FORCED CONVECTIVE HEAT TRANSFER ENHANCEMENT WITH PERFORATED PIN FINS SUBJECT TO AN IMPINGING FLOW ABSTRACT

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1 SEGi Reie ISSN Vol. 5, No. 1, Jl 01, 9-40 *Corresponding athor. FORCED CONVECIVE HEA RANSFER ENHANCEMEN WIH PERFORAED PIN FINS SUBJEC O AN IMPINGING FLOW *Ji-Jinn Foo 1,, Shng-Yh Pi 1, Yin-Ling Lai 1, See-Boon Chin 1 School of Engineering, SEGi Uniersit College, Selangor, Malasia; Department of Mechanical Engineering, Sheffield Uniersit, Sheffield, United Kingdom. ABSRAC he rapid groth in high speed mlti-fnctional miniatried electronics demands more stringent thermal management. he present ork nmericall inestigates the se of staggered perforated pin fins to enhance the rate of heat transfer hile sbject to a ertical impinging flo. In particlar, the nmber of horiontal perforations and the ertical and horiontal diameters of perforation on each pin are stdied. Reslts sho that the Nsselt nmber of pins ith horiontal and ertical perforations is abot 9% higher than that for the solid pins and it increases ith the nmber of horiontal perforations. Pressre drop ith perforated pins is redced b abot 10% compared ith that in solid pins. Perforation prodces smaller bt larger nmber of ortices donstream of the pins hich increases conectie heat transfer bt redces pressre losses. Hoeer, frther increasing the perforation diameters leads to a significant drop in thermal dissipation. Oerall, pin fins ith ertical and horiontal perforations are preferred for heat sink facing an oncoming ertical flo. 1.0 Introdction Heat sinks are emploed to dissipate thermal energ generated b electronic components to maintain a stable operation temperatre. A compact, efficient and easil fabricated heat sink is reqired. Hoeer, the design of heat sink deice is strongl dependent pon the need to balance thermal dissipation and pressre drop across the sstem sch that the oerall cost and efficienc ma be optimied. An eample of a familiar soltion is to appl pin fin arra onto a heat sink design. Kim et. al. [1] stdied eperimentall the thermal dissipation performance of plate fin and pin fin heat sinks hen sbject to a ertical impinging flo. heir reslts shoed that at small pmping poer, the heat sink thermal resistance is loer for pin fins compared ith that for the plate fins. he inlet geometr of confined impinging flo on a smooth channel is fond to be sensitie to heat transfer, here the inlet channel idth and nole-to-plate spacing decrease ith increasing Nsselt nmber and pressre drop []. Yang and Peng [3] inestigated nmericall the impinging heat transfer performance of heat sink ith nniform fin idth. he fond that the effect of fin dimensions on forced conectie heat transfer is more obios at high Renolds nmber. Sparro et. al. [4] obtained eperimentall the effects of in-line and staggered pin fin arras on thermal dissipation and pressre drop. he conclded that the heat transfer and pressre coefficients for staggered arras are higher than those for the in-line arrangement. ahat et. al. [5] optimied the lengthise and spanise arrangements of staggered and inline pins. Soodphakdee et. al. [6] reported nmericall that at lo Renolds nmber 9

2 (Re Dh <390), higher heat transfer coefficient is obtained ith elliptical pin fins. Hoeer, at high Re Dh circlar pin fins is more effectie. Yang et. al. [7] stdied nmericall forced conectie heat transfer in staggered alminm poros pin fin arras. he fond higher heat transfer rate in poros pin fins than in solid pins. Wake formation behind pin is minimal leeard of poros pin conseqentl minimiing pressre losses across the heat sink. heir reslts spported the earlier eperimental std carried ot b Sahin and Demir [8]. he pressre coefficient for staggered pin fin arra can be redced b either introdcing perforated pin-fins or pin-fin-dimple arras [9, 10]. Recentl, Yong et. al. [10] fond from eperimental and nmerical stdies that in horiontall perforated pin fin arras sbject to parallel incoming flo, increasing the nmber of perforation is more important than increasing perforation diameter. he present paper focses on nmerical std of forced conectie heat transfer in staggered perforated pin fins arra sbject to a ertical impinging flo. he effects of nmber of horiontal perforation and the horiontal and ertical perforation diameters on the rate of thermal dissipation and pressre drop are inestigated and compared ith those for the solid pins..0 Nmerical Method A proprietar softare package ANSYS-FLUEN (ersion 1.1.4, USA) as emploed to inestigate the three-dimensional (3D), laminar, stead-state and incompressible forced conectie heat transfer of staggered and perforated pin fins. he schematic diagram of the smmetric comptational domain is shon in Fig. 1. he ertical inlet internal channel dimensions are mm in length, idth and height, respectiel. he horiontal internal channel is mm. he srronding alls are of 3mm thick. Heat transfer performance as simlated on for sets of staggered pin fin arras, i (i) solid pins, Fig. (a), (ii) pins ith 1 to 5 horiontal perforation each of 4mm diameter, Fig. (b), (iii) pins of, 3, 4 and 5mm horiontal perforation diameter ith 5 perforations on each pin, Fig. (c), and (i) pins of, 3, 4 and 5mm ertical perforation diameter ith 5 horiontal perforations haing 4mm diameter on each pin, Fig. (d). In all cases, the pin fin arra contains 14 pins of 8mm diameter and 50mm height spaced niforml at 5mm in lengthise and spanise pitch. he pin arra is placed directl at the bottom of the ertical inlet channel. he smmetr in the comptational domain allos half of the channel to be analsed and nstrctred grids are sed. he channel and pins are assmed to be made of alminm ith thermal condctiit of 0Wm -1 K -1. All the alls ecept the heating srface are treated as adiabatic. For different inlet elocities are selected: 5, 10, 15 and 0ms -1, ith an inlet air temperatre of 300K. he otlet pressre is considered atmospheric. No-slip bondar is applied to the alls as ell as all the pin fin arras. A constant heat fl of 6000Wm - spplies energ nder the heat sink, Fig. 1. Laminar model is selected to particlarl focs at the thermal dissipatie performance of the pin fin arras. Phsical properties are assmed constant. 30

3 Fig. 1: 3D Nmerical Model (a) Solid (b) 3 Pf, D=4mm (c) 5 Pf, D=3mm (d) 5 Pf, D=3mm D hollo =4mm Fig. : Pins ith Different Perforation Nmber (Pf), Horiontal Diameters (D) and Vertical Diameters (D hollo ) 31

4 3 he folloing are the goerning eqations, Stead-state Naier-Stokes eqations, = P µ ρ (1) = P µ ρ () = P µ ρ (3) Heat condction eqation for the channel alls and pins, 0 = (4) Conseration of Energ eqations for the orking flid, = c p λ ρ (5) he Continit eqation, = 0 (6) here ρ is the air densit, P the pressre, μ the iscosit, the temperatre, c p the specific heat capacit of air, λ the thermal condctiit, (,, ) the elocit components, and (,, ) the coordinates. SIMPLE algorithm is sed to cople pressre and elocities. he flid flo and heat transfer are determined b soling iteratiel the goerning energ and momentm eqations in Eq.1-6. he conergence criteria are set to 10-3 for mass conseration together ith three elocit components, and at 10-6 for energ eqation. Simlations hae been carried ot ith trianglar meshes ithin to elements to ensre grid independent soltions. he highest nmber of element is sed for all the simlations. he calclated reslts confirm that the ariations of the srface temperatre distribtions along the heat sink srface are smaller than o C. Validations of the nmerical simlations are gien in a companion std [11]. he aerage Nsselt nmber, N, oerall thermal efficienc, η, pressre drop, P, friction factor, f, and Renolds Nmber, Re p, are defined as follo,

5 q" Dh N = (7) ot in kair (8) P = P in P ot N η = P f = L D h P 1 ρ o (9) (10) ρodp Re p = (11) µ here is the aerage base plate temperatre, in the inlet temperatre, ot the otlet temperatre, k air the thermal condctiit of air, q " the heat fl, D h the hdralic diameter of the inlet rectanglar channel, D p the pin fin diameter, o the inlet elocit, L the impinging affected distance beteen the inlet pressre P in and otlet pressre P ot. he related thermophsical properties of air are obtained sing the blk mean temperatre, m in ot = (1) 3.0 Reslts and Discssion 3.1 Pressre Drop Effect Fig. 3 shos the effects of the nmber of perforation, horiontal perforation diameter (D), and ertical perforation diameter (D hollo ) on f, as a fnction of Re p. In Fig. 3a, friction factor decreases ith increasing Re p de to the increase in kinetic energ of the flo (see Eq.10). Since pin fin arras restrict the flid flo passage casing mch energ dissipation, f are higher for both solid and perforated pin fin arras hen compared ith that in the smooth channel. Figs. 3(a), (b) and (c) also shos that f decreases ith increasing nmber of perforation as the perforations decrease the blockage effect. Since the nmber of perforation is restricted on a gien pin, f ma be frther redced b increasing the perforation diameter. It is important to note that erticall perforated pins are critical for heat sinks sbject to impinging flo. As shon in Fig. 3(d) pins ith horiontal and ertical perforations hae loer f than pins ithot, and pins ith ertical perforations hae the loest f. hs, at Re p = , pin fin arras ith 5Pf, D=3mm, and D hollo from, 3, 4 to 5mm diameter recorded f hich are 7%, 8%, 9% and 10%, respectiel, loer than that sing solid pin fin arra. Solid pin fin arra presents a higher impedance than perforated pins; the reslting ake old also be larger casing higher 33

6 pressre losses. As a reslt, it is eident that smaller f can be effectiel achieed sing perforated pin fins. (a) Nmber of Perforation (Pf) (b) Horiontal Perforation Diameter (D) (c) Vertical Perforation Diameter (D hollo ) (d) Pins With and Withot Vertical Perforations Fig. 3: he Effect of Nmber of Perforation, Horiontal, and Vertical Diameters on Pressre Drop 3. Heat ransfer Performance he effects of the nmber of perforation, horiontal diameter, and horiontal and ertical perforation diameter on N / N are shon in Figs. 4(a), (b), and (c), respectiel; here s N is the Nsselt nmber of smooth channel. Fig. 4(a) clearl sggests that s N / Ns increases ith increasing Re p. he solid and perforated pin fins heat sinks proide mch higher thermal dissipation compared ith the smooth channel ithot pin fin. More importantl, thermal dissipation is higher ith perforated pin fins than ith solid pins. It is fond that the larger the nmber of perforation on each pin fin the higher the N. Sch effect is de to the increase in heat transfer srface area hen the nmber of perforation 34

7 increases. Fig. 4(b) shos the effect of horiontal perforation diameter on pin fins ith fie perforations. he simlations sho that increasing the perforation diameter from to 3mm increases N. Hoeer, frther increasing the perforation diameter from 4 to 5mm redces N. Fig. 4(c) shos the effect of horiontall and erticall perforated pins ith 5 horiontal perforations of 3mm diameter. It is clear that increasing the ertical perforation diameter from mm to 3mm increases N, bt frther increasing it to 4mm redces N. hs, hen the perforation diameter is greater than 3mm, either horiontall or erticall N decreases. his is de to the decrease in the cross sectional area of the pin for heat condction along the pins. As shon in Fig. 4(d), b copling the effect of horiontal and ertical perforations, the heat transfer performance of the pins ma be optimied. Maimm heat transfer is obtained for pin fins ith 5Pf, D=3mm, and D hollo =3mm, e.g., at Re p = the N is 9.% higher than that ith solid pins. (a) Nmber of Perforation (Pf) (b) Horiontal Perforation Diameter (D) (c) Vertical Perforation Diameter (D hollo ) (d) Pins With and Withot Vertical Perforations Fig. 4: N s. Re : he Effect of Nmber of Perforation, Horiontal, and Vertical Diameters p 35

8 3.3 Heat ransfer Efficienc Oerall thermal efficienc is defined b the ratio of N, oer P [1] ith nit Pa -1. It describes the relatie cost (pressre drop hence pmping poer) to achiee a certain rate of heat transfer. Fig. 5 shos the range of the oerall thermal efficienc for to perforated pin fin arras hich are the best performing in each case. It is fond that the perforated pin fins hae higher efficienc than the solid pin fins. Clearl pin fin arras that cople both horiontal and ertical perforations are able to frther enhance the thermal dissipatie performance hen sbject to ertical impinging flo hilst loering the pmping poer needed b the heat sink. Since pressre drop significantl affects the thermal efficienc of a heat sink, perforated pin fin arra on the heat sink ma maimie the rate of heat transfer at minimal cost. Fig. 5: Dependent of hermal Efficienc on the Nmber of Perforation, Horiontal Diameter, and Vertical Diameter 3.4 Comparison: Effects of Nmber of Perforation and Perforation Diameter he geometr and dimensions of the pin fin limit the nmber of perforations and perforation diameter that ma be sed. hs, it is important to look into the relatie contribtion of both effects on heat transfer on pin fin arra ith the same srface area. In Fig. 6(a) the pin fin arra ith three perforations of 4mm diameter is compared ith fie perforation of mm diameter. It is fond that at Re p > the latter prodced a higher N hence a higher thermal dissipation rate. he difference ma be eplained b the present flo impinging effect as it is more difficlt for the flo stream to bend horiontall into a smaller perforation at a loer Re p, especiall for 5 Pf pins here the first and second perforations are too close to the heated srface. Hoeer, frther increasing the srface area as ell as perforation diameter, as shon in Fig. 6(b), the rate of heat transfer is higher for pins ith fie perforation of 3mm diameter than that ith three perforation of 36

9 4mm diameter. hs, effectie pin area for aial heat condction along the pin is larger for pins ith smaller perforations, proided that Re p > hen the first perforation of D=mm is 9mm aboe the heat sink srface. (a) 3 Pf, D=4mm s. 5 Pf, D=mm (b) 4 Pf, D=4mm s. 5 Pf, D=3mm Fig. 6: Effect of Nmber of Perforation and Horiontal Perforation Diameter at An Eqialent Pin Fin Arra Srface Area of 0.031m (a) and 0.03m (b) Respectiel Larger nmber of perforations ma redce the blockage effect on the flo prodcing smaller bt also larger nmber of akes behind the pins [11, 1]. his ma be seen in Figs. A1 and A. hese smaller akes are more effectie in remoing the flid aa from the pins and carring the heat ith it. Fig. A3 also sho that temperatre is generall loer in perforated pins (5 Pf, D=3mm, D hollo =3mm) than that in the solid pins. As a reslt, the nmber of perforation is more critical in enhancing thermal dissipation than the perforation diameter. Fig. A1: Wakes Behind Solid Pin Fins Fig. A: Wakes Behind Perforated Pin Fins 37

10 (a) (b) Fig. A3: hree Dimensional emperatre Distribtions beteen (a) Solid Pins and (b) Pins ith Horiontal and Vertical Perforations 4.0 Conclsion Stead-state forced conectie heat transfer in staggered pin fin arras in a rectanglar channel has been stdied sing nmerical simlation to qantif their heat transfer characteristics. hermal efficiencies are compared beteen solid and arios perforated pin fin heat sinks. he conclsions of this std are: 1. P across the heat sink is smaller ith increasing nmber of perforation and perforation diameter. In all cases, perforated pin fin arra performs better than the solid pins. Hence, perforated pin fins reqire less pmping poer than the solid pins for the same thermal performance.. Maimm N is obtained from pin fin arra ith 5 perforations, 3mm horiontal perforation diameter, and 3mm of ertical perforation. It is approimatel 9% higher than that for the solid pins at Re p = More importantl, the thermal energ is dissipated at a smaller pressre drop. 3. N increases ith the increasing (i) nmber of perforation, (ii) horiontal perforation diameter, and (iii) copling horiontal and ertical perforation diameters. Frther increasing the perforation diameters ill lead to a redction in thermal dissipation. his is de to the decrease in ertical heat condction along the perforated pin fins, as ell as the perforations indces reshaping of akes behind the pins. hs, hile designing a perforated pin fin arra, the balance beteen the perforation nmber and diameter shold be carefll taken into consideration. 5.0 Acknoledgement he athors old like to thank SEGi Uniersit College (Kota Damansara) for the financial spport of the research project (SCM ). 38

11 REFERENCES 1 D.K. Kim, S.J. Kim and J.J. Bae. International Jornal of Heat and Mass ransfer. 5, (009). Z.Q. Lo, A.S. Mjmdar and C. Yap. Applied hermal Engineering. 5, (005). 3 Y.. Yang and H.S. Peng. International Jornal of Heat and Mass rasnfer. 5, (009). 4 E.M. Sparro, J.W. Ramse and C.A.C. Altermani. ASME Jornal of Heat ransfer. 10, (1980). 5 M. ahat, Z.H. Kodah, B.A. Jarrah and S.D. Probert. Applied Energ. 67, (000). 6 D. Soodphakdee, M. Behnia and D.W. Copeland. he International Jornal of Microcircits and Electronic Packaging. 4, (001). 7 J. Yang, M. Zeng, Q. Wang and A, Nakaama. ASME Jornal of Heat ransfer. 13, (010). 8 B. Sahin and A. Demir. Energ Conersion and Management. 49, (008). 9 Y. Rao, C. Wan, Y. X and S.S. Zang. International Jornal of hermal Sciences. 50, (011). 10 K.K.. Yong, Y.L. Lai, J.J. Foo and S.B. Chin. nd International Conference on Mechanical and Manfactring Engineering, Malasia (011). 11 S.Y. Pi, Final Year Research hesis, SEGi Uniersit College (011). 1 H.R. Sef and M. Laeghi. ASME Jornal of Heat ransfer. 13, (010). 39

12 Nomenclatre c p specific heat capacit, Jkg -1 K -1 D horiontal perforation diameter, mm D hollo ertical perforation diameter, mm D p pin fin diameter, mm D h hdralic diameter, mm f friction factor k air thermal condctiit of air, Wm -1 K -1 L impinging affect distance, m N Nsselt nmber q" heat fl, Wm - in inlet temperatre, o C m blk mean temperatre, o C ot otlet temperatre, o C aerage base plate temperatre, o C P P Pf P in P ot Re p air pressre, Pa pressre drop, Pa nmber of perforation pressre inlet, Pa pressre otlet, Pa Renolds nmber based on pin fin diameter o inlet elocit, ms -1,, elocit components, ms -1,, coordinates Greek smbols η thermal efficienc, Pa -1 ρ densit of air, kgm -3 µ iscosit of air, kgm -1 s -1 40