Experimental and Theoretical Evaluation of On-Chip

Experimental and Theoretical Evaluation of On-Chip Closed Micro Heat Pipe System Pranab Kumar Kundua, Saikat Mondalb, Suman Chakrabortya, Sunando DasGuptab*

a

Department of Mechanical Engineering Department of Chemical Engineering Indian Institute of Technology, Kharagpur Kharagpur, India, 721302 * Corresponding Author Email: [email protected] Tel.: +91-3222- 283922, FAX: +91-3222-282250 b

Abstract The performance of a micro heat pipe is reported with an objective of enhancing the cooling potential. Triangular microgrooves are etched on a silicon wafer via lithographic process with two reservoirs at the two ends of the microchannel array. The top of the microgroove is closed by anodic bonding, resulting in an array of microchannels. Electrochemical spark erosion technique is used to create holes on the pyrex for vacuum connections and for coolant insertion. The cooling potential of the micro heat pipe is evaluated as a function of the supplied heat by accurately measuring the temperature distributions along the channel length. The capillary suction capability of the fabricated micro heat pipe is further evaluated by a mathematical model for the axial variation of the radius of curvature of the liquid film. The results clearly demonstrate the enhanced cooling potential of on-chip closed micro heat pipe system, as compared to dry systems of the same configurations.

Keywords Micro heat pipe, microfluidics, phase change, cooling

1. Introduction The rapid increase in the heat load signatures in electronic components in electronic packaging industry, micro gravity environments, and spacecraft thermal control systems demand effective and compact cooling strategies. Heat pipes have gained pertinence in this regards, primarily owing to their compact, on-board integrability and enhanced cooling performance. However, the presence of wicks in traditional heat pipes causes low form factor and large volume to surface area ratio that leads to inefficient control over interfacial transport. Further, due to the presence of porous structure along the entire length of the conventional heat pipe, and the viscous interaction between the vapour and liquid phases, major pressure losses may be associated with liquid flowing through it. The thermal performance of a heat pipe deteriorates as these losses adversely affect the heat transfer over a long distance. Furthermore, the performance of a conventional heat pipe is appreciably affected by gravity and hence on the orientation. The overall pressure losses in these heat pipes result in lower efficiency

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of the heat transfer process. The aforesaid limitations severely affect the performance of the conventional heat pipes. Furthermore, the miniaturization of the semiconductor devices and advent of high performance mobile computing platforms demand chip-cooling devices to have much smaller footprints ranging from micros to millimetres with on-chip integrability capabilities. The limitations of the conventional heat pipes, in conjunction with the need for miniaturization and demand for improved thermal performance in order to break the ever increasing heat-generation to heat-scavenging crossover barrier, have made micro-heat-pipes extremely relevant in the present scenario. The concept of micro heat pipe was first proposed by Cotter (1984), which essentially is a wickless heat pipe used to achieve the uniform temperature distribution in micromechanical and microelectronic devices and in various other applications, where a high degree of temperature consistency and uniformity are required (Faghri 1995; Vafai and Wang 1992;Vafal et al. 1995;Zhu and Vafai, 1998; Wang and Vafai 2000). The effect of geometry on the performance of heat pipe is high as the surface to volume ratio depends on the geometry, resulting in higher surface tension forces (Peterson 1994; Faghri 1995; Dunn and Reay 1982; Harirchian and Garimella 2009). Faghri and his co-workers (Rahman and Faghri 1992; Faghri et al. 1993) performed extensive research to evaluate the performance of radial micro heat pipes. The friction constant of the microchannels is greatly influenced by the cross-sectional aspect ratio. Experimental friction factor in smooth trapezoidal microchannels, fabricated on silicon, was estimated by Wu and Cheng (2003) for laminar flow of deionized water. A correlation of laminar friction constant for trapezoidal microchannels in terms of the cross-sectional aspect ratio was also derived by them. Ha and Peterson (1996, 1998) considered an uneven heat input and solved the evaporating film profile analytically. They used perturbation method to solve the main stream flow of an evaporative thin film of v-shaped microchannel considering the gravity effect. The capillary effects of coolant filled triangular microchannels was theoretically investigated by Sheu et al. (2004). The heat transfer from evaporating liquid thin film from triangular microchannels was characterized with help of an approximate analytical model proposed by Xu and Carey (1990). The fundamental physics governing the operation of micro heat pipe results from the difference in the capillary pressure across the liquid–vapour interfaces in the condenser and evaporator zone. Further, the performance greatly depends on the intermolecular interactions and wettability, as these microdevices exploit enhanced evaporation from curved microfilms on the microchannel surfaces. Because of the presence of long range intermolecular forces and due to its curvature, the liquid thin film on a solid substrate shows a different free energy from a bulk fluid (Derjaguin and Churaev 1978; Kundu et al. 2011; Pati et al. 2013). The excess potential known as disjoining pressure, was evaluated by Derjaguin and Churaev (1978), Wayner et al. (1976), Wayner (1991), Wang et al. (2007) and DasGupta et al. (1993, 1995). Kundu et al. (2011) quantified the shape of the liquid meniscus in the microgrooves using image analysing interferometry, as a function of heat input and opposing body forces. Hung and Tio (2012) have performed thermal analysis of a water-filled micro heat pipe with phase-change interfacial resistance. They have shown that heat transport capability of a micro heat pipe is dominated by phase-change heat transfer at the liquid–vapour interface. A detailed theoretical and experimental review of recent researches along with comparative analysis of the performance on micro heat pipes have been compiled by several researchers (Sobhan et al. 2007; Suman 2007). Garimella and his co-workers (Bertsch et al. 2008) have presented a thorough review of literature on flow boiling in miniaturized channels.

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In the present study, V-shaped microgroove arrays having reservoirs at the two ends are fabricated on a silicon wafer using chemical machining technique. The channels along with the reservoirs are closed from the top using a Pyrex 7740 glass via anodic bonding, to create micro heat pipe. A special technique, electrochemical spark erosion process, is used to generate holes on the pyrex glass for vacuum connection and coolant entry. The channels are degassed and subsequently filled by a small amount of deionized water and properly sealed. The sharp corners of the closed microchannels act as capillaries that provide the necessary suction for the coolant flow toward the heat source. The cooling potential of the micro heat pipe is evaluated as a function of the supplied heat flux. The capillary suction capability of the fabricated micro heat pipe is further evaluated by proposing a model for the axial variation of the radius of curvature of the liquid film and its numerical solution at specific experimental conditions. The results reaffirm the enhanced cooling potential of microchannels fabricated on the chip itself for in-situ applications. In the present study, the higher value of dimensionless radius of curvature at the hot end for a specific heat input also confirms that the capillary suction capacity is very high and the fabricated heat pipe can be utilized for large values of heat input without the occurrence of dry-out. The present micro heat pipes can also be used as the effective heat spreader for in-situ applications by fabricating microchannels on the unused surface of the silicon of a semiconductor device that generates high heat flux.

2. Materials and Methods 2.1 Fabrication of Micro heat pipe Fabrication of the microchannels One of the objectives of the present study is to fabricate micro heat pipe on the silicon wafer itself to provide direct, in-situ, change-of-phase cooling to the heat generating semiconductor devices. An array of fifteen V-grooved microchannels is chemically etched using standard lithographic process on 2 inch (1 inch ≈ 2.54 cm) diameter silicon wafer (DSP) with two reservoirs (10 mm × 5 mm) at the two ends of the array. The dimensions of each microchannel are 100 m in width, 70 m depth, 2.5 cm length, with a pitch of 400 m. The mask for lithography is designed in AutoCAD 2007 and replicated on a chromium-coated mask plate (3 inch × 3 inch) using Laser Mask writer with a precision of 1 m. The stable layer of oxide on silicon is grown in oxygen furnace under dry oxygen flow (dry oxidation process) followed by rapid oxidation using wet oxygen, and is finally completed in a dry oxygen ambience to obtain 1 m thick SiO2 layer. During photolithography, the layer of SiO2 is protected using photoresist of negative tone series (HNR-120) and is subsequently exposed to a controlled ultra violet light (Wave length - 360 nm, Mercury lamp) in double sided mask aligner (Karl Suss Make, MA6) through the mask. Developer WNRD is used to remove undesirable region of photoresist. The unwanted slices of SiO2 layer are then removed using buffer HF and subsequently the final etching (chemical) is performed using 40% KOH to form V-Groove channels and the reservoirs (Kundu et al. 2011).

Closed channel fabrication Heat shock resistant Pyrex 7740 glass is used to cover the top of the micro channels. Further, due to the low coefficient of thermal expansion (32.5 x 10-7/°C), Pyrex 7740 is suitable at high temperature applications. 3

Pyrex has high optical transmission over a wide wavelength range and is also resistant to most of the acids. Two holes are made on the Pyrex glass for vacuum connection and coolant entry by electrochemical spark erosion method. Platinum wires are used as electrodes and 60 V is applied from a variable dc power supply to produce a constant spark in an 8 M sodium hydroxide solution (Fig. 1). This produces a hole in the Pyrex glass with diameter same as that of the wire itself (Arora 2011).

NaOH Solution (8M) Pyrex

DC Power Source

Platinum Wires

+

Spark

_

Fig. 1: Electrochemical spark erosion method of drilling holes in Pyrex 7740

Bonding of Pyrex 7740 and Silicon Wafer Anodic bonding, as illustrated in Fig. 2, is used to attach the Pyrex 7740 and the wafer to obtain closed channels after perfect alignments (Wallis 1975; Gerlach et al. 1999; Lee et al. 2000; Wei et al. 2003). High strength bonding (typically 5-25 MPa) is achieved by exploiting electrostatic field at high temperature (Nese and Hanneborg 1993).

Top tool (Cathode) Bond interface

Na+ + Na+ Na+ Na + Na+ Pyrex 7740Na Na+ O- O- - O- O- O- OO

Vs

Silicon Chuck (Anode)

Fig. 2: Schematic of anodic bonding along with ion drifting in electric field

The Pyrex 7740 is placed on the wafer and both are kept in between the top tool, used as cathode and the chuck, used as anode, at temperature of 400°C. The mobility of positive ions in glass is always better for higher temperature. However, the temperature should always be kept below the softening point of Pyrex 7740. The applied electrical potential between the electrodes causes a diffusion of sodium ions (Na+) out of the bond interface to the backside of the Pyrex 7740 to the cathode. The applied high electrical potential also helps to support the drifting of the positive ions in Pyrex 7740 to the cathode. The Pyrex (NaO2) with its remaining oxygen ions (O-) is negatively charged at the bonding surface compared to the silicon. As a result, a high-impedance depletion region is developed at the bond barrier in the Pyrex, and a positive volume charge is formed on the silicon wafer side. The bond voltage drops in the gap between the silicon and Pyrex and the 4

bonding process starts as a combination of electrostatic and electrochemical phenomena (Nese and Hanneborg 1993; Wei et al. 2003).The oxygen ions drift to the bond interface and cross it due to very high intensity of the electrical field in the depletion region and later react with the silicon to form SiO2. The process is realized at temperatures 400°C for about 20 min. To ensure intimate contact between the surfaces of the bonding partners for good electrical conduction, pressure of 4.5 to 5 bar is applied. The photograph of the fabricated micro heat pipe without the connectors is shown in Fig. 3. Q si Q in b x

Q out

si

Q convective

Reservoir x

x

Triangular microchannels 100µm width and 70µm depth

Hole on the pyrex

  Fig 3: Closed microchannel arrays on silicon with reservoirs

Charging of the micro heat pipe Two Teflon tubes are aligned and connected with the ports of the reservoirs (Fig. 3) via connectors made especially for this purpose. The connectors are fitted to the reservoir using a combination of quick-set epoxy adhesive followed by high strength epoxy adhesive. Once the adhesive is cured, the system is evacuated to a pressure of less than 6 mTorr for a period of 24 hours to ensure complete removal of all non-condensable gases. The evacuated system is charged with a small amount (0.3 ml) of deionized water followed by thermal sealing of the two connectors to form the micro heat pipe. The axial variation of temperature is measured using nine thermocouples (T-type, sensitivity ~ 43 µV/C) attached on the reverse side of the silicon surface, beneath the microchannels, at intervals of 2.5 mm. The measured temperatures are recorded using a data acquisition unit (Yokogawa, Japan) at time intervals of 500 ms and with an accuracy of ±0.1°C. The hot region is simulated by attaching a standard strip heater with surface area of 15 × 6 mm2 to the bottom and the heater is powered through a DC power supply (Testronix make, Model 93c). Figure 4 shows the schematic of the experimental setup.

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DATA Processing Computer

DATA Acquisition System

Thermocouples

Sealing Pyrex 7740 x Silicon DC Power

Fig. 4: Schematic of experimental setup

2.2 Theoretical Model A thin slice of the V-grooved silicon substrate is considered with the heater below as shown in Fig. 3. The steady state energy balance can be written in a control volume of a differential element (Fig. 5) from the etched silicon substrate by considering net conductive heat input, convective losses and heat transfer from silicon to the coolant as:  dT   dT   K si Ac     K si Ac dx x   dx 

  –  bx  qsi –  bx  h Tx – Tamb   0 x  x 

(1)

where Ksi is the thermal conductivity of silicon, Ac is the cross sectional area of the silicon strip through which the conductive heat transfer takes place, b is the width of the strip, x is the thickness of the strip, qsi is the heat flux from the silicon substrate to the liquid, h is the natural convective heat transfer coefficient, Tx is the crosssectional average temperature at any axial location, and Tamb is the ambient temperature. The heat flux from the silicon substrate to the liquid coolant can be estimated from the energy balance and given as follows: K A qsi   si c  b

 d 2T  dx 2  h(Tx  Tamb ) 

(2)

The coupled momentum, mass and heat balance equations are presented next for the coolant liquid in a single microchannel, adopting an approach by Kumar and DasGupta (1997) and Suman et al. (2005a), with additional modifications and with the following assumptions. 

One-dimensional steady state incompressible flow of coolant water along the length of the micro heat pipe.



Uniform distribution of heat input.



Negligible viscous dissipation.



Constant pressure in the vapour region in the operating range of temperature.



Negligible shear stress at the liquid-vapor interface.

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

Negligible body force compared to the force due to pressure jump at the vapor-liquid interface (Suman et al. 2005a)

The heat flux qsi from the silicon substrate to the coolant liquid (Eq. 2) is utilized to (i) raise the temperature of the water and (ii) for evaporation ( qev )

qev

W

x

Vx+x Lh

Vx

x+x

q si

x

  Fig. 5: A schematic diagram of the differential element of a single microchannel from the micro heat pipe

The governing heat balance equation for the coolant of a channel length of Δx is given by

qsiW x 

 C

V Al 

pl l

x x

   C plVl Al   qev Rm x x

(3)

where W is the width at top of a single microchannel,  is the density of the liquid coolant, C pl is the heat capacity of the liquid at constant pressure, Vl is the liquid velocity, Al is the liquid cross sectional area (function of the radius of curvature, R), Tl is the liquid temperature, qev is the heat flux from the liquid coolant due to evaporation and Rm is the length of the curved surface at a particular x (function of the radius of curvature, R). Dividing both sides by Δx and in the limit when Δx approaches zero, the heat balance equation for the liquid yields the form

qsiW   C plVl Al

Tl  qev Rm x

(4)

T   Dropping the sensible heat term,   C plVl Al l  , as it is much smaller compared to the other two terms (as they x  

represent phase change, Kumar and DasGupta 1997), the equation takes the form qev Rm  qsiW

(5)

The mass balance for the element in differential form is  ( AV l l)  qev Rm  0 x

(6)

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The momentum balance equation of the coolant in the differential element is

 AV l l

dVl dP  Al l  2 Lh w  0 dx dx

(7)

where Pl is the liquid pressure, Lh is the wetted length and  w is the wall shear stress. Here, the first term represents the advective momentum transport, the second term is the pressure force acting on the differential element and the third term represents the wall shear stress. The pressure jump at the curved liquid-vapor interface can be expressed as a function of the radius of curvature at an axial position along the length of the heat pipe by the Young Laplace equation. Pv  Pl 



(8)

R

where, Pv is the vapour pressure, which is assumed to be constant and hence, the liquid pressure gradient is expressed in terms of the radius of curvature as Pl  R  x R 2 x

(9)

With the incorporation of equation (9), the momentum equation (7) takes the form

  AV l l

dV  dR  Al 2  2 Lh w  0 dx R dx

(10)

  Equation (10) is solved subjected to the boundary conditions at the hot and the cold ends. It is assumed that the velocity at the hot end (x=0) is zero as there is no evaporation beyond the hot end. At the cold end (x=L), the groove is filled with coolant liquid, with its radius of curvature obtained from the geometry for filled groove and is therefore constant. at x = 0,

Vl = 0

at x=L,

R = Ro

(11) and

Pl  Pvo – (

 Ro

(12)

)

where, Ro = Radius of curvature of the liquid with the channel filled with liquid as shown in Fig. A1 of the Appendix.

Non-dimensionalization Eqns. (2) to (10) are non-dimensionalized using the dimensionless parameters, defined as x*  P* 

Pl T Q  R , R*  , Tl *  l where Vr  , P  and Tr  32 C . Pr R0 R0  R0 2  r Tr

The non-dimensionalized governing equations take the form:

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V x , Vl *  l , Vr L

where,

QvVR RmV * B2VRV *  Al l ( Ro R* ) 2 R*  * VR 2V *2 x   2  l Ro R*2 L LR*

(13)

 Qv Rm L   2V * R*   V *     * *  x*  l Al l   R x  

(14)

P*  R*  * *2 x Ro PR R x*

(15)

f is the friction factor defined as

D V K , Re is the Reynolds number expressed as h l , Dh is the Re µ

hydraulic diameter of the microchannel specified as

4 Al , K ´ is constant for a specific geometry (Ayyaswamy 2 Lh

Vl 2 f

et al. 1974) and  is the wall shear stress given as

2

.The constants Al , Rm , B1 , B2 are defined in the

Appendix. Equations (13) and (14) are coupled and are solved numerically. The dimensionless boundary conditions are: at, x*  0, V *  0

(16a)

at, x *  1, R*  1

(16b)

   and at any x* , P*   Pvo    *   / Pr R R o   

(17)

Eqns. 13, 14 and 15 are valid for all the three regions of the heat pipe namely, evaporative, adiabatic and condenser.

Numerical implementation The governing equations are solved numerically with appropriate boundary conditions as described above. The input parameters are the experimentally obtained temperature profile, groove geometry, thermophysical properties of coolant liquid and substrate, and contact angle for the substrate and coolant liquid. The experimental temperature profiles, measured at nine different locations along the length of the heat pipe, are fitted to third degree polynomials. The entire heat pipe is discretized into 25,000 discrete elements with each element being 1 µm in length and the governing differential equations are solved using a finite difference scheme.

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The heat flux from the silicon substrate to the coolant is calculated by solving equation (2) adopting a central difference scheme. The non-dimensionalized heat, mass and momentum balance equations are coupled and solved simultaneously. The velocity of liquid at the hot end has been considered to be zero (Eq. 16a) and an initial guess value of dimensionless radius of curvature is assumed at the hot end. The solution of the coupled equations is obtained utilizing forward difference scheme to get the values of V * and R* at the next discrete point, till the condition R*  1 is satisfied at the cold end. Otherwise, a new value is assumed for R* at the hot end, and the calculations are repeated till the values are within a tolerance limit of 0.001. Extensive grid independence studies have also been carried out, so as to arrive at a compromise between numerical accuracy and computational economy.

3. Results and Discussions The cooling potential of the micro heat pipe is evaluated by measuring the temperature distribution and comparing the temperature profiles in presence and absence of the coolant at a fixed heat input. The performance is also evaluated at different values of the heat inputs. The measured temperature distribution is strongly influenced by the microscale transport processes taking place near the contact line (where the liquid, vapour and the solid are in close proximity) and augmented capillary suction provided by the microchannels. Nine T-type thermocouples placed at a gap of 2.5 mm are used to measure the temperature profiles for four different heat inputs. The method proposed by Kline and McClintock (1953) is used to determine the experimental uncertainties associated with the measurements of temperature and is found to be ± 0.25°C. Figure 6 depicts the substrate temperature measured from the edge of the strip heater at dry condition, whereas Fig. 7 represents the substrate temperature at the same locations when the micro heat pipe is sealed with the coolant. It is evident from these figures that having a properly sealed micro heat pipe not only reduces the temperature of the substrate significantly, but also homogenizes the temperature distribution over the substrate. For example, with respect to the dry substrate, the additional coolings achieved are 16, 13, 6, and 2°C, for heat inputs of 5, 4, 2, and 1 W, respectively. Additionally, the difference between the temperatures measured by the first and the last thermocouples is 17°C for the dry case as compared to 11°C with coolant at a heat input of 4W signifying enhanced temperature homogenization on the device. 350

1W 2W 4W 5W

Temperature (K)

340 330 320 310 300 0

0.005 0.01 0.015 0.02 0.025 Distance from the strip heater, x (m)

Fig. 6: Axial substrate temperature variation in absence of coolant

10

330

1W 2W 4W 5W

Temperature (K)

325 320 315 310 305 300 0

0.005 0.01 0.015 0.02 0.025 Distance from the strip heater, x (m) Fig. 7: Axial substrate temperature variation charged with coolant in the sealed heat pipe

The relative enhancement of cooling efficiency of the micro heat pipe is evaluated by introducing a dimensionless temperature (), defined as  

Td  Tw , where Td is the temperature of the substrate at dry Td  Tamb

condition, Tw is the temperature of the substrate in presence of coolant under identical heat input and location of measurement and Tamb is the prevalent ambient temperature. From Fig. 7, it is evident that Td– Tw is always lower than Td – Tamb (with Tamb being equal to 27°C) at any location along the microchannels of the heat pipe. However, higher values of  signify higher relative cooling because of the presence of liquid and enhanced capillary pumping. Figure 8 presents the variation of the axially averaged values of  (denoted by avg) as functions of the heat input. It is clear that avg increases with increase in heat input denoting more efficient operation even at higher values of the heat input. The designed micro heat pipe is effective for the heat input values used in the present study and the results suggest that additional capacity to pump liquid towards the hot spot also exists as will be discussed subsequently. 0.35

avg

0.3

0.25

0.2 0

1

2 4 Heat Input (W) Fig. 8: Variation of avg with heat inputs

11

5

In order to delve deeper towards understanding the underlying transport behaviour within the heat pipe, next, the results have been analysed from a theoretical perspective using the numerical route outlined in section 2.2. The primary objective of the numerical solution with temperature profiles as input, is to study the performance of the micro heat pipe for different heat inputs. The solutions of the above equations provide heat flux profiles and the results clearly show the presence of an evaporator section (positive value of heat flux) and a condensation zone (negative heat flux) with a narrow adiabatic zone in between where the heat flux is very close to zero. The variation of the adiabatic zone length with heat input is plotted in Fig. 9, which clearly indicates rapid decrease in the adiabatic zone length with increase in heat input. -3

1.6

x 10

Adiabatic length (m)

1.4 1.2 1 0.8 0.6 0.4 0

1

2

3 4 Heat Input (W)

5

6

Fig. 9: Variation of adiabatic length with heat inputs

The solution of the governing equations provide axial variation of the radius of curvature, which is primarily responsible for generating the capillary pressure gradient essential to maintain flow towards the hot spot. The profiles suggest a monotonically increasing radius of curvature profile towards the cold end (Fig. 10), thereby creating a favorable pressure gradient towards the hot end. A lower value of the radius of curvature also denotes a liquid film that has recessed well towards the corner of the grooves. It is also apparent that as the heat input increases, the radius of curvature at the hot end decreases, providing more suction towards the hot spot and greater coolant flow to replenish higher amounts of evaporation. Additionally, the minimum value of the radius of curvature at the hot end is calculated to be 0.845, and therefore, the fabricated heat pipe should be able to handle even higher heat inputs than those used herein and is far from reaching the capillary limit and subsequent dry-out phenomenon.

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Dimensionless Radius of Curvature (R*)

1.05 1 0.95 1W

0.9

2W

0.85

4W 5W

0.8 0

0.2

0.4 0.6 0.8 Dimensionless Length (x*)

1

Fig. 10: Axial variation of the dimensionless radius of curvature at different heat inputs The ensuing axial variation in liquid pressure is plotted in Fig. 11 for a heat input of 2W, demonstrating gradual decrease in liquid pressure as the hot end is approached. The differences between the pressure at the cold and the hot ends are calculated along with the axially averaged velocity as functions of heat input and are presented in Fig. 12. The results clearly indicate substantial increases in pressure difference (with concomitant increase in velocity) with increase in heat input, providing enhanced coolant flow towards the hot spot as can be seen quantitatively in Fig. 13, where the average mass flow rates are calculated as functions of heat inputs. It should be noted that, as the heat input is increased, the liquid velocity increases at all the points in the micro heat pipe. However, as the liquid will be more depressed towards the apex of the grooves at higher heat input, the cross-sectional area for flow will decrease (at a fixed axial location) with increase in heat input. The local values of coolant flow in the axial direction towards the hot spot however increases monotonically with increase in heat input.

2

Liquid Pressure (N/m )

6150

6100

6050 0

0.2 0.4 0.6 0.8 Dimensionless Length (x*)

1

Fig. 11: Plot of liquid pressure with dimensionless position for 2 W heat input

13

-4

P VMean

100

P (N/m2)

90 80

2

70 60 50 0

1

2

3 4 Heat Input (W)

Mean Liquid Velocity (m/s)

x 10 3

110

1 6

5

Fig. 12: Variation of liquid velocity and pressure differences with heat inputs

-10

Average Mass flow rate (kg/sec)

x 10 5.5 5 4.5 4 3.5 3 0

1

2 3 4 Heat Input (W)

5

6

Fig. 13: Variation of liquid average mass flow rate with heat inputs

4. Conclusions A micro heat pipe array with fifteen triangular microchannels is etched on silicon wafer and bonded with a thin pyrex 7740 glass using anodic bonding. Electro chemical spark erosion technique is used to make fine holes in the pyrex, for vacuum and coolant entry connections. The cooling potential of the micro heat pipe is evaluated as a function of supplied heat by accurately measuring the temperature distributions along the channel length, both in presence and absence of the coolant, using nine T-type thermocouples attached on the silicon. Experimental results demonstrate substantial reduction in temperature in presence of coolants. For example, with respect to the dry substrate, the additional cooling achieved are 16 and 13°C for heat inputs of 5 and 4W, respectively with the effect more pronounced at higher values of heat inputs. The micro heat pipe has also created temperature homogenization on the substrate, reducing the maximum temperature difference from 17°C (for the dry case) to 11°C at a heat input of 4W.

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The capillary suction capability of the fabricated micro heat pipe is further evaluated by a model developed to evaluate the axial variation of the radius of curvature of the liquid film and its numerical solution at specific experimental conditions. The capillary suction capacity of the heat pipe can be ascertained by the axial variation of the radius of curvature and the fabricated heat pipe remains operational without the occurrence of dry-out for all the heat inputs used herein. The liquid pressure profiles indicate increases in pressure difference (with a concomitant increase in liquid velocity) with increase in heat input, providing enhanced coolant flow towards the hot spot verifying the in-situ cooling potential of the fabricated micro heat pipe arrays. These results clearly demonstrate augmented cooling capabilities of integrated on-chip micro heat pipes, charged with coolants in sealed microfluidic environments, bearing far ranging consequences towards in-situ thermal management of electronic devices and systems.

Acknowledgements The authors gratefully acknowledge the financial support provided by Indian Space Research Organization [Sanction Letter no.: IIT/KCSTC/STC/CHAIR./NEW/P/11-12/01-05, Dt. 09-09-2011] and valuable discussions with Dr. AmritAmbirajan for carrying out this research.

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APPENDIX Calculation of Ro, Rm and Al  Curved line AB is the liquid meniscus when the groove is fully filled with coolant liquid.  AC and BC are tangents to the liquid meniscus.  α => Half apex angle of triangle.  γ => Contact angle of liquid (water) with the silicon. CAD   ; ADC   ACB  2(   ) AOB      2(   )

O

 R0

B

A

 C

Now, the radius of curvature at cold end when the groove is fully filled may be obtained as

a



R0 

a sin  2 cos     

D

Fig. A1: Radius of curvature when the groove is fully filled

O R

R

 a

A Lh

Fig. A2: Liquid partially filled and suction takes place through the 3 corners 

 

 

Lh  nR

cos(   ) sin 

 

 

 



D

 

 

C

B

 

Fig. A3: A single corner is shown for further calculation 

 

 

where n = no. of sides of a polygon (for a triangle, n  3 ) Rm  nRØ = Length of meniscus curve

16

 

 

 

 

 

Area of ACBD =

R 2 cot(   ) cos(   ) sin  sin 

Area of triangle ABC = R 2 cot(   ) cos(   ) sin  Area of sector AOB = ØR 2 / 2 Area of triangle AOB = R 2 cos(   ) sin(   ) Now, Al = cross section area of the liquid in the groove = n[Area of ACBD +area of ΔABC - (area of sector AOB – area of ΔAOB)] or, Al  B1 R

2

cot(   ) cos(   )sin    where, B1  n cot(   )  Ø / 2   sin    B2 

µl K ´cos 2(   )  cot(   ) cos(   ) sin   2sin    cot(   )  Ø / 2 sin   

2

2

References Arora A (2011) Rapid, inexpensive and stress free drilling in glass substrate or thermally bonded glass  chips  using  electrochemical  spark  erosion  method.  http://blogs.rsc.org/chipsandtips/2011/01/25/electrochemical‐spark‐erosion/.   Ayyaswamy  PS,  Catton  I,  Edwards  DK  (1974)  Capillary  Flow  in  Triangular  Grooves.  J  Appl  Mech  41:332. doi: 10.1115/1.3423288  Bertsch SS, Groll EA, Garimella S V. (2008) Review and Comparative Analysis of Studies on Saturated  Flow  Boiling  in  Small  Channels.  Nanoscale  Microscale  Thermophys  Eng  12:187–227.  doi:  10.1080/15567260802317357  Cotter TP (1984) Principles and Prospects of Micro Heat Pipes. Proc 5th Int Heat Pipe Conf, Tsukuba,  Japan 328–335.  Dasgupta  S,  Plawsky  JL,  Wayner  PC  (1995)  Interfacial  force  field  characterization  in  a  constrained  vapor bubble thermosyphon. AIChE J 41:2140–2149. doi: 10.1002/aic.690410913  DasGupta S, Schonberg JA, Kim IY, Wayner PC (1993) Use of the Augmented Young‐Laplace Equation  to  Model  Equilibrium  and  Evaporating  Extended  Menisci.  J  Colloid  Interface  Sci  157:332–342.  doi: 10.1006/jcis.1993.1194  Derjaguin B., Churaev N. (1978) On the question of determining the concept of disjoining pressure  and  its  role  in  the  equilibrium  and  flow  of  thin  films.  J  Colloid  Interface  Sci  66:389–398.  doi:  10.1016/0021‐9797(78)90056‐5  17

Dunn PD, Reay D (1982) Heat Pipes. 1:319.  Faghri A (1995) Heat pipe science and technology. 908.  Faghri A, Gogineni S, Thomas S (1993) Vapor flow analysis of an axially rotating heat pipe. Int J Heat  Mass Transf 36:2293–2303. doi: 10.1016/S0017‐9310(05)80114‐0  Gerlach  a.,  Maas  D,  Seidel  D,  et  al.  (1999)  Low‐temperature  anodic  bonding  of  silicon  to  silicon  wafers  by  means  of  intermediate  glass  layers.  Microsyst  Technol  5:144–149.  doi:  10.1007/s005420050154  Ha  JM,  Peterson  GP  (1996)  The  Interline  Heat  Transfer  of  Evaporating  Thin  Films  Along  a  Micro  Grooved Surface. J Heat Transfer 118:747. doi: 10.1115/1.2822695  Ha  JM,  Peterson  GP  (1998)  Capillary  Performance  of  Evaporating  Flow  in  Micro  Grooves:  An  Analytical Approach for Very Small Tilt Angles. J Heat Transfer 120:452. doi: 10.1115/1.2824270  Harirchian  T,  Garimella  S  V.  (2009)  Effects  of  channel  dimension,  heat  flux,  and  mass  flux  on  flow  boiling  regimes  in  microchannels.  Int  J  Multiph  Flow  35:349–362.  doi:  10.1016/j.ijmultiphaseflow.2009.01.003  Kline, S. J., McClintok IA (1953) Describing Uncertainties in Single Sample Experiments. Mech Engng  3–8.  Kumar  MR,  DasGupta  S  (1997)  Modeling  of  evaporation  from  V‐shaped  microgrooves.  Chem  Eng  Commun 160:225–248. doi: 10.1080/00986449708936615  Kundu P, Chakraborty S, DasGupta  S (2011) Experimental investigation of enhanced spreading and  cooling from a microgrooved surface. Microfluid Nanofluidics. doi: 10.1007/s10404‐011‐0814‐5  Lee  TM.,  Lee  DH.,  Liaw  CY.,  et  al.  (2000)  Detailed  characterization  of  anodic  bonding  process  between  glass  and  thin‐film  coated  silicon  substrates.  Sensors  Actuators  A  Phys  86:103–107.  doi: 10.1016/S0924‐4247(00)00418‐0  Mun Hung Y, Tio K‐K (2012) Thermal Analysis of a Water‐Filled Micro Heat Pipe With Phase‐Change  Interfacial Resistance. J Heat Transfer 134:112901. doi: 10.1115/1.4006898  Nese  M,  Hanneborg  A  (1993)  Anodic  bonding  of  silicon  to  silicon  wafers  coated  with  aluminium,  silicon  oxide,  polysilicon  or  silicon  nitride.  Sensors  Actuators  A  Phys  37‐38:61–67.  doi:  10.1016/0924‐4247(93)80013‐7  Pati S, Som SK, Chakraborty S (2013) Combined influences of electrostatic component of disjoining  pressure  and  interfacial  slip  on  thin  film  evaporation  in  nanopores.  Int  J  Heat  Mass  Transf  64:304–312. doi: 10.1016/j.ijheatmasstransfer.2013.04.049  Peterson GP (1994) An introduction to heat pipes: modeling, testing, and applications. 356.  Rahman MM, Faghri A (1992) Numerical simulation of fluid flow and heat transfer in a thin liquid film  over a rotating disk. Int J Heat Mass Transf 35:1441–1453. doi: 10.1016/0017‐9310(92)90035‐Q 

18

Sheu  T‐S,  Kuo  J‐S,  Ding  P‐P,  Chen  P‐H  (2004)  Theoretical  analysis  of  capillary  performance  of  triangular microgrooves. Microsyst Technol 10:315–322. doi: 10.1007/s00542‐003‐0332‐9  Sobhan  CB,  Rag  RL,  Peterson  GP  (2007)  A  review  and  comparative  study  of  the  investigations  on  micro heat pipes. Int J Energy Res 31:664–688. doi: 10.1002/er.1285  Suman  B  (2007)  Modeling,  Experiment,  and  Fabrication  of  Micro‐Grooved  Heat  Pipes:  An  Update.  Appl Mech Rev 60:107. doi: 10.1115/1.2730846  Suman B, De S, DasGupta S (2005a) Transient modeling of micro‐grooved heat pipe. Int J Heat Mass  Transf 48:1633–1646. doi: 10.1016/j.ijheatmasstransfer.2004.11.004  Suman B, De S, DasGupta S (2005b) A model of the capillary limit of a micro heat pipe and prediction  of  the  dry‐out  length.  Int  J  Heat  Fluid  Flow  26:495–505.  doi:  10.1016/j.ijheatfluidflow.2004.09.006  Vafai  K,  Wang  W  (1992)  Analysis  of  flow  and  heat  transfer  characteristics  of  an  asymmetrical  flat  plate heat pipe. Int J Heat Mass Transf 35:2087–2099. doi: 10.1016/0017‐9310(92)90054‐V  Vafal K, Zhu N, Wang W (1995) Analysis of Asymmetric Disk‐Shaped and Flat‐Plate Heat Pipes. J Heat  Transfer 117:209. doi: 10.1115/1.2822305  Wallis  G  (1975)  Field  Assisted  Glass  Sealing.  Electrocompon  Sci  Technol  2:45–53.  doi:  10.1155/APEC.2.45  Wang  H,  Garimella  S  V.,  Murthy  JY  (2007)  Characteristics  of  an  evaporating  thin  film  in  a  microchannel.  Int  J  Heat  Mass  Transf  50:3933–3942.  doi:  10.1016/j.ijheatmasstransfer.2007.01.052  Wang  Y,  Vafai  K  (2000)  An  experimental  investigation  of  the  thermal  performance  of  an  asymmetrical  flat  plate  heat  pipe.  Int  J  Heat  Mass  Transf  43:2657–2668.  doi:  10.1016/S0017‐ 9310(99)00300‐2  Wayner PC (1991) The effect of interfacial mass transport on flow in thin liquid films. Colloids and  Surfaces 52:71–84. doi: 10.1016/0166‐6622(91)80006‐A  Wayner  PC,  Kao  YK,  LaCroix  LV  (1976)  The  interline  heat‐transfer  coefficient  of  an  evaporating  wetting film. Int J Heat Mass Transf 19:487–492. doi: 10.1016/0017‐9310(76)90161‐7  Wei  J,  Xie  H,  Nai  ML,  et  al.  (2003)  Low  temperature  wafer  anodic  bonding.  J  Micromechanics  Microengineering 13:217–222. doi: 10.1088/0960‐1317/13/2/308  Wu  H.,  Cheng  P  (2003)  Friction  factors  in  smooth  trapezoidal  silicon  microchannels  with  different  aspect ratios. Int J Heat Mass Transf 46:2519–2525. doi: 10.1016/S0017‐9310(03)00106‐6  XU  X,  CAREY  VP  (1990)  Film  evaporation  from  a  micro‐grooved  surface  ‐  An  approximate  heat  transfer model and its comparison with experimental data. J Thermophys Heat Transf 4:512– 520. doi: 10.2514/3.215 

19

Zhu  N,  Vafai  K  (1998)  Analytical  modeling  of  the  startup  characteristics  of  asymmetrical  flat‐plate  and  diskshaped  heat  pipes.  Int  J  Heat  Mass  Transf  41:2619–2637.  doi:  10.1016/S0017‐ 9310(97)00325‐6 

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