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Extending the Heat Flux Limit with Enhanced Microchannels in Direct Single Phase Cooling of Computer Chips Satish G. Kandlikar1 and Harshal R. Upadhye Thermal Analysis and Microfluidics Laboratory, Mechanical Engineering Department, Rochester Institute of Technology, Rochester, NY 14623 1 [email protected] Abstract The high heat transfer coefficients in microchannels are attractive for direct cooling of computer chips requiring high heat-flux removal. However, the high heat removal capability of microchannels is associated with a severe pressure drop penalty. Channel size optimization therefore becomes necessary in selecting an appropriate channel geometry configuration. As the heat flux increases beyond about 2 MW/m2, the heat transfer and pressure drop characteristics of the plain channels dictate the use of turbulent flow through the channels, which suffers from an excessive pressure drop penalty. It therefore becomes essential to incorporate enhancement features in the microchannels and multiple passes with shorter flow lengths to provide the desired solution. Results obtained from a theoretical analysis are presented as parametric plots for the heat transfer and pressure drop performance of a 10×10-3 m × 10×10-3 m (10 mm x 10 mm) silicon chip incorporating plain microchannels. The enhanced microchannels with offset strip fins in single-pass and split-flow arrangements are also investigated. The results show that the enhanced structures are capable of dissipating heat fluxes extending beyond 3 MW/m2 using water as the coolant in a split-flow arrangement with a core pressure drop of around 35 kPa. Keywords Microchannels, Electronics Cooling, Channel Geometry, Pressure Drop, Optimization. Nomenclature Ac cross-sectional area of fin, m2 Adiv area offered by each division for heat transfer, m2 effective channel area for heat transfer considering Aw the fin efficiency effects, m2 a channel width, m b channel depth, m Cp specific heat at constant pressure, J/kg-°C d hydraulic diameter of the channels, m apparent friction factor fapp gc acceleration due to gravity, m/s2 h heat transfer coefficient, W/m2-°C k thermal conductivity of water, W/m-°C kf thermal conductivity of the fin material (silicon), W/m-°C L channel length, m m fin efficiency constant defined by Eq. (6) • mc n mass flow rate through a single channel, kg/s number of parallel microchannels 0-7803-8985-9/05/$20.00 ©2005 IEEE- Nu P Pr Q Qdiv q” Re s Tb Tout Tin Ts um W x Nusselt number perimeter of channel, m Prandtl number heat rate, W heat dissipated per element, W heat flux based on the base area, W/m2 Reynolds number thickness of the fin, m Fluid bulk temperature, °C temperature at the outlet of the microchannels, °C temperature at inlet of the microchannels, °C surface temperature at the base of the heat sink, °C mean fluid velocity through the microchannel, m/s width of the chip area being cooled, m axial distance from the entrance of the channel, m x+ x* hydrodynamic entry length thermal entry length Greek Symbols αc channel aspect ratio, a/b αf fin aspect ratio, s/b ∆p core frictional pressure microchannel, Pa ηf fin efficiency µ dynamic viscosity, N-s/m2 ρ drop across the density, kg/m3 1. Introduction Thermal management of electronic devices is one of the important aspects of electronics packaging. Air has been the fluid of choice in such cooling applications. With the rapid advances in microelectronics technology, the volume occupied by the devices has reduced considerably. But with increasing demand for faster and more efficient processors, the number of circuits and the power dissipation per unit volume has also increased. The combined effect of this has lead to an increase in the heat flux that needs to be removed from the chip surfaces. There is also a desire to reduce the junction temperature, as the increased temperature adversely affects the electrical performance of the devices and reduces their reliability. Possible damage involves junction fatigue, changes in electrical parameters and thermal runaway. Direct cooling of chips offers a practical solution to the heat dissipation problem. In such systems, water (with possible addition of antifreeze to allow cold weather shipments) is circulated in microchannels fabricated on the chip substrate. Such systems need to be carefully designed to meet the cooling requirements under the operational constraints. Pressure drop is an important parameter which 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. governs the pump selection, required pumping power, and the maximum pressure to which the chip is subjected. In the present work, an analysis is carried out to optimize the channel configuration that yields a minimum pressure drop for a given heat load. The constraints for the optimization are the maximum allowable chip temperature, heat dissipated, pressure drop for the fluid stream flowing through the channels, and the manufacturing constraints. The manufacturing constraints are not addressed in the present work. The analysis is extended to an enhanced microchannel incorporating offset strip-fin configuration in single-pass and split-flow arrangements. 2. Literature Review Microchannel heat sink concept was first introduced by Tuckerman and Pease [1]. The heat sink they manufactured was able to dissipate 7.9 MW/m2 with a maximum substrate temperature rise of 71 °C and a pressure drop of 186 kPa. Phillips [2] presented a detailed analysis of the forced convection liquid cooled microchannel heat sinks. Recent investigations include the work by Upadhye and Kandlikar [3], Kandlikar and Grande [4], Steinke and Kandlikar [5], Bergles et al. [6], Qu and Mudawar [7], and Ryu et al. [8]. Upadhye and Kandlikar [3] presented an analysis for optimizing the microchannel geometry for direct chip cooling using single-phase heat transfer with water as the working fluid. A chip with an active cooling area of 25.4×10-3 m × 25.4×10-3 m (25.4 mm × 25.4 mm) was analyzed. A fully developed laminar flow with constant channel wall temperature or constant heat flux condition was considered. The analysis showed that a narrow and deep channel is better than having a wide and shallow channel from the heat transfer and pressure drop perspectives. For the chip size considered, and with a heat load of 1 MW/m2, a channel width between 150×10-6 m (150 µm) and 250×10-6 m (250 µm) was found to result in the lowest pressure drop for a channel depth of 250×10-6 m (250 µm). Kandlikar and Grande [4] discussed the cooling limits of the plain rectangular microchannels with water cooling for high heat flux dissipation and illustrated the need for enhanced microchannels. Steinke and Kandlikar [5] carried out an extensive review of conventional single-phase heat transfer enhancement techniques. Several passive and active enhancement techniques for minichannels and microchannels were discussed. Some of their proposed enhancement techniques include fluid additives, secondary flows, vibrations, and flow pulsations. Bergles et al. [6] discussed the design considerations for small diameter internal flow channels. A design problem with a given heat rate and chip dimensions was studied in detail, the main focus being on pumping power and material thickness requirement. They concluded that cooling systems having smaller diameter channels result in a compact system and generally not impose a larger pumping power requirement. Qu and Mudawar [7] tested microchannel heat sinks 10×10-3 m (10 mm) in width and 48×10-3 m (48 mm) long. The microchannels machined in the heat sink were 231×10-6 m (231 µm) wide and 712×10-6 m (712 µm) deep. They also presented a numerical analysis for a unit cell containing a Kandlikar,et.al, Extending the Heat Flux Limit with ….. single microchannel and the surrounding heat sink material. The measured pressure drop across the channels and the temperature distribution showed good agreement with their 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. [8] performed a numerical optimization of thermal performance of microchannel heat sinks. The objective of the optimization was to minimize the convective thermal resistance of the fluid. They varied the channel width, channel depth, and fin thickness to arrive at an optimized solution. They observed that the channel width is the most important parameter governing the performance of a microchannel heat sink. Knight et al. [9] derived the governing equations for fluid flow and heat transfer in a microchannel heat sink in a dimensionless form and presented a scheme for solving these equations. Solution procedures for both laminar flow and turbulent flow were presented. 3. Objectives of the Present Work The objectives of the present work are: 1. Develop an algorithm to analyze the heat transfer and pressure drop characteristics of a given chip cooled with plain and enhanced microchannels by incorporating the developing flow effects. 2. Present the results in a parametric form to identify the optimum geometrical configuration that meets the cooling requirements and results in the lowest core frictional pressure drop. 3. Study the effects of enhanced microchannels incorporating the offset strip-fins. 4. Study the effects on incorporating a split-flow arrangement with enhanced microchannels. 4. Assumptions The heat transfer and pressure drop analysis are developed under the following major assumptions 1. 2. 3. 4. 5. Constant heat flux on the channel walls – The boundary condition on the microchannel walls is assumed to be axially constant wall heat flux with circumferentially constant wall temperature. The heat flux along the length of the channel is constant, while the wall temperature varies along the channel length in the flow direction. Heat losses from the cover plate are neglected – The cover plate on the microchannels is assumed to be insulated and hence the fin tip can be considered to be under adiabatic tip boundary condition. The solution obtained will be on the conservative side by neglecting the heat losses from the cover plate. The coolant flow is steady and incompressible – Since the working fluid is water and the maximum pressure drop is generally less than 100 kPa, the incompressible flow assumption should be valid. Uniform heat flux over the active chip surface area is assumed with no local hotspots. Constant properties are assumed for both the cooling fluid (water) and the wall material (silicon). 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. 6. A single-pass arrangement with plain microchannels is considered. The analysis is later modified to analyze enhanced microchannels and the split-flow arrangement. 5. Analysis A chip with L=10×10-3 m (10 mm) and W=10×10-3 m (10 mm) active cooling surface area and a microchannel depth b = 200×10-6 m (200 µm) is considered as shown in Fig. 1. Microchannels are fabricated on one side and the heat dissipating devices are placed on the other side of the chip. The maximum temperature of the channel walls is to be maintained below 360 K with an inlet water temperature of 300 K. The analysis uses the specified channel depth (as governed by the manufacturing constraints) and does not include the silicon thermal resistance between the channel bottom wall and the chip surface receiving heat. The analysis can however be extended to include this resistance if desired. Similarly, other chip geometries, channel depths, and fluid inlet temperatures can be readily handled. Cover plate The fin aspect ratio αf = L W Fig. 1 Microchannel geometry The dimensions of the microchannels, width a and fin thickness s, are the main parameters of interest. The length of the channels L is fixed by the prescribed geometry of the chip for which the cooling passages are designed. The channel depth b is assumed to be known. This is due to the fact that the channel depth is governed by the manufacturing process and the chip configuration. The channel width a and the fin thickness s together will determine the number of parallel channels that can be accommodated. The wall thickness s has a lower limit of 30×10-6 m (30 µm), which represents the minimum thickness that can be readily manufactured with the current microfabrication technology. In an effort to arrive at a common terminology in the microchannel heat sink application, three non-dimensional parameters – channel aspect ratio, fin aspect ratio and fin spacing ratio – are defined and described below. The channel aspect ratio αc is defined as the ratio of the a b from 0 to 1 ( 0 < α c ≤ 1 and 0 < α f ≤ 1 ). (1) αc αf Although α c and is >1 can be employed, this configuration is of little practical interest as narrow and deep channels (with α c <1) were shown to be more desirable for high heat flux dissipation, Upadhye and Kandlikar [3]. They also showed that the fin aspect ratio of α f >1 does not yield any benefits with the silicon substrate from fin efficiency considerations. The ratio of the fin aspect ratio to the channel aspect ratio plays an important role in the heat transfer analysis. It is defined as the fin spacing ratio β and is given by: αf s = αc a (3) The practical range for the fin spacing ratio is also β <1 because utilizing channels that are smaller than the fin thickness is not desirable from overall heat transfer and pressure drop considerations, and due to the danger of potential blockage of the channels with particulates. The channel width, chip width, number of channels, and the fin aspect ratio are related by the following equation. a= W n + (n + 1) β The channel aspect ratio (4) αc is an important parameter because the friction factor and the Nusselt number in the laminar flow region are both dependent on this ratio. The Nusselt number and friction factor information is derived from Kakac et al. [10]. For a particular Re and α c , the fappRe values are obtained from the appropriate charts. The constant heat flux (approximation, due to fin effects) on the channel walls is found by dividing the total design heat load by the available wall surface area. The effective channel wall heat transfer surface area, considering the fin efficiency effects, is given by: where ηf (5) is the fin efficiency. The fin efficiency for a rectangular, constant cross-sectional area fin under adiabatic fin tip boundary condition is given by: ηf = Kandlikar,et.al, Extending the Heat Flux Limit with ….. (2) Aw = (2η f b + a ) Ln channel width to the channel depth. It is given by: αc = s b The practical range of interest for both b a is defined as the ratio of the fin thickness to the fin height. It is given by: β= s αf tanh mb mb (6) 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. The fin parameter m is given by: x+ = hP k f Ac m= (7) where h is the heat transfer coefficient, P is the perimeter, and Ac is the fin cross-sectional area. The perimeter of the fin in contact with the fluid is given by: P = 2L (8) The cross-sectional area of the fin Ac = sL (9) Substituting the perimeter and the cross-sectional area from Eqs. (7) and (8) into Eq. (6), m reduces to 2h kfs m= (10) The heat transfer coefficient h is calculated from the Nusselt number. h = Nu k d (14) where x is the axial distance from the entrance along the channel length. Similarly, the local Nusselt numbers for thermally developing flows are obtained from Kakac et al. [10]. The data is presented in a tabular form for various values channel aspect ratio α c and x* given by: x* = Ac is given by: xd Re xd Re Pr (15) 7. Solution Procedure As mentioned in Section 5, the channel depth is decided by the manufacturing process. For the results presented in this paper, a channel depth of 200×10-6 m (200 µm) is considered. The minimum fin thickness is assumed to be 30×10-6 m (30 µm). The channel length is 10×10-3 m (10 mm). Since the non-dimensional lengths x+ and x* are functions of the axial distance from the entrance, the channel is divided into smaller divisions. The axial distance of each division from the channel entrance is the distance of the center of that particular division from the entrance. This is shown in Fig. 2. (11) where h is the heat transfer coefficient, and d is the hydraulic diameter given by the following equation for the rectangular microchannel shown in Fig. 1: d= 4ab 2(a + b ) (12) The Nusselt number and friction factor information is obtained from the literature in the developing flow region. Using this information, the microchannels are analyzed as heat exchangers. The details of the heat transfer and pressure drop calculations and the heat exchanger analysis are described in the following sections. 6. Nusselt Number and Friction Factor in the Laminar Developing Region Several investigators have studied the laminar developing flow in rectangular ducts. The developing flow effects are represented by an apparent friction factor between the inlet to a duct and the location of interest. The frictional pressure drop for fluid flow through a channel of length L is given by: ∆p = 2( f app Re )µu m L d2 (13) where fapp is the apparent friction factor that includes the effect of the developing flow. The apparent friction factors from Kakac et al. [10] for fappRe are presented as a function the channel aspect ratio α c and x+ given by: Kandlikar,et.al, Extending the Heat Flux Limit with ….. Fig. 2 Channel divided into smaller number of divisions along its length. The numbers indicate the division numbers and x indicates the distance of a particular division from the entrance. This x is used in Eq. (14) and Eq. (15) to get x+ and x* for the division. The results obtained from the analysis are plotted in the form of an operating envelope. The heat load and the channel depth are assumed to be known in this envelope. The important parameters to be determined are the channel width, the fin thickness, and the required mass flow rate. Once these parameters are known, the pressure drop can be calculated using Eq. (13). The objective in finding these parameters is to have the lowest value of the pressure drop under the given constraints. To solve this problem, the following algorithm is developed. 1. The number of channels, n, is assumed to be 50 in the beginning. If the number of channels is less than 50, it was found that the channels become too wide and require an excessive fluid flow rate with a high pressure drop to dissipate a given heat load. 2. The fin spacing ratio β is used as a parameter in plotting the results. Knowing the number of channels n and the fin 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. 3. 4. 5. 6. spacing ratio β , the channel width a, and the fin thickness s are calculated from Eqs. (1) to (4). The channel depth is assumed to be known. The hydraulic diameter is calculated from the known channel dimensions. The channel length is divided into a certain number of equal divisions, tentatively set as 10. A low starting value of the inlet Reynolds number is assumed (tentatively set as Re=50). Knowing Re, x* is calculated at the center of each division. Knowing this x*, Nu and h at each division is found from the look-up tables and charts [10]. This approach allows the use of variable fluid properties along the flow length. For a particular division, the energy balance equation is applied and outlet temperature of the coolant at that division is calculated. Tout = Qdiv + Tin m c C p (16) are needed to dissipate higher heat fluxes, Kandlikar and Grande [4]. Therefore an offset strip-fin construction is analyzed for dissipating heat fluxes above 3 MW/m2. In this type of construction, the continuous fin in the microchannels is broken down into several smaller fins that are placed offset to each other in the flow direction as shown in Fig. 3. In the fin arrangement analyzed, there is no gap or overlap with the downstream fins. The analysis of the strip-fin arrangement is carried out in a different manner than that described earlier for plain microchannels. In this arrangement, the fin length (i.e. length in the flow direction) is small and the heat transfer coefficient h is high over the fin (being in the initial developing region). The pressure drop is calculated using the fappRe over the fin length without breaking it down further into subdivisions. The values of h and fappRe are calculated in a similar fashion as explained previously. As a result significantly higher heat transfer coefficients are obtained, but with an increase in the pressure drop as well. where Qdiv is heat input per channel per division. This approach will allow extension of the analysis to non-uniform heat load conditions in the future work. The calculated Tout from Eq. (15) becomes Tin for the next division. The bulk temperature Tb for the division is the average of Tin and Tout. The fluid properties are calculated at this mean temperature. The Tin for the first division is the fluid inlet temperature and is assumed to be 300K. The process is repeated until the channel outlet is reached. The surface temperature at the exit of the channel is then given by: Ts = Qdiv + Tb hAdiv (17) Fig. 3 Offset strip-fins shown in the top view, with individual fin length l along the fin length. This temperature is compared to the maximum allowable surface temperature, assumed to be 360 K. If the exit surface temperature is above this allowable maximum temperature, the assumed value of Re is increased by a small increment (tentatively set at an increment of 5) and the calculations are repeated. Further refinements are made as the solution begins to converge. The calculations are stopped once the outlet surface temperature reaches a temperature within a certain limit below the maximum allowable temperature. 1. For the converged value of Re, the corresponding values of mass flow rate and pressure drop are calculated. The pressure drop is the summation of the pressure drops calculated in each division. 2. The entire procedure is repeated for different number of channels and different fin spacing ratios. 3. The results are plotted as parametric plots depicting number of channels versus fin spacing ratio, with channel frictional pressure drop, total fluid mass flow rate, and fin thickness as parameters. The plots are used to identify the desirable region from pressure drop considerations. 9. Split-flow Arrangement Another possible modification to the system is to reduce the fluid flow length in the microchannels. In the single-pass arrangement, fluid enters the microchannels at one end of the chip and exits on the other end as shown in Fig. 4. In the split-flow arrangement, also shown in Fig. 4, the fluid is introduced at the center and exits on the two sides. The inlet and exit locations could be interchanged if desired. 8. Enhanced Microchannels Although the heat transfer coefficients are very high with water flow in microchannels, higher heat transfer coefficients Fig. 4 Schematics of single-pass and split flow arrangements showing fluid flow through microchannels. Kandlikar,et.al, Extending the Heat Flux Limit with ….. (a) Single-pass arrangement (b) Split-flow arrangement 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. The split-flow arrangement is advantageous over the single-pass arrangement in two ways: (i) the flow length of the fluid stream in the microchannels is reduced by half, and (ii) the fluid flow rate through the microchannels is also halved. Both these factors contribute to reducing the pressure drop. Furthermore, the reduction in the flow rate does not lower the heat transfer coefficient significantly (being in the laminar region); some reduction in h however is expected as the enhancement due to the developing flow is lower for the lower Reynolds number in the split-flow arrangement. The analysis is also carried out to investigate the combined effects of enhanced microchannels and the split-flow arrangement. The area reduction due to the central inlet manifold is however neglected. 10. Results and Discussion A chip with a cooling area of 10×10-3 m × 10×10-3 m (10mm × 10mm) is considered with a heat load of 300 W. The channel depth is 200×10-6 m (200 µm). The analysis is carried out for developing a design envelope. The resulting envelope for the above conditions is presented in Fig. 5. The x-axis represents the number of channels and the y-axis represents the fin spacing ratio. The contour plot shows the pressure drop in kPa (dash-dot lines). The solid lines indicate the fin thickness in µm. Since the minimum thickness that can be fabricated for a fin is 30×10-6 m (30 µm), the configurations represented by the region below 30×10-6 m (30 µm) are not feasible. For the region above the 30×10-6 m (30 µm) line, a pressure drop of less than 25 kPa can be obtained with the number of channels between 72 and 96. The resulting fin spacing ratio is between 0.25 and 0.4. All the configurations in between these numbers will yield a lower pressure drop than any other configuration under the given design constraints. Once the fin spacing ratio and the number of channels are selected, the actual channel width and the fin thickness can be calculated from Eqs. (1) to (4). As an example, select 80 channels (n=80) and a fin spacing ratio of 0.35 (β=0.35) with a pressure drop of 25 kPa from Fig. 5. Substituting these values in Eqs. (1) to (4), we get a channel width of 92 µm and a fin thickness of 32×10-6 m (32 µm). A similar contour plot developed for water flow rate is shown in Fig. 6 for the same heat flux of 3 MW/m2 and a channel depth of 200×10-6 m (200 µm). The dash-dot lines in Fig. 6 show contours for mass flow rates in 10-3 kg/s. The solid lines indicate the fin thickness. For the design point considered earlier, with n=80, β =0.35, a=92×10-6 m (92 µm), b=32 ×10-6 m (32 µm), the flow rate is seen to be 1.6x10-3 kg/s. Kandlikar,et.al, Extending the Heat Flux Limit with ….. Fig. 5 Contour plot of fin spacing ratio β vs. number of channels with pressure drop (dash-dot lines) and fin thickness in µm (solid lines) as parameters for water flow in plain rectangular microchannels in single-pass arrangement at a heat flux of 3MW/m2. Fig. 6 Contour plot of fin spacing ratio β vs. number of channels with water flow rate in 10-3 kg/s (dash-dot lines) and fin thickness in µm (solid lines) as parameters for water flow in plain rectangular microchannels in single-pass arrangement at a heat flux of 3MW/m2. A similar contour plot for pumping power is shown in Fig. 7 with contour lines for pumping power shown in mW. The pumping power plot shown in Fig. 7 completes the design solution as now we have all the information needed to define the microchannel cooling system that will satisfy the specified constraints with a minimum pressure drop. Similar plots can be constructed for any other heat load, channel depth, or overall chip size. 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. pressure drop remains almost the same in both configurations because the reduction in the mass flow rate is countered by an increase in the friction factor for the enhanced geometry. The reduced mass flow rate and pressure drop lead to a reduced pumping power requirement for the enhanced microchannel configuration as compared to the plain microchannels. The enhanced microcrochannels are analyzed next in the split flow arrangement shown in Fig. 4b. Figure 10 shows the pressure drop comparison between the single-pass and splitflow arrangements for the enhanced microchannels. The split-flow arrangement yields a significantly lower pressure drop as compared to the single-pass arrangement for the same heat load. In the split-flow arrangement, the pressure drop is reduced significantly because of the reduction in the flow length as well as a reduction in the mass flow rate. Fig. 7 Contour plot of fin spacing ratio β vs. number of channels with pumping power in mW (dash-dot lines) and fin thickness in µm (solid lines) as parameters for water flow in plain rectangular microchannels in single-pass arrangement at a heat flux of 3MW/m2. For the enhanced microchannel configuration, the offset strip-fin arrangement shown in Fig. 3 is used with a channel width of 200×10-6 m ( 200 µm) and a channel depth of 200×10-6 m (200 µm). A fin thickness of 100×10-6 m (100 µm) is employed. A higher fin thickness is used as the fins in this configuration may not be as strong as the long continuous fins. With this configuration, 33 channels can be constructed in 10×10-3 m (10 mm) width. The fin length in the flow direction is l=0.5×10-3 m (0.5 mm), see Fig. 3. Fig. 9 Heat load versus mass flow rate, in 10-3 kg/s, for plain (l=10 mm) and enhanced offset strip-fin microchannels (l=0.5 mm) in single-pass arrangement on a 10 mm × 10 mm chip. Fig. 8 Heat load versus pressure drop for plain (l=10 mm) and enhanced offset-strip fin microchannels (l=0.5 mm) in single-pass arrangement on a 10 mm × 10 mm chip. Figures 8 and 9 show a comparison between the enhanced offset strip-fin microchannels (fin length 0.5 mm) and the plain microchannels (fin length 10 mm) with a channel width of 200×10-6 m (200 µm) and a depth of 200×10-6 m (200 µm). Figure 8 shows the pressure drop as a function of the heat load, while Fig. 9 depicts the mass flow rate as a function of the heat load. The pressure drop for the enhanced microchannels is slightly lower than the plain microchannels for the same heat load, while the mass flow rate is seen to be considerably lower for the enhanced microchannels. The Kandlikar,et.al, Extending the Heat Flux Limit with ….. Fig. 10 Comparison of pressure drops for the enhanced microchannels with offset strip-fins (l=0.5 mm) in single-pass and split-flow arrangements on a 10 mm × 10 mm chip. The split-flow arrangement yields a definite improvement over the single-pass arrangement. The heat dissipation capacity for a specified pressure drop is significantly higher than the single-pass arrangement for the enhanced microchannels as seen from Fig. 10. This improvement can be attributed to the increased heat transfer coefficient leading 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply. to a reduced mass flow rate, and the reduced fluid flow length for each fluid stream. The header arrangement however may become somewhat more complex. 11. Additional Considerations i. The results are presented for a temperature difference of 60 °C between the maximum allowable chip temperature and the inlet water temperature. The corresponding fluid thermal resistance can be readily calculated and applied to other temperature difference conditions (a slight error will result due to differences in the water properties at the different operating temperatures). ii. The results are expected to be different for different working fluids, such as antifreeze mixtures or with mineral oils. Similar analysis is recommended with the actual properties of the fluid used. Similarly, slight differences are expected to result when these results are applied to copper heat sinks. iii. The results presented in this paper consider the frictional pressure drop in the microchannel core only. The pressure drops due to the entrance and exit area changes between the header and the microchannels, and the pressure drops in the headers are not included in the analysis. iv. More aggressive strip-fin designs could be implemented with shorter fin lengths and shorter microchannel widths for dissipating higher heat fluxes. Both the heat transfer coefficient and the friction factor will increase accordingly. Multiple inlet and outlet manifolds will be beneficial with such aggressive designs to reduce the pressure drops by limiting each individual fluid stream length through the microchannel passages. v. Another consideration that plays a major role is the pressure drop introduced by the filtering system. As the microchannel dimensions become smaller, the filters will be required to remove smaller particles from the fluid stream to avoid blockage of the microchannel flow passages. This will further increase the pressure drop with narrower microchannels due to finer filters employed. 12. Conclusions • An analysis is presented for evaluating the thermohydraulic performance of microchannels in direct chip cooling application by considering the developing flow effects. The analysis includes only the core frictional pressure drop and does not include the entrance and exit contraction and expansion losses. • The results are presented as parametric plots to identify the desired channel width, fin thickness, and mass flow rate for a given heat load and channel depth using water as the cooling fluid. • Plain rectangular microchannels and enhanced microchannels with offset strip-fins are considered. The enhanced microchannel configuration is further evaluated under single-pass and split-flow arrangements. • Direct cooling of chips with water in microchannels offers a viable solution from a thermohydraulic viewpoint. Plain microchannels of 200×10-6 m (200 µm) depth and between 100×10-6 m (100 µm) and 200×10-6 m (200 µm) width are able to dissipate heat fluxes of up to 3 Kandlikar,et.al, Extending the Heat Flux Limit with ….. • • MW/m2 with a frictional pressure drop of under 35 kPa in the core. For higher heat fluxes beyond 3 MW/m2, plain microchannels require excessive water flow rates that impose higher pressure drop penalties. Providing enhanced offset-strip fins with a split-flow arrangement enables accommodating such high heat fluxes with a core pressure drop of around 35 kPa. Enhanced offset strip-fin configuration in a split-flow arrangement provides an attractive option for extending the heat flux limit in direct chip cooling application. Further splitting the flow into multiple inlets and outlets may be considered, along with more aggressive split-fin designs. References 1. Tuckerman, D. B., and Pease, R. F. W., “HighPerformance Heat Sinking for VLSI,” IEEE Electron Device Letters, Vol. EDL-2, No 5, pp 126-129, 1981. 2. Phillips, R. J., Forced Convection, Liquid Cooled, Microchannel Heat Sinks, M.S. Thesis, Dept. of Mechanical Engineering, Massachusetts Institute of Technology (Cambridge, MA, 1987). 3. Upadhye, H. R. and Kandlikar, S. G, "Optimization of Microchannel Geometry for Direct Chip Cooling Using Single Phase Heat Transfer," Proceedings of the Second International Conference on Microchannels and Minichannels, June 17-19, 2004, Rochester, NY USA ASME Publications, pp 679-68, 2004. 4. Kandlikar, S. G., and Grande, W. J., “Evaluation of Single Phase Flow in Microchannels for High Flux Chip Cooling – Thermohydraulic Performance Evaluation and Fabrication Technology,” Heat Transfer Engineering, Vol. 25, No. 8, pp. 5-16, 2004. 5. Steinke, M. E. and Kandlikar, S. G, "Single-Phase Heat Transfer Enhancement Techniques in Microchannel and Minichannel Flows," Proceedings of the Second International Conference on Microchannels and Minichannels, June 17-19, 2004, Rochester, NY USA ASME Publications, pp 141-148, 2004. 6. Bergles, A. E., Lienhard, J. H., V, Kendall, G. E., and Griffith, P., “Boiling and Condensation in Small Diameter Channels,” Heat Transfer Engineering, Vol. 24, No.1, pp. 18-40, 2003. 7. Qu, W., and Mudawar, I., “Experimental and Numerical Study of Pressure Drop and Heat Transfer in a Singlephase Micro-channel Heat Sink,” Int. J. Heat and Mass Transfer, Vol.45, pp.2549-2565, 2002. 8. Ryu, J. H., Choi, D. H. and Kim, S. J., “Numerical Optimization of the Thermal Performance of a Microchannel Heat Sink,” Int. J. Heat and Mass Transfer, Vol.45, pp.2823-2827, 2002. 9. Knight, R. W., Hall, D. J., Goodling, J. S., Jaeger, R. C, “Heat Sink Optimization with Application to Microchannels,” IEEE Transactions on Components, Hybrids, and Manufacturing Technology, Vol. 15, No. 5. pp. 832-842, 1992. 10. Kakac, S., Shah, R. K and Aung, W., Handbook of Single-Phase Convective Heat Transfer, John Wiley & Sons, (New York, 1987). 21st IEEE SEMI-THERM Symposium Authorized licensed use limited to: Rochester Institute of Technology. Downloaded on June 14,2010 at 19:06:32 UTC from IEEE Xplore. Restrictions apply.