Design Optimization of Micro-Channel Heat Exchanger ... - IMAPSource

45th International Symposium on Microelectronics | September 9-13, 2012 | San Diego, California USA

Design Optimization of Micro-channel Heat Exchanger embedded in LTCC Aparna Aravelli1, Singiresu S. Rao1, Hari K. Adluru2 1

2

University of Miami Department of Mechanical and Aerospace Engineering Coral Gables, Florida, USA 33146 305-284-2571, 305 284 2580 FAX, [email protected]

Florida International University, Department of Mechanical and Materials Engineering Miami, Florida, USA 33199 305-348-1932 FAX, [email protected]

Abstract Increase in the density of electronic packaging leads to the investigation of highly efficient thermal management systems. The challenge in these micro-systems is to maximize heat transfer per unit volume. In the author’s previous work, experimental and computational analysis has been performed on LTCC substrates using embedded silver vias. This novel technique of embedding silver vias along with forced convection resulted in higher heat transfer rates. The present work further investigates into the optimization of this model. A Multi-objective optimization problem has been formulated for the heat transfer in the LTCC model. The Log Mean Temperature Difference (LMTD) method of heat exchangers has been used in the formulation. Optimization is done based on maximization of the total heat transferred and minimization of the coolant pumping power. Structural and thermal design variables are considered to meet the manufacturability and energy requirements. Demanded pressure loss and volume of the silver metal are used as constraints. The classical optimization technique Sequential Quadratic Programming (SQP) is used to solve the micro-heat exchanger problem. The optimal design is presented and sensitivity analysis results are discussed. Keywords: electronic cooling, micro-channel, LTCC, optimization, micro heat exchanger.

Introduction The conventional method of forced air cooling with passive heat sink can handle heat fluxes up-to 3-5W/cm2; however current microprocessors are operating at levels of 100W/cm2 and greater. This demands the innovation of novel thermalmanagement systems. Micro-channel heat sink cooling is a promising means of heat removal because of its high ratio of surface area to volume and a compact design. Heat transfer in micro-channel heat sinks has been studied for almost three decades now. Tuckerman and Pease [1] were the first to experimentally study the heat removed using three different micro-channel heat sinks with varying channels heights and widths. Their work was followed by many researchers performing experimental and theoretical studies on microchannel heat sinks. Kliener et al., [8] used a parallel plate-fin heat sink to perform experimental and theoretical investigation in micro-channels. Philips [9] suggested an analytical model for the estimation of thermal resistance in a micro-channel and validated the model with experiments. Theory based correlations for thermal resistances in microchannels were reported by Samalam [10]. Numerical simulation of heat transfer in solid and liquid

Increased device density, switching speeds of integrated circuits and decrease in electronic packaging size is placing new demands for high power thermal-management. The thermal management system employed is extremely important because this system controls the temperatures of the micro-circuits and microprocessors on the chips. These chip temperatures in turn affect the performance and reliability of the system. Often heat transfer systems coincide with the electrical circuit and so design of thermal management systems has always been a challenge. In general, the thermal management system considers the complete thermal path from heat source to the heat sink. Most of the heat removal is by conduction and convection with the lowest possible thermal resistance at all levels of assembly. Depending on the application, a wide range of cooling methods are in use, which include forced air convection, external/internal heat pipes, water cooled heat sinks, immersion cooling and refrigeration cycles. All these cooling methods can be broadly classified as heat pipe cooling, thermoelectric cooling, phase change cooling and micro-channel heat sink cooling.

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substrate micro-channel heat exchangers was conducted by Weisburg et al., [11]. Manifold microchannel heat sinks were first proposed in [12] and numerically studied in [13]. The studies conclude that the manifold micro-channel heat sinks have a less pressure drop when compared to the conventional micro-channels heat sinks for a fixed flow rate. Different geometries of micro-channels like grooves, pin-fins, dimples and ribs have also been studied by many researchers [7, 3]. A comparative analysis of studies on heat transfer and fluid flow in micro-channels is detailed in [14].

compared. One of the shortcomings in this study is that convection is neglected. Design optimization of four types of cooling technologies using two coolants was studied by Ndao and Jenson [3]. The four types considered are the micro-channel heat sinks, circular pin-fin heat sinks, offset-strip fin heat sinks and submerged impinging jets and the coolants were water and HFE-7000. The technologies were compared for total thermal resistance and pumping power based on constant pressure drop. It is concluded that the offset strip-fin heat sink is better than the other three types considered.

Optimization in micro-channels was conducted by Bau [15] to minimize the temperature gradient and the overall thermal resistance. Upadhye [16] optimized the geometry of micro-channels heat sink from a heat transfer and pressure drop perspective. It is concluded that the higher the aspect ratio, the better is the performance of the micro-channel heat exchanger. The effect of the width of the microchannel in transferring heat is numerically studied by Ryu[17]. Thermal resistance was considered as the objective for optimization. Another important optimization study was based on laminar and turbulent flows in the micro-channel heat sinks by Knight [18]. The governing fluid flow and heat transfer equations were solved numerically and the optimal channel dimensions were found. Optimization of stacked micro-channel heat sinks was studied by Wei and Joshi [7]. A thermal resistance network model was developed and single objective optimization of the model was done using genetic algorithms. Overall thermal resistance was minimized based on the maximum pressure drop and coolant flow rate constraints. The effect of the number of layers in the stacks, pumping power and channel length were investigated. Ansari et al., [2] investigated the shape optimization of micro-channel heat sink. Grooved structure is considered for optimization based on thermal resistance and pumping power. Results obtained were compared to that of a smooth structure micro-channel. It is concluded that the grooved structure showed a decrease in thermal resistance and an increase in Nusselt number at the expense of pumping power. Pareto optimal solutions were generated for the multi-objective optimization problem and the sensitivity of design variables is shown. Design optimization of single phase liquid cooled microchannel heat sink was investigated by Biswal et al., [4]. A systematical robust analytical method was developed for optimization considering nonconventional design variables, like the footprint of the heat source, its eccentricity and thickness of heat sink base. Experimental and analytical results were

Most of the literature in micro-channels is based on inbuilt channels of the base material (Silicon, Cu, and LTCC). This is usually done to ease the fabrication/manufacturability. In order to further decrease the thermal resistance and enhance the heat transfer, thermal vias made of materials made of high thermal conductivity can be used. The model used in the present study is based on a novel micro-channel heat sink using silver vias. A water-cooled heat exchanger, with active in-built heat sink using vertical free standing silver columns acting as pin fins, is embedded in the LTCC substrate. The concern with fabricating is also addressed in the author’s previous work [6, 20]. LTCC Heat Exchanger Model Fabrication In the author’s previous work [6, 20], it was proved that micro heat-exchangers using silver (Ag) vias can be fabricated in LTCC materials. A commercially available Dupont 951 cofirable green tape and modified Dupont 6141 Ag via ink with additional silver has been used. Thermal vias were built by drilling vias in the LTCC tape using a hig-speed numerically controlled micro-drilling system, screen printing Ag ink into these vias using vacuum. These tapes in green state were laminated together using an isostatic laminator. A wax insert was placed in the channel cavity before laminating to minimize sagging and maximize green density during lamination. The free standing Ag columns were built by drilling holes in the wax insert and filling Ag via ink into the holes with the assistance of vacuum. These pieces were stacked carefully on top of one another and the entire structure was finally laminated at a pressure of 20.6Mpa and temperature of 70oC for 10 minutes. This final structure in the green state was fired using manufacturer’s specifications, with a peak firing temperature of 850oC with an intermediate hold of two hours at 450oC for organic binder burnout. To ensure complete burnout of organic binders in LTCC and any residual wax, the burnout cycle was slightly modified to hold at 130oC for one hour before

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reaching the peak firing temperature. The final structure of the LTCC substrate is shown in Figure 1. The cross section of the sample is shown in Figure 2.

LTCC Heat Exchanger Model Description The schematic of the cross sectional view of the LTCC heat exchanger is shown in Figure 3. Constant amount of heat is provided to the copper shim on the top, which replicates a constant wall temperature heat source. Thermal vias filled with silver ink form columns inside the LTCC substrate. A silver pad is inserted at the inner surface of the rectangular duct to increase the heat transfer area. The thermal vias extend further down to form free standing silver columns in the rectangular duct which act as pin fins. The coolant is pumped into the rectangular duct at the center. LTCC Heat Exchanger Optimization Problem In the optimization of the LTCC heat exchanger, the main aim is to design an energy efficient heat exchanger configuration based on the maximum possible heat transfer from the source to the heat sink while minimizing the coolant pumping power. In the present example, heat source is the top surface of the LTCC sample and the heat sink is the cooling liquid (water).

Figure 1 LTCC heat exchanger with thermal via array (top view) [20]

The problem can be expressed as Min

(1)

where

Figure 2 LTCC heat exchanger with Ag columns (cross section) [20]

with the following constraints: i)

Pressure drop across the duct (2)

ii)

Volume of silver

This constraint is essential for cost effective design. (3) iii) Figure 3 Schematic of LTCC heat exchanger model

Upper and lower bounds on the design variables

The design variables have to be limited to certain bounds based on manufacturability and size

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

restrictions. In this problem, the bounds are specified as:

find X to minimize f

hk

0

 X  subject to 

 X   0 , k  1, 2, , p 

the Lagrangian function, L

(4)

 

(13)

 X ,  , is given by 

 

p   L  f X   k hk X

10.03

(14)

k 1

The thermodynamic, heat transfer and fluid flow relations used for calculations are given as:

where

k

is the Lagrange multiplier for the kth

equality constraint. The Kuhn-Tucker conditions can be stated as

(5)

F Y   0

(6)

(15)

(7)

where

(8)

 L  X  ,Y  , F     h  n p   1    n p   1

(9)

0 0   0  n p   1

Energy balance equation gives (10)

(16)

Equation (15) can be solved using Newton’s iterative method [19] as

Hence, Tout is given by

   Y j 1  Y j   Y j

(11)

(17)

Total heat transfer

with (12)

  F  Tj

 Yj   F  Yj



(18)

where Y j is the solution at the start of jth iteration

Optimization - Solution Method

and  Y j is the change in Y j necessary to generate

The developed optimization model is solved using the robust and classical optimization techniquesequential quadratic programming (SQP). Sequential quadratic programming (SQP) is an efficient direct optimization method for solving constrained nonlinear programming problems [19]. This method is based on the solution of a set of non-linear equations using Newton’s method and derivation of simultaneous non-linear equations using the Kuhn-Tucker conditions to the Lagrangian of the constrained optimization problem. For a problem with equality constraints of the form:

the

improved

solution,

Y j 1 ,

and

[ F ] j  [  F (Y j ) ] is the n  p   n  p  Jacobian matrix of the nonlinear equations whose ith column denotes the gradient of the function Fi (Y ) with respect to the vector Y. By substituting Eqs. (15) and (16) into Eq.(18), we obtain [ 2 L] [ H ]  X j   f j  (19)    T   [0]  j   j 1   h j   [H ]

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H  is updated to improve the quadratic approximation in Eq. (20). H  is chosen

Eq. (19) can be solved to find the change in the design vector  X j and the new values of the

 j 1 .

Lagrange multipliers,

the Hessian matrix

The iterative process

as the identity matrix at the beginning. The matrix H is updated using the modified Broyden Fletcher Goldfarb Shanno (BFGS) approach [19].

 

indicated by Eq.(19) can be continued until convergence is achieved. The solution of the problem in Eq. (13) can be found through the solution of a quadratic programming program iteratively.

SQP is a procedure to solve the single objective optimization problems. The present heat exchanger model is a multi-objective optimization problem since the number of objective functions is more than one (Maximization of heat transfer and minimization of pumping power). There are many procedures available in literature for solving multi-objective optimization problems. Some of them are the weighted sum, global criterion, bounded objective, lexicographic, goal programming, goal attainment and trade–off curve methods. In this study, the widely used approach of weighted sum is used to solve the multi-objective optimization model.

By using a similar analysis, the solution of a problem involving equality and inequality constraints can be determined by solving the following quadratic programming problem iteratively: find X which minimizes

1 Q  f T X  X T [ H ] X 2 subject to the linear equality and inequality constraints

g j   g Tj X  0 , j  1, 2, , m

Results and Discussion LTCC heat exchanger model has been solved using the SQP method. The design constants considered for the design are: Tin = 20oC; T1 = 35.5oC; tAgpad = 0.1 mm; k ltcc = 3.3 W/m K; k Ag = 247 W/m K; Cp,w = 4178 J/kg K; ρw = 997 kg/m3; µw = 8.9*10-4 kg/ms; Pr = 5.68.

hk   hkT X  0 , k  1, 2, , p (20) By treating X in Eq. (20) as the search direction S , standard quadratic programming techniques can be used to find S . Once S is determined, the design vector is updated as

X j 1  X j   * S

Table 1 Results of Optimization Design Variables

(21)

where  is the optimal step length along the direction S found by minimizing the function (using an exterior penalty function approach): *

m

p

j 1

j 1

  f  X     j ( max [ 0, g j ( X ) ] )   mk hk  X 

, j  1, 2, , m  p in first iteration





1 ~     j ,  j ,  j  in subsequent iterations 2  

(22) and

~

j  j

0.8 1.6 2.0 8 25.4

Bounds Lower 0.2 0.5 1.5 4 10.1

Upper 1.0 2.0 2.5 20 30.5

Optimum Design 0.3 0.6 2.5 16 23.2

The results of optimization are shown in Table 1. An initial design is randomly chosen in between the upper and lower bounds of the design variables. The value of the objective function (combining heat transferred and pumping power) converges to 38.37 W. The heat transferred is 43.75 W and the pump consumes 5.38 W. At the optimum design, the diameter of the silver column converges to 0.3 mm and is close to the lower bound value of 0.2 mm. The pitch of the silver columns is 0.6 mm. Also, the number of silver columns converges to 16, which is closer to the upper bound design (20). This means that the total energy (combining the heat transferred

with  j  j   max 

Initial Design

of the previous iteration. The step

length  can be found using a cubic interpolationbased approach. Once X j 1 is found from Eq. (22), *

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and the pumping power) is optimum at lower diameters and pitch and higher number of silver columns. Hence, for energy savings, the silver vias should be thin and closely placed. This results in an increase in the surface area of heat transfer and so more heat flows from the metal into the coolant. Also, such a design results in an increase in the total number of silver vias for a specified heat source footprint area. The duct height converges to the upper bound value (maximum value) of 2.5 mm. This result is in agreement with the basics of heat transfer: the larger the length of the fin, the greater is the heat transfer. But due to available space restrictions, the upper bound is chosen to be 2.5mm in the present design. Mass flow rate of the coolant affects the pumping power and also the heat absorbed. The optimum mass flow rate converges to a value of 23.2 g/s. So for an optimum flow of 23.2 g/s, the heat absorbed by the coolant is maximum with minimum pumping power.

Figure 4 Optimization Results (function evaluations)

The convergence of the optimization algorithm is shown in Figure 4, which gives the total number of function evaluations at each iteration during optimization. From the figure, it is evident that the total number of iterations required for convergence to the optimum solution is 21. The variation of the objective function value (combined heat transfer and pumping power) at each iteration is shown in Figure 5. It is to be noted that the objective function value is negative because the heat dissipated is to be maximized and the pumping power is to be minimized. The variation of total thermal resistance and the pumping power during the optimization is shown in Figures 6 and 7.The pump power varies from an initial value of 6.5 W to an optimum value of 5.38 W at the end of the optimization. This value is in agreement with the range of the pump chosen in this study and also with the current microelectronics standards. The total thermal resistance value at the optimum point is found to be 0.325 oC/W. Thus this optimum design gives a very low thermal resistance.

Figure 5 Convergence of the objective function

Figure 6 Variation of total thermal resistance

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amount of silver metal, the thermal conductivity increases and hence more heat is transferred from the source to the coolant. This sensitivity analysis is useful to a designer to choose from the results and prioritize modifications in designs based on the requirement. Conclusions In this work, optimization of a novel LTCC heat exchanger using silver vias is performed. The multiobjective optimization model is developed and is solved using a robust optimization algorithm. Five design variables namely, the diameter of the silver vias, the pitch of the silver vias, the number of silver columns and the mass flow rate of the coolant are considered. The two conflicting objective functions chosen are the total heat transferred and the pumping power. An optimum design is found which satisfies the given constraints. Sensitivity of the optimum design is studied as well. Diameter and number of silver columns and the height of the duct proved to be the most sensitive parameters, while the pitch of the silver columns proved to be least sensitive. Weighted sum method of multi-objective optimization is used in the present study. Although this method provides with a reasonable solution, other more accurate methods like game theory and genetic algorithms can be used in future. In this work, a basic heat transfer model is optimized. The model uses one dimensional heat transfer relations. In reality, although most of the heat is transferred in one direction, other dimensions are also to be considered for maximum energy savings. Also, only the important design variables such as structural and flow variables are considered in this study. In future, additional analyses considering thermal stresses, vibration analysis and structural failure can be included for refinement and accuracy of the model and thus the optimum designs.

Figure 7 Variation of pumping power

70 60

Objective (-f)

50 40 30 20 10 0

-40

-20

0

20

40

% Change in design variables dia of Ag columns

pitch

duct height

# of Ag columns

mass flowrate Figure 8 Sensitivity analysis

Acknowledgements

Sensitivity Analysis

The authors would like to express their gratitude to Dr. Kinzy W. Jones from Florida Interantional University (FIU) for his support in the present study.

To further understand the effect of different designs close to the optimum design, sensitivity analysis of the optimum design is considered. The design variables are varied about ±30% of their optimum values. Variation of the objective function (heat transfer) with changes in the optimum values of the design variables is shown in Figure 8. It is evident from the figure, that diameter of the silver column; number of silver columns and the duct height are among the most sensitive variables. The least sensitive variable is the pitch of the silver columns. This is as expected, because with increase in the

References [1] Tuckerman D. B. and Pease R. F. W., “HighPerformance Heat Sinking for VLSI”, IEEE Electron Device Lett., Vol. 2, No. 5, pp. 126-129, May 1981. [2] Ansari D., Hussain A. and Kim K.Y., “Multiobjective Optimization of a Grooved MicroChannel Heat Sink”, IEEE Transactions on Components and Packaging Technologies, Vol. 33, No. 4, pp. 767-776, December, 2010.

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[13] Ng E. Y. K. and Poh S.T., “Investigate Study of Manifold Micro-Channel heat sinks for Electronic Cooling Design”, Journal of Electronic Manufacturing, Vol. 9, No. 2, pp. 155-166, 1999.

[3] Ndao S., Peles Y. and Jensen M. K., “Multiobjective Thermal Design Optimization and Comparative Analysis of Electronic Cooling Technologies”, International Journal of Heat and Mass Transfer, Vol. 52, No. 19-20, pp. 4317-4326, 2009.

[14]Sobhan C. B. and Garimella S. V., “A Comparative Analysis of Studies on Heat Transfer and Fluid Flow in Micro-channels”, Microscale Thermophysical Engineering”, Vol. 15, pp. 293-311, 2001.

[4] Biswal L., Chakraborty S., and Som S. K., “Design Optimization of Single-Phase Liquid Cooled Microchannel Heat Sink”, IEEE Transactions on Components and Packaging Technologies, Vol. 32, No. 4, pp. 876-886, December, 2009.

[15] Bau H. H., “Optimization of Conduit’s shape in Micro-heat Exchangers”, International Journal of Heat and Mass Transfer, Vol. 41, pp. 2717-2723, 1998.

[5] Dulikravich G. S. and Martin T. J., “Optimization of 3D Branching Networks of Microchannels for Microelectronic Device Cooling”, Proceedings of the International Heat Transfer Conference, Washington, DC , August 8-13, 2010.

[16] Upadhye H. R. and Kandlikar S. G., “Optimization of micro-channel geometry for direct chip cooling using single phase heat transfer”, Proceedings of 2nd International Conference on Microchannels and Minichannels, pp. 679-685, June 2004.

[6] Zampino M. A., Adluru H., Liu Y. and Jones W. K., “LTCC Substrates with Internal Cooling Channel and Heat Exchangers” Proceedings of the 36th International Symposium on Microelectronics, IMAPS, Boston, 2003.

[17] Ryu J. H., Choi D. H. and Kim S. J., “Numerical Optimization of the Thermal Performance of a Microchannel Heat Sink”, International Journal of Heat and Mass Transfer, Vol. 45, No. 13, pp. 28232827, 2002.

[7] Wei X. and Joshi Y., “Optimization Study of Stacked Micro-Channel Heat Sinks for MicroElectronic Cooling”, IEEE Transactions on Components and Packaging Technologies, Vol. 26, No. 1, pp. 55-61, March, 2003.

[18] Knight R. W., Hall D. J., Goodling J. S. and Jaeger R. C., “ Heat Sink Optimization with Applications to Micro-channels”, IEEE Transactions on Components Hybrids and Manufacturing Technology, Vol. 15, No. 5, pp. 832-842, October 1992.

[8] Kleiner M. B., Stefan A. K. and Haberger K., “High Performance Forced Air Cooling Scheme employing Microchannel Heat Exchangers”, IEEE Transactions on Component Packaging Technology: Part A, Vol. 18, No. 4, pp. 795-804, December 1995.

[19] Rao, S.S., “Engineering Optimization: Theory and Practice”, John Wiley and Sons Inc., Fourth Edition, New York, 2009.

[9] Philips R.J., “Micro-channel Heat Sinks”, in Advances in Thermal Modeling of Electronic Components and Systems, A. Bar-Cohen and A. D. Kraus, Eds., Vol. 2, pp. 109-184, 1990.

[20] Adluru Hari, “Design and Analysis of MicroChannel Heat Exchanger embedded in low temperature co-fire ceramic (LTCC)”, M.S. Thesis, Florida International University, Miami, FL, 2004.

[10] Samalam V. K., “Convective Heat Transfer in Microchannels”, Journal of Electronic Materials, Vol. 18, No. 5, pp. 611-618, 1989. [11] Weisburg A., Bau H. H. and Zemel J. N., “Analysis of Microchannels for Integrated Cooling”, International Journal of Heat and Mass Transfer, Vol. 35, No. 10, pp. 2465-2474, 1992. [12] Harpole G. M. and Eninger J. E., “Microchannel Heat Exchanger Optimization”, Proceedings of 7th IEEE Semi Thermal Symposium, Scottsdale, AZ, February 12-14, pp. 59-63, 1991.

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Nomenclature

Cp Deq f h k L

N

Pr Re R S T

V

Density in kg/m3 Pressure drop in N/m2 Specific heat in J/KgoC Diameter of the Ag column in mm Equivalent diameter in m Friction factor Height of the duct in mm convective heat transfer coefficient in W/m2K Thermal conductivity in W/mK Equivalent length in m Coolant mass flow rate in g/s Number of silver columns (row/column) Nusselt number constant Heat dissipated or transferred in W Coolant pumping power in W Pitch of the silver column in mm Prandtl Number Rate of Heat transferred in W/s Reynolds number Thermal resistance in oC/W Area in m2 Thickness of Ag pad Temperature in oC Constant wall source temperature in oC Coolant inlet temperature in oC Coolant outlet temperature in oC Bulk mean temperature of coolant in oC Velocity of the coolant in m/s Volume of silver metal in m3

000865