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Journal of Microelectronics and Electronic Packaging (2013) 10, 40-47 Copyright © International Microelectronics And Packaging Society ISSN: 1551-4897

Multiobjective Design Optimization of Microchannel Cooling System Using High Performance Thermal Vias in LTCC Substrates Aparna Aravelli,1 Singiresu S. Rao,1 and Hari K. Adluru*,2

AbstractIncreased heat generation in semiconductor devices for demanding applications leads to the investigation of highly efficient cooling solutions. Effective options for thermal management include passing of cooling liquid through the microchannel heat sink and using highly conductive materials. In the author’s previous work, experimental and computational analyses were performed on LTCC substrates using embedded silver vias and silver columns forming microchannels. This novel technique of embedding silver vias along with forced convection using a coolant resulted in higher heat transfer rates. The present work investigates the design optimization of this cooling system (microheat exchanger) using systems optimization theory. A new multiobjective optimization problem was formulated for the heat transfer in the LTCC model using the log mean temperature difference (LMTD) method of heat exchangers. The goal is to maximize the total heat transferred and to minimize the coolant pumping power. Structural and thermal design variables are considered to meet the manufacturability and energy requirements. Pressure loss and volume of the silver metal are used as constraints. A hybrid optimization technique using sequential quadratic programming (SQP) and branch and bound method of integer programming has been developed to solve the microheat exchanger problem. The optimal design is presented and sensitivity analysis results are discussed. KeywordsElectronic cooling, microchannel, LTCC, micro heat exchanger, optimization

INTRODUCTION ncreased 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 microcircuits and microprocessors on the chips. These chip temperatures in turn affect the performance and reliability of the system. Often, heat transfer systems coincide

I

The manuscript was received on October 10, 2012; revised on January 8, 2013; accepted on January 8, 2013 1 University of Miami, Department of Mechanical and Aerospace Engineering, Coral Gables, Florida, 33146, USA 2 Florida International University, Department of Mechanical and Materials Engineering, Miami, Florida, 33199, USA *Corresponding author; email: [email protected] doi:10.4071/imaps.360

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 microchannel heat sink cooling. The conventional method of forced air cooling with a passive heat sink can handle heat fluxes up to 3-5 W/cm2; however, at present, microprocessors are operating at levels of 100 W/cm2 and greater. This demands the innovation of novel thermal management systems. Microchannel 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 microchannel 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 microchannel heat sinks with varying channel heights and widths. Their work was followed by many researchers performing experimental and theoretical studies on microchannel heat sinks. Kliener et al. [2] used a parallel plate fin heat sink to perform experimental and theoretical investigation in microchannels. Philips [3] suggested an analytical model for the estimation of thermal resistance in a microchannel and validated the model with experiments. Theory-based correlations for thermal resistances in microchannels were reported by Samalam et al. [4]. Numerical simulation of heat transfer in solid and liquid substrate microchannel heat exchangers was conducted by Weisburg et al. [5]. Manifold microchannel heat sinks were first proposed in Harpole and Eninger [6] and numerically studied in Ng and Po [7]. The studies conclude that the manifold microchannel heat sinks have a reduced pressure drop when compared with the conventional microchannel heat sinks for a fixed flow rate. Different geometries of microchannels, such as grooves, pin-fins, dimples, and ribs, have also been studied by many researchers [8, 9]. A comparative analysis of studies on heat transfer and fluid flow in microchannels is detailed in Sobhan and Garimella [10].

1551-4897 © 2013 International Microelectronics And Packaging Society

A. Aravelli et al.: Optimization of Microchannel Cooling System in LTCC

Optimization in microchannels was conducted by Bau et al. [11] to minimize the temperature gradient and the overall thermal resistance. Upadhye et al. [12] optimized the geometry of microchannel heat sinks from a heat transfer and pressure drop perspective. The conclusion is that the higher the aspect ratio, the better is the performance of the microchannel heat exchanger. The effect of the width of the microchannel in transferring heat is numerically studied by Ryu et al. [13]. Thermal resistance was considered as the objective for optimization. Another important optimization study was based on laminar and turbulent flows in the microchannel heat sinks by Knight et al. [14]. The governing fluid flow and heat transfer equations were solved numerically and the optimal channel dimensions were found. Optimization of stacked microchannel heat sinks was studied by Wei and Joshi [8]. 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. [15] investigated the shape optimization of the microchannel heat sink. Grooved structure was considered for optimization based on thermal resistance and pumping power. The results obtained were compared with those obtained from a smooth structure microchannel. 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 multiobjective optimization problem and the sensitivity of design variables is shown. Design optimization of a single phase liquid cooled microchannel heat sink was investigated by Biswal et al. [16]. A systematic robust analytical method was developed for optimization considering nonconventional design variables, such as the footprint of the heat source, its eccentricity, and the thickness of the heat sink base. Experimental and analytical results were 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 et al. [9]. The four types considered are the microchannel 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. The conclusion was that the offset strip fin heat sink is better than the other three types considered. Most of the literature in microchannels 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 with high thermal conductivity can be used. The model used in the present optimization study is based on a novel microchannel heat sink using silver vias. A water-cooled heat exchanger, with an active in-built heat sink using vertical freestanding Ag columns acting as pin fins, is embedded in the LTCC substrate. The fabrication of the model is addressed in the author’s previous work [17, 18].

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MODEL FABRICATION OF THE MICROCHANNEL COOLING SYSTEM In the author’s previous work [17, 18], it was proven that micro heat exchangers using 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 Ag was used. Thermal vias were built by drilling vias in the LTCC tape using a high-speed numerically controlled microdrilling system, screen printing Ag ink into these vias with vacuum assist. These tapes in the green state were laminated together using an isostatic laminator. The freestanding Ag columns were built by drilling holes in the wax insert and filling Ag via ink into the holes with the assistance of vacuum. The wax insert was placed in the channel cavity before laminating to minimize sagging and maximize green density during lamination. The pieces were stacked carefully on top of one another and the entire structure was finally laminated at a pressure of 20.6 MPa and a temperature of 70 C for 10 min. A general layout of the fabrication process is shown in Fig. 1. This final structure in the green state was fired using the manufacturer’s specifications, with a peak firing temperature of 850 C with an intermediate hold of 2 h at 450 C for organic binder burnout (Table I). To ensure complete burnout of the organic binders in LTCC and any residual wax, the burnout cycle was slightly modified to hold at 130 C for 1 h before reaching the peak firing temperature. The final structure of a sample LTCC substrate is shown in Fig. 2 and its cross section is shown in Fig. 3.

MODEL DESCRIPTION OF THE MICROCHANNEL COOLING SYSTEM A schematic of the cross-sectional view of the LTCC heat exchanger used in the current study is shown in Fig. 4. Kapton heaters are used to provide heat to the copper shim on the top

Fig. 1. Layout of the fabrication process [18]. Table I Sintering Profiles for the LTCC Materials [18]

Material

Lamination pressure

Burnout Burnout

450 C Dupont 3000 psi @ for 1-2 h, 951 70 C, hold for 10 min 2 C/min to 450 C

Sinter

Dwelling

Ramp

Cooling

2 C to 6 C/min Furnace to 850 C to cooling 875 C, hold for 15 min

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Journal of Microelectronics and Electronic Packaging, Vol. 10, No. 1, 1st Qtr 2013

Fig. 2. LTCC heat exchanger with thermal via array (top view) [18].

shim and is powered by a regulated DC supply. The power dissipated is measured by recording the potential drop and the current drawn through the heater. Coolant (water) is pumped into the test sample using a peristaltic pump through silicone tubing. The temperature of the inlet water is maintained at a constant level using a large temperature-controlled water bath. The temperature of coolant at the inlet and outlet of the cooling system (duct) is measured by inserting thermocouples directly into the flow regimen by making small holes in the barb fittings. The entire cooling system is wrapped in fiberglass foam to provide insulation and thus reduce the heat loss to the surroundings. The testing is done by adjusting the pump speed to the desired flow rate and observing the inlet and outlet temperatures, and also the temperature below the heating coil and on the surface of the copper shim. The DC power supply is then adjusted to the desired input power. The temperatures at the inlet, outlet, and on the surface of the copper shim are monitored until the steady state condition is reached. The steady state is considered to be established when there is no change in the inlet and outlet temperatures for a period of 15 min. By adjusting parameters such as flow and power, different sets of temperature are measured at steady state conditions and the experimental data are collected for further analysis and optimization. Further details on the experimental setup and procedure can be found in Adluru [18].

Fig. 3. LTCC heat exchanger with Ag columns (cross section) [18].

MICROCHANNEL HEAT EXCHANGER OPTIMIZATION PROBLEM

Fig. 4. Schematic of the microchannel cooling system.

surface, which replicates a constant wall temperature source. Thermal vias filled with Ag ink form columns inside the LTCC substrate. A silver pad is inserted at the inner surface of the rectangular duct to reduce the thermal resistance and thus increase the heat transfer. The thermal vias extend further down to form freestanding silver columns in the rectangular duct which act as pin fins. The coolant (water) is pumped into the rectangular duct at the center.

EXPERIMENTAL PROCEDURE A copper shim is attached to the top surface of the LTCC substrate using thermal conductive epoxy. A small notch is made into the copper shim and a thermocouple is fixed using thermally conductive epoxy. The thermocouple measures the substrate’s surface temperature near the center of the heater. A kapton type foil heater is mounted on top of the copper

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). The problem can be expressed as ~ þ Pp X ~ ~ ¼ Pheat X ð1Þ Min f X ~ is the objective function which includes the total Where f X heat transferred from the source to the coolant (Pheat) and ~ is given as the pumping power (Pp). The design vector X 9 8 DAg > > > > > > > = < PtAg > ~¼ : X hdct > > > > n > > Ag > > ; : m_ coolant The design vector consists of the design variables, the diameter of the Ag column DAg, the pitch of the Ag column PtAg, the height of the duct hdct , number of Ag columns nAg, and the mass flow rate of the coolant m_ coolant . The constraints in the optimization problem are given as below: 1. The pressure drop across the duct (D p) is within the lower and upper bounds ðD pÞl Dp ðD pÞu

ð2Þ

2. Volume of silver (VAg ) is within the lower and upper bounds ðVAg Þl VAg ðVAg Þu

ð3Þ


43

where m_ denotes the mass flow rate, Cp is the specific heat of Ag, and s is the wetted surface area. The pumping power Pp is given by

This constraint is essential for cost-effective design. 3. Upper and lower bounds on the design variables The design variables have to be limited to certain bounds based on manufacturability and size restrictions. In this problem, the bounds are specified as:

Pp ¼

0:5 PtAg 2:0

10:03 m_ coolant 30:5 The basic thermodynamic, heat transfer, and fluid flow relations used for calculations are briefly given as follows. The total heat transferred from the source to the coolant (Pheat ) is a function of the total thermal resistance (RTotal); and the difference in temperature between the source and the coolant is denoted as DT. Hence, ð5aÞ

where the total thermal resistance is calculated as a summation of the conductive resistance (Rconduction þ RAgpad ) and convective resistance (Rconvection ), and is given by RTotal ¼ R conduction þ RAgpad þ R convention

ð5bÞ

Also, the rate of convective heat transfer Q_ is calculated as Q_ ¼ hSDTavg

ð6Þ

where S is the convective surface area, and h is the convective heat transfer coefficient. The variable h is a function of the Nusselt number Nu and is given as h¼

NuK x

ð8Þ

where Tbulkmean denotes the average of the inlet (Tin ) and outlet (Tout ) temperatures of the coolant. Tbulkmean

Tin þ Tout ¼ 2

ð9Þ

ð10Þ

The solution of the optimization problem is based on a developed hybrid optimization algorithm. The algorithm uses the classical optimization technique of Sequential Quadratic Programming (SQP) for continuous optimization along with the Branch and Bound (B&B) method of integer programming. The SQP method is an efficient direct optimization method for solving constrained nonlinear programming problems [19]. This method is based on the solution of a set of nonlinear equations using Newton’s method and derivation of simultaneous nonlinear equations using the Kuhn-Tucker conditions to the Lagrangian of the constrained optimization problem. For a problem with equality constraints of the form: ~ to minimize f X ~ subject to find X ~ ¼ 0; k ¼ 1; 2; ; p ð13Þ hk X ~; ~ the Lagrangian function, L X l , is given by p X ~ þ ~ lk hk X L¼f X

hs Tout ¼ T1 T1 Tin e mCp

ð11Þ

ð14Þ

k¼1

where lk is the Lagrange multiplier for the kth equality constraint. The Kuhn-Tucker conditions can be stated as F ðY Þ ¼ 0 where F¼

ÑL h

ðnþpÞ ´1

;Y ¼

X l

ð15Þ

ðnþpÞ ´1

;0¼

0 0 ðnþpÞ ´1 ð16Þ

A solution to eq. (15) can be found by using Newton’s iterative method [19] as ~ Yjþ1 ¼ ~ Yj þ D ~ Yj with ½ Ñ F Tj D Yj ¼ F

Solution of eq. (10) gives

ð12bÞ

HYBRID OPTIMIZATION ALGORITHM FOR SOLVING THE OPTIMIZATION PROBLEM

Considering energy balance in fins (Ag columns in the rectangular duct) _ p dT ¼ hðT1 Tbulkmean Þds mC

L V2 r Deq 2

where N is the number of Ag columns in a row, f is the friction factor, L is the length of the duct, Deq is the equivalent diameter of the duct, V is the velocity of the coolant, r is the density of the coolant, and h is the efficiency of the pump.

ð7Þ

where K is the thermal conductivity of the coolant and x is the equivalent length of the duct. The value of DTavg is calculated using the constant wall source temperature T1 and the bulk mean temperature of the coolant Tbulkmean DTavg ¼ T1 Tbulkmean

Dp ¼ N f

ð4Þ

1:5 hdct 2:5 4 nAg 20

DT RTotal

ð12aÞ

Where the pressure drop across the system, Dp, is given by

0:2 DAg 1:0

P heat ¼

_ mDp rh

ð17Þ

Yj

ð18Þ

where Yj is the solution at the start of jth iteration and D Yj is the change in Yj necessary to generate the improved solution,

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Yj+1, and [ÑF ] j = [ÑF(Yj)] is the ðn þ pÞ´ðn þ pÞ 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 DXj Ñfj ½Ñ L ½H ¼ ð19Þ hj ½HT ½0 j ljþ1 The solution to eq. (19) results in the change to the design vector D Xj and the new values of the Lagrangian multipliers, lj+1. The iterative process 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. 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. 1 find D X which minimizes Q ¼ Ñf T DX þ D X T ½H DX 2 subject to the linear equality and inequality constraints gj þ Ñ gjT DX 0; j ¼ 1; 2; ; m

(B&B) method of integer programming. The details of the B&B method can be found in Rao [19]. The flowchart for the developed hybrid optimization algorithm is shown in Fig. 5. The optimization algorithm for the LTCC heat exchanger problem involves two main steps. In the first step, the optimization problem is solved using SQP, assuming all the variables to be continuous in nature. Once the optimum solution to step one is obtained, the design variable (number of Ag columns) is checked for discreteness (integer in this case). If the condition is satisfied, then the program is terminated and the results are printed. If the condition of discreteness is not satisfied, the next step of the algorithm is implemented, which involves the B&B method. The discrete variable (number of Ag columns) is set for lower and upper bound integers based on the results obtained in the first step. In this way, two subproblems for optimization are formed. These subproblems have the same objective and constraints as the initial problem with an additional equality constraint. Then the two suboptimization problems are solved using SQP. At each stage, the branching (dividing into subproblems) is continued until an infeasible solution is found. Each time, the best feasible solution obtained up to that point

ð20Þ

hk þ Ñ hTk D X ¼ 0; k ¼ 1; 2; ; p

By treating DX 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 Xjþ1 ¼ Xj þ a S

ð21Þ

where a is the optimal step length along the direction S found by minimizing the function (using an exterior penalty function approach): p m X X þ lj ðmax½0; gj X lm þ k hk X j¼f X þ j¼1

j¼1

with

8 > > < lj ; j ¼ 1; 2; ; m þ p in first iteration lj ¼ 1 ~ > > lj ; lj in subsequent iterations : max lj ; 2 ð22Þ

~j is equivalent to lj of the previous iteration. The step and l length a can be found using a cubic interpolation-based approach. Once Xj+1 is found from eq. (22), the Hessian matrix [H ] is updated to improve the quadratic approximation in eq. (20). [H ] is chosen as the identity matrix at the beginning. The matrix [H ] is updated using the modified Broyden Fletcher Goldfarb Shanno (BFGS) approach [19]. SQP is a procedure to solve single objective optimization problems with continuous design variables (not discrete values). However, it is evident that the heat exchanger problem has a design variable (number of silver columns) which takes only integer values within the bounds. Hence, SQP cannot be directly used. Therefore, in this study, a hybrid optimization algorithm is developed using the SQP and branch and bound

Fig. 5. Flowchart for microchannel heat exchanger optimization using the hybrid optimization method.


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is updated and the branching and bounding and the SQP optimization is continued until the optimum solution is obtained. The present heat exchanger model is a multiobjective 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 the literature for solving multiobjective optimization problems. Some of these are the weighted sum, global criterion, bounded objective, lexicographic, goal programming, goal attainment, and tradeoff curve methods [19]. In this study, the widely-used approach of the weighted sum is used to solve the multiobjective optimization model. In the weighted sum approach, multiple objectives are combined together into a single objective based on the relative importance of each of them. In the current study, equal importance is given to the total heat transferred and the power required to pump the coolant into the system.

RESULTS AND DISCUSSION An LTCC heat exchanger model has been solved using the hybrid optimization method detailed in the previous section. The design constants considered for the design are: Tin ¼ 20 C; T1 ¼ 35.5 C; thickness of the Ag pad (tAgpad) ¼ 0.1 mm; thermal conductivity of LTCC (kLTCC) ¼ 3.3 W/mK; thermal conductivity of Ag (kAg) ¼ 247 W/mK; specific heat of water (Cp,w) ¼ 4178 J/kgK; density of water (rw) ¼ 997 kg/m3; viscosity mw ¼ 8.9 ´ 104 kg/ms; Prandtl number (Pr) ¼ 5.68. The results of optimization are shown in Table II. 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 and the pumping power) is optimum at lower diameters and pitch and a higher number of silver columns. Hence, for energy saving, the silver vias should be thin and closely placed. This results in an increase in the surface area of heat transfer, 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

Fig. 6. Optimization Results (function evaluations).

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 2.5 mm in the present design. The 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. Thus, for an optimum flow of 23.2 g/s, the heat absorbed by the coolant is at maximum with minimum pumping power. The convergence of the optimization algorithm is shown in Fig. 6, which gives the total number of function evaluations for every 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 Fig. 7. Note 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 Figs. 8 and 9. 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 C/W. Thus this optimum design gives a very low thermal resistance. The effect of coolant flow rate on the total thermal resistance and the pressure drop is shown in Fig. 10. Total thermal

Table II Results of Optimization Bounds

Design variables

Initial design

Lower

Upper

Optimum design

DAg PtAg hdct nAg m_ coolant

0.8 1.6 2.0 8 25.4

0.2 0.5 1.5 4 10.1

1.0 2.0 2.5 20 30.5

0.3 0.6 2.5 16 23.2 Fig. 7. Convergence of the objective function.

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Fig. 11.

Fig. 8. Variation of total thermal resistance.

Sensitivity analysis.

increasing the flow rate does not result in a significant reduction in thermal resistance. This optimum value is found based on thermal resistance, pressure drop, and flow calculations for a particular physical configuration (based on experimental data) of the microchannel heat exchanger model. But when additional parameters like the volume of the silver metal and the number of silver columns (i.e., the geometric variables) are considered and the model is optimized, the optimum flow rate is found to be 1397 mL/min (23.2 g/s) as shown in Table I. Hence, there is a 9.9% increase in the flow rate of the coolant.

SENSITIVITY ANALYSIS

Fig. 9. Variation of pumping power.

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 Fig. 11. It is evident from the figure that diameter of the silver column, the 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, since with an increase in the 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

Fig. 10. Variation of total thermal resistance and pressure drop with coolant flow rate.

resistance of the heat sink decreases from 0.413-0.335 C/W and the pressure drop increases from 160-278 kPa. As the flow rate of the coolant increases, the thermal resistance decreases and the pressure drop increases. Hence, there is a tradeoff between the two and so the optimum point is where the curves intersect. The optimum value of the coolant flow rate is found to be 1275 mL/min (21.1 g/s). Beyond this point,

In this work, optimization of a novel microchannel cooling system (heat exchanger) using silver vias in LTCC substrates is performed. The multiobjective optimization model is developed and is solved using a hybrid optimization technique. The design variables of 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. The sensitivity of the optimum design is studied as well. The diameter and the 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. The weighted sum method of multiobjective optimization is used in the current study.


Although this method provides a reasonably accurate solution, other methods such as game theory and genetic algorithms can be used for further refinement of the solution. 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, considering 2D and 3D models would result in 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, which would result in more optimum designs.

ACKNOWLEDGMENTS The authors thank to Dr. Kinzy W. Jones from Florida International University (FIU) for his support in the present study.

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[7] E.Y.K. Ng and S.T. Poh, “Investigate study of manifold micro-channel heat sinks for electronic cooling design,” Journal of Electronics Manufacturing, Vol. 9, No. 2, pp. 155-166, 1999. [8] X. Wei and Y. Joshi, “Optimization study of stacked micro-channel heat sinks for micro-electronic cooling,” IEEE Transactions on Components and Packaging Technologies, Vol. 26, No. 1, pp. 55-61, 2003. [9] S. Ndao, Y. Peles, and M.K. Jensen, “Multi-objective 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. [10] C.B. Sobhan and S.V. Garimella, “A comparative analysis of studies on heat transfer and fluid flow in micro-channels,” Microscale Thermophysical Engineering, Vol. 15, pp. 293-311, 2001. [11] H.H. Bau, “Optimization of conduit’s shape in micro-heat exchangers,” International Journal of Heat and Mass Transfer, Vol. 41, pp. 2717-2723, 1998. [12] H.R. Upadhye and S.G. Kandlikar, “Optimization of micro-channel geometry for direct chip cooling using single phase heat transfer,” Proceedings of the 2nd International Conference on Microchannels and Minichannels, pp. 679-685, 2004. [13] J.H. Ryu, D.H. Choi, and S.J. Kim, “Numerical optimization of the thermal performance of a microchannel heat sink,” International Journal of Heat and Mass Transfer, Vol. 45, No. 13, pp. 2823-2827, 2002. [14] R.W. Knight, D.J. Hall, J.S. Goodling, and R.C. Jaeger, “Heat sink optimization with applications to micro-channels,” IEEE Transactions on Components Hybrids and Manufacturing Technology, Vol. 15, No. 5, pp. 832-842, 1992. [15] D. Ansari, A. Hussain, and K.Y. Kim, “Multiobjective optimization of a grooved micro-channel heat sink,” IEEE Transactions on Components and Packaging Technologies, Vol. 33, No. 4, pp. 767-776, 2010. [16] L. Biswal, S. Chakraborty, and S.K. Som, “Design optimization of single-phase liquid cooled microchannel heat sink,” IEEE Transactions on Components and Packaging Technologies, Vol. 32, No. 4, pp. 876-886, 2009. [17] M.A. Zampino, H. Adluru, Y. Liu, and W.K. Jones, “LTCC substrates with internal cooling channel and heat exchangers,” Proceedings of the 36th International Symposium on Microelectronics, IMAPS, Boston, 2003. [18] H. Adluru, “Design and analysis of micro-channel heat exchanger embedded in low temperature co-fire ceramic (LTCC),” Masters Thesis, Florida International University, Miami, FL, 2004. [19] S.S. Rao, “Engineering Optimization: Theory and Practice,” 4th ed., John Wiley and Sons Inc., NY, 2009.