Microchannels and Minichannels - 2004 June 17-19, 2004, Rochester, New York, USA Copyright © 2004 by ASME
ICMM2004 – xxxx
OPTIMIZATION OF MICROCHANNEL GEOMETRY FOR DIRECT CHIP COOLING USING SINGLE PHASE HEAT TRANSFER
Harshal R. Upadhye1 and Satish G. Kandlikar2 Thermal Analysis and Microfluidics Laboratory, Mechanical Engineering Department, Rochester Institute of Technology, Rochester NY 14623. 1
[email protected] 2
[email protected]
ABSTRACT Direct cooling of an electronic chip of 25mm x 25mm in size is analyzed as a function of channel geometry for single-phase flow of water through small hydraulic diameters. Fully developed laminar flow is considered with both constant wall temperature and constant channel wall heat flux boundary conditions. The effect of channel dimensions on the pressure drop, the outlet temperature of the cooling fluid and the heat transfer rate are presented. The results indicate that a narrow and deep channel results in improved heat transfer performance for a given pressure drop constraint. INTRODUCTION One of the most important parameters affecting the performance of silicon integrated circuits is the circuit temperature. Maintaining the circuit temperature below certain limit of about 850 C is very important. Air cooling has been the most commonly used cooling method for majority of chips used in computer applications. Current trends indicate that as the fabrication technology improves, silicon chips with millions of devices can be fabricated. These trends point to very high heat fluxes in chip modules. To maintain temperature of the circuit in such a scenario is a daunting task and fabrication of such devices might be limited by their cooling capability.
Direct Chip cooling with microchannels or minichannels is a good solution for cooling of such devices. These chips have machined microchannels through which cooling liquid such as water is circulated. The cooling water removes heat by single-phase forced convection. The cooling passages within these chips can be fabricated along with the circuit components, or as a follow-on process. Liquid cooling, especially with water, will give additional benefits of superior thermal properties. The design and optimization of such microchannel passages in a direct heat sink is important from an operational standpoint. Pressure drop considerations will further determine the pumping power required and the operating pressure to which the chips will be subjected. The microchannels must be optimized using the range of flow channel dimensions that can be fabricated. Fabrication methods will also play a major role in the overall design of the direct heat sink. The current work consists of studying the effects of varying channel dimensions on pressure drop and the heat transfer characteristics of such a chip for a given heat duty. Basic equations are presented and the performance characteristics are obtained for a specific chip size of 25mm x 25mm as an example. Traditionally, air has been the preferred fluid for cooling electronic components, either a single chip or an entire printed circuit board consisting of numerous chips. With heat fluxes going beyond 100W/cm2, air cooling may no longer be possible. The low heat transfer coefficient coupled with a low specific heat makes air as a poor choice in microchannel flow passages. Liquids, especially water,
as compared to air or gases, offer a very good alternative due to their higher heat transfer coefficient, higher specific heat and lower specific volume compared to air. Water in particular is highly desirable because of its thermal properties as well as other characteristics such as low cost and extensive experience in other systems. Figure 1 shows a schematic of the microchannel geometry investigated in the present study. Microchannels are machined or etched in silicon substrate and closed by a cover plate on top to form flow passages. Cooling liquid flows through these channels. As is shown later, such a configuration is capable dissipating heat fluxes in excess of 100W/cm2. The microchannel flow geometry offers large surface area for heat transfer and a high convective heat transfer coefficient. But the small channel dimensions result in a very high pressure drop. The objective of this study is to investigate the thermal and pressure drop characteristics of these passages in an attempt toward obtaining optimized channel dimensions to match the given heat transfer and pressure drop requirement.
important parameter dictating the performance of a microchannel heat sink. Knight et al. (1992) presented the governing equations for fluid dynamics and heat transfer in the heat sink in a dimensionless form and then presented a scheme for solving these equations. Solution procedure for both laminar flow and turbulent flow through the channels was presented. ANALYSIS A chip with 25mm × 25mm active cooling surface area covered with microchannels machined on one side and heat dissipating devices on the other side, as shown in Fig. 1, is considered. Cover plate
b LITERATURE REVIEW
L
a W
Figure 1 Microchannel’s machined in Silicon. The dimensions of the microchannels, width a and depth b are the main parameters of interest. The length of the channels L is fixed by the geometry of the chip for which the cooling passages are designed. The channel width a will decide how many channels can be fitted. The wall thickness s is assumed to be 35µm, which represents the minimum thickness that can be easily manufactured with current fabrication technology.
1
0.95
Fin Efficiency
Microchannel heat sink concept was first introduced by Tuckerman and Pease (1981). The heat sink they manufactured was able to dissipate 790W/cm2. Phillips, (1987) presented a detailed analysis of the forced convection, liquid cooled microchannel heat sinks. Recent work includes work by Bergles et al. (2003), Qu and Mudawar (2002) and by Ryu et al.(2002). Bergles et al. (2003) discussed the design considerations for small diameter internal flow channels. A design problem with given heat rate and chip dimensions was studied in detail, the main focus being on pumping power and material thickness required. They concluded that cooling systems having smaller diameter channels result in a compact system and generally does not impose a larger pumping power requirement. Fin effects were found to be significant in designs where thin solid sections were utilized. Qu and Mudawar (2002) tested microchannel heat sink 1cm wide and 4.8cm long. The microchannels machined in the heat sink were 231µm wide and 712µm deep. Apart from this they also presented numerical analysis for a unit cell containing a single microchannel and surrounding solid. The measured pressure drop across the channels and temperature distribution showed good agreement with the numerical results. They concluded that the conventional Navier-Stokes and energy equations remain valid for predicting fluid flow and heat transfer characteristics in microchannels. Ryu et al. (2002) performed numerical optimization of thermal performance of microchannel heat sinks. The objective of the optimization was to minimize thermal resistance. They varied the channel width, channel depth and the fin thickness to come up with an optimized solution. Their observation was that the channel width is the most
s
0.9
0.85
0.8
0.75
0.7
0
20
40
60
Fin Thickness (microns)
80
Figure 2 Fin efficiency for various fin thickness for a channel depth of 300µm.
The number of channels that can be accommodated in given width is given by W n= a+s
h = Nu
(1)
From Eq. (1) we can see that the number of channels that can be fitted in a given width is dependent on channel width a and the spacing s. The spacing s is fixed to 35µm, as a result the channel width is the deciding factor for number of channels that can be fixed in the given width W. Figure 2 shows the fin efficiency as a function of the fin thickness for a maximum fin height (channel depth) of 300 µm. A thick fin will have a better fin efficiency, but the number of channels decreases with an increase in the fin thickness, and the area available for heat transfer also decreases. With a fin thickness of 35 µm, the fin efficiency is above 90 percent. Although including fin thickness as a variable would lead to further refinements, the fabrication limit is believed to be the limiting factor. The analysis is done considering two boundary conditions – (i) constant channel wall temperature and (ii) a constant heat flux boundary condition. In both cases heat transfer from the top cover plate is neglected. The flow through the channel is assumed to be laminar and fully developed. Water is used as a coolant having constant properties and the heat sink material is silicon. The hydraulic diameter is calculated from the channel dimensions:
4ab d= 2( a + b )
From the definition of Nusselt number
(2)
b a
ηf =
Constant Channel Wall Temperature Case The constant temperature Ts of the channel walls is assumed to be the design temperature that should not be exceeded in the unit. In case of electronic circuits it can be the maximum allowable temperature in the circuit. In this study we have assumed it to be 358 K. As a result the maximum water temperature at the outlet theoretically possible will be 358K. Water temperature at the inlet Tin is 300K. The entrance region effects are neglected and the Nusselt number is assumed to be constant (single-phase laminar flow). The value of Nusselt number is obtained from Kakac et al. (1987). The Nusselt number is for circumferentially and axially constant wall temperature at all four walls of a rectangular channel.
Nu = 7.541(1 − 2.610α + 4.970α 2 − 5.119α 3 + 2.702α 4 − 0.548α 5 )
tanh( mb) mb
(4)
(6)
where
m=
hP k f Ac
(7)
The perimeter of the rectangular fin is assumed to be twice the passage length.
P = 2L
(8)
The cross section area of the fin is (9)
Ac = Ls
Substituting Eqs. (8) and (9) into the expression for m in Eq. (7),
m=
(3)
(5)
where k is the thermal conductivity of the fluid. The walls separating the channels can be treated as rectangular fins of uniform cross-section. From Incropera and DeWitt (2002) the fin efficiency is given as
The channel aspect ratio is given by
α =
k d
2h kf s
(10)
An iterative technique is followed to calculate the mass flow rate and the water outlet temperature. The initial assumption is made that the liquid enters the microchannels at temperature Tin and leaves the microchannels at a temperature Tout =Ts. With this assumption and knowing the heat rate, mass flow rate required can be found out. •
m=
Q
(11)
C p (Tout − Tin )
& can now be used to calculate Tout by rearranging the This m logarithmic mean temperature difference equation. − hAn •
Tout = Ts − (Ts − Tout )e
mCp
(12)
where the product hA is
hA = haL + 2 Lbhη f
(13)
The Tout obtained from Eq.(12) is compared with the assumed Tout and then the Tout is adjusted. The process is iterated until Tout value is converged. Knowing Tout the mass flow rate required is calculated from Eq.(11). The mass
in Eq.(5) the value of convective heat transfer coefficient h can be found out. The maximum allowable surface temperature is again a constraint here. The outlet temperature of the fluid is given by
•
flow rate per channel
m c is found by the total mass flow
Tout = Ts −
•
m by the number of channels n. The velocity of fluid through each channel is •
V=
mc ρab
(14)
and the Reynolds number for the flow is
Re =
Vd
ν
2CLρV 2 Re d
(15)
(16)
where
C = f Re
(17)
The value of C from Kakac et al. (1987) is
C = 24(1 − 1.3553α + 1.9467α 2 − 1.7012α 3 + 0.9564α 4 − 0.2537α 5 )
(22)
Once the outlet temperature is known we can easily find out the mass flow rate required from Eq. (11). Equations (14)(16) give us the flow velocity, the Reynolds number and the pressure drop through the channels. RESULTS AND DISCUSSION
The pressure drop across the channels is given by the following equation –
∆p =
q" h
(18)
The fluid outlet temperature, flow Reynolds number, the mass flow rate and the pressure drop in a direct heat sink for a given heat rate are calculated for various channel dimensions. The effect of geometrical parameters on the channel heat transfer and pressure drop performance is discussed in the following sections. Constant Channel Wall Temperature As the channel width changes for a given thickness, the aspect ratio also changes. This affects the Nusselt number, as seen from Eq. (4). Figure 3 shows the variation of Nusselt number with channel aspect ratio for both constant heat flux and constant channel wall temperature boundary conditions. At aspect ratio of 1 (i.e. a square channel) the Nu is lowest. As the channel gets more skewed, Nu increases. 8
Constant Heat Flux Case
7
In constant heat flux condition the wall heat flux is found by dividing the channel wall area by the desired heat rate. Q Aw
(19)
2
(20)
− 2.4765α 3 + 1.0578α 4 − 0.1861α 5 )
1 0
The Nusselt number from Kakac et al (1987) is
Nu = 8.235(1 − 2.0421α + 3.0853α 2
4 3
The area of wall Aw is
Aw = (2η f b + a ) L.n
5
Nu
q" =
Constant heat flux Constant channel wall temperature
6
0
0.25
0.5
0.75
1
Aspect Ratio
(21)
The Nusselt number given by the above equation is valid for circumferentially constant wall temperature and axially constant wall heat flux for channels with rectangular geometry. From the definition of the Nusselt number given
Figure 3 Variation of Nusselt number with aspect ratio. The effect of channel width on heat transfer coefficient is result of the changing Nusselt number with channel width as well the change in the hydraulic diameter. The combined effect of these two parameters on h is plotted in Figure 4. It is seen that the heat transfer coefficient goes through a
1
0.8
0.6
T*
minimum at a channel width somewhat larger than that corresponding to an aspect ratio of 1. The heat transfer coefficient decreases with the channel width up to this minimum value, before rising slowly for larger channel widths. For the deepest channel of 300 µm plotted in Fig. 4, a channel width below about 100 µm results in a significant improvement in the heat transfer coefficient. However, the heat transfer performance needs to be considered in conjunction with the associated pressure drop. The effect of channel width on the outlet water temperature is considered next.
0.4
Channel Depth (microns)
50 100 150 200 250 300
0.2
40000 Channel Depth (microns)
50 100 150 200 250 300
30000
2
h (W/m K)
35000
0
25000
100
200
300
Channel Width (microns)
400
Figure 5 Dimensionless Coolant Outlet Temperatures (Constant Channel Wall Temperature, Chip heat flux 100W/cm2)
20000 15000 10000 100
200
300
Channel Width (microns)
400
Figure 4 Variation of h with channel width for various channel Depths. (Constant Surface Temperature) Figure 5 shows the variation of T* as a function of channel width, for various channel depths. The dimensionless temperature is defined as
T* =
Tout − Tin Ts − Tin
As seen from Fig. 6, the pressure drop for a very narrow channel is high, but it decreases with increasing depth. Still there exist some better solutions to the problem. A slightly wider channel and a deeper channel offer less pressure drop. For example – in Fig. 6, at a channel width of 60 µm and depth of 150 µm the pressure drop is 62100 Pa. An increase in width to about 120 µm results in pressure drop of 21100 Pa for the same depth. Increase in depth also lowers the pressure drop. At 120 µm channel width and channel depth of 300 µm the pressure drop is 6500 Pa. As the chip heat flux is increased, the mass flow rate required for taking out the heat increases. As a result the
(23)
300000 Channel Depth (microns)
50 100 150 200 250 300
2
The outlet temperature is very close to the surface temperature for a narrow and deeper channel. As the channel becomes wide, the outlet temperature decreases. The wider channel therefore causes two problems. As the outlet temperature decreases the mass flow rate required to carry away the specified amount of heat, increases. Another factor is the number of channels. Since the width of each channel is large, the total number of channels that can be fitted decreases. As a result the mass flow through each channel increases. Therefore pressure drop increases. Figure 6 shows the pressure drop values for various channel dimensions for a constant channel wall temperature case with a chip heat flux of 100 W/cm2. Only the frictional pressure drop considering fully developed flow is considered here. The entrance region effect and the inlet and outlet losses will affect the pressure drop characteristics somewhat, but their effect is expected to be relatively small compared to the frictional pressure drop in the channel.
Pressure Drop (N/m )
250000
200000
150000
100000
50000
0
100
200
300
Channel Width (microns)
400
Figure 6 Pressure Drop for Constant Channel Wall Temperature Reynolds number and the pressure drop also increase. In Fig. 7, pressure drop is plotted against channel width for a
chip heat flux of 200 W/cm2. The pressure drop has increased for all the channel configurations considered.
300000
Channel Depth (microns)
50 100 150 200 250 300
Pressure Drop (N/m2)
250000
predicted by using constant temperature boundary condition. Figure 9 shows the variation of pressure drop as a function of channel geometry for a constant heat flux condition. The pressure drop for a 50 µm deep channel, from Fig. 9, is far more as compared to deeper channels for the same width. 300000
250000
Pressure Drop (N/m2 )
200000
200000
150000
Channel Depth (microns)
150000
100000
50 100 150 200 250 300
100000
50000
0 50
75
100
125
150
Channel Width (microns)
50000
0
Figure 7 Pressure Drop for Constant Channel Wall Temperature For an assumed maximum allowable pressure drop of 30000 Pa, a 50 µm deep channel does not provide us with an acceptable solution. Also channels having width beyond 125 µm do not offer practical solution because of the high pressure drop except for channels with 250 µm and 300 µm width. Constant Heat Flux For the constant heat flux boundary condition, h values are shown in Fig. 8. The values are slightly higher than the h values for constant surface temperature boundary condition.
100
200
300
Channel Width (microns)
400
Figure 9 Pressure Drop for Constant Heat Flux. (Chip heat flux 100W/cm2) As in the constant surface temperature case, a deeper channel offers a lesser pressure drop. Hence deeper channels should be employed. The width of the channel has significant effect on the pressure drop. A very narrow channel offers a relatively higher pressure drop than a wider channel. But beyond a certain critical value, which depends on the chip heat flux and the channel depth, the pressure drop increases. CONCLUSIONS 1.
45000 40000
Channel Width (microns) 50 100 150 200 250 300
30000
2
h (W/m K)
35000
2.
25000 20000
3.
15000 10000 5000 0
4. 100
200
300
Channel Width (microns)
400
5. Figure 8 Variation of h with channel width for various channel Depths. (Constant Heat Flux) The predicted pressure drop for the constant heat flux boundary condition is slightly higher than the pressure drop
Heat transfer and pressure drop characteristics for single phase flow in direct heat sinks are analyzed. The results are presented for a chip with an active cooling area of 25mm x 25mm. The fin effect of channel walls separating adjacent flow channels was analyzed. A wall thickness of 35 µm resulted in fin efficiencies above 90 percent. This wall thickness was the minimum that is recommended from fabrication point of view. Pressure drop, an important parameter for microchannel heat sink design is a strong function of the channel geometry. From both heat transfer and pressure drop perspectives, a narrow and a deep channel is better than having a wide and shallow channel. For a constant wall temperature case and for a chip heat flux of 100W/cm2 we can definitely narrow down on particular channel dimensions which will give a lower pressure drop. Channel width in between 150µm and 250µm definitely seems to be a better choice with channel depth of 250µm.
6.
Channel width larger or smaller than this range increases the pressure drop. Increasing the channel depth any further does not substantially reduce the pressure drop. The constant heat flux condition also indicates towards a similar trend with a slight difference in pressure drop values. From the above analysis we can identify a region of possible channel configurations that can help in designing microchannels. The current work only considers a chip of 25mm × 25mm. The methodology and equations presented here can be applied to other chip sizes in arriving at the desirable channel configurations.
Future work is planned to include the effects of entrance region and entry and exit losses on pressure drop. ACKNOWLEDGEMENTS The work was carried out at the Thermal Analysis and Microfluidics Laboratory at RIT. NOMENCLATURE Ac Aw a b C Cp d f h k kf L m
cross sectional area of fin area offered by the channel walls for heat transfer channel width channel depth constant defined by Eq. 17 specific heat at constant pressure hydraulic diameter of the channel fully developed fanning friction factor heat transfer coefficient thermal conductivity of water thermal conductivity of fin material (silicon) channel length fin efficiency constant defined by Eq. 10
•
m
mass flow rate
•
mc n Nu P Q q” Re s
mass flow rate through single channel number of channels that can be fitted in heat sink Nusselt number perimeter of channel heat rate heat flux Reynolds number thickness of the fin
T* Tout Tin Ts V W
dimensionless temperature temperature at the outlet of the microchannels temperature at inlet of the microchannels surface temperature of the heat sink fluid velocity through the microchannel width of the chip to be cooled
Greek Symbols α ηf ρ ν
channel aspect ratio fin efficiency density kinematic viscosity
REFERENCES Bergles, A.E., Lienhard, J.H. V, Kendall, G.E., and Griffith, P., 2003, “Boiling and Condensation in Small Diameter Channels”, Heat Transfer Engineering, Vol 24(1), pp. 18-40. Incropera, F.P., and DeWitt, D.P., 2002, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York. Kakac, S., Shah, R.K and Aung, W., 1987, Handbook of Single-Phase Convective Heat Transfer, John Wiley & Sons, New York. Knight, R.W., Hall, D.J., Goodling, J.S., Jaeger, R.C, 1992, “Heat Sink Optimization with Application to Microchannels”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, Vol. 15, No. 5. pp. 832-842. Mishra, R., Keimasi, M., and Das, D., 2004, “The temperature ratings of electronic parts”, Electronics Cooling, Vol. 10, No 1, pp 20-26. Mudawar, I., and Qu, W., 2002, “Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink”, Int. J. Heat and Mass Transfer, Vol.45, pp.2549-2565. Phillips, R.J., 1987, Forced Convection, Liquid Cooled, Microchannel Heat Sinks, M.S. Thesis, Dept. of Mechanical Engineering, Massachusetts Institute of Technology. Ryu, J.H., Choi, D.H. and Kim, S.J., 2002, “Numerical Optimization of the thermal performance of a microchannel heat sink”, Int. J. Heat and Mass Transfer, Vol.45, pp.28232827. Tuckerman, D.B., and Pease, R.F.W., 1981, “HighPerformance Heat Sinking for VLSI”, IEEE Electron Device Letters, Vol. EDL-2, No 5, pp 126-129.
