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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

FLOW AND HEAT TRANSFER SIMULATION INMINI CHANNEL

Twinkal M Bhavsar1* and Manish Maisuria1

*Corresponding Author: Twinkal M Bhavsar, twinkal7107@gmail.com

This paper presents the a numerical simulation of a front side of mini channel (for z = 0 surface)to investigate the temperature distribution obtained by solid domain using boundary conditions .Here uniform heat flux is applied to the bottom side of the mini channel top surface is assumedto be adiabatic and remaining two surfaces are selected to be symmetric. The variation ofmaximum temperature of the periphery of the mini channel with the different values of the flux isillustrated in this study. Here thermal characteristics of the mini channel is represented bymaximum temperature obtained by the periphery of the mini channel. In order to obtain thebehaviour of thermal conductivity of the material in heat transfer characteristics of the minichannel three different solid material is used one is copper which has highest thermal conductivitysecond one is stainless steel which is lower thermal conductive material and third one is siliconwhose thermal conductivity ranges between the thermal conductivity of the other two solidmaterials copper and stainless steel. For the cooling purpose of the mini channel three differentcooling fluids are taken into analysis water, engine oil and mercury. And also comparing theresults of the best fluid and solid to that of the results obtained by researchers.

Keywords: laminar flow, Mini channel, Fluent, Mercury, Water, Engine oil

INTRODUCTIONMini Channel Heat ExchangerClassification of heat exchangers are basedon the working principles, geometry ofconstruction, heat transfer mechanisms, fluidflow arrangements, and transfer processes.They can also be classified based on sizesand surface area to volume ratio. Based on

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Int. J. Mech. Eng. & Rob. Res. 2014

1 Department of Mechanical Engineering, Chhotubhai Gopalbhai Patel Institute of Technology, Bardoli.

channel dimensions, especially thecharacteristic length or hydraulic diameter, twomain classification schemes are available inopen the literature which is shown in tablebelow.

Channels are of different cross sectionsmay be its circular, triangular, rectangular,trapezoidal, etc. Channel used for the current

Research Paper

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

study is the circular shape mini channel.Circular channels are most likely as shown inFigure 1. The MICHX used in the current studyis of rectangular shape and holes are placedin this rectangular space of different materialsand mini channels are placed inside the holesof this rectangular block. There is no gap inbetween adjacent channels for fluid interaction.Flat heat transfer surfaces at the top and thebottom faces of each holes offer the fluid flowan excellent contact with the heating surfaces,which leads to elevated heat transfer over theconventional heat exchangers of isolated tuberows. Flow, in a cross-flow orientation, overtubes in inline or staggered arrangement, which

is widely used in many conventional heatexchangers applications forms a wake regionat the rear of each tube when fluid is flowing inthe tube. Figures 1 and 2 illustrate thedifferences between tubes and monolithicchannels structures inside heat exchangercore.

Why to Choose Smaller FlowPassages?Fluid flow inside channels is at the heart ofmany natural systems. Heat and mass transferis accomplished across the channel walls inbiological systems as well as in many man-made systems. In general, in mini channeltransportation of heat occurs through the solidregion and fluid is passing through the fluidregion means through holes of the block. Assome surface of the slab is heated so muchso that the need of cooling this plate or slab isnecessary so for that this mini channels areused block is placed on that heated surfaceand cold fluid is passing through this holes asthe fluid is passing through this holes hotsurfaces exchanges heat from hot surface tothe cold fluid so the fluid get heated and thenthis fluid is removed and new fluid is insertedagain and again.

A channel serves to accomplish twoobjectives:

1. Bring a fluid into intimate contact with thechannel walls; and

2. Bring fresh fluid to the walls and remove fluidaway from the walls as the transport processis accomplished.

Classification of ChannelsA classification of the channels is describedin given table:

Figure 1: Circular Shapes Mini ChannelFlow Passage

Figure 2: Circular Channels Inside SolidDomain

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

Special characteristics of the mini channelare a s discussed below:

• High surface area per unit volume and highheat transfer coefficient.

• The ratio of area cross- section of the solidsubstrate to that of the fluid domain is quitesmall. And as a result of high heat transfercoefficient with high conductive material,the conduction resistance of the substrateis comparable to the convective resistance.

• Considering a single cell from many parallelcells forming the minichannel heat sink, theheat is supplied to one side of the substrate(at the bottom side) while the other threesides are considered as adiabatic surface(assuming the channel is cut from two sidedwhile the topside is assumed to have anegligible heat losses). The result of thisarrangement dictates the mini/microchannel to have variable heat flux aroundthe channel perimeter.

All the above mentioned concerns imposesthat the heat transfer condition which the fluid

actually experiences at the solid-fluid interfacesignificantly deviates from the conventionaluniform heat flux or uniform wall temperatureheat transfer problem heat transfer problem.

Here in this study addressing the effect ofheat flux magnitude which is applied on one ofthe surface of the mini channel, on the heattransfer characteristics. and for thisrepresentation discussion effect of heat fluxvalues are compared with maximumperipheral temperature. Here analysis isperformed with the help of three solid substratematerials copper, silicon and stainless still. Theanalysis is performed with three differentcooling liquids mercury, water and engine oil.

MATHEMATICAL MODELLINGFor investigation about the heat transfer in minichannel heat sink, the geometricalconfiguration of the mini channel heat sink isas shown in Figure 3.

It is a plate of length L, width W and heightH in which number of cells are there from whichfluid is flowing and all the cells are of samediameter and distance between two cells isalso same for all.

Microchannels 1-100 m

Meso-channel 100 m-1 mm

Compact passages 1-6 mm

Conventional passages > 6 mm

Table 1: Channel Classification Accordingto Mehendale

Conventional Passages > 3 mm

Minichannels 3 mm > D > 200 m

Microchannels 200 m > D > 10 m

Transitional Microchannels 10 m > D > 1 m

Transitional Nanochannels 1 m > D > 0.1 m

Nanochannels 0.1 m > D

Table 2: Channel Classification Accordingto Kandlinkar

Figure 3: Geometrical Configurationof the Two Different Heat Sink

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

The assumptions which have been takeninto account are as follows:

1. The fluid is newtonian and incompressiblewith constant physical properties in steadystate heat transfer problem.

2. Negligible viscous heat dissipation.

3. The flow is laminar.

4. Hydrodynamic and thermal developing flow.

5. Body force is neglected and no externalforce is applied.

6. The radiation heat transfer is neglected.

7. Thermal conductivity of the solid substrateis constant.

8. No heat generation.

Here this problem of heat transfer in minichannel, conjugate heat transfer problem isconsisting of the flowing fluid and the channelwall is governed by the respective energyequations in 3D form. Here, we are selectingone cell for the calculation of temperaturedistribution in solid region as show in Figure4. This is attributed to the symmetrical designof the many cells forming the mini channelheat sink.

Here, Heat is supplied to the bottom sideof the substrate, the top side of the substrateis assumed to be adiabatic (negligible heat

loss) and the other two sides are consideredas symmetry boundary condition.

The governing equations for theconservation of mass, momentum and energyin the solid and liquid regions in circular minichannels are as follows:

Governing Equation for FluidDomain

011

zVV

rV

rrV z

r ...(1)

rP

fV

rzVVV

rV

rVV zr

11 2

Vrr

VzV

rrV

rrVv 222

2

22

2 211...(2)

rP

frVV

zVVV

rV

rVV rzr

1

rVrr

VzV

rrV

rrVv 222

2

22

2 211

...(3)

zP

fzVVV

rV

rVV z

zzz

r

1

2

2

2

2

22

2 11zV

zV

rrV

rrVv zzz ...(4)

zTVT

rV

rTV f

zff

r

2

2

2

2

22

2 11

ffff TTrr

Trr

T...(5)

Solid DomainNow for solid domain, assuming steady stateconditions and constant properties of the wall,the energy equation for this region is as follows:

02

2

2

2

2

2

zT

yT

xT sss ...(6)

Figure 4: Geometrical Configurationof Domain for the Unit Cell

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

Since it is a mini channel simulation problemwe have to use cylindrical coordinate systemto simulate the model convection within thecircular channel while the cartesian coordinatesystem is used to simulate the conductionwithin the solid substrate domain.

Boundary ConditionsAt Inlet SectionAt the inlet section of the fluid domain,

• Velocity and temperature are considered asuniform,

• For the solid domain velocity is zero, and

• Wall is adiabatic.

At ininin fffzr TTVVVVdrz ,,0,0,2

0,0

At ,0,0,2

,0 HyWxdrz

0,0

zTVVV s

zyx

At Outlet SectionFlow is assumed to be a fully developed at thechannel outlet and the outlet boundaries for thesolid domain are same as that of the inletsection:

At 0,0,2

0, 2

2

zT

zVV

rVdrLz fzr

At ,0,0,2

, HyWxdrLz

0,0

zTVVV s

zyx

At Solid-Fluid InterfaceNo slip condition is assumed at the wallinterface between the solid and fluid domain:

At ,0,2

,0 zr VVVdrLz

rTK

rTKTT s

sf

fsf

,

At Solid WallsAdiabatic boundary conditions are applied toall the boundaries of the solid region exceptthe heat sink bottom wall , where a constantheat flux is assumed:

At ,0,0,0 LzHyx

0,0

zyxss VVV

zT

yT

At ,0,0, LzHyWx

0,0

zyxss VVV

zT

yT

At LzyWx 0,0,0

0,

zyxs

ss

s VVVqzTK

xTK

At LzHyWx 0,,0

0,0

zyxss VVV

zT

xT

RESULTS AND DISCUSIONThe numerical analysis and simulation usingANSYS software is discussed in previouschapter. Now here discussion is taken out forthe thermal characteristics of the mini channelin terms of temperature distribution. Heredifferent fluids and different solid materials aretaken one by one to each other for thesimulation. Water as cooling liquid and siliconas a substrate material are selected as thebase operating condition for mini channel heatsink with the variation of heat flux. Two fluidselection is taken out with the help of thermalproperty of the fluid. Here mercury is selecteddue to its high thermal property with respect to

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

water and other fluid engine oil acts as coolantwhich has poorer thermal properties ascompared to water. And in solid materialselection of material is done with respect tothermal conductivity. Copper has higherthermal conductivity with respect to silicon andsteel has lower thermal conductivity ascompared to silicon. So behaviour of thermalproperty (temperature distribution) isdiscussed in this section by changing fluxvalues. Surface temperature is calculated fromthe outlet temperature of the fluid domain.

At higher heat flux value, it is interesting tonote that surface temperature of periphery ofthe mini channel for coolant engine oil is higheras compared to other liquid coolant water andmercury which we have used.

Figure 5 shows the surface temperature ofmini channel periphery for copper as substratematerial used for solid domain, with changesin value of heat flux. It is seen from the figurethat engine oil has highest value of peripherytemperature as respect to other fluids waterand mercury. When fluid is water or mercury

peripheral temperature of mini channel isalmost same for both fluids when solid materialis copper. Figure 6 shows the surfacetemperature of mini channel periphery forstainless steel as substrate material used forsolid domain, with changes in value of heatflux. It is seen from the figure that engine oilhas highest value of periphery temperature asrespect to other fluids water and mercury.When fluid is water or mercury peripheral

Figure 5: Peripheral TemperatureDistribution for Copper as Substrate

Material

Figure 6: Peripheral TemperatureDistribution for Steel as Substrate

Material

Figure 7: Peripheral TemperatureDistribution for Silicon as Substrate

Material

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

temperature of mini channel is almost samefor both fluids when solid material is stainlesssteel. Figure 7 shows the surface temperatureof mini channel periphery for silicon assubstrate material used for solid domain, withchanges in value of heat flux. It is seen fromthe figure that engine oil has highest value ofperiphery temperature as respect to otherfluids water and mercury. When fluid is wateror mercury peripheral temperature of minichannel is almost same for both fluids whensolid material is silicon. Figure 8 shows thesurface temperature of mini channel peripheryfor water used as fluid for fluid domain, withchanges in value of heat flux. It is seen fromthe figure that stainless steel has highest valueof periphery temperature as respect to othersolid materials copper and silicon. When solidsubstrate material is copper or siliconperipheral temperature of mini channel isalmost same for both solids when fluid used iswater. Figure 9 shows the surface temperatureof mini channel periphery for mercury used asfluid for fluid domain, with changes in value ofheat flux. It is seen from the figure that stainless

steel has highest value of peripherytemperature as respect to other solidmaterials copper and silicon. When solidsubstrate material is copper or siliconperipheral temperature of mini channel isalmost same for both solids when fluid used ismercury. Figure 10 shows the surfacetemperature of mini channel periphery forengine oil used as fluid for fluid domain, withchanges in value of heat flux. It is seen from

Figure 8: Peripheral TemperatureDistribution for Water as Coolant Medium

Figure 9: Peripheral TemperatureDistribution for Mercury as Coolant

Medium

Figure 10: Peripheral TemperatureDistribution for Engine Oil as Coolant

Medium

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

the figure that stainless steel has highest valueof periphery temperature as respect to othersolid materials copper and silicon. When solidsubstrate material is copper or siliconperipheral temperature of mini channel isalmost same for both solids when fluid used isengine oil. As shown in the graph wheneverhigh thermal conductive material is used forsolid domain (stainless steel) the peripheraltemperature difference is higher as comparedto the lower thermal conductive material.Copper as substrate material comes in thecentre of the other two solid substrate materialwhen using all fluids which is discussed earlierone by one as shown in the Figures 8-10. Andthe results of the copper material obtained bysimulation is nearly same as that of silicon tillthe results of the silicon is so good ascompared to other solid materials.

As the fluid is selected one by one for allsolid substrate materials from the graph ofdifferent values of heat flux against themaximum peripheral temperature of the minichannel, the results of the mercury as fluid isselected as best since it gives highest heat

transfer coefficient value as compared to otherfluids. And also temperature distribution on theperiphery of the mini channel is also lowest asshown in graph of mercury as fluid. So if thevalue of the maximum peripheral temperatureof the mini channel and heat transfer coefficientis lower and higher respectively. Figure 11shows the peripheral temperature distributionfor copper as solid substrate material andmercury as fluid since it gives best results forcooling purpose. Figure12 shows the variationof average bottom surface temperature of themini channel to that of the obtained byresearcher M. Khamis Mansour. This Figure11 shows that as the area of the solid substrateis increases the average bottom surface of themini channel is also increases. as shown inFigure 12 there is about 168.6 K temperaturedifference obtained when area of the soliddomain is increases from 3.3 × 4.0 mm to 8.13× 8.13 mm. Since the area used by researcherM. Khamis Mansour is small as compared tothe domain used in this study, average oftemperature of bottom surface is obtainedabout 393.14 K and average of the bottom

Figure 11: Peripheral TemperatureDistribution of Silicon and Mercury

Figure 12: Average Bottom Surface Temp.for Silicon and Mercury as Solid and Fluid

Material

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Int. J. Mech. Eng. & Rob. Res. 2014 Twinkal M Bhavsar and Manish Maisuria, 2014

surface temperature of the domain used forthe study is 561.75 K. So as the area of thesolid domain increases heat transfer area alsoincreases and therefore higher temperatureobtained in this study. So, Whenever channelused for cooling purpose select lowest crosssection as possible of the solid domain so thataverage surface temperature of the bottomsurface is low and it cools the domain.

CONCLUSIONFrom the above study following conclusionsmay occur:

• The behaviour of the periphery of the minichannel is very different when domain issubjected to the higher heat flux value orwhen it is subjected to lower heat fluxvalue.

• Temperature difference of the periphery ofthe mini channel is higher when the soliddomain is of the higher thermal conductivematerial.

• At maximum value of the heat flux (320 KW/m²) steel with engine oil has highestperipheral temperature and silicon andmercury has lowest peripheral temperature.

• With the increase in the area of the soliddomain, average bottom surfacetemperature of the mini channel is alsoincreases.

REFERENCES1. Al Omari S-A B (2011), “Enhancement

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2. Amador M Guzman, Maximiliano P Beiza,Andres J Diaz, Paul F Fischer and JuanC Ramos (2013), “Flow and Heat TransferCharacteristics in Micro and MiniCommunicating Pressure Driven ChannelFlows by Numerical Simulations”,International Journal of Heat and MassTransfer, Vol. 58, pp. 568-577.

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4. Khamis Mansour M (2013), “NumericalAnalysis of Conjugate Heat Transfer forCircular Liquid Mini Channel”, JPJournal of Heat and Mass Transfer,Vol. 7, pp. 85-111.

5. Mostafa Keshavarz Moraveji, RezaMohammadi Ardehali and Ali Ijam C F D(2013), “Investigation of Nanofluid Effects(Cooling Performance and PressureDrop) in Mini-Channel Heat Sink”,International Communications in Heatand Mass Transfer, Vol. 40, pp. 58-66.

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