Optimization of Heat Sink Design and Fan Selection in Portable Electronics Environment


 Kerry Harmon
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1 Optimization o Heat Sink Desin and Fan Selection in Portable Electronics Environment Abstract Modern portable electronics have seen component heat loads increasin, while the space available or heat dissipation has decreased, both actors workin aainst the thermal desiner. This requires that the thermal manaement system be optimized to attain the hihest perormance in the iven space. While addin ins to the heat sink increases surace area, it also increases the pressure drop. This reduces the volumetric airlow, which also reduces the heat transer coeicient. There exists a point at which the number o ins in a iven area can be optimized to obtain the hihest perormance or a iven an. The primary oal o this paper is to ind the optimization points or several dierent anheat sink desins. The secondary oal is to ind a theoretical methodoloy that will accurately predict the optimization point and the expected perormance. Key Words: thermal resistance, ap/lenth ratio, pressure drop, optimization and anheat sink system. Nomenclature A d Duct cross sectional area, mm A b Heat sink base area, mm A Fin surace area, mm A m Fin proile area, mm A sc Heat source contact area, mm D h Hydraulic Diameter, mm Friction actor app Apparent riction actor Channel width, mm h Convection heat transer coeicient, W/m K h Fin heiht, mm k air Air thermal conductivity, W/mK k m Material thermal conductivity, W/mK K c Contraction coeicient K cd Duct Contraction Coeicient K e Expansion coeicient K ed Duct Expansion Coeicient L Fin lenth, mm L c Corrected lenth, mm Nu Nusselt number P Total input power, W Pr Prandtl Number Re Dh Hydraulic Diameter Reynolds Number Re Channel Reynolds number Re a Approach velocity Reynolds number T amb Ambient temperature, C T b Heat sink base temperature, C t Fin thickness, mm t b Heat sink base thickness, mm w Fin pitch, mm x l Channel lenth, mm x Dimensionless hydrodynamic entry lenth Channel velocity, m/s V V s V a Free stream velocity, m/s Actual approach velocity, m/s P Heat sink pressure drop, N/m P th Theoretical Heat sink pressure drop, N/m λ Spreadin resistance variable, m  η Fin eiciency ρ Fluid density, K/m 3 ν Fluid viscosity, m /s Θave Averae heat sink thermal resistance, C/W Θba Experimental thermal resistance, C/W Θ Fin thermal resistance, C/W Θ s Base spreadin resistance, C/W Total resistance, C/W Θ t Introduction Rapid development in packain technoloy allows portable electronics to ain aster processin speed and enhanced capabilities. However, thermal manaement in the portable electronics environment is becomin increasinly diicult due to hih heat load and dimensional constraints. Proper selection o ans and in pitch in the heat sink is crucial to ensure the thermal desin o the system is optimized. Fiures and show the common thermal solutions ound in today s portable computer environment. The micro blowerheat sink heat pipe assembly shown in Fiure is mounted on a slim cold plate. Heat pipes transport the heat enerated by the chip, where it is dissipated to the environment with the aid o the airlow produced by the micro blower. This type o thermal desin is deployed in a system with limited space. The in desins are optimized to assure maximum heat transer occurs between the ins and the surroundin ambient. The micro blower is capable o supplyin suicient airlow to cool the system while maintainin a low proile to ulill the space restriction []. The axial an heat pipeheat sink assembly shown in Fiure is used when space is less constrictive. A heat pipe transports heat rom the source to the hih eiciency ins enclosed in a square block with an axial an attached at one end to pull airlow throuh the ins. Fiure : Micro blowerheat sink system or portable computer.
2 To evaluate the total pressure drop across the heat sink, we must irst determine the hydraulic diameter and channel velocity. They are iven as ollows: D h h = () h t V = Vs () Fiure : Axial anheat sinks systems or portable computer. The main objective o this paper is to investiate the eects on thermal perormance under axial an and micro blower airlow or dierent ap/lenth ratio heat sinks. In doin so, the optimization point between the dierent types o ans or blowers under certain in ap/lenth ratio can be obtained. In addition, the experimental results are used to compare with theoretical methodoloy developed by Copeland [], Biber [3], and Teertstra [4]. Analytical Model A anheat sink model can be characterize based on the ollowin assumptions: No low bypassin since the heat sink is ully ducted Isotropic material Fin tips are adiabatic Uniorm approach velocity This model can be urther broken down into two sections, the calculation o pressure drop across the heat sink and indin the overall thermal resistance o the heat sink. Total Heat Sink Pressure Drop The acceleratin lows inside the heat sink channel produces a pressure drop between the channel entrance and exit reion. This pressure drop across the heat sink is also known as the system resistance. System resistance aects the overall thermal perormance o heat sink. Hiher system resistance causes less airlow throuh the heat sink channel, attainin lower convection heat transer rate between the ins and the surroundin air and increases the in thermal resistance. When the heat sink system resistance is known, the actual volumetric low rate can be ound rom the an/blower perormance curve with a iven total heat sink pressure drop. This point alon the an/blower curve is called the system operatin point. The system operatin point shits up and down alon the perormance curve dependin on the constraints (hydrodynamic head, eometry o heat sink and luid properties) imposed upon the system [5]. When the an perormance is balanced by the system perormance to deliver the most eicient combination o airlow and heat sink surace area. The system is said to be optimized at that operatin point. The channel velocity is related to the ree stream velocity and the ratio o in thickness and the channel width. Usin these variables with luid properties, the Reynolds number is ound to be: D h V Re = (3) ν Generally, the velocity proile in the heat sink channel is laminar, in which the Reynolds number is below 300. Also, in most cases, the channel lenth is not lon enouh or the low in the channel to become ully developed, and hence, the low is a mixture o ully developed and developin low. The apparent riction actor or this mixture o low is a unction o riction actor o the ully developed low and the hydrodynamic entrance lenth. The approximate equation is taken rom Shah and London [6]: / 3. appre = { Re } 0.57 (4) ( x ) The ully developed low riction actor, Re, is obtained rom Kays and London [7]. Since the low is laminar, the dimensionless hydrodynamic entrance lenth is deined as a unction o Reynolds number, hydraulic diameter and the lenth o the channel as ollows [8]: x x l = Re D D h h laminar The laminar low contraction and expansion loss coeicients are deined as []: (8) c ( w) [ ( w) ] 0.4( w) (5) K = (6) K e = (7) The total heat sink pressure drop is ormulated as: P = ( ) ρv K 4 x K c app e
3 For our case, we added the contraction and expansion loss coeicients o the duct to closely represent the experiment. These coeicients are ound in Munson, Youn and Okiishi [9]. Thereore, the total heat sink pressure drop equation (8) becomes: Pth = (9) ( ) ρv K K 4 x K K c cd app e ed The theoretical total heat sink pressure drop can be inserted into any commercially available an perormance curve to determine the volumetric low rate at that iven point. The actual approach velocity can be calculated by dividin the volumetric low rate with duct cross sectional area. V a = Volumetric Flow Rate A d (0) The newly ound approach velocity is then used to compute the heat sink thermal resistance. Total Thermal Resistance The total thermal resistance is the product o the in thermal resistance and the base spreadin resistance, expressed as ollow: Θ = Θ Θ () t s Fin Thermal Resistance With the adiabatic in tip assumption, the in thermal resistance is iven by: Θ = () η A h In order to compute the coeicient o heat transer, h, the approach velocity Reynolds number, Re a, must be calculated irst. The approach velocity Reynolds number is evaluated by takin the aspect ratio o the channel width to lenth and it is deined as: Re a Va = ν L (3) Since the channel low is partly ully developed and developin low, the composite model proposed by Teertsra is used to calculate the averae Nusselt number in the channel [4]: Nu 3 3 * ReaPr * = Re a Pr * (4) Re a 3 Nu k air h = (5) L With the assumption that the in width is suiciently lare compared with the in thickness, and alon with the coeicient o heat transer and in eometry, the in eiciency, η, is iven as [0]: tanh ml c η = (6) ml where ml c is deined as: c h 3 ml c = L c (7) k A m m and the corrected in lenth and in proile area are ound usin these equations: t L c = L (8) A m = L ct (9) Base Spreadin Resistance As heat lows across the cross sectional area o the base, it encounters resistance and thereore ives rise to the base temperature. Dependin on the size o the heat source, the smaller the heat source, the hiher the base spreadin resistance. The empirical solution by Lee is shown as ollows []: Θ s = k m A b where λ is iven as: A sc λk ma bθ ave tanh πa k ma bθ avetanh b A sc λ 3 b sc ( λt b ) ( λt ) b (0) λ = π A () A In our study, the averae thermal resistance, Θave, is assumed to be equal to the in thermal resistance, Θ. Experimental Method Fiure 3 shows the test sample experimental setup. There are total o 8 heat sink samples with varyin pitches. Three thermocouples are inserted into the pilot holes in the base to monitor the base temperature. Usin the above approximation, the coeicient o heat transer, h, can be expressed as:
4 Fiure 5 shows the wind tunnel assembly with micro blower attachment. The experimental procedures or micro blower are the same as the DC axial an. Fiure 3. Experimental Setup o Test Sample Thermal rease is used as an interace material between the heat source and heat sink base. The thermoelectric module serves as heat source in this experiment. The desin speciications o heat sink sample are listed in Table. Table. Heat Sink Sample Desin Speciications Fin Material Aluminum A3003 Fin Thickness 0.mm Fin Pitch 0.95mm,.05mm,.0mm,.30mm,.45mm,.55mm,.70mm,.80mm Base Material Copper C0 Base Thickness 6mm Overall Sample Dimension 0L x 40W x 0H mm The wind tunnel assembly used or heat sink characterization is shown in Fiure 4. The DC axial an module is attached to one end o the wind tunnel to deliver airlow throuh the duct. The test sample in Fiure 3 is mounted in the closely ducted test section o the wind tunnel. Temperature measurements taken rom the base are output to the data loer or recordin. The test samples are tested under dierent DC axial ans with dierent volumetric low rates and head pressure. Fiure 5. Schematic o Experimental Setup with Micro Blower Table provides the ans and blowers speciication used in this experiment. Table. Blowers and Fans Speciications Type Power (W) Dimension (mm) Hih Power Blower Low Power Blower Hih Power Axial Fan Low Power Axial Fan Max Flow Rate (CFM) Max Static Pressure (mmh O) x 40 x x 40 x x 30 x x 30 x The experimental thermal resistance, Θba, is a measure o the temperature dierence between the base and ambient air over the power delivered by the thermoelectric module. It is deined as: Tb Tamb Θ ba = () P Discussion o Results Fiure 6 shows the experimental thermal resistances versus the channel width/lenth ratio or the 4 dierent an types. It is observed that the low power blower has the worst thermal perormance and the hih power axial an turned out to be the overall best perormer. The hih power blower perormed nearly as well as the hih power axial an. Fiure 6 also shows that the order o the ans perormance matches the ans maximum volumetric low rate. Fiure 4. Schematic o Experimental Setup with Axial Fan
5 Thermal Resistance, C/W Hih Power Axial Fan Low Power Axial Fan Channel Width/Lenth Hih Power Blower Low Power Blower Fiure 6. Experimental Total Thermal Resistance vs. The Channel Width/Lenth Ratios with dierent types o Micro Blower and Axial Fan Comparin between the optimization points o the blowers and axial ans, both blowers produced a local minima at width/lenth ratio. As or the hih and low power axial ans, optimizations are ound on the points o and width/lenth ratio respectively. This suests that the mass low rate o the axial ans is more reatly hindered by the pressure drop o the heat sink as compared to the blowers. In Fiure 6, it is also clearly indicated that there is an optimization point or all our cases that have been investiated in this experiment. Because the optimization point varies between the heat sink eometries and an types, it is concluded that both o the actors eect the heat sink optimization. In order to attain the optimum perormance, the heat sink and system desin, coupled with the an selection is considered to be a critical path. Thermal Resistance, C/W Experimental (Low Power) Theoretical (Low Power) Experimental (Hih Power) Theoretical (Hih Power) Channel Width/Lenth Fiure 7. Total Thermal Resistance vs. The Channel Width/Lenth Ratio with Micro Blower The blower theoretical and experimental thermal resistance is shown in Fiure 7. Both o sets o data exhibit similar trends, and it is observed that the optimized point or both theoretical and experimental data aree. The theoretical data or the low power blower shows an averae o 9% better perormance than the experimental data. The theoretical data or the hih power blower showed an averae o 8% better perormance over the experimental data. Thermal Resistance, C/W Experimental (Low Power) 4.80 Theoretical (Low Power) 4.50 Experimental (Hih Power) 4.0 Theoretical (Hih Power) Channel Width/Lenth Fiure 8. Total Thermal Resistance vs. The Channel Width/Lenth Ratio with Axial Fan Fiure 8 shows the comparison o thermal resistance and channel width/lenth ratio or the axial ans. In these cases, the experimental and theoretical or both axial ans exhibit the same trends. The theoretical and experimental optimization point or the hih power axial an did not match, however the optimization points identiied were very close. As with the blowers, the theoretical axial ans outperormed the experimental results. The theoretical low power axial an perormed about 8% better and the theoretical hih power axial an perormed about 6% better, compared with their correspondin experimental counterparts. It is also noted that the theoretical data did ind the experimental optimums in three o the our cases. This suests that the methodoloy has the ability to determine the optimization point or the systems in the rane tested. However, due to increased perormance o the theoretical data, caution must be used i usin the theoretical methodoloy to simulate the perormance o a real world application. Future methodoloies should also take into account minor resistances, such as in to base bondin resistance, to build a more accurate picture o actual perormance. Conclusions In this experiment, the primary oal was to characterize the perormance o several anheat sink desins. In doin so, the optimization point can be ound or the iven space constraints. The thermal characterization and optimization points were ound experimentally. The secondary oal was to ind a theoretical methodoloy that would accurately predict both the optimization point or a iven space as well as the perormance o the solution. The chosen methodoloy did accurately predict the optimization point, however, it predicted better perormance o the system on averae by 60%.
6 Reerences [] Nelson, Daniel, Enertron Inc. Enertron s contribution the evolution o portable electronics coolin, Electronics Coolin, Vol. 6, Num., pp. 8, January 000. [] Copeland, D., Optimization o Parallel Plate Heatsinks or Forced Convection, Proceedins o 6 th IEEE Semiconductor Thermal Measurement & Manaement Symposium, pp. 667, San Jose, CA, March 3, 000. [3] Biber, C.R., and Fijol, S., FanplusHeatsink Optimization Mechanical and Thermal Desin with Reality, Proceedins o the International Systems Packain Symposium, pp , 999. [4] Teertstra, P., Yovanovich, M.M., Culham, J.R., and Lemczyk, T., Analytical Forced Convection Modelin o Plate Fin Heat Sinks, Proceedins o 5 th IEEE Semiconductor Thermal Measurement & Manaement Symposium, pp. 344, San Dieo, CA, March 9, 999. [5] Bleier, P. Frank, FAN HANDBOOK Selection, Application and Desin, st Edition, McGrawHill, New York, 998. [6] Shah, R.K., and London, A.L., Laminar Flow Forced Convection in Ducts, Advances in Heat Transer, Supplement, Academic Press, 978. [7] Kays, William M., and London, A.L., Analytic Solutions or Flow in Tubes, Compact Heat Exchaners, 3 rd Edition, McGrawHill, New York, 984. [8] Incropera, Frank P., and Dewitt, David P., Internal Flow, Fundamentals o Heat and Mass Transer, 4 th Edition, John Wiley & Sons, New York, 996. [9] Munson, Bruce R., Youn, Donlad F., and Okiishi, Theodore H., Fundamentals o Fluid Mechanics, nd Edition, John Wiley & Sons, New York, 994. [0] Loh, C.K., Chou, BorBin, Nelson, Dan and Chou, D.J., Thermal Behavior o SolderBonded and Adhesive Bonded Folded Fin Assemblies, Proceedins o 6 th IEEE Semiconductor Thermal Measurement & Manaement Symposium, pp. 334, San Jose, CA, March 3, 000. [] Lee, Seri, Calculatin Spreadin Resistance in Heat Sinks, Electronics Coolin, Vol. 4, Num., pp , January 998.
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