately the heats through the vertical inlet passages (region a), the cylindrical chamber (region b) and the vertical outlet passages (region c) of the heat sink as well

419


Hot Air

Hot Air

Cold Air

Hot Air

Cold Air

Hot Air

Cold Air

(a) Model A

Cold Air

(b) Model B

Hot Air

Cold Air

Hot Air

Hot Air

Hot Air

Cold Air

Cold Air

(c) Model C1

Hot Air

Cold Air

Cold Air

(d) Model C2

Cold Air

Hot Air

Cold Air Hot Air

Hot Air Cold Air

Cold Air

Cold Air

Cold Air

(e) Model D

(f) Model E

Fig. 8. Schematic diagrams of air flows for various test models.

as the second path (the external cooling path); A1a, A1b, A1c and Aext are separately the surface areas of the region a, region b, region c and the external part of the heat sink; Ts1 is the representatively external surface temperature of the heat sink; Ts2 is the representatively internal surface temperature of the heat sink; T0, T⁄0, T⁄⁄ 0 and T⁄⁄⁄ are separately the ambient temperature as well as the bulk 0 mean temperatures of air through the region a, region b and region c; qf is the density of air; Cp is the specific heat; Qflow is the volumetric air flow rate; F^ is the effective radiation view factor of all the exposed surface of the heat sink and reasonably set as 0.3 by citing Ref. [31]; r is the Stefan–Boltzmann constant, and h1a,fc, h1b,fc, h1c,fc and hvp,nc are separately the heat transfer coefficients at region a, region b, region c and the external cooling path. And set

where g1 is the fin efficiency of the internal cooling path and set as 1 herein; g2 is the fin efficiency of the external cooling path and set as 0.74–0.83 dependent on the measured temperatures herein. Then the heats through the present two coupled heat transfer paths can be expressed separately as follows: " ! !# b b c c Q 1a þ Q 1b þ Q 1c ¼ a 1 þ 1þ a qf C p Q flow b qf C p Q flow g1 ðT w T 0 Þ ¼ Aheat h1;fc ðT w T 0 Þ Q 2 ¼ Aext hv p;nc g ðT w T 0 Þ þ Aext F^ r f½T 0 þ g ðT w T 0 Þ4 T 4 g 2

¼ Aheat h2;ncþrd ðT w T 0 Þ

2

ð8aÞ

0

ð8bÞ

T s1 T 0 ¼ g1 ðT w T 0 Þ

ð7aÞ

T s2 T 0 ¼ g2 ðT w T 0 Þ

ð7bÞ

Where Aheat is the surface area of the film heater, and h1,fc and h2,nc+rd are separately the heat transfer coefficients of the internal and external cooling paths based on Aheat and (Tw–T0). Therefore, the total Nusselt number can be theoretically expressed as follows.

ð7cÞ

Nu ¼

a¼ b¼

c¼

1 1 þ A1a h1a;fc 2qf C p Q flow

!1

!1 1 1 þ A1b h1b;fc 2qf C p Q flow !1 1 1 þ A1c h1c;fc 2qf C p Q flow

ð7dÞ

ð7eÞ

ðh1;fc þ h2;ncþrd Þ D kf

ð9Þ

In the above-mentioned equations, only the forced convection heat transfer coefficients are employed at the internal cooling path (i.e. the first heat path, see Fig. 11). It is because of the neutralized effect between the assisting and opposing flows of buoyancy-induced and forced motions separately at the inlet part (including the vertical inlet passages (region a) and half of the cylindrical chamber (region

420


500

400

Model A, Re=0 Model B, Re=0 Model C1, Re=18 Model C2, Re=87 Model D, Re=263 Model E, Re=260

Free convection (Churchill & Chu, 1975) + radiation heat transfer (Khor et al., 2010)

300

Nu

Model A (T0=31.1

)

Model B (T0=32.1

200

)

100 Churchill & Chu, 1975 Free convection from a vertical plate

0

Model C1 (T0=32.7

)

Model C2 (T0=29.6

200000

)

400000

600000

Gr

(a) Motor fan built in heat sink 500 Free convection (Churchill & Chu, 1975) + radiation heat transfer (Khor et al., 2010)

400

Model D (T0=33.2

)

Model E (T0=29.3

)

Fig. 9. Infrared thermal images for various test models with/without motor fan (Qt = 15.48 W).

b)) as well as the outlet part (including the vertical outlet passages (region c) and half of the cylindrical chamber (region b)). In order to obtain the prediction value of Nusselt number by using Eqs. (6)-(9), the h1a,fc of region a, the h1b,fc of region b, the h1c,fc of region c and the hvp,nc of the external cooling path need to know. As shown in Eq. (10a), the empirical formula of fully developing laminar flow through the circular duct with iso-temperature wall, proposed by Hausen [32] and reported by Holman [33], was used for predicting h1a,fc and h1c,fc herein. As shown in Eq. (10b), the empirical correlation of laminar free convection from a vertical plate, provided by Churchill and Chu [34], was employed for the prediction of hvp,nc since that the most of the external part of the heat sink could be considered as vertical surface. For the h1b,fc of region b, there is no adaptive empirical formula due to the very unique configuration of inlet and outlet. Therefore, a test section for determining the h1b,fc of region b was manufactured (as shown in Fig. 12) and the similar heat transfer experimental method reported by Jeng et al. [35] was used. Finally, the empirical formula of h1b,fc could be obtained as shown in Eqs. (10c) and (10d).

h1a;fc ¼ h1c;fc ¼ 3:66 þ

0:0668ðd=H1 ÞRePr 1 þ 0:04½ðd=H1 ÞRePr

for laminar flow hv p;nc ¼ 0:68 þ

0:670ðgGrPrÞ

ðkf =dÞ ð10aÞ

!

1=4

½1 þ ð0:492=PrÞ9=16

2=3

!

4=9

ðkf =Hf Þ

for gGr Pr 6 109 " 0:675 # nd =D Þ ¼ 1:459 Re h1b;fc ¼ 1:459Re0:675 ðk in f Din Din

ð10bÞ

ðkf =Din Þ for Re ¼ 76:5—343 and GrDin ¼ 2:7 105 —6:4 105 ð10cÞ GrDin ¼ ReDin ¼

3 b g ðT w T 0 Þ Din

ðl=qf Þ2

;

qf ½2Q flow =ðpD2in =4Þ Din l

ð10dÞ

Heat sink with built-in motor fan Model C2 Model D Model E Re=87; Re=263; Re=260

300

Symbol

Re 0 76.5 127 179 233 291 343

Nu 200

100

Curve fit of present data Nu nc+rd =2.45 Gr 0.317

Churchill & Chu, 1975 Free convection from a vertical plate

0 200000

400000

600000

Gr

(b) Compressed air blown in heat sink Fig. 10. Relationship between total Nusselt number and Grashof number.

Where ReDin is the jet Reynolds number of the region b; H1 is the length of the vertical passages; d is the diameter of the vertical passages; Hf is the height of the heat sink; n is the number of the vertical passages, and Din is the inner diameter of the cylindrical chamber of the heat sink. Notably, although the Richardson number (GrDin/ReDin2) of Eq. (10c) ranged from 0.87–54.7, the deviation of h1b,fc was within 5% for the case with the same ReDin but various GrDin. It validates the above mentioned statement that the neutralized effect between the assisting and opposing flows of buoyancy-induced and forced motions happened at the cylindrical chamber (region b). Using the Eqs. (6d), (7b), (8b), (9) and (10b), the predicted Nu value of the heat sink with Re = 0 was obtained. It was also plotted in Fig. 10. The predicting results generally agree with those experimental data with Re = 0 plotted in Fig. 10. It was overrated by maximum 11% when the radiation heat was considered in the predicting result. However, according to the data shown in Fig. 10(b), the predicting results excluding radiation heat were 22% lower than the experimental data herein. Besides, a more simple Nu correlation for the heat sink with Re = 0 (i.e. at the natural convection coupling with radiation condition) can be formulized as follows:

Nuncþrd ¼ 2:45Gr0:317

ð11Þ

421


ks

Ts1

h1,fc Aheat

h1c , fc A1c

ks

Ts2

hvp,nc Aext hrd

h2 Aheat

Forced convection

Tw

T0** Natural convection

h1b , fc A1b h1a , fc A1a

T0***

T0* T0

T0 c

T0

Radiation heat transfer

a b

T0

Ts2

h, Aheat

Ts1

T0

Tw

Fig. 11. Schematic diagram of thermal network for the present active heat sink.

Fig. 12. The test section for the heat transfer experiment to determine the h1b,fc of region b.

The applied range of Eq. (11) is Gr = 2.37 105–5.92 105. The maximum deviation between the predictions of Eq. (11) and the experimental data is ±5%. Fig. 13 depicts the relationship between the total Nusselt number and the vertical-passage Reynolds number for the cases with compressed air blown in heat sink. According to the discussions in Fig. 11, the total Nusselt number is generally the sum of the Nusselt number of the externally natural convection coupling with radiation (Nunc+rd) and the Nusselt number of the internally forced convection (Nufc). Therefore, the Nufc empirical formula of the present heat sink can be obtained by Eq. (11) and Fig. 13(a). 0:808

Nufc ¼ 1:38Re

ð12Þ

The applied range of Eq. (12) is Re 5 343. The maximum deviation between the Nufc predictions of Eq. (12) and the experimental data is ±15%. Using Eqs. (11) and (12) to predict the total Nusselt number, the maximum deviation between the predictions and the experimental data is ±6.1%. In addition, the predicted Nu value of the heat sink is also obtained by using the Eqs. (6)–(10) and plotted in Fig. 13(b). The applied range is Gr = 1.86 105–4.66 105 and

Re 5 343. The average deviation between Nufc prediction of Eqs. (6)–(10) and the experimental data is ±17%. However, using Eqs. (6)–(10) to predict the total Nusselt number, the maximum deviation between the predictions and the experimental data is ±11%. 4. Conclusion This study proposed the design and implementation of an innovative LED lamp cooling device with a motor fan and multiple vertical passages. The major conclusions are listed as follows: (1) Comparing to the heat sink without built-in motor fan, the heat sink with motor fan can enhance the overall Nusselt number by 28–102%. The wide range of heat transfer enhancement is attributed to the very different air flow rates driven by various motor fans. (2) The overall heat transfer mechanism of the present active LED cooling device is theoretically and experimentally demonstrated that it is the combination of the internally forced convection and the externally natural convection coupling with radiation heat transfer.

422


Acknowledgement

500 Symbol

Gr

data of Nufc

1.86E5-2.37E5 2.72E5-3.70E5 3.71E5-4.66E5

400

0.808

Nu fc =1.38 Re

Correlation, Nu=Nunc+rd+Nufc

0.317

Nu nc+rd =2.45 Gr

2.25E5 3.27E5 4.26E5

300

Nu

The author would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract Nos. NSC 102-2221-E-270-003 and NSC 102-2622-E-270005-CC3. Also, the author appreciates Dr. Sheng-Chung Tzeng for his useful comments and Mr. Chi-Huang Liu for his assistance in some tests.

200

References 100

0 0

100

200

300

400

Re

(a) Correlation I 500 Symbol

Gr

data of Nufc

1.86E5-2.37E5 2.72E5-3.70E5 3.71E5-4.66E5

400

Nu fc=Eqs.(6)~(10)

Correlation, Nu=Nu nc+rd +Nufc

Nu nc+rd =Eqs.(6)~(10)

1.86E5-2.37E5 2.72E5-3.70E5 3.71E5-4.66E5

300

Nu 200

100

0 0

100

200

300

400

Re

(b) Correlation II Fig. 13. Relationship between total Nusselt number and vertical-passage Reynolds number for the cases with compressed air blown in heat sink.

(3) A theoretically empirical formula is proposed to predict the Nusselt numbers of the present combined convection and radiation heat transfer. The applied range is Grashof number Gr = 2.37 105–5.92 105 and Reynolds number Re 5 343. When the Reynolds number of driven air flow equals zero, there is more than 30% deviation between the predicted values of Nusselt numbers including and excluding radiation heat transfer. The maximum deviation of the total Nusselt number between the predictions and the experimental data is ±11%. (4) This study found that the integration effect of the motor fan and vertical passages as well as the separation completeness can affect the overall heat transfer. Therefore, the impact of the number, dimension and opening position of vertical passages on the heat transfer performance of the present active heat sink is worthy of the systematic discussions in the future. Conflict of interest None declared.

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