Simulation of the Macroscopic Heat Transfer and Flow Behaviours in Microchannel Heat Sinks using Porous Media Approximation

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1 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) Simulation o the Macrocopic Heat Traner and Flow Behaviour in Microchannel Heat Sink uing Porou Media Approximation F.Y. LIM 1, S. ABDULLAH 1, I. AHMAD 3, B.Y. MAJLIS 1 AND K.SOPIAN 1 Intitute o Micro Engineering & Nanoelectronic (IMEN) Solar Energy Reearch Intitute Univeriti Kebangaan Malayia, UKM Bangi, Malayia 3 Univeriti Tenaga Naional (UNITEN) Km 7, Jalan Kajang-Puchong, Puchong, Selangor, Malayia. angyau@eng.ukm.my; hahrir@eng.ukm.my,kopian@vli.eng.ukm.my Abtract: - Due to the high perormance o electronic component, the heat generated i increaing dramatically and cooling ytem or uch component become one o the mot important iue to diipate heat that generated in electronic component. In the preent analyi, a microchannel heat ink coniguration i imulated by modelling the tacked microchannel heat ink in macrocopic cale a i it i a luid aturated porou medium. The olution are obtained numerical uing a Brinkmann-baed ormulation. In order to accurately predict the permeability o the tacked microchannel, the imulation are compared with imulated ingle microchannel heat ink auming incompreible low and good agreement wa ound with the imulation a well a experimental reult perormed by other reearcher. Then the veriied porou-media-like-microchannel are combined to be part o a computational domain o a CFD imulation where olution to the imulation can be ued to deign and optimize the gating ytem or the heat ink. Key-Word: - Microchannel heat ink; Porou media approximation; Heat traner; Thermal management; Watercooled 1 Introduction Recent advance in emiconductor technology have led to the igniicant increae in power denitie encounter in microelectronic equipment. According to the International Roadmap or Semiconductor (ITRS), the maximum power o ingle chip package will reach 173 W/cm in 0 [1]. The increae o heat that generate within the microelectronic equipment ha led to many cooling method that propoed by other reearcher. One o the promiing poible method or removing high heat lux i by uing orce convection microchannel heat ink which i abricated a an integral part o the ilicon waer. The microchannel heat ink wa irt propoed over 7 year ago by Tuckerman and Peae [,3]. Since it emergence, many numerical tudy and experimental tudy had been conducted. For example, experimental work were conducted by Miaggia et al. [4]. Kleiner et al. [5], and Laance and Simon [6]. Theoretical and numerical work were perormed by Samalam [7] and Weiberg et al. [8] who invetigate claical one-layer microchannel heat ink. Philip [9] and Morini [10] preented critical review paper on the numerical tudy and experimental work. However, mot o the tudie were limited to conventional method utilizing CFD code. Even i it i poible, mapping the whole microchannel can lead to very high computing cot and uch method are limited by number o imulated channel and dimenion o apparatu, uch method requet much more numerical eort to handle complex geometrie in detail. In the middle o 1980, Koh and Colony [11] have modelled microchannel heat ink a luid-aturated porou medium by uing Darcy law to decribe the low. Thi approach later i applied to the microchannel by Tien and Kuo [1], and later extended by Kim and co-worker [13-15] by uing averaging approach or the velocity and temperature ditribution in microchannel. In thi paper, the luid low and heat traner or ingle microchannel wa imulated to invetigate temperature proile a well a low characteritic inide the microchannel. Then, the reult o luid low or the ingle microchannel i analyed and compared with the Brinkman equation model. For veriication o the reult, the imulation outcome are compared with the reult obtained by Kim and co-worker [13,14]. Problem Decription and Model Deinition In thi tudy, water i ued a the working luid in the microchannel heatink operation. Silicon wa ued a the material o the microchannel. The microchannel have a width W ch and depth H. The wall that eparate ISSN: ISBN:

2 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) between the channel are reerred to a in and ha a width W in. The top wall o the mocrochannel i aummed inulated while the bottom wall receive a uniorm heat lux q w. The heat lux repreent the heat that needed to be diipated rom electronic chip. The coolant water i orced to enter the open channel in the x-direction to achieve heat diipation a hown in Fig. 1. o the ingle microchannel i elected a computational domain a hown in Fig 3. For the computational meh, in order to increae accuracy, quadrilateral element ha been ued to generate the volume meh, a hown in Fig.3 or ingle microchannel coniguration. Fig Geometry or Single Microchannel Fig 1 Schematic diagram o the microchannel heat ink Here, it i aumed that water i incompreible, ingle phae-luid and ha been ully developed laminar low in a ingle microchannel. The teady-tate governing equation can be written in vector orm a ollow: Ma: ρ u = 0 (1) Momentum: T ρ u ( u) = p + μ [ u + ( u) ] () Energy: ρ C u T = k T ( ) p. or luid (3) k T = or conduction in ubtrate (3) ( ) 0 The governing equation are olved uing the COMSOL Multiphyic otware, which ue the inite element method in olving the governing equation. In order to tudy the luid low and heat traner o ingle microchannel, the model employ the general teady convective heat traner analyi with incompreible luid a the medium. The domain i made o two ub-domain coniting o a cuboid and a L-hape a depicted in Fig.. Silicon wa ued to contruct the microchannel tructure. The dimenion or the ingle- microchannel i tabulated in Table 1.The dimenion i et with the apect ratio H/Wc = 6 in order to compare with the reult obtained by Kim and coworker [13-15]. Due to ymmetry o the problem, hal Fig. 3 Meh or microchannel Table 1 Dimenion o the microchannel. Dimenion (mm) Lc Wc Ww Hc Hw A propoed by Kim and co-worker [13-15], the microchannel heat ink can be modelled a porou media. The governing equation or the luid low and heat traner i etablihed by applying volume-averaged technique a hown a below [1]: Fluid low: d d μ p + μ u ε u dx dy κ = 0 (5) Energy in olid phae: k T = ha( T T ) y (6) Energy in luid phae: ISSN: ISBN:

3 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) ( ρ C p, ) u T = ha( T T ) ε (7) x Hence, the microchannel heat ink hown in Fig. 1 wa modelled a a porou medium with poroity ε, permeability κ and wetted area per volume a can be expreed a [16]: ( + H ) ( W + W ) ε ε =, κ =, a = (8) + Win 1 ch in H The above parameter wa ued in the imulation to model the porou media. The porou ubdomain, the low variable and luid propertie are deined at a point inide the medium by mean o averaging o the actual variable and propertie over a certain volume urrounding the point. To invetigate the luid low o microchannel a porou media, a teady-tate imulation baed on Brinkmann equation wa perormed. A coniguration o microchannel wa generated a hown in Fig. 4 and Fig. 5, with the dimenion 1cm 1cm 300µm repreenting a ingle microchannel hear ink a luid aturated porou media. The Brinkman equation wa then employed throughout the whole porou media uing the parameter propoed by Bejan [16]. Fig 4. Mapped quadrilateral meh or microchannel (a) (b) Fig. 5 (a) Slice view in the porou media; (b) zoomed lice view o the meh 3 Phyic o the Model The material propertie ued to model the ingle microchannel and the porou media are lited in Table. The parameter or poroity and permeability wa calculated a ollow: 50μm ε = = = Win 50μm+ 50μm μm κ = ε = = ( ) 10 Table Propertie or water ued a coolant Material Water (at 93K) Thermal conductivity (W/m K) Heat capacity (J/kg K) m Denity (kg/m 3 ) Silicon Thee value were ued or the porou medium imulation. The dimenion o the ingle microchannel and the porou media were ued to in order to acilitate comparion in the next ection. In thi work, model o ame height and length have been ued with the apect ratio o 6 i ued in thi paper. 3.1 Single Microchannel Boundary Condition The bottom part o the L-hape wa et to a contant heat lux with 0.4 MW/m with the ambient temperature with 93K, accounting or typical heat lux o a imilar lip-chip. Temperature wa peciied at the inlet, while the outlet and the ymmetry plane o the luid domain were et a convective lux and thermal inulation, repectively. For the inlet velocity, the inlet and preure outlet wa et 0.001m/ and 0 Pa repectively. The ymmetry part wa et to ymmetry. All other part wa et to nolip condition. The no-lip condition i eential in the veriication or etablihing a correct tranvere velocity proile inide the microchannel Model Implementation and Computation In thi numerical tudy, mapped meh wa irtly generated at inlet urace o the microchannel.. Boundary layer meh wa alo generated at wall or the top and bottom part. Later, the boundary layer meh wa generated with the intention to get accurate velocity gradient near the wall. The all domain meh wa later wept with 50 number o element layer. Lagrange quadratic element were ued during all the mehing operation. Uing a mapped meh hown in Fig. 4, the microchannel model now conit o 4,350 hexahedral element. The imulation wa executed in tationary mode. ISSN: ISBN:

4 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) 3. Porou media 3..1 Boundary Condition For the porou media, imilar to the ingle microchannel, the inlet velocity, the inlet and preure outlet wa et m/ and 0 Pa, repectively, wherea all other part were et to no lip condition Model Implementation and Computation For the porou media, a mapped quad meh wa generated a hown in Fig 4. A number o 50 element wa generated at inlet urace and later the urace wa wept with 10element layer. By uing thi mapped meh,,500 hexahedral element were generated. H, Height o Microchannle (m) Velocity, m/ Fig. 7 Tranvere velocity proile in the ingle microchannel 4 Reult and Dicuion Two et o reult are hown; the irt i or laminar low in the ingle microchannel and the econd i the low in the porou media. A hown in ee Fig. 6, the preure drop or ingle channel i Pa, while the preure drop along porou media i Pa. Thi i expected a the preure drop in porou media include the drop in the olid. The velocity proile acro the microchannel i hown in Fig. 7 which mimic ome power law, and no-lip condition i viible rom the proile. For heat traner, the temperature ditribution i given in Fig. 8, which how a dominant convective mode o heat traner where the heat rom the bae plate i being removed by the lowing coolant. 60 Preure, Pa Preure, Pa Microchannel Length, X (a) Porou Media Length, X (b) Fig. 6 Preure drop along (a) the ingle microchannel, and (b) the porou media Fig 8 Temperature ditribution in the ingle microchannel To invetigate how accurate the porou media model can repreent an array o microchannel heat ink, the method etablihed by Kim and co-worker [13-15] i reerred. The reult or the ingle microchannel with the conventional Navier-Stoke ormulation were compared and converted into non-dimenionalied orm by uing the ollowing dimenionle relation, u κ 1 y U =, Da =, =, Y = (9) um εh α H where u m i the mean velocity in luid region, α i the apect ratio o the microchannel H/W c and Y i the dimenionle vertical coordinate. For ingle microchannel, u m wa calculated by divided volume over the integration o the luid domain with the velocity ield expreion. The value or u m i m/. Then, the velocity data wa extracted rom point (0.5 mm, 75 µm, 100 µm) to point (0.5 mm, 75 µm, 300 µm), which i at the middle plane o the microchannel length. To get the average u in microchannel, the ollowing relation wa ued: ISSN: ISBN:

5 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) u = u (Poieuille low or parallel plate) microchannel 3 For the porou media, u m wa alo calculated by dividing the volume over the integration o the luid domain with the velocity ield expreion. The velocity data wa extracted rom the point, (5.0 mm, 5.0 mm, 0) to the point (5.0 mm, 5.0 mm, 300 µm), and the value obtained or u m i m/. Thereore, the imulation or the ingle microchannel model and the porou media were veriied and compared and preented in Fig. 9. a a luid aturated porou media, the reult hown to predict the volume-averaged microcopic velocity proile agree quite well. Thu the porou media approach ha an advantage in imulated the luid behaviour o microchannel compared to modelling every ingle microchannel with a drawback o very high numerical eort. By uing thi approach, it can igniicantly reduce the computational requirement, a well a enable the imulation be taken into the next level, uch a optimiing the gating ytem and the overall coolant ytem. Normalized velocity (<u>/um) Kim and kim (1999) The Brinkman Equation (Porou media) Single Microchannel Fig 9. Comparion velocity with olution rom conventional method (Da =0.001). Fig. 9 depict the reult or the non-dimenionle velocitie or the developed low proile acro the microchannel along the x-direction. From Fig 9, an average o 7.5 percent deviation o the Brinkman equation model reult and 7.8 percent deviation o the ingle microchannel compared to the Kim and Kim reult. The preent reult how appreciable agreement with Kim and Kim numerical reult which ha been validated with experimental reult. Thereore, by uing the correct permeability, the velocity o the luid low in tatured porou medium can be obtained. 5 Concluion In the preceding analyi, a ull three-dimenional imulation or luid low and heat traner or ingle microchannel heat ink wa developed. Propoed porou media have been alo modelled. In order to veriy the aumption o porou media a approximation to microchannel, both reult were ued and compared with other reearcher inding. The variable in nondimenionle orm have been ued or comparion. The reult indicate that or luid low agree well with other reearcher inding. By treating the microchannel Y Acknowledgement The author grateully acknowledge the inancial upport o Minitry o Science, Technology and Innovation, Malayia under the project SF0318. Reerence: [1] International Technology Roadmap For Semiconductor (ITRS): 008 Update, [] Tuckerman, D.B., and Peae, R.F.W., Highperormance heat inking or VLSI, IEEE Electron Device Letter, Vol., 1981, pp [3] Tuckerman, D.B., and Peae, R.F. W., Ultrahigh thermal conductance microtructure or integrated circuit, IEEE Proc. 3 nd Electronic Conerence, 198, pp [4] Miaggia, L.J., Walpole, J.N., Liau, Z.L. and Phillip, R.J., Microchannel heat ink or twodimenional high-power-denity diode laer array, IEEE J. Quantum Electron. Vol. 5, No. 9, 1989, pp [5] Kleiner MB, High perormance orced air cooling cheme employing microchannel heat exchanger. IEEE Tran Compon Packag Manu Technol Vol. 18, 1995, pp [6] Laance, C.J.M., and Simon, R.E., Advance in high-perormance cooling or electronic, Electronic Cooling, Vol. 11, No. 4, 005. [7] Samalam, V.K. Convective heat traner in microchannel, Journal o Electronic Material, Vol. 18, 1989, pp [8] Weiberg A., Analyi o Microchannel or Integrated Cooling, Int. J. Heat Ma Traner, Vol. 35, No. 10, 199, pp [9] Philip, R. J., Micro-channel heat ink, Advance in Thermal Modeling o electronic Componenet and Sytem, Vol., A. bar-cohen and A. D. Krau, ed, ASME, New York, Chapter 3, ISSN: ISBN:

6 Proceeding o the 4th IASME / WSEAS International Conerence on ENERGY & ENVIRONMENT (EE'09) [10] Morini, G.L., Single-phae convective heat traner in microchannel: a review o experimental reult, International Journal o Thermal Science, Vol 43, No. 7, 004, pp [11] Koh, J.C.Y., and Colony, R., Heat traner o microctructure or integrated Circuit, Int. Comm. Heat Ma Traner, Vol.13, 1986, pp [1] Tien, C.L., and Kuo, S.M., Analyi o orced convection in microtructure or electronic ytem cooling. In Proceeding o the International Sympoium on Cooling Technology or Electronic Equipment, Honolulu, Hl, 1987, pp [13] Kim, S.J., and Kim, D., Forced Convection in microtructure or electronic equipment cooling, J. Heat Traner, Vol. 11, 1999, pp [14] Kim, S.J., Kim, D., and Lee, D.Y., On the local thermal equilibrium in microchannel heat ink, Int. J. Heat Ma Traner, Vol. 43, 000, pp [15] Kim, S.J., and Kim, D., Averaging approach or microchannel heat ink ubjected to the uniorm wall temperature condition, Electronic Packaging Technology Conerence, 004. [16] Bejan, A. Convection Heat Traner. John Wiley & Son, New York ISSN: ISBN: