The Effect of a Metal Plate Barrier with Holes Blocking Channelin the Forced Convection of Rectangular Modules

Masao Fujii and Toru SawaiDepartment of Biomechanical and Human Factors Engineering, Kinki University, Japan

The experimental work reported here has provided an analysis of the effect ofa perforated barrier, fully spanning the flow passage upstream of a pair of modules ina duct, on heat transfer and pressure drop characteristics of heated, rectangular modulesthat are commonly encountered in electronic equipment. The barrier has been shown to be an effective means towards providing heattransfer enhancement. Heat transfer was increased with increasing barrier hole diame-ter d, and decreasing barrier porosity σ and module-barrier distance L. The enhancingeffect of the barrier was found to change dramatically at L/d = 3.5 and 18. Experimentaldata on heat transfer coefficients were correlated as a function of L/d, σ, and Reynoldsnumber. The pressure loss coefficient of the barrier is influenced by porosity σ, and isinsensitive to the other factors experimentally investigated. The average pressure losscoefficient was correlated as a function of σ. © 2011 Wiley Periodicals, Inc. HeatTrans Asian Res, 40(4), 340–351, 2011; Published online 28 March 2011 in WileyOnline Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20348

Key words: heat transfer, forced convection, electronic cooling, barrier, hole

1. Introduction

Electronic devices produce a large amount of heat as a by-product of normal operations. Whenelectrical current flows through a semiconductor or a passive device, a portion of the power dissipatesas heat energy. When a device exceeds its specified temperature, its performance, life-expectancy,and reliability are greatly reduced. Therefore, heat transfer from electronic components is of primeimportance in the design of digital electronic equipment, particularly those that produce high densitiesof dissipated electrical power [1].

Forced convection air cooling of electronic equipment is one technique mostly common usedin practice. Flow passages surrounding devices are frequently irregular, often being bounded bycomponents of various sizes and shapes. Furthermore, electronic equipment is usually covered witha solid or perforated metal casing to protect components from mechanical or electromagnetic damage.The combinations of components and casing together work either to hinder or promote heat transferof the components.

© 2011 Wiley Periodicals, Inc.

Heat Transfer—Asian Research, 40 (4), 2011

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Sparrow et al. [2–4] have studied the most common generic configuration possible forelectronic cooling, in which an array of rectangular heat-generating modules deployed along one wallof a flat rectangular duct is cooled by forced convection airflow. In various reports, a turbulence-pro-moting barrier positioned between modules was shown to enhance heat transfer of a trailing module.Shiina et al. [5] studied the effect of thin-plated obstacles oriented parallel to the duct, and Tanazawaet al. [6] reported that a perforated plate promoted turbulence. Fujii et al. [7, 8] presented the effectof perforations of a heat exchanger with passage enlargement and contraction. The above-mentionedresearch was intended to appraise the effectiveness of a barrier in enhancing heat transfer.

The work reported here focuses on the effect of perforated metal barriers commonly using ascasings on heat transfer from a hot rectangular module that has particularly high heat dissipationand/or a crucial temperature limitation, such as a central processing unit. Since the air flow behindthe barrier is extremely complicated — involving flow separation, recirculation, and reattachment —the barrier itself does not always enhance heat transfer from modules situated in its proximity.Addressing device integrity and reliability concerns of electronic equipment, it is important to studythermal management in devices, particularly the effect of perforated barriers on the effectiveness offorced convection air cooling in promoting heat transfer from modules. We have previously reportedon the effect of a metal plate barrier without holes partially blocking an air passage on heat transferfrom a pair of modules [9], in which heat transfer at the 2nd row module was enhanced, but wasreduced at the 1st row module. Furthermore, using a perforated metal plate barrier with circular holes,partially blocking the air passage, heat transfer from modules was reduced [10].

In the work described here, we quantify the heat transfer coefficients of both modules in thepresence of a perforated metal plate as the barrier placed upstream of the modules and fully blockingthe flow passage. These measurements were performed under changes in various parameter valuessuch as module-barrier separation, hole diameter, and barrier porosity.

Nomenclature

A: per-module heat transfer area except bottom surface area of the module, m2

C: constantD: characteristic length, md: hole diameter of the barrier, mh: per-module heat transfer coefficient, W/(m2K)K: pressure loss coefficientk: thermal conductivity of air, W/(m⋅K) L: module-barrier separation, mmm, Y: constantsNu: Nusselt numberPr: Prandtl number of airQ: heat flow rate, WRe: Reynolds numberTa: inlet air temperature, KTw: temperature of module, Kv: mean air velocity, m/s∆P: pressure loss, Pa

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n: kinematic viscosity of air, m2/sρ: density of air, kg/m3

σ: porosity

Subscripts

i: module number (i = 1: 1st module, i = 2: 2nd module)b: barrierav: average value

2. Experimental Apparatus and Procedure

We employ a typical arrangement to study active cooling of heat-dissipating electroniccomponents. A schematic diagram of the top and side views of the experimental apparatus is presentedin Fig. 1. A pair of rectangular heat-generating block-like elements representing electronic moduleswas deployed along one wall of a flat rectangular duct and subject to active cooling from a forcedconvective airflow.

The rectangular duct, made of acrylic resin, was 600 mm long, 100 mm wide, and 85 mmhigh. Each module consisted of a square aluminum block of fixed dimensions; specifically a sidelength of 30 mm and a thickness of 15 mm. A 2.0-mm-thick acrylic resin plate was placed on the baseof each module, and the modules were attached to the bottom plate of the duct with 1.0-mm-thickadhesive tape. Under these conditions, heat dissipated from the upper surface and the four side surfacesof the module.

The modules were heated simultaneously via a rubber heater implanted in each module. Heatrates were 3.0 to 8.0 W within an uncertainty of ±0.45%. Temperatures of each module Twi weremeasured with a 0.2-mm outer diameter copper constantan thermocouple, and found to be in the rangeof 328 to 342 K. Air temperatures Ta entering the duct were about 301 K. The temperature difference

Fig. 1. Experimental apparatus.

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(Twi – Ta) was within a percentage uncertainty of ±0.21%. A 13-mm-thick air gap set under thebottom plate of the duct thermally insulated the modules from heat flow (heat loss) from below.Thermocouples were placed on the underneath of the bottom plate, under each module, and tempera-ture Tsi recorded. Heat loss from each module into the air gap was estimated by the temperaturedifference (Twi – Tsi), as described in detail in Refs. 9 and 10. The mean air velocity v in the ductwithout modules was 0.54 to 2.7 m/s within an uncertainty of ±1%, and determined the characteristicvelocity used to evaluate the Reynolds number defined below in Section 3. We recall that as theReynolds number increases, heat loss decreases. The heat loss was used to obtain the heat flow rateQi from each module into air flowing through the duct.

Figure 2 shows a diagram of a barrier which consisted of a perforated aluminum plate, 0.5 mmthick, patterned with uniform circular holes of constant pitch corresponding to a porosity of 16.3,32.6, or 65.2%. These holes were distributed in a staggered array at the apices of a centered equilateraltriangle; different barriers had different hole diameters d of 1.5, 3.0, 6.0, or 12.0 mm. Each barrierfully spanned the duct passage upstream of the modules as shown in Fig. 1.

Geometric parameters that could be varied were module-barrier separation, hole diameter, andbarrier porosity. As shown in Fig.1, the distance L1 between the front edge of the 1st module and thebarrier was set at 10, 20, 30, 50, or 100 mm; the separation between the front edges of the two moduleswas set at L2 – L1 = 60 mm.

The pressure drop ∆P was measured with a pressure gauge with a resolution of ±0.1 Pa, andobtained by measuring the pressure difference between the wall static pressure at 270 mm ahead ofthe front edge of the 1st module and the atmospheric pressure in the laboratory.

3. Experimental Results and Discussion on Heat Transfer

The heat transfer coefficients hi for each module were obtained from the defining relation

hi = Qi/{A(Twi – Ta)} (1)

Heat transfer and pressure drop characteristics are presented in terms of dimensionlessparameter grouping, i.e., the Nusselt and Reynolds numbers respectively:

Nui = hiD/k

Fig. 2. Perforated metal plate barrier with circular holes.

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Re = vD/n

The characteristic length D = 30 mm corresponds to the side length of the module. Averagescorresponding to the inlet air temperature Ta and the heating surface temperatures Twi of the modulewere used in the data reduction.

3.1 Module characteristics in the absence of a barrier [9]

The dimensionless correlations for the module pairing were obtained in the absence of a barrierwithin an uncertainty of ±3%:

Nu1 = 0.168Re0.719Pr1/3 for the 1st module (2)

Nu2 = 0.284Re0.637Pr1/3 for the 2nd module (3)

where 940 ≤ Re ≤ 4400.

3.2 Module characteristics in the presence of a barrier

Experimental data for each experimental setting were correlated by Eq. (4) within anuncertainty of ±3%:

Nubi = CRenPr1/3 (4)

Here, Nubi corresponds to the Nusselt number of the module with barrier present.

Figure 3 shows the effect of hole diameter d, barrier porosity σ, and module-barrier separationL on the heat transfer of each module for Reynolds numbers of 1000 and 4000; L is plotted along theabscissa, the ratio Nubi/Nui plotted along the ordinate. This ratio characterizes the effect of the barrierand can be calculated from Eqs. (2), (3), and (4). The departure of this ratio from unity indicates theenhancing/reducing extent in heat transfer performance.

From the figure, this ratio exceeded 1 for both modules so that the barrier has enhanced theheat transfer of each module. For all settings, a common pattern appears wherein the ratio decreaseswith increasing distance L and porosity σ but increases with increasing hole diameter d.

With σ = 16.3% and d = 12.0 mm, it is predicted that the heat transfer performance will beinfluenced by the relative orientation of the barrier perforations to the module, as can be seen in Fig.4. In Fig. 3, the experimental results are also shown for orientations (a) and (b) in Fig. 4. The heattransfer performance of orientation (a) (K, /) is better than that for (b) (+, ×). In orientation (a), theair flow through the perforations at the lowest and central positions impinges on the front side of the1st module enhancing the heat transfer and at the same time promoting turbulence, while in orientation(b), the air flow through the perforations brushes the sides of the modules.

Figure 5 shows the clear influence of hole diameter and barrier porosity on the ratio of Nubi/Nui

given L1 = 10 mm (L2 = 70 mm). This ratio increases with increasing hole diameter and decreasing

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porosity. For the 1st module, there is no influence of Reynolds number on this ratio, while for the 2ndmodule the ratio becomes larger as the Reynolds number increases. This result shows that barrierenhancements extend further downstream at higher Reynolds numbers.

To obtain an alternative perspective on these heat transfer results, flow visualization studieswere performed. For this purpose, we employed the tuft technique. Representative photographs oftypical flow fields are presented in Fig. 6, all of which correspond to settings L1 = 20 mm, d = 3.0mm, and v = 2 m/s. As seen in Figs. 6(a) and 6(c), the tuft length was set long to observe the air flowaround the 2nd module, while in Figs. 6(b) and 6(d), the tuft length was set short to observe the airflow around the 1st module. In Figs. 6(a) and 6(b), where barrier porosity is 16.3%, the tuft vibrated

Fig. 4. Relative orientation of the barrier perforations to the module.

Fig. 3. Effect of distance, hole diameter, and porosity.

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vigorously, indicating that a barrier with smaller porosity promotes turbulent flow. With a porosityof 65.2%, the end of the tuft is not oscillating as much in Figs. 6(c) and 6(d), so that we conclude thata barrier with large porosity promotes smooth laminar flow.

3.3 Dimensionless correlation of the heat transfer in the presence of the barrier with circularholes

The exponent n of Re in Eq. (4) indicates the flow pattern in the duct; in general, n = 0.5 isindicative of laminar flow, while n = 0.8 is indicative of turbulent flow. The experimental data werecorrelated by Eq. (4), and Fig. 7 shows the effect of dimensionless number L/d on n in Eq. (4). Fromthe experimental data, the mean value of n for the 1st module was 0.717, while that for the 2nd modulewas 0.688. The mean value of n over all experimental data was 0.70 with an experimental uncertaintyof ±15% as shown in Fig. 7. From Figs. 6 and 7, the barrier functions to promote turbulence and toimprove heat transfer from the modules. The exponent n is nearly constant up until value L/d = 107,so that the characteristics of the bulk fluid motion established by the barrier is maintained over a widerange of L/d = 0.83 to 107.

Figure 8 shows the dimensionless correlation of the heat transfer coefficient of the modules.The abscissa gives the dimensionless number L/d, while the ordinate plots the dimensionless numberdefined by:

Zi = Nubi/(Re0.70Pr1/3) (5)

Fig. 5. Effect of hole diameter.

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With increasing L/d, Zi decreases (plotted by the thick solid line in Fig. 8), wherein theinfluence of L/d on Zi is seen to change dramatically at L/d = 3.5 and 18, as shown by the verticaldash-dotted lines. The physical meaning of these figures is unclear but they are of practical use inthermal control design.

To analyze the effect of L/d on the heat transfer performance for practical application, Eq. (6)was used to correlate the experimental data:

Fig. 6. Flow visualization.

Fig. 7. Effect of L/d on the exponent n of Reynolds number in Eq. (4).

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Zi = Y(L/d)–m (6)

For given barrier porosity, the following empirical equations were obtained as shown by thin solid

lines.

Zi = 0.497(L/d)–0.219 for σ = 16.3% (7)

Zi = 0.363(L/d)–0.177 for σ = 32.6% (8)

Zi = 0.240(L/d)–0.0648 for σ = 65.2% (9)

Fig. 8. Effect of L/d on heat transfer performance.

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With increasing σ, the exponent m decreases, indicating that the influence of L/d on heattransfer performance becomes small. The intensity of the bulk fluid motion generated through theholes is stronger with large hole diameters than that with small hole diameters. Although the amountof bulk fluid increases with increasing σ, the intensity of the bulk fluid motion is small. The intensityof bulk fluid motion also decreases with an increase in L because of friction losses within the fluid.

By using porosity σ, the following empirical equations were obtained for constants Y and min Eq. (6).

Y = 0.679 – 1.27σ + 0.910σ2 (10)

m = 0.252 – 0.171σ – 0.177σ2 (11)

Finally, we obtained the following empirical relation for the heat transfer coefficients of the modulesin the presence of a barrier:

Nubi = Y(L/d)–mRe0.70Pr1/3 (12)

where 870 ≤ Re ≤ 4900.

4. Experimental Results and Discussion on Pressure Loss

Figure 9 shows the relationship between the pressure loss coefficient K defined by Eq. (13)and Reynolds number Remax defined by Eq. (14):

K = 2∆Pb/(ρv2) (13)

Remax = vmaxd/n (14)

Fig. 9. Pressure loss coefficient.

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The presence of the barrier gives rise to a substantial pressure drop relative to that in theabsence of a barrier. Therefore, the net incremental pressure loss ∆P due to the barrier is of practicalinterest. This pressure loss was obtained by subtracting the pressure loss of the modules from the totalexperimental pressure loss of the modules and the barrier [9]. The velocity vmax is the maximumvelocity through the barrier perforations. The characteristic length and velocity in Eqs. (13) and (14)were selected to correlate the experimental data clearly. The pressure loss coefficient increased withdecreasing porosity σ, whereas no dependence was seen with respect to distance L, hole diameter d,and Reynolds number in the range investigated. If Fig. 8 is considered in conjunction with Fig. 9, itis seen that the higher pressure losses caused by smaller porosity are compensated by somewhat higherheat transfer coefficients. Since pressure loss is quite insensitive to hole diameter, it is preferable touse a barrier with large hole diameters at the same porosity.

The pressure loss coefficient of the barrier showed a minimum value at Remax of about 500for a porosity of 65.2%, which is a similar tendency to the results in Ref. 11. The figures Kav in Fig.9 show the average values of the pressure loss coefficients. The average pressure loss coefficientswere correlated with respect to porosity within an uncertainty of ±30% to be

Kav = 0.893σ–2.43 (15)

5. Conclusions

The experimental work reported on here has provided an analysis of the effect of a perforatedbarrier, fully spanning the flow passage upstream of a pair of modules in a duct, on heat transfer andpressure drop characteristics of heated, rectangular modules that are commonly encountered inelectronic equipment.

The barrier has been shown to be an effective means towards providing heat transferenhancement. Heat transfer was improved with increasing hole diameter d, and decreasing barrierporosity σ and module-barrier distance L. The enhancing effect of the barrier was found to changedramatically at L/d = 3.5 and 18. Experimental data on heat transfer coefficients were correlated byEq. (12) as a function of L/d, σ, and Reynolds number.

The pressure loss coefficient of the barrier is influenced by porosity σ, but is insensitive tothe distance L, hole diameter d, and Reynolds number. The average pressure loss coefficient wasgiven by Eq. (15) as a function of σ.

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"F F F"

Originally published in Trans JSME Ser B 76, 2010, 1579–1585.Translated by Masao Fujii, Department of Biomechanical and Human Factors Engineering, Kinki

University, Nishimitani, Kinokawa, Wakayama 649-6493 Japan.

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