salman 2013 renewable and sustainable energy reviews

5/21/2018 Salman 2013 Renewable and Sustainable Energy Reviews

Characteristics of heat transfer and uid ow in microtube andmicrochannel using conventional uids and nanouids: A review

B.H. Salman a,n, H.A. Mohammed b,n, K.M. Munisamy a, A. Sh. Kherbeet a

a Mechanical Engineering Department, College of Engineering, Universiti Tenaga Nasional, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysiab Department of Thermouids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia

a r t i c l e i n f o

Article history:

Received 7 September 2012Received in revised form25 July 2013Accepted 11 August 2013Available online 13 September 2013

Keywords:

MicrotubeMicrochannelHeat transferNanouidsNanoparticles

a b s t r a c t

Research on convective heat transfer on internal microtube and microchannel has been extensively

conducted in the past decade. This review summarizes numerous researches on two topics; the rstsection focuses on studying the uid ow and heat transfer behavior of different types of microtubes(MT) and microchannel (MC) at different orientations. The second section concentrates on nanouids; itspreparation, properties, behavior, and many others. The purpose of this article is to get a clear view anddetailed summary of the inuence of several parameters such as the geometrical specications,boundary conditions, and type of uids. The maximum Nusselt number is the main target of suchresearch where correlation equations were developed in experimental and numerical studies arereported. The heat transfer enhancement of nanouids along with the nanouids preparation technique,types and shapes of nanoparticles, base uids and additives, transport mechanisms, and stability of thesuspension are also discussed.

&2013 Elsevier Ltd. All rights reserved.

Contents

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8492. Microtube (MT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849

2.1. Experimental studies on MT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8492.2. Numerical studies on MT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851

3. Microchannel (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8543.1. Experimental studies on MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8543.2. Numerical studies on MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 860

4. Nanouids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8624.1. Preparation of nanofulids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8624.2. Experimental studies on nanouids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862

4.2.1. Thermal conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8624.2.2. Effects of thermal conductivity on heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866

4.3. Viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8685. Numerical studies on nanouids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870

6. Theoretical studies on nanouids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8717. Single phase and two phase models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8728. Mechanism of heat conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872

8.1. Brownian motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8728.2. Nature of heat transport in nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8738.3. Nanolayer thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8738.4. Effects of clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873

9. Heat transfer enhancement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87410. Rheological behavior of nanouids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87411. Challenges of using nanouids to enhance the heat transfer for MT and MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875

Contents lists available atScienceDirect

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1364-0321/$- see front matter& 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.rser.2013.08.012

n Corresponding authors. Tel.: 60 755 34716; fax: 60 755 66 159.E-mail addresses:[email protected] (B.H. Salman),[email protected] (H.A. Mohammed).

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11.1. long term stability of nanoparticles dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87511.2. Increased pressure drop and pumping power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87511.3. Thermal performance of nanouids in turbulent ow and fully developed region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87511.4. Higher viscosity and lower specic heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87611.5. High cost of nanouids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87611.6. Difculties in production process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876

12. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876

1. Introduction

The characteristics of ow and heat transfer in microchannelsand microtubes have attracted much attention of researchersbecause of the rapid developments of micro-electromechanicalsystems (MEMS) and micrototal analysis system. These develop-ments have great impacts on the microelectronic cooling techni-ques, the microheat exchanger, bioengineering, human genomeproject, medicine engineering, etc. It is evident that the under-standing of the microscale phenomena is very important fordesigning efcient micro-devices. To explore the fundamental

physical mechanisms ofuidow and heat transfer in microchan-nels, many effects, including the size effect, rarefaction effect,surface roughness, viscous effect, electrostatic force effect, axialheat conduction in the channel wall, surface geometry, themeasurement errors, etc. should be taken into account [1]. A largenumber of experimental and numerical studies focus on ow andheat transfer behavior in microtube and microchannel have beenreported. These vast results and information have dealt withdifferent conditions, parameters, geometry dimensions, and instru-mentation, which indeed used for comparison purposes to indicatemore accurate methodology for solving the case studies.

The purpose of this paper is threefold. The primary purposeis to review the available results of the ow and heat transferpresented in previously published data for microtubes and micro-

channels. The results of massive number of different parametersaffect the uid ow and heat transfer characteristics are summar-ized and presented to predict the peaks of the ow and heattransfer. The second purpose is to understand the characteristicsand functions of nanouids, to expect their effects and heattransfer enhancement in such geometries. The third purpose isto open a gate for new researches and propose suggestionsthat could lead to improve the ability to enhance the heat transferin MT and MC using nanouids. The review starts with anextensive review on the ow and heat transfer in microtube andmicrochannel. Then nish with a comprehensive review fornanouids and its characteristics.

2. Microtube (MT)

2.1. Experimental studies on MT

In last few years, large number of researchers intend to study theheat transfer and uid ow in MT. Zhou et al. [1] investigatedexperimentally and numerically the ow and heat transfer char-acteristics of liquid laminar ow in MT. They used the smooth fusedsilica and rough stainless steel microtubes with the hydraulicdiameters of 50100mm and 3731570 mm, respectively. Deionizedwater was used as the working uid. The dimensions and surfaceroughness for the fused silica tubes and stainless steel are ranged50mm, 75mm and 100 mm. The Reynolds numbers was ranged from20 to 2400. The friction factors for smooth fused silica tubes are in

good agreement with the prediction of the conventional theory. For

the rough stainless steel tubes, the friction factor was higher thanthe prediction of the conventional theory. The results indicated thatthe conventional friction prediction is valid for water ow throughMT with a relative surface roughness less than 1.5%. The experi-mental results show that the Nusselt number along the axiadirection do not accord with the conventional results especiallywhen the Reynolds number is low and the relative tube walthickness is high.

Lelea et al.[2]investigated experimentally and numerically theheat transfer and uid ow characteristics in a microchannel. The

diameters of the microchannel used were 0.1 mm, 0.3 mm and0.5 mm, the ow regime was laminar and the Reynolds numberrange was up to 800. The tube material was stainless steel SUS304. The distilled water was used as a working uid. They foundthat the results conrm that the conventional or classical theoriesare applicable for water ow through microchannel of above sizes

Ding et al. [3] investigated experimentally the heat transfebehavior of aqueous suspensions of multi-walled carbon nanotubes (CNT nanouids) owing through a horizontal tube. Astraight copper tube with 970 mm length, 4.5 mm inner diameterand 6.35 mm outer diameter was used as the test section. Distilledwater and multi-walled carbon nanotubes were used to producenanouids. Fig. 1 shows a SEM image of the dispersed sampleSignicant enhancement was observed of the convective heattransfer in compared with pure water as the working uid. Theyfound this enhancement depends on the ow condition, CNTconcentration and the pH level. The axial position of the maximumenhancement increases with the CNT concentration and theReynolds number. The results indicate that the Reynolds numbercauses a signicant increase in the convective heat transfecoefcient.

Yang and Lin[4] investigated experimentally the forced con-vective heat transfer performance of water ow through six microstainless steel tubes with inner diameters ranging from 123 mm to962mm. The results indicate that the conventional heat transfercorrelations for laminar and turbulent ows can be well appliedfor predicting the fully developed heat transfer performance in theMT. The transition occurs at Reynolds number from 2300 to 3000The surface temperature uctuation in transition regime is much

larger than that in laminar and turbulent ow regimes. Theyobserved that the heat loss is less than 4% and 1% of the total heainput for 123 mm and 962 mm tubes, respectively. At the lowestReynolds number in the 123mm tube, a 4% heat loss cause 25%heat transfer coefcient overestimate.

Celata et al. [5] investigated experimentally the inuence ochannel wall roughness and the channel wall hydrophobicity onadiabaticow in circular microchannels. Different diameters of MTranges from 70 mm to 326 mm were used with Reynolds numberless than 300 for all diameters. The experiments were carried outon sooth glass/fused silica and a Teon capillary tubes used withwater. The results indicate that, with degassed water, there was noeffect of slip ow noted due to hydrophobic channel walls even at70 m inner diameter. For roughened glass channels, an increased

in friction factor above 64/Re was observed only at the smallest

B.H. Salman et al. / Renewable and Sustainable Energy Reviews 28 (2013) 848880 849


diameter of 126 m. The higher factor was caused by actualdeformation of channel circularity rather than increased frictionat the rougher wall, and similar behavior was observed in aTeon tube.

Peng et al.[6]investigated water ow in a fused glass microtubewith inner diameter of 230 m and the outer diameter is about500 m. The Reynolds number was ranged from 1540 to 2960. Theresults indicates that, the ow transition from laminar to turbulentoccurs at Reynolds number 1700 to 1900, and the turbulencebecomes fully developed at Re42500. The details of the owstructure such as stream wise streaks and transverse vortices wereobserved in the transitional ow elds for 1800oReo2100.The instantaneous velocity which observed by micro-PIV reveal largescale coherent structures in the turbulent ow in MT.

Celata et al.[7] investigated experimentally the characteristics ofthe adiabatic behavior of single-phase laminar ow in circular micro-tube. The diameters were used from 528 down to 120 mm. Theexperiments were carried out using water, which was degassed bypassing through a very small and continuous of helium. The resultindicates that, the Nusselt number decreased with decreasing thediameter. The smaller MT shows progressively less evidence ofow inthe course of thermal development. The decreased in heat transferperformance with respect to the conventional value of Nusselt number(Nu4.36) was more marked for decreasing the Reynolds number.

Sara et al. [8] investigated experimentally the laminar con-vective mass transfer and friction factor in MT with diameter of0.20 mm andL/Din the range of 100 to 500. The Reynolds numberwas ranged from 40 to 1400. The distilled water was used as aworking uid. The results reveal that the friction factor was in avery good agreement with the HagenPoiseuille theory in thelaminar regime and the conventional correlations can be used todetermine the friction factor for MT with IDZ0.20 mm. For masstransfer, the Sherwood number for MT was smaller than thoseobtained from the correlations developed for macrotubes.

Zhang and Fu[9] investigated experimentally the characteris-tics of two-phase ow of liquid nitrogen in vertically upward

micro-tubes with inner diameters 0.531 and 1.042 mm. The resultsindicate that, the main two-phase ow patterns of liquid nitrogenin MT were bubbly ow, slug ow, churn ow and annular ow.The conned bubble ow was observed in 0.531 mm and1.042 mm MT. The dry-out easily happened in 0.531 mm diametertube and led to high vapor quality and mist ow appeared. Theow regime transition lines moved to lower supercial vaporvelocity as the diameter of MT decreased. In addition, there wasquite large divergence between the experimental results and theexisted theoretical models, and it seemed that there was not yet atheoretical model which can predict the ow regime transitionwell for the two-phase ow. The slip ratio between two phasesbecame larger as the inner diameter of the MT decreased.

Liu et al.[10]investigated experimentally the forced convective

heat transfer characteristics in quartz microtubes with innerFig. 1. SEM image of a dispersed sample of carbon nanotubes [3].

Nomenclature

Al2O3 Aluminum oxideCp Specic heat of the uid (J/kg K)CuO Copper oxidedf Diameter of base uid moleculedp Nanoparticle diameter (m)

g Gravitational acceleration (m/s2

)k Thermal conductivity (W/m K)keff Effective thermal conductivityk sf wall-to-uid thermal conductivity ratioL Length of the tube (m)M Molecular weight of base uidN Avogadro number (N6.022 1023 mol1)Nu Nusselt number (NuhD/K)P Pressure ofuid (Pa)Pr Prandtl number (PrCp0/k)qx Heat ux (W/m

2)Re Reynolds number (Re0V0D/0)Rnp Nanoparticle radius (m)SiO2 Silicon oxide

T Temperature of

uid (K)T Bulk temperature (K)T0 Reference temperatureU, V Velocities inxand ydirections (m/s)

U, V Dimensionless velocities inx and y directionsU0 Average jet velocity at the entrance (m/s)V Axial velocity (m/s)ZnO Zinc oxide

Greek symbols

eff Effective viscosity Thermal diffusivity (m2/s) Dynamic viscosity ofuid (kg/ms) Kinematic viscosity ofuid (m2/s) Inclination of tilted wall Fluid density (kg/m3)1 Nanouid density (kg/m

3) Volume fraction of nanoparticles Non-dimensional wall thickness Relative roughness height

Subscript

bf base-uid

nf nanouidsnp nanoparticleeff effective

B.H. Salman et al. / Renewable and Sustainable Energy Reviews 28 (2013) 848880850


diameters of 242 m, 315 m and 520 m. The de-ionized waterwas used as the working uid. The Reynolds number was rangedfrom 100 to 7000. The results indicate that, the experimentalNusselt number is a good agreement with that of the laminarcorrelations when the ow state was laminar. The Reynoldsnumber of the laminar to turbulent transition region may beabout 15004000, 16004500 and 19005500 for MT with innerdiameters of 242 m, 315 m and 520 m, respectively.

Celata et al. [11] investigated experimentally the effects ofcompressibility for helium ow through fused silica micro-tubes.The MT diameter was ranged from 30 m to 254 m. Reynoldsnumber was ranged from 0.8 to 500. Two hydrodynamic modelsfor compressible ow (isothermal and adiabatic) were confrontedat normal conditions. Local friction factor was devised to comparewith the global friction factor to quantify the effect of compres-sibility. The results reveal that, the friction factor has remarkablyaccurate prediction by the reference curve of HagenPoiseuille anda very close agreement between the incompressible and quasi-compressible correlations was obtained. The effect of density-change-induced acceleration was extremely limited on the particlescale and that an incompressible characterization ofow.

Qi et al.[12,13]investigated experimentally the ow boiling of

liquid nitrogen in the MT with the diameter range from 0.531 mmto 1.931 mm. They investigated the heat transfer characteristicsand the critical heat ux (CHF). The results reveal that, the wallincreased in the single-phase ow region, drops abruptly at ONBand then decreased monotonically in the two-phase ow regionand this decreased was a result of large two-phase ow pressuredrop. For low mass quality region, heat transfer was governed bynucleate boiling and heat transfer coefcient was dependent onheat ux and pressure. In addition, the heat transfer coefcientincreases with mass quality at low and medium heat uxes. CHFincreased with the mass ux whereas the critical mass qualitydecreased with mass ux. The CHF was governed by the liquidlmnear the inner wall.

Wen and Ding [14] investigated experimentally the effects ofconvective heat transfer of nanouids at the entrance region of thecopper tube with 970 mm length. The de-ionized water with Al2O3nanoparticles were used as working uids. Reynolds number wasranged from 500 to 2100. The results indicate that, the use of Al2O3nanoparticles as the dispersed phase in water signicantlyenhanced the convective heat transfer in the laminar ow regimeand this enhancement increased with Reynolds number and theparticle concentration. The enhancement was particularly signi-cant in the entrance region and decreased with the axial distance.The thermal developing length of nanouids was greater than thatof pure base liquid and increased with an increase in particleconcentration.

2.2. Numerical studies on MT

Xiong and Chung[15]proposed a novel bottom-up approach togenerate a three-dimensional random roughness on a MT surface.They used Gaussian random number generator to generate thecorner points in the space with random heights and the bi-cubicCoons patch to create the boundary curves and surface based onthe corner points. Many tiny generated surfaces were used to formthe random rough of MT. Computational uid dynamics (CFD)solver was used to isolate the roughness effect and to solve thethree dimensional equations for the waterow through generatedthe rough MT with 50 m diameter and 100 m length. Theyassumed N points in space, and it is connected one by one usingstraight lines to form the bones of the rough surface in step two. Atthe third step, they created the curve surface and in the last step,they created two more surfaces for the inlet and outlet and then

they used it to form a volume as shown in Fig. 2. Reynolds

numbers ranged from 40 to 2000 and the viscous dissipation isnot considered. They observed that the temperature has largevalues at the peaks and small values at the valleys of the MTsurface. The roughness has a negligible on the averaged Nusseltnumber because the effects of peaks and valleys counteract eachother for the whole MT surface. The local Nusselt numbers doesnot have a large uctuation away from the theoretical value and itrandomly distributes along the MT. For the hydraulic diamete

they noticed, the improper use of the hydraulic diameter canresult in increasing or decreasing the friction factor and Nunumber.

Zhang et al.[16]investigated numerically the effects of wall axiaheat conduction and uid axial conduction for simultaneouslydeveloping the laminar ow and heat transfer in the wall of MTwith constant outside wall temperature. The results indicated thatthe heat transfer process is most sensitive to wall-to-uid con-ductivity ration ksf, and in condition when 30rRePrr11,560 andksf425; But when the conditions were used 30rRePrr11,560 andksfr25, the increasing tube thickness and the decreasing ksfcouldmake the inner wall surface approaching the uniform heat uxcondition. The maximum Nusselt number they obtained is about4.3. It turns out that the basic function of the wall axial hea

conduction is to unify the inner wall surface heat

ux.Giulio and Paola[17] investigated numerically the roughnesseffects on the heat transfer and pressure loss performances omicroscale tubes and channels. The nite element was used basedon the fractional step or projection approach. The surface rough-ness was modeled through a number of peaks and valleys alongthe ideal smooth surface. Different peak shapes and distributionwas considered to arrive to the real roughness. The relativeroughness height () ranged from 0.0% to 5.3% was used and thegeometrical parameter which representative of the tubes is thediameter ranged from 50 m to 150 m. The results indicated thatfor both congurations, a signicant increase in Poiseuille numberwas detected. While the inuence of roughness on the heatransfer is smaller and more sensitive to the geometry of bothduct and roughness obstruction and it is highly dependent on thetube shape.

Kamali and Binesh[18]investigated numerically the effects oheat transfer for multi-wall carbon nanotube (MWCNT) basednanouids in a straight tube under constant wall heat ux condi-tion. The tube length was 914.4 mm and the tube diameter was1.55 mm. Both water base uid and aqueous 1% CNT nanouid wereused as uids in simulations. The single phase model was used oftwo dimensional axisymmetric steady, forced laminar convectionows of nanouids inside a straight circular tube. The resultsindicate that the heat transfer coefcient is dominated by the walregion due to non-Newtonian behavior of CNT nanouid.

Hong and Asako [19] investigated the heat transfer character-istics of gaseous ows in a MT with constant heat ux whose valueis positive or negative on 2D compressible laminar ow for no-slip

regime. The tube diameter range was from 10mm to 100 mm and thelength to diameter ratio was 200. The constant heat ux range wasfrom 104 W/m2 to 104 W/m2. The numerical methodology wasbased on the ArbitraryLagrangingEulerian (ALE) method. Theyselected stagnation pressure in such a way that the Mach number atexit ranged from 0.1 to 0.7 and the outlet pressure wasxed at theatmosphere pressure. The results indicated that, in the case of slowow, the wall and bulk temperatures normalized by heat uxesincrease for both positive and negative heat ux. A correlation forthe prediction of the wall temperature of the gaseous ow in theMT was proposed. Supplementary runs with slip boundary condi-tions for the case of D10mm were conducted and rarefactioneffect was discussed. With increased Ma number, the compressi-bility effects are more dominant and the rarefaction effect is

relatively insignicant whereKn number is less than 0.0096.



Bianco et al.[20]investigated numerically the development oflaminar forced convection ow of a waterAl2O3 nanouid in acircular tube with a constant heat ux at the wall. Single and two-phase model were employed with either constant or temperature-dependent properties. The Re number was ranged from 250 to1050. The heat ux was ranged from 5000 W/m2 to 10,000 W/m2

and, (the nanoparticle volume fraction) was ranged from 1% to4% for both constant and temperature-dependent properties. In allcases the size for the spherical particles was considered to equal100 nm. The results indicate that the inclusion of nanoparticlesproduced a considerable increase of the heat transfer with respectto that of the base liquid. The heat transfer enhancement wasincreased with the concentration of particle volume and thisincrease was accompanied by increase wall shear stress values.The results of single and two-phase models were quite similar, themaximum difference detected was 11% for the average heattransfer coefcient especially for 4%.

Xiao et al.[21]investigated numerically the effects of gas owin microtube. The results indicate that, the heat transfer effectsassociated with rareed ow were reduced for the second-ordermodel and the effects of the second order terms was mostsignicant at the upper of the slip regime. For the airow atstandard conditions, the maximum second-order changes ofNusselt number was on the order of 15%. Nusselt number wasincreased relative to the values of no-slip when the temperature

jump effect was small.Koo and Kleinstreuer [22] investigated the effects of viscous

dissipation on the temperature eld and the friction factor inmicrotube (MT) and microchannel (MC). Three working uids wereused, water, methanol and iso-propanol. The results indicate that,the viscous dissipation effect on the friction factor was increased asthe system size decreases. For water ow in a tube withDo50mm,viscous dissipation becomes signicant and should be considered forall experimental and computational analyses. In addition, the aspectratio of a channel plays an important role in viscous dissipation, asthe aspect ratio deviates from unity, the viscous dissipation effectsincrease. Ignoring the viscous dissipation effects could ultimatelyaffect the friction factor measurements for ow in MT.

Lelea and Cioabla[23,24]investigated numerically the effects of

viscous dissipation on heat transfer and uid ow in micro-tubes.

Three different uids, water and two dielectric uids, HFE-7600 andFC-70 with temperature dependent uid properties were used. Thediameter ratio of the MT was Di/D0(0.1/0.33)mm with a tubelength L100 mm. Two different heat transfer conditions, coolingand heating and three different Brinkman number 0.01, 0.1 and0.5 was used. Non-dimensional parameters were obtained, forwater Re 2581684; Pr 6:46:9, HFE-7600 Re 1861130;Pr 29:332:2 and FC-70 Re 7:243:2; Pr 189:8317:4.

The results reveal that, the friction factor and Poiseuille constantPoare affected atBr 0:5 for water and start with Br 0:1 for highlyviscous uids HFE-7600 and FC-70. The Nusselt number for thecooling case for Br 0:5 was about three times higher than forheating case, regardless the uid type.

Satapathy[25]investigated forced convection for gaseous slipow in an innite microtube with mixed boundary conditions.The results indicate that for both the hot and cold wall situation inthe thermal entrance region, the local bulk-mean temperatureincreased as Peclet number or Knudsen number increases andvice-versa. The local Nusselt number increased with the increasein Peclet number and decreased with the increase in Knudsennumber. The fully-developed Nusselt number decreased with theincrease in Knudsen number. For a xed value of Knudsen number,it reaches to constant value for all Peclet numbers.

Wang and Wang[26]investigated numerically the inuences ofthree-dimensional wall roughness on the laminar ow in micro-

tube. The relative roughness was ranged from 0 to 0.05 and thewave number from 0 to 30. Reynolds number was ranged from1 to 500. The results reveal that if the wave number of roughfunction or Reynolds number decreased, the disturbed areas ofow eld becomes larger. The variation of disturbed area wasindependent of the variation of relative roughness if the relativeroughness is a small quantity. In addition, the dimensionlesspressure drop increased with the increases of relative roughness,Reynolds number or wave number of wall function. The inuenceof wall roughness on the ow pattern was different from those onthe pressure drop.

Aziz and Niedbalski[27]investigated numerically the rst andsecond order slip ow effects on the thermal development ofdilute gas ow in a micro-tube with axial conduction and viscous

dissipation. The results indicate that for the fully developed

Fig. 2. Four steps to form the rough microtube: (a) points (b) lines (c) surfaces and (d) volume[15].



hydrodynamic condition, the analytical solution for the velocity withthe second-order slip model predicts higher velocities in the centralregion of the ow but the trend was reversed near the wall region. Inaddition, the local Nusselt number decreased as the uid owsthrough the cooled section of the tube. However, as the viscousdissipation gathers strength, the Nusselt number reaches a minimumand then increases again as the effect of viscous dissipation continuesto prevail over the cooling effect. Salman et al. [28] investigated

numerically laminar convective heat transfer in a microtube (MT) with50 m diameter and 250 m length with constant heat ux usingnite volume method (FVM). Different types of nanouids Al2O3, CuO,SiO2 and ZnO, with different nanoparticle sizes 25, 45, 65 and 80nm,and different volume fractions ranged from 1% to 4% using ethyleneglycol as base uids were used. This investigation covers Reynoldsnumber in the range of 10 to 1500. The results have shown that SiO2-EG nanouid has the highest Nusselt number, followed by ZnO-EG,CuO-EG, Al2O3-EG, and lastly pure EG. The Nusselt number for allcases increases with the volume fraction but it decreases with the risein the diameter of nanoparticles. In all congurations, the Nusseltnumber increases with Reynolds number. A summary for the experi-mental and numerical studies in MT is shown inTable 1.

3. Microchannel (MC)

3.1. Experimental studies on MC

Jung et al.[29]measured experimentally the heat transfer coef-cient and friction factor of nanouids in rectangular microchannel(MC). Aluminum dioxide (Al2O3) with diameter of 170 nm nanouidswith various particle volume fractions of 0.6%, 1.2% and 1.8% were usedas working uids. The Reynolds number was tasted in the range of

5 and 300. The results indicated that the convective heat transfercoefcient of Al2O3nanouid in laminar ow regime was increased upto 32% compared to the distilled water at a volume fraction of 1.8%without major friction loss. The Nusselt number increases withincreasing the Reynolds number in laminar ow regime. The Nusseltnumber was successfully correlated with Reynolds number andPrandtl number based on the thermal conductivity of nanouids.

Cheng et al. [30] reported a novel concept to control the

interface location of the pressure driven multi-phase ow inmicrochannel. An H-shape microuidic device was used todemonstrate the concept of interface control as shown inFig. 3.Two uids, aqueous NaCl solution and diluted glycerol wereintroduced through the inlets by a syringe pump. The ow ratesfor NaCl solution and diluted glycerol was maintained at the samevalue. For a purely pressure driven two-uid ow, the aqueousNaCl solution with a lower viscosity ows faster and occupied asmaller width of the microchannel. The results show that thismethod is effective for low ow rates, and small viscosity ratioclose to 1. The experimental results demonstrate a new method tosolve the unmatched viscosity problem of the two-uid ow inmicrochannel.

Agarwal et al.[31]investigated experimentally the heat trans-

fer coef

cients in six non-circular horizontal MC with diametersranged from 0.424 mm to 0.939 mm of different shapes duringcondensation of refrigerant R134a over the mass ux in the rangeof 150 kg/m2/s to 750 kg/m2/s. The channels included barrel-shape, N-shape, rectangular, square, and triangular extruded tubesas shown inFig. 4. The results reveal that the models developedfor larger tubes result in signicant deviations from the measureddata, because the models were not intended for and could notaccount the ow phenomena and interfacial shear behaviorspecic to MC. For square, rectangular, and barrel-shaped channelsan annular-lm ow based model was developed. For triangular,N-shaped, and W-insert channels, it was assumed that the liquidfraction was retained at the corners, with the ow at the rest of thewall and in the core being approximated as mist ow. The annular-ow-based model recommended to be used for the square, barrel-shaped and rectangular channels, while the mist-ow correlationshould be used for channels with sharp corners.

Roland et al.[32]investigated experimentally and numerically thehydrodynamics in two-dimensional MC having 700 m and 200 mheight. Reynolds number used was ranged from 200 to 8000. Thetesteduids were demineralized water with an electrical conductivityof 300 S/cm. In addition, two-dimensional numerical model corre-sponding to the symmetry plane of the test section was developed.The model accounted for free convection heat transfer with surround-ing air at the outside walls of the test section. The results indicate thata reduction in the Nusselt number for laminar ow at the microscale isoccurred. In the laminar regime, the validity of the conventionaltransport phenomena theory may be extended to the small scales(200 m). Transition to turbulence was observed both in the global

pressure losses measurements and in the Nuwith Reevolutions. Inaddition, the critical Reynolds numbers were found to vary from 3500to 4500 which are consistent with the values observed at the largerscales. The experimental corrected data matched both with the Blasiushydrodynamic law and the Dittus and Boelter heat transfer correlation.

Wu and Cheng[33] investigated experimentally laminar heattransfer and pressure drop of water through 13 different trape-zoidal silicon micro-channels with different geometry, surfaceroughness and surface hydrophilic properties. The results indicatethat the bottom to top width ratio, the height to top width ratioand the length to diameter ratio have a great effect on the laminarNusselt number and apparent friction constant of the trapezoidalMCs. The laminar Nusselt number and apparent friction constantof the trapezoidal MCs increased with the increase of surface

roughness and this increase is more obvious at large Reynolds

Fig. 3. Schematic of an H-shaped microuidic device[30].

Fig. 4. Tube shapes[31].



numbers. The Nusselt Number and apparent friction constant arehigher when using strong hydrophilic surfaces than those withweak hydrophilic surfaces (silicon surfaces). In addition, thelaminar convective heat transfer shows two different character-istics at low and high Reynolds number ranges. For very lowReynolds number ow (0oReo100), the Nusselt numberincreased almost linearly with the rise of Reynolds number.However, the increased of the Nusselt number after Re 100 was

gentle with the rice of Reynolds number.Park and Punch [34] investigated experimentally the frictionfactor and heat transfer in multiple MCs with hydraulic diametersfrom 106 m to 307 m for single phase liquid ow. The Reynoldsnumber used was ranged from 69 to 800. Deionized water wasused as a working uid. The results indicate that the frictionfactors obtained by experiments on the MC prove that theconventional theory for fully-developed ow was applicablewithin the range of the values of parameters they used. In orderto predict heat transfer rate accurately, they proposed an empiricalcorrelation in terms of Nu=Re0:62Pr0:33and Brinkman numberconned to the experimental range. The correlation was expectedto be useful to design the MC devices related to heat transfer.

Quan et al. [35] investigated experimentally in determination

annular condensation heat transfer coef

cient of steam in two siliconmicrochannels with hydraulic diameters of 127 m and 173 m withtrapezoidal cross sections. The air was used as the coolant for thesteam owing in the MC. The results indicate that the annularcondensation heat transfer coefcient in MC increased with mass uxand quality and decreased with the hydraulic diameter. The annularcondensation heat transfer coefcient based on a semi-analyticalapproach of turbulent liquid lm with correlations for two-phasepressure drop and void fraction are valid in MC.

Lee et al. [36] investigated experimentally and numerically thebehavior in single-phase ow through rectangular microchannels withwidth range from 194 m to 534 m. Deionized water was used as aworkinguid. Reynolds number was ranged from 300 to 3500. Theresult indicates that the heat transfer coefcient increased with thedecrease of the channel size depending on the ow rate. Theexperimental results were compared against conventional correlationsto evaluate their applicability in predicting MC heat transfer. The widedisparities revealed that the mismatch in the boundary and inletconditions between the MC experiments and the conventional corre-lations precluded their use for predictions. The numerical resultsagreed with the experimental data, suggesting that such approacheswhen coupled with carefully matched entrance and boundary condi-tions can be employed with condence for predicting heat transferbehavior in MC. The results also conrm that the simplied thin wallanalysis can be used as a computationally economical alternative to afull 3D conjugate analysis.

Harirchian and Garimella [37] investigated experimentally the localow boiling heat transfer of a dielectric uid (Fluorinert FC-77) inmicrochannel heat sinks as shown inFig. 5. The mass ux used was

ranged from 250 kg/m2/s to 1600 kg/m2/s. Seven different test piecesmade from silicon and consisting of parallel MCs with nominal widthranged from 100 m to 5850 m with a nominal depth of 400 mwere obtained. The results indicate that for MCs of width 400 m andgreater, the heat transfer coefcients corresponded to a xed wall heatux as well as the boiling curves was independent of channel size. Theheat transfer coefcients and boiling curves was independent of massux in the nucleate boiling region for a xed channel size, but affectedby mass ux as convective boiling dominates. In addition, a strongdependence of pressure drop on both channel size and mass ux wasobserved.

Ergu et al. [38]investigated experimentally the pressure dropand point mass transfer in a rectangular microchannel with awidth of 3.70 mm, height of 0.107 mm and length of 35 mm.

Distilled water was used as a working uid. Reynolds number

used was ranged from 100 to 845. The results indicate that thefriction factor values were slightly higher than those calculated bytheoretical correlation and these values increased with increasingReynolds number. The classical laminar ow equations can be usedfor the calculation of the friction factor in MCs.

Owhaib et al. [39]investigated experimentally saturated owboiling in MCs. Heat transfer coefcients were measured fosaturated boiling of working uid (R 134a) in vertical circula

tubes with internal diameters ranged from 0.862 mm to 1.7 mmwith a uniform heating length of 220 mm. Heat transfer coef-cients were obtained for a heat ux ranged from 3 kW/m2 to34 kW/m2 and a mass ux was ranged from 50 kW/m2/s to400 kW/m2/s and vapor qualities up to 0.6. The results reveal thatthe saturated ow boiling heat transfer coefcient was more orless independent of vapor quality and mass ux, but it is highlydependent on the heat ux for vapor fraction xo0.6. The con-tribution of forced convection heat transfer to the overall transferrate was small and that heat transfer by a mechanism similar tothat in nucleate boiling was dominant. In addition, ow boilingheat transfer coefcients was higher for smaller diameter tubesAlso, an increase in the system pressure improves the heat transferperformance.

Chiu et al. [40] investigated experimentally and numericallythe heat transfer performance and characteristics of liquid coolingheat sink microchnnels. The height of MCs was constantThe aspect ratio was set from 1.67 to 14.29 and the porosity wasfrom 25% to 85%. The imposed pressure drop used was rangedfrom 490 Pa and 2940 Pa. The result indicate that the overalaveraged Reynolds number in MCs decreased with both increasingthe aspect ratio and cross-sectional porosity under same pressuredrop. The aspect ratio for the lowest effective thermal resistancewas dependent on the pressure drop between the inlet and theoutlet of heatsink. In addition, the heat transfer enhancemendue to raising pressure drop was more signicant on MCs withhigh aspect ratio hence thinner channels are more advantageousunder high pressure drop. The local Nusselt number in a channedecreased with increasing the aspect ratio. The value of Numonotonically decreased along the channel for high aspect ratio.

Shen et al.[41] investigated experimentally the single phase heatransfer in a compact heat sink consisting of 2 rectangular MCs of300 m width and 800 m depths. The relative roughness was rangedfrom 4% to 6%. Deinonized water was used as the working uid. TheReynolds number used was ranged from 162 to 1257. The inlet liquidtemperature used was ranged from 30 1C to 70 1C and the heatingpowers were used from 140 W to 450 W. The results indicate that thesurface roughness has a great effect on the laminar ow in rough MCsFor developed ow, the Poiseuille number in the regime of highReynolds numbers was higher than the conventional theory predic-tions and increase with increasing the Reynolds number, rather thanremaining constant. In addition, the average Nusselt number increasedwith the increase of Reynolds number and Prandtl number. Both the

local and the average Nusselt numbers were signicantly lower thanthe conventional theory predictions for all ow rates and this wasattributed to two main factors, the cross-sectional aspect ratio and thesurface roughness.

Barber et al. [42] investigated experimentally the effects ohydrodynamics and heat transfer during ow boiling instabilitiesin a single MC with a hydraulic diameter of 727 m. The uniformheatux used was 4.26 kW/m2 and the inlet liquid mass ow rateheld constant at 1.13 105 kg/s. The results reveal that the owpressure and temperature conditions leading to nucleate boilingow instabilities and transition regimes during ow boiling in aMC. A quantify and characterize the timescales of various observedinstabilities during ow boiling in a MC. High speed imagingrevealed some of the controlling physical mechanisms responsible

for the observed instabilities.



Lee and Garimella [43] investigated experimentally the owboiling in arrays of parallel MCs by using a silicon test piece withimbedded discrete heat sources and integrated local temperaturesensors. The MCs width used was ranged from 102 m to 997 m

and the width was 400m. Deionized water was used as aworking uid. The results reveal that the pressure drop acrossthe MCs increased rapidly with the heat ux when the incipienceheat ux (for the onset of nucleate boiling) was exceeded. At lowto medium heat uxes, the local heat coefcient increased almostlinearly with heat ux. While, at higher heat uxes, the saturatedheat transfer coefcient becomes largely insensitive to heat uxfor the range tested.

Celata et al. [44] investigated experimentally heat transfercharacteristics of subcooled ow boiling of FC-72 in a singlehorizontal circular cross section MC with 480 m inner diameter,800 m outer diameter and 102 mm long. Different ow patterns,both in the stable and unstable ow boiling regimes were con-sidered. The results indicate that the stable ow boiling with

alternating bubbly/slug ow, slug/annular ow and annular/mist

ow was observed for heat ux of 150 kW/m2 or higher and massux of 1500 kg/m2 s or higher. Back and forth oscillations with owinstabilities were observed in cases of lower heat and mass uxes.No complete reverse ow was observed in upstream direction. In

addition, the heat transfer coefcient increased with the increasesof vapor quality at higher vapor quality, and at lower vapor quality,the heat transfer coefcient was rather independent of heat ux.

Megahed[45] investigated experimentally ow boiling charac-teristics in a cross-linked MC heat sink at low massuxes and highheat uxes. The heat sink used consists of 45 straight MCs with ahydraulic diameter of 248 m and heated length of 16 mm. Thedielectric coolant FC-72 was used as a working uid. The heat uxused was ranged from 7.2 kW/m2 to104.2 kW/m2, mass ux from99 kg/m2/s to 290 kg/m2/s, and exit quality from 0.01 to 0.71. Theresults indicate that the instability increased with decreasing themass ux. The inlet pressure and outlet saturation temperatureoscillate with higher amplitudes as the mass ux decreases. Thetwo-phase pressure drop through MC heat sinks with cross-links

was much higher compared to the straight MC heat sinks due to the

Fig. 5. (a) Microchannel test section and (b) integrated heaters and temperature sensors in the microchannel test piece [37].



cross-link effect. The two-phase heat transfer coefcient wasstrongly increased with the exit quality because of the dominationof the nucleation boiling mechanism in the cross-link region.

Diaz and Schmidt[46]investigated experimentallyow boilingheat transfer in a single rectangular MC made of the nickel alloyInconel 600 with 0.3 mm height, 12.7 mm width and 200 mmlength. Water and ethanol were used as test uids. The mass uxesused ranged between 50 kg/m2/s and 500 kg/m2/s and heat uxes

up to 400 kW/m2

at an outlet pressure of 0.1 MPa. The resultsreveal that, high amplitude oscillations for water were found inthe region of subcooled boiling at qualities slightly below zero. Theamplitude decreased as quality increases and no characteristicfrequency was observed. Flow boiling of ethanol yielded lowamplitude oscillations of the wall temperature, even within thesubcooled boiling region. Increase in quality resulted in increasingoscillation amplitude. In addition, the heat transfer coefcientdecreased with increasing quality for water. Different observed forethanol after the low quality region. The heat transfer coefcientincreased with increasing quality at low heat uxes. With increas-ing heat ux, the heat transfer coefcient decreased with quality.

Chen et al. [47]investigated experimentally the condensationof steam in a series of triangular silicon MCs with hydraulic

diameters ranged from 100 to 250 m. The number of channelsin each silicon chip was 10 and the length for each channel was56.7 mm. The results indicate that the droplet, annular, injectionand slugbubblyow are the dominant ow patterns in triangularsilicon MCs. The ow of condensation instability was higher withincreased inlet vapor Reynolds number, condensate Webernumber and the prolongation of the injection location, or with adecrease in the hydraulic diameter of the channel. In addition, thewall temperature of the channel decreased along the condensationstream. The total pressure drop, the average condensation heattransfer coefcient and the average Nusselt number wereobserved to be larger with increased inlet vapor Reynolds number.Moreover, it was found that the condensation heat transfer wasenhanced by a reduction in the channel scale.

Betz and Attinger[48]investigated experimentally heat transferenhancement in MC heat sink with the introduction of segmentow. The segmented ow pattern was created by the periodicinjection of air bubbles into water-lled channels. Reynolds numberused was ranged from 160 to 1580. The results reveal that thesegmented ow would provide an intermediate step betweensingle-phase and boiling ow for the purpose of electronic cooling.The segmented ow increases the Nusselt number of laminar owby more than 100%. The heat transfer enhancement only occurs fora specic range of ow rates and capillary numbers. At lower orhigher capillary numbers, there was no signicant heat transferenhancement observed because segmented ow was replaced bybubbly or churn ow, respectively.

Wojtan et al. [49] investigated experimentally the saturatedcritical heat ux (CHF) in 0.5 mm and 0.8 mm internal diameter

MC tubes as a function of refrigerant mass velocity, heated length,saturation temperature and inlet liquid subcooling. The testedrefrigerants were R-134a and R-245fa and the heated length of MCwas varied between 20 mm and 70 mm. The results reveal that astrong dependence of CHF on mass velocity, heated length and MCdiameter but no inuence of liquid subcooling (2151C) wasobserved. A new MC version of the KattoOhno correlation wasdeveloped to predict the CHF in circular, uniformly heated MCs.

Asthana et al.[50]investigated experimentally convective heattransfer in serpentine MCs cross section 100 m with a segmentedow of two immiscible liquids for ow rates up to 130 l/min. Theresults reveal that for slug ow, the movement of the oil slugsinduces intensive uid recirculation in the carrier water phasebetween the slugs, which disrupts the formation of a boundary

layer and improves mixing, more so for increasing oil volume

fractions. In addition, the local temperature of the water regionseparating the droplets was higher than in the case of pure waterow. For segmented ow, up to a four-fold increased the Nusseltnumber compared to pure water ow was observed. Increasedheat removal increased the pressure drop, which was stronglyaffected by the uid temperature.

Wang and Cheng [51] investigated experimentally stable andunstable ow boiling phenomena of deionized water in a single

MC with hydraulic diameter of 155 m. The results reveal thastable ow boiling occurred in a single MC if exit vapor qualityxeo0.013, where vapor bubbles generated and pushed away bythe incoming subcooled liquid. Single-phase liquid ow, bubblyow and elongated bubbly/slug ow were observed sequentiallyin the stable ow boiling mode. In addition, unstable ow boilingoccurred in a single MC ifxe40.013, where vapor plug expandedupstream resulting in oscillations of temperature and pressure. Inthis unstable ow boiling mode, bubbly ow, elongated bubblyslug ow, semiannular ow and annular/mist ow were observedat different times near the outlet depending on the mass ux.

Wu et al.[52]investigated experimentally steam condensationow in wide rectangular silicon MCs with the hydraulic diameterof 90.6 m, 483.4 m width and 50 m depth. The results revea

that droplet-annular compound

ow, injection

ow, and vaporslugbubbly ow were observed along the channel, which differfrom that in other cross-sectional shape MCs. In the dropletannular compound ow region, the vertical walls (short side) ofthe channel were completely covered by the condensate, whiledroplet condensation still exists on the horizontal wall (long sideof the channel. The location of the injection ow postponed withthe increasing inlet vapor Reynolds number. The injectionfrequency increased with increasing the inlet vapor Reynoldsnumber and condensate Weber number. In addition, the frequencyin the wide rectangular MCs was lower than that in triangular MCswith the same hydraulic diameter. It is conrmed that the crosssectional shape of the MC plays a signicant role on the instabilityof condensation ow. The correlation of Nusselt number was alsoobtained.

Steinke and Kandlikar [53] investigated experimentally thedifferent components of the total pressure drop measuremenfor adiabatic and single-phase degassed water in MC with a widthof 200 m, a depth of 250 m and a length of 10 mm. An in-depthcomparison of previous experimental data was performed toidentify the discrepancies in reported literature. The Reynoldsnumber used was ranged from 14 to 789. The results reveal thatthe procedure for correcting the measured pressure drop, the datawas corrected for inlet and exit losses and then it was corrected fordeveloping ows. The corrected data shows good preliminaryagreement in value and trend with the conventional theory forlaminar uid ow. The conventional Stokes and Poiseuille owtheories apply for single-phase liquid ow in MC ows.

Wu et al. [54]investigated experimentally static and dynamicow instability of a parallel MC heat sink consisting of 26rectangular MCs with 300 m width, 800 m depth, at high heatuxes. Water and methanol were used as a working uid withmass uxes of 201200 kg/m2/s. The inlet temperature used wasranged from 3001C to 70 1C. The results indicate that the onset oow instability occurs at the outlet uid temperature of 93961Cwhich were several degrees lower than the saturated temperaturecorresponding to the exit pressure of the MCs. In addition, theoutlet temperature and inlet pressure were always in phase, butthey were out of phase with the pressure drop across the MCs. Thewall temperatures generally match the oscillation trends of theinlet pressure and the outlet temperature, but a time delay occursdue to the thermal inertia of the copper block.

Zhang et al. [55] investigated experimentally the control o

pressure-drop ow instabilities in boiling microchannel systems with



61 m width, 272 m height and 15 mm length. Deionized water wasused as a working uid. The results reveal that the predictions fromthe ow oscillation model were agreed well with the experimentalpressure-drop observations across a ow meter and a MCHS. Inaddition, a family of state and dynamic output-feedback active owcontrollers was developed and evaluated for the dynamic pressure-drop instability suppression. The ow oscillation amplitude can beregulated to whatever level is desired under certain conditions.

Kohl et al. [56] investigated experimentally the ow withinternal pressure measurements in straight microchannel testsection with hydraulic diameters ranged from 25 m to 100 m.The Reynolds number used was ranged from 4.9 to 18,814. Theresults suggest that friction factors for MCs can be accuratelydetermined from data for standard large channels.

Rosengarten et al.[57]investigated experimentally the effect ofcontract angle (surface wettability) on the convective heat transfercoefcient in microchannels using thin lm coating technology.Distilled water was used as a working uid. The results reveal that,the pressure drop decreases relative to that expected with non-sliptheory above a critical shear rate and this decrease was dependenton the contact angle. Associated with the decrease in pressuredrop was a concurrent decrease in the convective heat transfer

coef

cient which again was more pronounced for hydrophobicsurfaces. Slip ow was an extremely important for micro and inparticular nano heat exchanger designs as heat transfer rates maydecrease more than 10% at high shear rates.

Tang et al.[58]investigated experimentally compressibility, rough-ness and rarefaction inuences for nitrogen and helium in stainlesssteel MTs with diameters ranged from 119 m to 300 m, fused silicaMTs with hydraulic diameter ranged from 52 m to 201 m and fusedsilica square MCs with diameters ranged from 52 m to 100 m. TheReynolds number used was ranged from 3 to 6300. The tested outletKnudsen number used was ranged from 1.4 104 to 4 103, andthe tested outlet Mach number was ranged from 0.01 to 0.6. Theresults indicate that the gaseous ow friction factor in stainless steeltube (SST) was observed to be much higher than the theoreticalprediction for conventional size tubes. The friction factor in the fusedsilica tubes and fused silica channels (FST, FSC) agreed well with thetheoretical prediction. In addition, the increase in friction factor wasattributed to the dense roughness distribution in the inner surface ofthe stainless steel tubes. Surface roughness in MCs was found to affectthe friction factor. It is suggested that for gaseous ow in MCs with arelative surface roughness less than 1%, the conventional laminarprediction should still be applied.

Huh et al. [59]investigated experimentally the unique character-istics of ow boiling in a polydimethylsiloxane (PDMS) rectangularsingle microchannel with a hydraulic diameter of 103.5 m and lengthof 40 mm. Deionized water was used as a working uid. The massuxes used were 170 kg/m2 and 360 kg/m2 and the heat uxes wereranged from 200 kW/m2 to 530 kW/m2. The results indicate that owboilinguctuations with a very long period and large amplitude were

observed. Both the pressure drop and mass ux had these uctuations,but a phase shift occurred between them that controlled the owpatterns. The uctuation of wall temperature and heat ux had thesame period as that of the mass ux. In addition, the variation intemperatures, pressure, and mass ux exactly matched the owpattern transitions between bubbly/slug ow and elongated slug/semiannular ow. The ow pattern transition instabilities in the singleMC caused the cyclic behavior of the wall temperature, pressure drop,and mass ux. As the supplied heat ux and vapor quality increased,the period of the unstable uctuations lengthened and the amplitudealso increased.

Mokrani et al. [60] investigated experimentally the uid owand convective heat transfer in at microchannels with constantwidth, height ranged between 50 m and 500 m and the hydrau-

lic diameter was varying between 1 m and 100 m. The tap water

was used as working uid with ow rate ranged from 0.04 ml/minto 240 ml/min. Reynolds number used was ranged from 100 to5000. The results reveal that the conventional laws and correla-tions describing the ow and convective heat transfer in ducts oflarge dimension were directly applicable to the MCs of heightsbetween 500 m and 50 m. In addition, the transition from thelaminar to turbulent regime occurred in a range of Reynoldsnumbers similar to that observed in ducts of large sizes.

Bertsch et al.[61]investigated experimentally the ow boilingheat transfer with the refrigerants R-134a and R-245fa in coppermicrochannel cold plate evaporators. Array of MCs were used withhydraulic diameter 1.09 mm and 0.54 mm. The aspect ratio of therectangular cross section of the channels in both test section was2.5. The saturation temperatures used were ranged from 8 1C to301C, mass ux from 20 kg/m2/s to 350 kg/m2/s and the heatuxwas ranged from 0 W/cm2 to 22 W/cm2. The results indicate thatthe heat transfer coefcient for R-245fa in comparison with R-134ain single-phase ow was higher. The pool boiling heat transfer forR-245fa was lower as a result of its higher molecular mass andsurface tension. In addition, the ow boiling heat transfer coef-cient strongly increased with the increase of the heat ux and wasdominated by nucleate boiling. It also shows a strong dependence

on thermodynamic vapor quality with a rapid decrease at qualitiesabove 0.5. The maximum heat transfer coefcient occurs at vaporqualities between 0.1 and 0.5 depending on uid, geometry andow conditions. The heat transfer coefcient increased weaklywith increases mass ux and was almost constant. However, acomparison of the measurements against predictions from severalcorrelations showed reasonable agreement only with a very fewcorrelations except of a pool boiling equation that were developedspecically for small channels did not predict the heat transfercoefcient better.

Ngo et al.[62]investigated experimentally the thermal-hydrauliccharacteristics of microchannel heat exchangers (MCHEs) withS-shaped and zigzag ns by varying Prandtl number widely from0.75 to 2.2. The results indicate that the pressure-drop factor of theMCHE with S-shaped ns was 45 times less than that of MCHEwith zigzag ns, although Nu was 2434% less, depending on theReynolds number within its range. However, the Nucorrelation ofthe MCHE with S-shaped ns reproduces the experimental data ofoverall heat transfer coefcients with a standard deviation of72.3%, although it is 73.0% for the MCHE with zigzag ns. Thecalculated pressure drops obtained from pressure-drop factor corre-lations agreed with the experimental data within a standard devia-tion of 716.6% and 713.5% for the MCHEs with S-shaped andzigzag ns, respectively.

Wei and Joshi[63]investigated experimentally and numericallythe sidewall prole effects on ow and heat transfer inside micro-channels with diameter ranged from 53 m to 112 m. Numericalmodeling was conducted for conjugate heat transfer inside MCs. Tosimulate the practical application conditions such as those in

electronic cooling, uniform heat ux condition was applied at thebottom region while the interface of the channel was assumedadiabatic. Three different cases were considered in which thechannel proles were rectangular, positively tapered and re-entrant respectively. The results reveal that the location of themaximum velocity deviates from the mid-plane along the depthdirection due to the wall taper. In addition, for constant heat uxcondition, serious degradation in overall heat transfer occurs forchannel with 51slope. For conjugate heat transfer, the degradationin heat transfer was much less and re-entrant channel has betterheat transfer performance than positively tapered channel. It wasconcluded that for MCs with large aspect ratio the transportcharacteristics very sensitive to the channel proles, therefore,careful design and control of the micro-fabrication process were

crucial to the performance of the micro-scale devices.



Fang et al. [64] investigated experimentally the inuences oflm thickness and cross-sectional geometry on hydrophilic micro-channel condensation, with aspect ratios ranged from 1 to 5 andhydraulic diameters ranged from 100m through 300 m. Theresults reveal that the experimental measurement qualitativelymatches the prediction of previous theoretical models accountingfor the surface tension effect, which highlights the importance ofsurface tension force and channel geometry in the MC condensa-

tion. In addition, the pressure drop increased linearly with bothinlet vapor mass ux and inlet vapor mass owrate. Under thesame vapor ow rate and aspect ratio, the channel with thesmaller hydraulic diameter exhibits the higher pressure drop.While the pressure drop reduced with increases the hydraulicdiameters so does the mean heat ux. Therefore, the optimizationof hydrophilic channel geometry for lm condensation enhance-ment lies in the trade-off between these two factors. If thepumping power of the compact heat exchanger is primary con-cern, a larger channel was more desirable considering its smallpressure drop. In contrast, if heat exchanger size or channel lengthis the primary limit, a smaller channel was more favorable due toits high mean heat ux.

Bogojevic et al.[65]investigated experimentally the effects of non-

uniform heating on

ow boiling instabilities in microchannel-basedheat sink using water as the cooling liquid. The results indicate thatthe onset of boiling caused metastable non-uniform ow distribution,with boiling in some channels and single-phaseow in others, leadingto transverse variations in temperature that were less severe when thehotspot was at the downstream position. The non-uniformity wasattributed to statistical variations in the small numbers of stablebubble nucleation sites per channel. In addition, the oscillations weresuperimposed on the non-uniform ow distributions. At low hotspotheat ux, there were high amplitude oscillations at a dominant lowfrequency (HALF). With increasing heat ux, this changed progres-

sively to lower amplitude oscillations at higher frequency (LAHF). Inthe HALF regime, synchronized uctuations in the wall temperatureoccurred in channels with and without boiling, indicating that theoscillations were not driven by the growth of conned bubbles inindividual channels.

Wang et al. [66]investigated experimentally the effects of inlet/outlet congurations onow boiling instability in parallel microchan-nels have a 30 mm length and a hydraulic diameter of 186 m. Three

types of inlet/outlet congurations were obtained. In Type-A connec-tion, inlet and outlet conduits were perpendicular to the parallel MCsin the test section. In Type-B connection, uid could ow into and exifrom the parallel MCs without any restriction, and in Type-C connec-tion, uid entered each of the MCs through an inlet restriction. Theresults indicate that the amplitudes of temperature and pressureoscillations in Type-B connection was much smaller than those inType-A connection under the same heat ux and massux conditionsNearly steady ow boiling exists in the parallel MCs with Type-Cconnection under the experimental conditions as shown in Fig. 6Therefore, this conguration was recommended for high-heatux MCapplications. The experimental data of pressure drop was higher andheat transfer coefcients was lower for boiling ow at high vaporquality in MCs than those predicted from correlation equations for

boiling

ow in MCs, due to local dryout.Hernando et al. [67] investigated experimentally uid owand heat transfer in a single-phase liquid ow micro-heaexchanger, characterized by MCs of 100 100 m and200 200 m square cross section. The deionized water waused as a working uid. The results show good agreement withthe general theory and no special effect related to the smaldimension of the channels was observed. In addition, no heattransfer increment appeared as a result of the small channeldimensions. For very low Reynolds numbers, the results showdiscrepancies with the available models and correlations, which

Fig. 6. Parallel microchannels with three different inlet/outlet connections [66]. (a) Type-A connections: ow entering and exiting from paral microchannels withrestrications because inlet/outlet conduit perpendicular to microchannels, (b) Type-B connection: ow entering to and exiting from microchannels freely withuot restriction

and (c) Type-C connection: ow entering with restriction and exiting without restriction in microchannels.



overestimate the convection coefcients which related withthe adequacy of the boundary conditions. On the other hand,the plate conduction thermal resistance was a major restrictionfor micro-heat exchanger performance. The plate thicknessand plate material were critical in the design of micro-heatexchangers.

3.2. Numerical studies on MC

Yang and Lai[68]investigated numerically the effects of forcedconvection ow of Al2O3water nanouids in the radial owcooling system using a single-phase approach. The geometricalconguration of the conned radial ow was used shown inFig. 7.The two plates separated by a gap were parallel and stationary.The lower disk (with nozzle) acts as the insulated connementplate, while the upper one (wafer) was subjected to a constantheatux. The numerical simulations were performed based on thefollowing conditions: volume concentration of 47 nm Al2O3nano-particle suspended within water is from 0% to 10%, ow Reynoldsnumber range from 300 to 900 with the heat ux 2438 W/m2 and3900 W/m2. The inlet uid temperature To296 K. The resultsindicate that the heat transfer coefcient increased with theincreases of Reynolds number and particle volume fraction.

Wu et al. [69] proposed a new correlation for the saturated-ow boiling critical heat ux (CHF) in microchannel for both multiand single channel congurations. The saturated CHF correlationwas proposed by using the boiling number, length to diameterratio and the exit quality. The results reveal that the boilingnumber at CHF decreased greatly with a small increase in lengthto diameter ratio Lh /dhewhen this ratio r50. The transition wasappeared in the range of 50oLh /dher150. This correlation canpredict the overall MC database accurately. This method almostpredicts 97% of the non-aqueous data and 94% of the water datawithin the 730% error band.

Shevade and Rahman [70] investigated numerically the con-vective heat transfer in rectangular and square cross sections MCsfor volumetric heat generation. Gadolinium was used as thesubstrate material and water as the working uid. The resultsreveal that the Nusselt number decreased along the x or y-axisfrom the mid-section of the channel to the corner due to smalleruid velocity which caused by larger frictional resistance at thecorner. In rectangular channels, the heat transfer coefcient valuesare higher on the longer side than on the shorter side. At a smallerow rate, the local Nusselt number decreased and the outlettemperature increased as the low velocity uid remains in contactwith the solid for a longer period of time. The pressure drop in thechannel increased as the Reynolds number increased. Nusseltnumber increased as the channel dimensions increased. For the

same channel, Nusselt number increased with Reynolds number.

Gamrat et al. [71] investigated numerically the roughnesseffects on heat transfer in thermally fully-developed laminar owsthrough microchannels. The models considered parallelepipedicelements periodically distributed on the plane walls of a micro-channel of innite span. Three-dimensional numerical simulationswere rst conducted in a computational domain extending overone wavelength in streamwise and spanwise directions. Thenumerical results reveal that the Poiseuille number Po and the

Nusselt number (Nu) increased with the relative roughness andnearly independent of Reynolds number in the laminar regime(Reo2000). In addition, the roughness increase the friction factormore than the heat transfer coefcient for a relative roughnessheight expected in the fabrication of MCs.

Mlcak et al. [72]investigated numerically the heat transfer andlaminar uidow in an array of parallel microchannels etched on asilicon substrate with water as the circulating uid. The hydraulicdiameter used was 85.6 m and aspect rations ranged from 0.10 to1.0. Reynolds number used was ranged from 50 to 400. The resultsreveal that the linearly increasing friction coefcient that wasobserved between Reynolds numbers 50 and 400 as a result ofincreased hydraulic entrance length. Friction coefcient values werefound to monotonically increase for aspect ratios approaching 0.10.

The values of inlet and outlet thermal resistance decreased foraspect ratios approaching 0.10, for the same hydraulic diameter theinlet and outlet thermal resistance and friction coefcient valueschanged very little for aspect ratios larger than 0.50.

Chen et al. [73] investigated numerically the heat transfer anduidow in noncircular microchannel heat sink. The cooling uid inthe channel used was deionized water. The geometries for thetriangular, rectangular and trapezoidal channel were used, 129.6m,40 m and 158 m, respectively. The results reveal that, the circum-ferential average Nusselt number has a much higher value at the inletregion but it quickly approaches the constant fully developed value.The liquid and solid temperature increased along the ow direction.In addition, the Poiseuille number in MCs with a certain cross sectionremained almost constant and independent with the Reynoldsnumber for fully developed laminar ow which was similar to uidow in MCs. Triangular MC heat sink has the highest thermalefciency among the three heat sinks, the trapezoidal MC was inferiorto triangular but superior to rectangular.

Zhu and Liao[74]investigated theoretically the laminar forcedheat transfer for a gas ow through a microchannel of arbitrarycross section with axial constant heat ux and circumferentialvaried wall temperature boundary condition in the slip ow andtemperature-jump regime. The inuences of Knudsen number, thechannel aspect ratio, and the thermal boundary condition on heattransfer behavior were estimated. The results indicate that for arectangular and triangular microchannel, the average Nusseltnumbers were smaller than those of a macrochannel with thesame thermal boundary conditions and it decreases with increas-ing Knudsen number. Knudsen number has more signicant

inuences on the average Nusselt number of the rectangularmicrochannel with a smaller channel aspect ratio. The varyingtrends of the average Nusselt number with the channel aspectratio were similar at various Kn numbers. The channel aspect ratiohas few effects on the average Nusselt number ratio at a xedKnudsen number within a moderate range of channel aspect ratio.

Ji et al. [75] investigated numerically the wall roughness ongaseous ow and heat transfer in a microchannel with lengthrange from 1 m to 100 m. The effect was examined for gas owsunder inlet Mach number ranged from 0.0055 to 0.202. TheReynolds number used was ranged from 0.001 to 100. The resultsindicated that the rough elements restrict the upstream gas owand cause more pressure drop and increase the Poiseuille numberdue to the obstruction effect and formation of recirculation

regions. Rareed ow was sensitive to the shape of roughness

Fig. 7. geometrical conguration[68].



elements. The average Poiseuille number increased not only as theroughness height increases but also as the spacing distancebetween the roughness elements was decreased. However, thiseffect was much stronger on the gas ow with a lower Knudsennumber. In addition, for a highly compressible ow, the averageNusselt number does not change much or increases slightly. Theexistence of wall roughness enhances the heat transfer.

Sui et al. [76] investigated numerically laminar liquid water

ow and heat transfer in three-dimensional wavy MCs withrectangular cross section under constant wall heat ux. In theconjugate simulation, a uniform heat ux was applied at thebottom wall of the silicon substrate and on the upper surfaceadiabatic boundary condition was employed. The results revealthat when liquid coolant ows through the wavy MCs, second-ary ow (Dean vortices) was generated. The quantity and thelocation of the vortices may change along the ow direction,leading to chaotic advection, which can greatly enhance theconvectiveuid mixing, and thus the heat transfer performanceof the wavy MCs was much better than that of straight MCs withthe same cross section. In addition, the pressure drop penaltyof the wavy MCs was much smaller than the heat transferenhancement.

Muhammad et al.[77]investigated numerically the convectiveheat transfer in a composite trapezoidal microchannel with length23 mm during magnetic heating. The channel was formed byetching a silicon 100 m wafer and bonding it with a slab ofgadolinium with height varied between 1.5 mm and 5 mm. Rey-nolds number used was ranged from 1000 to 3000. The roughnessheight used was 0.35 nm for silicon MC surface and 1 nmfor gadolinium. Magnetic eld used was ranged from 2.5 T to10 T. The results reveal that for a smaller ow rate, the outlettemperature increased as a lower velocity uid remains incontact with the solid for a longer period of time. The peripheralaverage heat transfer coefcient and Nusselt number decreasedalong the length of the channel due to the development ofthermal boundary layer. Increasing the channel spacing slightlyincreased the local Nusselt number all along the length of thechannel. The Nusselt number increased with decrease of channelhydraulic diameter at any given Reynolds number due to higheruid velocity. Compared to helium and FC-72, water providesbetter thermal performance with higher values of Nusseltnumber.

Liu et al. [78] investigated numerically uid ow and heattransfer in MC cooling passages. Two-dimensional simulation wasperformed for low Reynolds number ow of liquid water withdiameterD 100m of single channel subjected to localized heatux boundary conditions. The results reveal that the heat transferenhancement due to viscosity-variation was pronounced, thoughthe axial conduction introduced by thermal-conductivity-variationwas insignicant unless for the cases with very low Reynoldsnumbers.

Renksizbulut et al. [79] investigated numerically rareed gasow and heat transfer in the entrance region of rectangular MC inthe slip-ow regime. The Reynolds number used was ranged from0.1 to 10, channel aspect ratio ranged from 0 to 1 and the Knudsennumber wasKnr0.1. The results indicate that the slip-ow regimewas associated with very large reductions in wall friction and heattransfer in the entrance region. Fully developed values of frictioncoefcient and heat transfer rates were more inuenced withrarefaction effects in a at channel than a square duct due to themajor inuence of channel corners where rarefaction effectslargely vanish.

Niazmand et al.[80]investigated numerically the velocity andtemperature elds in the slip-ow regime in trapezoidal MCs withconstant wall temperatures. The range of channel aspect ratio used

was from 0.25 to 2, side angles from 301to 901and the Reynolds

number ranged from 0.1 to 10. The prandtl Number used wasPr1. The results reveal that the major reductions in the frictionand heat transfer coefcients were observed in the entranceregion due to large amounts of velocity-slip and temperature

jump. The friction coefcient decreased strongly both withincreasing the Knudsen number and aspect ratio but has a weakerdependence on the side angle.

Khadem et al.[81]investigated numericallyuidow and heat

transfer characteristics in MCs at slip ow regime with considera-tion of slip and temperature-jump. The results reveal that therough elements restrict the upstream gas ow and cause morepressure drop and increases in the Poiseuille number due to theobstruction effect. Roughness has more signicant effect on higherKnudsen number ows with higher relative roughness. The chan-ging in roughness shape leads to extremely different ow patternsexcept for small relative roughness.

Zade et al. [82] investigated numerically the effects ovariable physical properties on the ow and heat transfecharacteristics of simultaneously developing slip-ow in rec-tangular MCs with constant wall temperature. The Reynoldnumber used was set equal to 0.1. The inlet gas temperature inall simulations was specied to be Tin300 K, and the wal

temperature was Tw350 K. The results indicate that in theentrance region, Nusselt number was only affected by thechange in the Knudsen number and was higher in variable-density slip-ow cases. The Nusselt number was generallyhigher in the variable-property simulations. In the fully-developed region, since the effect of density change diminishesfriction coefcient and Nusselt number predictions of thevariable-property simulations were higher in comparison tothose of the constant-property cases.

Shokouhmand and Bigham [83] investigated numerically theeffects of Knudsen number and geometry on thermal and hydro-dynamic characteristics of ow in the wavy microchannel aconstant Reynolds number. The results reveal that the Nusselnumber and Cf. Re decreased with Knudsen number. In thedivergent parts, Nusselt number experiences a rapid decreaseThe very high heat transfer rate andCf.Reat the entrance declinesrapidly as the thermally-hydraulically developingow approachesfully developed ow. In addition, the effect of viscous dissipationhas a considerable effect in MCs and this effect can be moresignicant by increasing Knudsen number.

Mohammed et al. [84,85] investigated numerically the inu-ence of channel shapes (zigzag, curvy, wavy) on the thermal andhydraulic performance of microchannel heat sink (MCHS). TheReynolds number used was ranged from 100 to 1000 for alchannel ow shapes. Water was used as a working uid. The inlettemperature of water used was 293 K and the heat ux at the topplate of MCHS was 100 W/m2. The results reveal that, the tem-perature and the heat transfer coefcient of the zigzag MCHS wasthe least and greatest, respectively, comparing to other channe

shapes. The second best thermal performance was provided bycurvy channels after the wavy channels. The zigzag MCHS was thebest channel for the best thermal performance, while the stepMCHS was the best channel for the hydraulic performance withmoderate degradation of heat transfer compared to conventionastraight MCHS

Kosar [86] investigated numerically the effect of substratethickness and material on heat transfer in microchannels heasink. The size of the MCs used (200 m 200 m, 5 cm long)The substrate thickness was ranged from 100 m to 1000 mand the MEMS materials used (polyimide, Silica Glass, Quartzsteel, silicon and copper). Temperature, pressure and velocitydistributions across a MC heat sink were found under a broadrange of Reynolds number and heat transfer using water as a

working uid. The results reveal that a very good agreement



between the model results and the theoretical predictioncorresponding to constant heat ux boundary condition forReynolds number Reo976 was observed, beyond Re 1000Nusselt number results were greater than the theoretical valueof Nusselt number for developed ows due to developingeffects. The Nusselt number was lower for low thermal con-ductivity materials than the Nusselt number obtained from highconductivity materials. The weaker dependence of substrate

thickness on Nusselt number compared to the effect of thermalconductivity was because of the existing constraint in the ratioof substrate thickness to the MC size.

Mohammed et al.[87,88]investigated numerically the inu-ences of nanouids on parallel ow square and rectangularmicrochannel heat exchanger (MCHE) performance. Four differ-ent nanouids (aluminum oxide (Al2O3), silicon dioxide (SiO2),silver (Ag) and titanium dioxide (TiO2) with three nanoparticlevolume fraction of 2%, 5% and 10% were used with water asbase uid. Reynolds number used was ranged from 100 to 800.The results reveal that as the nanoparticle volume fractionincreased, the bulk average temperature of the cold uidincreased and the heat transfer rate decreased. On the otherhand, as the Reynolds number increased, the average bulk

temperature of the cold

uid decreased and the heat transferrate increased. In addition, aluminum oxide nanouid has thehighest heat transfer coefcient among all the nanouidstested. The presence of nanoparticles increase the pressuredrop slightly with silver nanouid has the lowest pressure drop,while the highest difference of pressure drop f

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