Numerical study of metal foam heat sinks under uniform impinging flow

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1 Journal o Phyic: Conerence Serie PAPER OPEN ACCESS Numerical tudy o metal oam heat ink under uniorm impinging low To cite thi article: A Andreozzi et al 17 J. Phy.: Con. Ser View the article online or update and enhancement. Related content - Bubbly ree and impinging jet: experimental tudy by mean o PIV and PFBI K S Pervunin and M V Timohevkiy - Numerical tudy o heat traner o emboed plate ined heat ink Suliman Mohamed Mohamed Ali, Waleed Fekry Fari and Ahmed Fari Imail - Experimental invetigation o olidiication in metal oam enhanced phae change material W Beyne, O Baci, H Huieune et al. Recent citation - Comparative Study o the Heating Surace Impact on Porou-material-involved Spray Sytem or Electronic Cooling - an Experimental Approach Ji-Xiang Wang et al - Aniotropy eect on convective heat traner and preure drop in Kelvin open-cell oam M Iaiello et al Thi content wa downloaded rom IP addre on 8/7/18 at 1:13

2 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 International Conerence on Recent Trend in Phyic 16 (ICRTP16) Journal o Phyic: Conerence Serie 755 (16) 111 IOP Publihing doi:1.188/ /755/1/111 Numerical tudy o metal oam heat ink under uniorm impinging low A Andreozzi 1, N Bianco, M Iaiello and V Nao Dipartimento di Ingegneria Indutriale, Univerità degli tudi di Napoli Federico II, P.le Tecchio 8, 815, Napoli, Italy 1 aunta.andreozzi@unina.it Abtract. The ever-increaing demand or perormance improvement and miniaturization o electronic ha led to a igniicant generation o wate heat that mut be diipated to enure a reliable device operation. The miniaturization o the component complicate thi tak. In act, reducing the heat traner area, at the ame required heat rate, it i neceary to increae the heat lux, o that the material operate in a temperature range uitable to it proper unctioning. Traditional heat ink are no longer capable o diipating the generated heat and innovative approache are needed to addre the emerging thermal management challenge. Recently, heat traner in open-cell metal oam under an impinging jet ha received attention due to the coniderable heat traner potential o combining two cooling technologie: impinging jet and porou medium. Thi paper preent a numerical tudy on Finned Metal Foam () and Metal Foam () heat ink under impinging air jet cooling. The analyi i carried out by mean o the commercial otware COMSOL Multiphyic. The purpoe i to analyze the thermal perormance o the metal oam heat ink, inned or not, varying it geometric parameter. Reult are preented in term o predicted diipated heat rate, convective heat traner coeicient and preure loe. Nomenclature A, b Coeicient Re Reynold number C p Heat capacity at contant preure (J/kg K) Re c Cell Reynold number d c Cell ize (m) Fin pitch (m) d Strut thickne (m) t Fin thickne (m) D Inlet ection diameter (m) T Temperature (K) Inertial actor u Velocity vector (m/) h c Heat traner coeicient (W/m K) W Heated plate ide (m) h v Volumetric heat traner coeicient (W/m 3 K) H Heat ink height (m) Greek ymbol k Thermal conductivity (W/m K) ε Poroity k p Fin thermal conductivity (W/m K) μ Dynamic vicoity (kg/m ) K Permeability (m ) ρ Denity (kg/m 3 ) n Normal vector Shear tre (N/m ) p Preure (Pa) Subcript PPI Pore per inch (1/in) Ambient Pr Prandtl number e Eective Q Heat rate (W) Fluid Content rom thi work may be ued under the term o the Creative Common Attribution 3. licence. Any urther ditribution o thi work mut maintain attribution to the author() and the title o the work, journal citation and DOI. Publihed under licence by IOP Publihing Ltd 1

3 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 Solid Solid Supercript Other ymbol Fluid <> Volume average 1. Introduction With the advent o modern electronic computer, cooling electronic chip have become one o the principal ubject or heat traner cience and engineering. The technological progre in the ield o microchip ha long ocued on miniaturization and on increaing the computational peed. The demand o high peed and miniaturization o electronic component reult in increaed power diipation requirement or thermal management. Among variou cooling technique or electronic component, orced convective cooling with air eature advantage o convenience and low cot. Limitation o the orced convective cooling with air, however, lie in the relatively low heat removal rate. In act, traditional heat ink are no longer capable o diipating the generated heat and innovative approache are needed to addre the emerging thermal management challenge. The heat diipation o a heat traner medium i a complex unction o many actor, e.g., available heat traner area, heat conduction, heat traner coeicient, and low reitance characteritic. Thee actor are trongly dependent on the tructure o the heat traner medium; and they conlict with each other; or example, higher urace area and tronger heat conduction capability uually lead to larger low reitance. Recently, heat traner in open-cell metal oam under an impinging jet ha received much attention due to the coniderable heat traner potential o combining two dierent cooling technologie: impinging jet and porou medium. Extenive tudie have been carried out to enhance the orced convective cooling with air by utilizing heat ink with dierent hape, material, low pattern, etc... Aluminum metal-oam heat ink have proven to be uitable in the thermal control o high-power electronic component, with excellent cooling perormance under orced convective condition [1]. Bhattacharya and Mahajan [] propoed a heat ink made up by a inned metal oam heat exchanger. They inerted block o aluminium-oam between variou parallel plate in, and invetigated the orced convection or oam ample with dierent poroitie and PPI. The heat traner coeicient turned out to be ix time that in a conventional longitudinal inned heat ink. Kim et al. [3] invetigated experimentally the heat traner in a channel partially illed with an aluminium-oam heat ink, with an impoed uniorm heat lux at it bai. Experiment were made or dierent PPI and Reynold number, and reult howed that the lowet thermal reitance wa obtained with the lowet PPI oam. The comparion with a conventional parallel-plate heat ink howed the advantage to ue an aluminium-oam baed heat ink. Hieh et al. [4] obtained Nuelt number correlation or dierent velocitie, PPI and poroitie, with an experimental apparatu imilar to a proceor cooling heat ink, with the heat ource orthogonally inveted by a tream o air. Shih et al. [5] howed that the perormance o an aluminium-oam heat ink i aected by the height o a ink under impinging-jet low condition. The Nuelt number wa no monotonically correlated with the height and an optimal height wa ound, a a unction o PPI and poroity. Succeively Shih et al. [6] demontrated that the heat traner perormance o the ame aluminium-oam heat ink improved by uing an annular lowretricting mak, that reduced the low outlet ection. Recently, uing 3-D printing and invetment cating technique, Krihnan et al. [7] abricated and tudied heat ink with regular oam tructure, and concluded that on an equal pumping power bai, heat ink outperorm conventional plate-in heat ink. Feng et al. [8] carried out a combined experimental and numerical tudy on inned metal oam () and metal oam () heat ink under impinging air jet cooling. Comparion o experimental and numerical reult reveal that uing the laminar Darcy extended model can predict airly both the heat traner and preure drop o and heat ink under high Reynold number. A numerical invetigation wa carried out to characterize the thermal perormance o inned metal oam heat ink ubject to an impinging air low by Feng et al [9]. The main objective o the tudy wa to quantiy the eect o all relevant conigurational parameter (channel length, channel width, in thickne, and in height) o the heat ink upon the thermal perormance. Variou imulation cae or dierent combination o channel

4 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 parameter were carried out to obtain the Nuelt number correlation. Baed on the invicid impinging low, a preure drop correlation wa derivedd or impinging low in inned metal oam heat ink. By uing the above reerred correlation, the thermal perormance o inned metal oam heat ink wa compared with that o conventional plate-in heat ink. It wa demontrated that the inned metal oam heat ink outperormed the plate-in heat ink on the bai o given weight or given pumping power. Thi paper preent a numerical tudy on inned metal oam () and metal oam () heat ink under impinging air jet cooling. The numerical analyi i carried out by mean o the commercial otware COMSOL Multiphyic. The purpoe i to analyze the thermal perormance o the metal oam heat ink, inned or not, varying it geometric parameter. Reult are preented in term o diipated heat rate, convective heat traner coeicient and preure loe.. Mathematical model The Finned Metal Foam () heat ink i repreented in Fig.1. The heated plate i located at the bottom o the heat ink. The air low come rom a circular ection located on the top, take heat rom the plate and exit rom the heat ink lateral ide. The Metal Foam () heat ink ha the ame coniguration but without in. The heated plate i a 68 x 68 mm quare. The ratio o the impinging low ection diameter, D, to the heated plate ide, W, i.5,.5,.75, 1.. The height o the computational domain, H, i 1,, 3, 4 mm. The in thickne, t, i and 4 mm. The number o in ued in the computation i 1,, 4, 6, 8, and 1. The poroity and the PPI o the aluminum oam are.88,.91,.94,.97 and 5, 1,, 4, repectively..1. Governing equation The porou mediumm i treated a an equivalent homogeneou medium, and governing equation are written by uing the Volume Averaging Technique (VAT). Due to the phyic o the problem, a Local Thermal non-equilibrium (LTNE) model i employed. The low i aumed to be teady and laminar. Eect o buoyancy, thermal diperion and thermal tortuoity are neglected. Thermophyical propertie are conidered to be independent o the temperature. The governing equation or the porou domain are: Figure 1. Finned Metal Foam () heat ink. 3

5 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 u = (1) u u p u u u u () K K C, p T k e T hv T T u (3) ke, T hv T T (4) while the Laplace equation i ued or the aluminium in... Cloing coeicient In order to olve porou medium governing equation, cloing coeicient are required or permeability, K, inertial coeicient,, thermal conductivitie, k e, and k e,, and volumetric heat traner coeicient, h v. Permeability and inertial coeicient are obtained rom the ollowing equation [1]: d c K (5) K (6) d c where d c i the cell ize. For the energy equation, the eective thermal conductivitie, k e,, k e,, and the volumetric heat traner coeicient, h v, are required. The eective thermal conductivity, k e, i [11]: k 1 ke ke, ke, k (7) 3 The volumetric heat traner coeicient, h v, i obtained rom the ollowing correlation [1]: k h (8) v Re c dc where Re c = u d c / i the cell Reynold number..3. Boundary condition Boundary condition o the problem are reumed in Table 1. A rectangular coordinate ytem with the origin located at the bottom-let corner i employed or the three-dimenional model. For the heated plate, a 7 C uniorm temperature i impoed. The thermal conductivity o the aluminium in i et equal to 17 W/m K. In the inlet low ection, a Robin boundary condition i ued or both olid phae o the oam energy equation and aluminium in equation. In particular, or the olid phae oam equation, a correlation or taggered cylinder in crolow i ued [13]: k b.37 hc ARe Pr (9) d 4

6 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 where the Reynold number i deined a Re = u d /, with d the trut thickne, and the contant A and b depending on the Reynold number [13]. Table 1. Boundary condition o the problem. Momentum Energy (luid) Energy (olid) Fin Inlet uu n T C T T ke, hc T T kp hct T n n Other u T T T n n n Heat ink p 11 kpa T T T ide i, j n n n Foam/in u T k 1 T T Interace ke, kp n 3 n n Bottom u T T T 7 C For the aluminium in, the ollowing equation i ued [14]: k.5 hc.6re (1) t where the Reynold number i deined by uing the in thickne a the characteritic length. 3. Reult The olid-phae dimenionle temperature on the heated plate, or D/W = 1 and D/W =.5, are reported in Fig.. It i hown that at higher D/W value the air reache the whole heat ink, while, at lower D/W value not the whole heat ink i employed, ince mot o the heated plate remain at <T > /<T > y= = 1. Thi mean that, when the impinging ection i larger, the eiciency o the heat ink i improved ince all the heated plate contribute to heat traner. However, it hould be pointed out that reducing the impinging ection make the central region o the heat ink colder than that o the larger impinging ection cae, ince the air velocity locally increae. Reult are reported in term o the heat traner coeicient, evaluated with the ollowing equation: h c Q W T T (11) where Q i the heat rate and W the area o the heated plate. The heat traner coeicient i calculated on the heated plate. Diipated heat rate a a unction o the velocity, or the and heat ink, together with data by Feng et al. [8], are reported in Fig. 3. The igure exhibit dierence between prediction by the preent model and Feng et al. model le than 8% or the FM model and le than 18% or the. 5

7 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 T T y T T y (a) (b) Figure. Solid-phae dimenionle temperature on the heated plate: a) D/W = 1; b) D/W =.5. Convection heat traner coeicient and preure drop are evaluated or =.9, PPI = 1, u =.5 m/, t = mm, H = mm and D/W = 1. The heat traner coeicient and the preure drop a a unction o the number o in, or t = mm and 4 mm, are preented in Fig. 4. The igure point out that, both or and 4 in, the heat traner coeicient increae, attain a maximum and then decreae. Thi behaviour i due to a competition between two actor: the increae in the number o in, which enhance the diipated heat rate, and the reduction in the oam inert volume. In the irt part o the curve, the increae in the in number improve the heat ink perormance, but it reduce the oam volume, thu reducing the diipated heat. A to the preure drop, more in mean le oam volume, thu le preure drop due to the reduction o oam inert volume. The heat traner coeicient and preure drop a a unction o the ink height, or and heat ink with our in, are reported in Fig.5. The heat traner coeicient reduce with height becaue the impinging jet reache the hot plate more diicultly, and alo preure drop reduce ince a larger raction o the luid exit the heat ink rom the ide wall o the oam. The comparion o the heat ink with the heat ink how that the latter exhibit a higher heat traner coeicient but alo a higher preure drop. Heat rate (W) u (m/) Feng et al. [8] () Preent tudy () Feng et al. [8] () Preent tudy () Figure 3. Diipated heat rate v. the velocity, or the and heat ink. 6

8 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 hc (W / m K) t = mm t = 4 mm n in p (Pa) t = mm t = 4 mm n in Figure 4. Heat traner coeicient and preure drop v. the number o in, or t = mm and 4 mm. The heat traner coeicient and preure drop a a unction o the ratio o the impinging jet diameter to the ide length o the heated plate, or and ink with our in, are reported in Fig.6. We notice that the larger the ection the larger the heat traner coeicient, ince increaing the plate ize decreae the velocity o the luid but allow the luid to reach the plate in an eaier way. The coniguration perorm better than the one at low value o D/W becaue it i inned and ha a maller ree area; thu the contribution o cold air i dratically reduced. Preure drop in the coniguration i unaected by the ize o the impinging ection ince the ma low rate i unchanged, while preure drop in i aected by the ize o impinging ection becaue o the in, that induce a concentrated preure drop. The heat traner coeicient and preure drop a a unction o the poroity, or and ink with our in, are reported in Fig.7. The igure how that increaing the poroity reduce the heat traner coeicient, becaue it i inverely proportional to the poroity, a well it reduce alo the preure drop, ince the oam contain a decreaing raction o olid. The convection heat traner coeicient and preure drop a a unction o PPI, or and ink with our in, are reported in Fig.8. The igure exhibit a light increae in heat traner coeicient and a marked increae in preure drop at increaing PPI. Heat traner in coniguration i almot independent o PPI, ince at high value o the volumetric heat traner coeicient a LTE condition i attained and enhancing PPI i uele. hc (W / m K) H (mm) p (Pa) H (mm) Figure 5. Heat traner coeicient and preure drop v. the ink height, or and heat ink with our in. 7

9 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 hc (W / m K) D/W p (Pa) D/W Figure 6. Heat traner coeicient and preure drop v. the ratio o the impinging jet diameter to the ide length o the heated plate, or and ink with our in. hc (W / m K) Figure 7. Heat traner coeicient and preure drop v. the poroity, or and ink with our in. p (Pa) hc (W / m K) PPI p (Pa) PPI Figure 8. Heat traner coeicient and preure drop v. PPI, or and ink with our in. 8

10 34th UIT Heat Traner Conerence 16 IOP Con. Serie: Journal o Phyic: Con. Serie 796 (17) 1 IOP Publihing doi:1.188/ /796/1/1 4. Concluion In thi paper a numerical analyi o heat traner and preure drop in a heat ink under impinging air jet cooling i carried out. Two dierent heat ink coniguration have been invetigated: a metal oam heat ink and a inned metal oam heat ink. The air-aturated oam i treated a an equivalent homogenou medium, by employing the Local Thermal non-equilibrium model. The problem i numerically olved by mean o the COMSOL Multiphyic code. The eect o the ratio o the impinging jet diameter to the heated plate ide, the height o the heat ink, the in thickne, the number o in, the oam poroity and PPI are analyzed. Reult how that when the impinging jet diameter i equal to the heated plate ide, both the heat traner coeicient and preure drop in the inned metal oam heat ink are larger than thoe in the metal oam heat ink. The metal oam heat ink perorm better than the inned metal oam heat ink when the impinging jet diameter i maller than the heated plate ide. 5. Reerence [1] Sathe S and Sammakia B 1998 A review o recent development in ome practical apect o air cooled electronic package Tran. ASME, J. Heat Tran [] Bhattacharya A and Mahajan R L Finned metal oam heat ink or electronic cooling in orced convection J. Electron. Pack [3] Kim S Y, Paek J W and Kang B H 3 Thermal perormance o aluminum-oam heat ink by orced air cooling IEEE T. Compon. Pack. T [4] Hieh W H, Wu J Y, Shih W H and Chiu W C 4 Experimental invetigation o heat-traner characteritic o aluminum-oam heat ink Int. J. Heat Ma Tran [5] Shih W H, Chiu W C and Hieh W H 6 Height eect on heat-traner characteritic o aluminum-oam heat ink J. Heat Tran-T. ASME [6] Shih W H, Chou F C and Hieh W H 7 Experimental invetigation o the heat traner characteritic o aluminum-oam heat ink with retricted low outlet, J. Heat Tran-T. ASME [7] Krihnan S, Hernon D, Hode M, Mullin J and Lyon A M 1 Deign o complex tructured monolithic heat ink or enhanced air cooling IEEE Tran. Compon. Packag. Manu. Technol. () [8] Feng S S, Kuang J J, Wen T, Lu T J and Ichimiya K 14 An experimental and numerical tudy o inned metal oam heat ink under impinging air jet cooling Int. J. Heat Ma Tran [9] Feng S S, Kuang J J, Lu T J and Ichimiya K 15 Heat traner and preure drop characteritic o inned metal oam heat ink under uniorm impinging low Journal o Electronic Packaging, Tran. ASME 137 paper number 114 [1] Wu Z, Caliot C, Bai F, Flamant G, Wang Z, Zhang J and Tian C 1 Experimental and numerical tudie o the preure drop in ceramic oam or volumetric olar receiver application Appl. Energy [11] Kamiuto K 8 Modeling o Compoite Heat Traner in Open-Cellular Porou Material at High Temperature Cellular and Porou Material: Thermal Propertie, Simulation and Prediction, ed A Öchner, G E Murch and M J S de Lemo (Weinheim: Wiley-VCH) chapter 6 pp [1] Wu Z, Caliot C, Flamant G and Wang Z 11 Coupled radiation and low modeling in ceramic oam volumetric olar air receiver Sol. Energy [13] Zukauka A. A Convective heat traner in cro-low Handbook o Single-Phae Convective Heat Traner, ed S Kakac, R K Shah and W Aung (New York, NY: Wiley) [14] Eckert E R G and Drake R M 197 Analyi o Heat and Ma Traner (New York, NY: McGraw-Hill) 9