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Applied Thermal Engineering 78 (2015) 30e38

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Research paper

Stepwise varying width microchannel cooling device for uniform walltemperature: Experimental and numerical study

Sara Riera a, 1, J�erome Barrau a, *, Mohamed Omri b, Luc G. Fr�echette c, Joan I. Rosell a, 2

a Applied Physics Section of the Environmental Science Department, University of Lleida, C/Pere Cabrera s/n, 25001 Lleida, Spainb King Abdulaziz Univ, Dept Mech Engn, POB 80204, Jeddah 21589, Saudi Arabiac Universit�e de Sherbrooke, D�ept g�enie m�ecanique, 2500 boul. Universit�e, QC J1K 2R1, Canada

h i g h l i g h t s

� A design procedure of a cooling device in micrometrical scale has been developed.� Thermal resistance coefficient is near three times lower than at millimetre scale.� The stepwise varying width microchannel scheme provides high temperature uniformity.� The TIM layer causes a smoothing of the temperature distribution.

a r t i c l e i n f o

Article history:Received 23 July 2014Accepted 3 December 2014Available online 18 December 2014

Keywords:MicrochannelTemperature uniformityCooling deviceCFD modeling

* Corresponding author. Tel.: þ34 973003703.E-mail addresses: sriera@macs.udl.cat (S. Ri

(J. Barrau), omrimoha2002@yahoo.fr (M. Omri), L(L.G. Fr�echette), rosell@macs.udl.cat (J.I. Rosell).

1 Tel.: þ34 973003580.2 Tel.: þ34 973003568.

http://dx.doi.org/10.1016/j.applthermaleng.2014.12.011359-4311/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Within the high heat extraction cooling technologies, stepwise varying width microchannel coolingschemes have demonstrated their capacity to provide high temperature uniformities with low pressuredrops. In this study, a method to tailor the design of this kind of cooling device to the needs on anapplication is developed. The resulting geometry is experimentally tested. A global thermal resistancecoefficient of 2.35$10�5 m2 K/W has been found, improving near three-fold the performance in a mil-limetrical scale for the same flow rate. The temperature profile of the wall temperature is quite uniform,validating the design of the cooling device. A numerical model is developed and validated throughcomparison with experimental results. It shows the smoothing effect of the Thermal Interface Material(TIM) on the temperature profile and the improvement of both the thermal resistance coefficient and thetemperature uniformity with the increase of the flow velocity.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The operation of most semiconductor devices is sensitive totemperature, so thermal management strategies are of increasingimportance as chips achieve higher power densities. As a conse-quence, efficient and innovative cooling systems must be imple-mented and become more relevant to the design of thesetechnologies. The main requirement is to provide a low thermalresistance to maintain an acceptable operating temperature, asneeded for high power microelectronic components, for example.

era), jerome.barrau@udl.catuc.Frechette@usherbrooke.ca

2

Temperature uniformity is also a key requirement to preserve theirreliability and/or efficiency. Uniformity is especially critical fordensely packed photovoltaic cells that operate under high sunlightconcentration, referred to as concentrated photovoltaics (or CPV).The reliability of the CPV receivers is reduced by temperature non-uniformity, as they provoke difference of thermal expansion alongthe surface and, as a consequence, mechanical stress within thereceiver. Also the performance of thewhole CPV receiver is reduced[1,2] when the temperature uniformity decreases, although at alower rate than the non-uniformity of illumination.

Within the cooling technologies that have high heat fluxremoval capacities, liquid flow in microchannels is one of the mostcommonly used approaches [3,4]. Heat sinks based on micro-channels were first suggested by Tuckerman and Pease [5], whodemonstrated low thermal resistance with this approach. Theimprovement in cooling performance at micro-scale is based on thefact that the convective heat transfer coefficient scales inversely

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e38 31

with channel width. The major drawbacks of this cooling schemeare the temperature non-uniformity and the relatively large pres-sure drop that they generate. Indeed, since the fluid rises in tem-perature as it collects heat along the heat sink, it is difficult tomaintain a uniform temperature across the device. Higher flowrates can reduce the temperature variation, but to the expense ofincreased pressure drop.

Two-phase systems, that enhance the heat extraction capacitywith respect to single-phase regime, can also improve the tem-perature uniformity since the fluid isothermally absorbs heat as itevaporates. Recent studies, focused onmicrochannels in two-phaseflow with enhanced geometries, used mixing to increase the heattransfer rate and reduce the pressure drops [6] and flow separationtechniques to, in addition, improve the temperature uniformity [7].Nevertheless, the formation of bubbles in microchannels leads toinstabilities and, as a consequence, to a less reliable and control-lable process than single phase cooling in microchannels [8]. Thiswork therefore studies the combination of microchannels for highheat flux with a novel configuration to achieve uniform tempera-ture with minimal pressure drop in single-phase regime.

Various shapes, configurations, and derivatives of micro-channels have been proposed to reduce the temperature non uni-formity of the cooled object in single-phase regime. Ryu et al. [9]proposed to alternate inlets and outlets along the microchannels,adding some manifold dividers. Maximum temperature variationon the heated wall is reduced by tenfold while the thermal resis-tance is lowered by more than 50%, compared to a traditionalmicrochannel cooling system. Missagia and Walpole [10] reducedtemperature non-uniformity by alternating flow directions throughthe channels in a single layer. They found a resistance of1.1$10�5 K m2/W for a laminar flow of 28 mL/s, and a pressure dropof 452 kPa for 10 cm long microchannel. Vafai and Zhu [11], pro-posed a two-layered microchannel heat sink structure, with flowloop bifurcation and allowing the coolant to flow from oppositedirections. The maximum temperature difference in the stream-wise direction in the two-layer structure is around 5� C, comparedto the 15� C observed in the one-layer structure.

Lee et al. [12] replaced the conventional microchannel heat sinkwith continuous fins, implementing oblique fins into a micro-channel. This enhances the heat transfer performance as the ther-mal boundary layer development along the channel surface isdisrupted and a secondary fluid flow is created. There's an increaseof 80% in the heat transfer coefficient compared to conventionalchannels, and with little effects on pressure drop. Nonino et al. [13]also studied uniformwall heat flux in amicrochannel with differentcross sections with developing laminar flux. Results show that theshape of the channel can influence the performance. However, itdoes not have much influence on the effect of pressure drop, whichis mainly influenced by the temperature-dependent viscosity.

In other research lines, some authors analyzed the use ofnanofluids in microtubes with tangential impingement [14,15]. Theresults showed an improvement of both the temperature unifor-mity and the heat transfer, but with a slightly higher cost in termsof pressure drop. Other researchers analyzed the performance ofmicro pin-fins heat sinks [16,17], showing that this kind of struc-tures improve both the temperature uniformity and the heattransfer, but implies, for Reynolds numbers higher than 1500, anincrease of the pressure drops.

With the aim of improving the whole performance of thecooling devices, Barrau et al. [18] developed a new cooling scheme.In order to improve the temperature uniformity of the cooled ob-ject, the design counteracts the increase in water temperature byincreasing the local heat transfer coefficient to maintain constantthe heat flux removal capacity. This is done by making the coolantflow through a series of millimetre-scale channels with a stepwise

varying width along the flow path. Simultaneously, this approachreduces the pressure drop since channel widths are not constrainedto the smallest required diameter, but are locally increased where alow thermal resistance is not necessary. The authors demonstratedthe capacity of the proposed heat sink to achieve temperatureprofiles of the target object that may even decrease in the fluid flowdirection of the cooling fluid. This performance, as commentedbefore, cannot be reached by conventional channels, and representsthe main highlight of the proposed cooling scheme. Furthermore,this design maintains the global high heat removal capabilityinherent to microchannel technologies. Numerical parametricstudies [19,20] also showed that the temperature distributionprovided by the variable width microchannel heat sink can betailored, through the non-uniform distribution of its local heatremoval capability, according to the cooling needs of the system.

Some subsequent studies such as that conducted by Kar-athanassis et al. [21] and Dede and Liu [22] confirmed that theintroduction of stepwise varying channels increases the thermalperformance of this heat-sink configuration without introducing asevere pressure drop penalty. For a heat flux of 28.3 kW/m2 and avolumetrical flow rate of 30 mL/s, the thermal resistance reached isof 0.018 K/W with low pressure drops. The ability of this design toprovide a quite uniform temperature profile of the cooled objecthas been confirmed by Ji et al. [23], who studied experimentallyand numerically a hybrid system based on the design of Barrau et al.[18] but with a radial disposition of the channels.

Those last investigations display the enhancement of imple-menting variable microchannel width along the coolant flow path,implemented here in a silicon microfabricated heat sink withmicrometer-scale channels. In this study, a method to tailor thedesign of the cooling device to the needs of an application isdeveloped. The performance of the resulting geometry is experi-mentally tested. The thermal resistance coefficients of the coolingdevice are compared, for several coolant flow rates, to the previousstudies, made at millimeter scale. The temperature distribution andits uniformity are also studied. Finally, a numerical model isdeveloped and experimentally validated in order to study the effectof the Thermal Interface Material (TIM) thermal resistance and theflow velocity on both the cooling performance and the temperatureuniformity.

2. Heat sink design procedure

To increase the thermal performance of the stepwise varyingwidth microchannel heat sink, a design procedure of the coolingscheme has been developed. Themain objective of this procedure isto improve the temperature uniformity of the cooled object, whilemaintaining thermal resistance levels achieved in the previousworks [18,19].

The first step is to define the design specifications, which are:

� The inlet water temperature (Tf,in) is at ambient temperature.� The heat flux ðq00 Þ is determined according to the dissipation ratein the application fields of our study, concentrated photovol-taic's, electronic systems and other similar devices.

� The water flow rate (Q) is established within the availablecommercial pumps.

� The wall temperature (Ts) and heat sink area (S) of the cooledsurface are determined with the usual operation parameters inelectronic devices.

To define the design space, the following constraints must bedefined and respected, based on microfabrication considerations:the number of microchannel sections (N), the fins width (Wf) and

Table 1Set up design conditions.

Parameter Unit Value

Design specifications Tf,in K 293q

00W/cm2 50

Q mL/s 8.73Ts K 313S m2 5.00$10�4

Design constraints N e 5H mm 300Wf mm 100

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e3832

their height (H). The values of all these parameters are listed inTable 1.

The energetic balance gives the local temperature of the fluid(Tf,i) along the flow path through the following equation.

Tf ;i ¼ Tf ;in þq

00$Si

r$CP$Q(1)

where Si is the area of the heated surface up to the microchannelsection Ni. At the inlet (i ¼ 1), S1 ¼ 0 m2 and so Tf,i ¼ Tf,in and, at theoutlet (i ¼ 5), S5 ¼ S and so Tf,i ¼ Tf,out.

The heat transfer coefficient (hi, with 1 � i � N) of the Nmicrochannel sections (Ni, with 1 � i � N) along the flow path canbe calculated with the following equation:

hi ¼q

00

Ts � Tf ;i; (2)

As an objective function, the solid wall temperature, Ts, isconsidered constant along the whole flow path.

At this point, the distribution of the heat transfer coefficientsneeded to obtain a constant temperature profile of the cooled ob-ject along the flow path is defined. by adjusting the microchannelswidth in order to maintain constant the solid wall temperature (Ts)along the path. In the next step of the design procedure, these localheat transfer coefficients are associated to equivalent hydraulicdiameters.

The previous studies, experimental and numerical, made atmillimetric and micrometric scales, represent a database that al-lows us to associate, in fixed conditions (those of the design con-ditions, Table 1), the local heat transfer coefficient with thehydraulic diameter of themicrochannels (Fig.1). These results werefound after validating the CFD model with the experimental dataextracted from the heat sink device proposed in a previous study

Fig. 1. Relation between hydraulic diameter and local heat transfer coefficient:q

00 ¼ 50 W/cm2, Q ¼ 8.73 mL/s, from Barrau et al [20].

[19]. Generally, such a correlation is required to guide the design,and could be obtained by experimental measurements or para-metric CFD studies for different channels widths.

The correlation, based on the previous data, is proposed inequation (3):

dh ¼ 185;416$h�1:8797 (3)

with the following formula of hydraulic diameter for rectangularsections:

dh ¼ 4$H$W2$H þW

(4)

This will allow the width of the channels en each section (Wi) tobe calculated once the microchannel height is defined:

Wi ¼2$H$dhi4$H � dhi

(5)

The number of sections (N) is limited to 5 in order to minimizethe impact of the entrance effect on the overall performance of thedesign. The cooling device is 50 mm long, in order to allow thevisualization of the variation of the temperature along the coolantflow path, and 10 mm wide, in order to reduce the impact of theedge effects on the experimental temperature measurements(made in the centreline of the cooling device).

The results of the design procedure, when applied in the designconditions defined in Table 1, are presented in Table 2 and Fig. 2.

3. Description of the experimental setup

Fig. 3 shows the experimental setup used for this study. Water,used as the coolant fluid, is stored in a reservoir with a thermostaticbath so as to maintain a constant temperature. The water is circu-lated in the closed loop with the aid of a variable speed peristalticpump (JP Selecta PERCOM N-M) and passes through a 3-mm filterbefore entering the test module. The heat flux is generated by anadvanced ceramic heater completely covered by the microchannelchip (Watlow Ultramic 600).

The cooling device is sealed on the copper layer of the testmodule (Fig. 5) through a thin layer of the Thermal interface Ma-terial (TIM). The thickness of the TIM layer has been measured witha microscope (50 mm, ±5 mm) and its thermal conductivity has beenverified (lTIM ¼ 0.82 W/m$K). The ceramic heater resistance, thatprovides the heat flux to the system, is located directly below thecopper layer.

The microchannel test module and the flow path through it arerepresented in Fig. 4.

The fluid is introduced to the heat sink through the central slotof the slot plate (2), located below the entry volume of the coolantdistributor (1). After impacting on the middle zone of the device,the water flow is divided in two (3) and passes through thestepwise-varying width microchannel sections until the two out-lets of the heat sink (4). Finally, the fluid comes out the coolant testmodule through the outlet volumes (5). The lower face of the slotplate seals the top of the microchannels.

Type-K thermocouples are used to measure the water temper-ature at the inlet and outlet of the cooling device and the tem-perature distribution of the copper layer along the flow path, atdifferent positions (x) along the centerline (y ¼ 0 mm) of thecooling device. All this information is acquired by a datalogger(Campbell CR23X) and sent to a computer to be stored and analyzed.

The microchannel pattern has been etched in silicon by lithog-raphy and Deep Reactive-Ion Etching (DRIE) [24], creating a con-stant depth (300 mm) microchannel array. To do so, a thick

Table 2Results of the design procedure (for design conditions in Table 1).

Parameter Unit Values

N1 (i ¼ 1) N2 (i ¼ 2) N3 (i ¼ 3) N4 (i ¼ 4) N5 (i ¼ 5)

Tf,i K 20 22.9 25.1 26.8 28.2hi W/m2 K 25,000 29,303 33,605 37,908 42,210dhi mm 1003 744 575 459 375Wi mm 1528 490 276 186 136

Fig. 3. Microchannel heat sink test setup, which temperature uniformitymeasurements.

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e38 33

photoresist is applied on a 100 mm Si wafer by spin casting, pre-baked, exposed to UV light through an optical mask with themicrochannel features, and developed. The exposed silicon is thenetched anisotropically with vertical walls using the Bosch processfor DRIE. The photoresist is then remove by O2 plasma and the chipsare separated by dicing.

4. Experimental results

To study the temperature distribution and thermal resistance ofthe heat sink described previously, various tests were performedunder the conditions listed in Table 3. Temperature profiles, flowrates, heat rates were measured, which will first be used to validatethe test apparatus.

4.1. Energy balance

The data acquired allows checking the energy balance of thesystem and validate the extracted information from the tests. It hasto be verified that all the electric power (Pw) supplied and thereforetransmitted in the form of heat by the ceramic heater, is absorbedby the cooling fluid (Pf), since the test module is otherwise wellinsulated:

Pf ¼ Pw (6)

The energy transferred to the refrigerating liquid is:

Pf ¼ r$Cp$Q$�Tf ;out � Tf ;in

�(7)

Fig. 2. Cooling device geometry (dimensions in

The experimental setup is validated through comparison of thetheoretical temperature difference between the inlet and outlet ofthe cooling liquid with the experimental data (Fig. 6).

The Reynolds number is calculated at the inlet as:

Re ¼ v$dhy

(8)

As the section through which the fluid flows before the first rowof microchannels is an elongated section with a form factor x, thehydraulic diameter is calculated according to the expression:

mm) for q00 ¼ 50 W/cm2, Q ¼ 8.73 mL/s.

Fig. 4. Exploded view of the microchannel test module. The sequence of the flow path is represented by the numbered arrows.

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e3834

dh ¼ 2$Wcool

1þ x(9)

whereWcool is the width of the cooling device and the form factor xis defined as:

x ¼ WcoolH

(10)

Considering the uncertainty on the experimental temperaturemeasurements, we find a good agreement between the energybalance prediction and the experimental data acquired. Since theenergy balance is verified, the analysis of the experimental resultscan be done.

Fig. 5. Detail of the test module and

4.2. Temperature uniformity measurements

As the design procedurewas oriented to reduce the temperaturenon uniformity of the cooling device, the temperature maps for thedifferent tests are presented in Fig. 7. The temperatures are dis-played only for one side of the heat sink, as the distribution issymmetric with respect to the central (y,z) plane.

The uncertainty owing to the error of the TIM thickness mea-surement of ±5 mmcan be valuedwith amargin of ±1.1 �C. Added tothe uncertainty due to thermocouples measurement of ±0.5 �C, thetotal margin of error represented in the figure is ±1.6 �C.

A quite uniform temperature distribution (slightly decreasing) isobserved. As the proposed stepwise varying width microchannelscheme is able to counteract the coolant temperature increase, its

position of the thermocouples.

Table 3Tests conditions.

Test 1 Test 2 Test 3

Q mL/s 8.8 11.23 15.97q

00W/cm2 50 50 50

Tf,in �C 21.7 21.9 22.6

Fig. 6. Comparison of the theoretical temperature difference between the inlet andoutlet of the cooling liquid with the experimental data.

Table 4Temperature uniformity at copper layer height.

Symbol Unit Test 1 Test 2 Test 3

DTf,in-out �C 5.8 5.6 4.1Ts �C 77.5 75.7 66.6DTs (minemax)

�C 2.7 3.0 2.1sT

�C 0.9 1.2 0.8

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e38 35

effectiveness to maintain the wall temperature more uniform or totailor the temperature distribution to the user's need is proved.

Table 4 presents the results of temperature uniformity withinthe thin copper layer below the heat sink, expressed through thestandard deviation sT with respect to average temperature and itsdifference to each data point. The calculation of the average tem-perature of the studied surface, Ts, is done with the arithmeticmean of the 6 measured temperatures.

The standard deviation of the temperature (sT), which repre-sents the temperature uniformity, varies between 0.9 and 1.2 �Calong the 5 cm length of the cooling device. These results enhancewidely the ones obtained by Sung and Mudawar [25] with anotherhybrid jet impingement/microchannel cooling device. These au-thors, which designed and studied this design with the aim ofimproving the temperature uniformity of the cooled object,reached, at the same heat flux (50W/cm2) and at a similar flow rate(13 mL/s), a temperature uniformity of 2 �C along a cooling devicelength of only 2 cm.

Fig. 7. Temperature distribution of the experimental cooling device for a heat flux of50 W/cm2. The longitudinal distribution of microchannels is represented on the lowestpart of the graph.

4.3. Scale effect

The average thermal resistance coefficient Rt of the system, iscalculated by the following equation:

Rt ¼�Ts � Tfin

�q00

(11)

The values used to calculate the thermal resistance coefficientare the experimental ones taken in the three test conditions. But,the thermal resistance coefficient obtained directly by these mea-surements (Rt) includes the thermal resistance of the TIM and thecopper layers (RTIM and RCu, respectively), located between the baseof the cooling device and the thermocouples location as it'sdescribed in the Test module setup section. As a consequence, theperformance of the cooling device, expressed by thermal resistancecoefficient (Rcool), must be calculated through the expression:

Rcool ¼ Rt � ðRCu þ RTIMÞ (12)

The average thermal resistance coefficients for the threedifferent tests conditions listed are calculated and shown in Table 5.

For a flow rate of 15.97 mL/s and heat flux of 50 W/cm2, the newstepwise varying width microchannel device (made at micro-metrical scale) has a thermal resistance coefficient of2.35$10�5 m2 K/W, whereas a similar design, made at a millimetricalscale [18], had a thermal resistance coefficient of 7.2$10�5 m2 K/W.These values are in concordance with the existing reports andliterature on this topic, showing that microchannel heat transfert isenhanced compared to millimetrical scale results found.

5. Numerical study

A numerical model has been developed and experimentallyvalidated in order to carry out a parametric study of the coolingdevice, with the objective of predicting the effect of variations of agiven parameter of the system. With this in mind, simulations withdifferent flow rates of coolant are done so as to analyze the influ-ence of this factor in the cooling device performance. Also theimpact of the different layers located between the heat sink and theheat source is studied by displaying the temperature profiles atdifferent heights of the cooling system.

5.1. Description of the numerical model

As indicated in Fig. 5 the heat exchanger presents two sym-metries (both in xz and yz planes), thus only the quarter of the

Table 5Thermal resistance coefficient of the cooling device.

Test 1 Test 2 Test 3

Q mL/s 8.8 11.23 15.97Tf,in �C 21.7 21.9 22.6q

00W/cm2 50 50 50

Rt m2 K/W 1.11$10�4 1.08$10�4 8.81$10�5

RCu þ RTIM m2 K/W 6.46$10�5 6.46$10�5 6.46$10�5

Rcool m2 K/W 4.68$10�5 4.29$10�5 2.35$10�5

Fig. 8. Comparison between experimental and numerical temperature distributionsfor Test 1 and Test 3, at thermocouples height (z ¼ �1.25 mm).

Fig. 10. Impact of the Reynolds number on the thermal resistance coefficient andtemperature standard deviation. Tf,in ¼ 20 �C; q

00 ¼ 50 W/cm2; flow rates (Q) from8.80 mL/s to 3.00 mL/s.

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e3836

device is considered as the numerical domain. The layers includedin the numerical model are the copper base plate, the TIM layer andthe microchanneled cooling device.

The NaviereStokes equations are solved in the fluid domainwith the assumption of laminar flow. The thermophysical proper-ties of the solid constituting the domain (Silicium, TIM and copper)are considered to be uniform and constant. The only requiredboundary conditions are the imposed mass flow, the temperatureat the inlet and the heat flux on the bottom wall. The energyequation is solved in the fluid and solid domains. The coupledpartial differential equations describing the flow field are dis-cretized with the finite volume method, using a commercial solver(Ansys Fluent). Second order upwind discretization is used. Therectangular staggered grid is non-uniform in both directions withinthe fluid domain: it is finer in the boundary layers where gradientsare more important. Also the mesh is refined in order to take intoaccount the jet impingement. The first grid node from each wall ofthe domain is situated at yþ ¼ 1.

First, a grid independence study was done for each micro-channel to obtain the minimum required grid, and after a vali-dation of the whole domain is done. This validation step was alsofollowed by another one which consists of doubling the mesh ineach direction: it was verified that doubling the grid modifies thetemperature less than 1%. This validationmethod was successfullyused in previous studies [19]. Thus, a total number of seven mil-lions nodes are used. Convergence is declared when the cumula-tive residuals for all conservation equations are less than at least10�10.

Fig. 9. Temperature distribution at thermocouples height along the device's centre-line, z ¼ �1.25 mm and y ¼ 0 mm, for different inlet velocities; Tf,in ¼ 20 �C; q00 ¼ 50 W/cm2.

5.2. Validation of the numerical model

The CFD model is validated by comparison with two experi-mental sets of measurements (Tests 1 and 3).

Taking into account the margin of error explained in Section 4.2,the comparison between the experimental and numerical tem-perature profile shows the same trends in each section of thecooling device (Fig. 8).

5.3. Numerical parametric study

5.3.1. Effect of the flow velocityThe numerical results show that the general trend of the tem-

perature distribution along the flow path is very similar for all thecases studied (Fig. 9). The impact of the Reynolds number on boththe thermal resistance coefficient and the temperature uniformityis represented in Fig. 10.

The thermal resistance coefficient, as well as the temperaturestandard deviation decreases with the increase of Reynolds num-ber. Both the standard deviation and the thermal resistance relationwith the Reynolds number are not linear. The tendency shows achange around Re ¼ 3000 as, within the microchannel sections, thelaminar flow turns to a turbulent one. Indeed, from this value, theturbulence intensity is found to be higher than 10%. For higherReynolds numbers (Re > 4000), the improvement of the thermalresistance coefficient of the cooling device is not so significant thanfor lower Reynolds numbers.

Fig. 11. Temperature distribution in centrelines of the cooling device (y ¼ 0 mm).Conditions of Test 1 (Tf,in ¼ 21.7 �C; q00 ¼ 50 W/cm2; Q ¼ 8.80 mL/s).

Fig. 12. Average temperature and temperature standard deviation vs. thermal resis-tance. Conditions of Test 1 (Tf,in ¼ 21.7 �C; q00 ¼ 50 W/cm2; Q ¼ 8.80 mL/s).

S. Riera et al. / Applied Thermal Engineering 78 (2015) 30e38 37

5.3.2. Impact of the TIM thermal resistance coefficientFig. 11 shows the different temperature distribution along the

centrelines of the cooling device (y ¼ 0) at several depth for theconditions of Test 1; from the bottom of the cooling device(z ¼ 0 mm) to thermocouples depth (z ¼ �1.25 mm).

The impact of the thermal resistance of the TIM layer on thetemperature distribution is clearly not negligible. The copper layerhas a less remarkable effect, but is also perceptible. On one hand,these additional thermal resistances associated to these layerscause an increase of the total thermal resistance coefficient (Rt). Onthe other hand, both layers cause a strong smoothing effect on thetemperature distribution.

As expected, the average temperature increases with the ther-mal resistance, while the temperature standard deviation scalesinversely (Fig. 12). These features imply both a higher averagetemperature of the cooled object and better temperatureuniformity.

As the objective of the cooling device is to provide high tem-perature uniformity while keeping the temperature in the oper-ating range, the benefits of the TIM layer in terms of temperatureuniformity must be balanced by the inconvenient of the higheraverage temperature. So the design procedure should also take intoaccount the TIM layer effects.

6. Conclusions

A design procedure of a stepwise varying width microchannelcooling device in micrometrical scale has been developed andapplied. The objective was to improve the temperature uniformityof the cooled object while keeping a high heat extraction capacity.The key findings of this study are as follows:

1 The thermal resistance coefficient of the tested device was2.35$10�5 m2 K/W for a flow rate of 1.60 mL/s, enhancing nearthree-fold the performance at the millimetre scale for the sameflow rate.

2 The cooling device provides high temperature uniformity. Atemperature standard deviation of 0.8 �C has been experimen-tally found.

3 The slightly decreasing trend in the direction of the flow pathshows the effectiveness of the proposed concept, as it has thecapacity to counteract the effect of the coolant temperatureincrease.

4 The TIM layer causes a smoothing of the temperature distribu-tion of the cooled object and an increase of its averagetemperature.

The results show that the design procedure for future devicescan tailor the temperature distribution to the specific needs of thecooled object, by modifying the microchannel distribution alongthe flow path. The effect of the TIM layer between the cooling de-vice and the cooled object should be kept into account at the designstage.

Acknowledgements

This work is supported by the Project ENE2010-18357, funded bythe Spanish Ministry of Science and Innovation (MICINN).

Nomenclature

CP Specific heat at constant pressure (J/kg K)dh Hydraulic diameter (m)h Heat transfer coefficient (W/m2 K)H Height of microchannels (mm)N Number of microchannel sections (�)Pf Power transferred to the refrigerating liquid (W)Pw Electric power (W)q

00Heat flux (W/m2)

Q Flow rate (m3/s)Rcool Thermal resistance coefficient of the cooling device

(m2 K/W)RCu Thermal resistance coefficient of the copper layer (m2 K/

W)RTIM Thermal resistance coefficient of the TIM layer (m2 K/W)Rt Average thermal resistance coefficient (m2 K/W)Re Reynolds number at the inlet (�)S Area of the heat sink (m2)Tf Fluid temperature (K)Ts Wall temperature (K)Ts Average wall temperature (K)v fluid velocity (m/s)Wcool Width of the cooling device (mm)W Width of microchannel path (mm)Wf Width of microchannel fins (mm)

Greek symbolsx form factor (�)l thermal conductivity (W/m K)r Density (kg/m3)sT Temperature standard deviation (K)y kinematic viscosity (m2/s)

Subscriptsi position number of the sections (�)in inlet (�)out outlet (�)

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