Research Article CFD Simulation of Heat Transfer and ...Simulations were carried out using ANSYS...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 895374 10 pageshttpdxdoiorg1011552013895374

Research ArticleCFD Simulation of Heat Transfer and Turbulent Fluid Flow overa Double Forward-Facing Step

Hussein Togun12 Ahmed Jassim Shkarah23 S N Kazi1 and A Badarudin1

1 Department of Mechanical Engineering University of Malaya 50603 Kuala Lumpur Malaysia2 Department of Mechanical Engineering University of Thi-Qar 64001 Nassiriya Iraq3 Department of Mechanical Engineering Universiti Teknikal Malaysia Melaka 75450 Melaka Malaysia

Correspondence should be addressed to Hussein Togun htokan 2004yahoocom

Received 31 August 2013 Revised 10 November 2013 Accepted 10 November 2013

Academic Editor Oluwole Daniel Makinde

Copyright copy 2013 Hussein Togun et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Heat transfer and turbulent water flow over a double forward-facing step were investigated numerically The finite volume methodwas used to solve the corresponding continuity momentum and energy equations using the119870-120576modelThree cases correspondingto three different step heights were investigated for Reynolds numbers ranging from 30000 to 100000 and temperatures rangingfrom 313 to 343K The bottom of the wall was heated whereas the top was insulated The results show that the Nusselt numberincreased with the Reynolds number and step height The maximum Nusselt number was observed for case 3 with a Reynoldsnumber of 100000 and temperature of 343K occurring at the second step The behavior of the Nusselt number was similar for allcases at a given Reynolds number and temperature A recirculation zone was observed before and after the first and second stepsin the contour maps of the velocity field In addition the results indicate that the coefficient pressure increased with increasingReynolds number and step height ANSYS FLUENT 14 (CFD) software was employed to run the simulations

1 Introduction

The goal of this study is to investigate two-dimensionaldouble forward-facing step flows and the results of numericalcomputations for different step heights temperatures andReynolds numbers are presented herein Numerous studieshave been performed on single forward- and backward-facing steps however the literature on double forward-and backward-facing steps is very limited and the phys-ical basis of flow separation and vortex creation remainsunclear Fluid flow over a backward- or forward-facing stepgenerates recirculation zones and subsequent reattachmentregions due to sudden contraction or expansion in flowpassages Many practical engineering applications such asthe cooling of electronic devices open channels power-generating equipment heat exchangers combustion cham-bers and building aerodynamics involve separating flowsThe first attempts to study heat transfer and fluid flow overforward- or backward-facing steps were made in the 1950rsquosLater researchers were able to analyze complex flows in three

dimensions due to the development of CFD software Sebanet al [1] and Seban [2] pioneered the study of fluid flowover backward- and forward-facing steps from a heat transferperspective The authors discovered that the maximum heattransfer coefficients occur at the reattachment point anddecrease toward the outlet The effect of stream turbulenceon the heat transfer rate in the reattachment region on thebottom surface of a backward-facing step was demonstratedby Mabuchi et al [3] Improvements in device capabilitieshave allowed researchers tomeasure reattachment points andheat transfer characteristics Mori et al [4] used a thermaltuft probe Kawamura et al [5 6] obtained the temporaland spatial parameters of heat transfer in the reattachmentregion using a new heat flux probe and Oyakawa et al [7 8]employed jet discharge The hydrodynamic characteristics ofgas flows past a rib and a downward step in feature separationflow regions were studied by Terekhov et al [9] The heattransfer coefficients temperature distributions and pressuresbehind the obstacles aswell as the 5ndash10enhancement of heattransfer at the maximum recirculation reported also agree

2 Mathematical Problems in Engineering

with the results reported by Alemasov et al [10] Aung [11]Vogel and Eaton [12] Sparrow and Chuck [13] Chen et al[14] Masatoshi and Kenichiro [15] and Khanafer et al [16]conducted numerical and experimental studies on the airflowover a horizontal backward-facing step with uniform heatflux or uniform temperatureThe authors observed a decreasein the Nusselt number and recirculation zone with increasingbuoyancy force and noted that themaximumNusselt numberwas observed at the reattachment point Abu-Mulaweh [17]experimentally studied the turbulent fluid flow and heattransfer of a mixed convection boundary-layer of air flowingover a vertical forward-facing step The effect of the stepheight on the local Nusselt number distribution namelythe increase in the local Nusselt number with increasingstep height reached a maximum value at the reattachmentpoint Both the inclination angle and step height affected heattransfer and flow behavior for the single forward-facing stepstudied numerically by Nassab et al [18]

An early study on turbulent heat transfer and airflow overa double forward-facing step was reported by Yilmaz andOztop [19] The top of the wall and steps were insulated andthe bottom of the wall was heated The authors used 119870-120576model and found that the step ratio affected the heat transferand flow more strongly than the length ratio Later Oztopet al [20] presented a numerical study of heat transfer andturbulent airflow over a double forward-facing step with anobstacle The bottom of the wall and steps were heated andthe top of the wall was insulated The results showed that theobstacle aspect ratio (Ar) affected the heat transfer with themaximum Nusselt number corresponding to Ar = 1

The objective of this paper is to contribute new dataregarding water flow over double forward-facing steps toimprove the design of heat exchangers

To the best of the authorsrsquo knowledge turbulent waterflow and heat transfer over double forward-facing steps havenot been reported in the literature thus this work is the firstsuch study

2 Numerical Model

21 Physical Model A schematic diagram of the doubleforward-facing step and the flow shape employed in this studyis presented in Figure 1The bottoms of the wall and the stepswere heated to a given temperature (119879ℎ) while the top of thewall was adiabaticThe first step height (ℎ1)was varied from 2to 6 cmwhereas the second step height (ℎ2)was fixed at 2 cmThe entrance width (119867) was 10 cm while the exit width (1198672)

was 6 4 and 2 cm according to the first step height Threecases corresponding to three step heightswere investigated asshown Table 1 In addition the Reynolds number was variedfrom 30000 to 100000 and calculated based on entrancewidth (119867) and four different temperatures from 313 to 343Kwere adopted

22 Governing Equations The SIMPLE algorithm couplesvelocity and pressure [21 22] and links the momentum andmass conservation equations using pressure corrections [23]Therefore in this study the SIMPLE algorithmwas combined

Insulated

H1 H2H

a b c

Water flow

L

Heated Th

Figure 1 Physical model

0 02 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

Grid 1Grid 2Grid 3

Nu x

X (m)

Figure 2 Comparison of Nusselt number case 1 with Re = 30000and 119879 = 313K for grid independent

with the finite volume method to discretize continuity119883119884 momentum and energy equations in the computa-tional domain The conservation equations (1) assuming twodimensions steady flowand aNewtonian fluid can bewrittenas follows Yilmaz and Oztop [19]

120597119906

120597119909+120597V

120597119910= 0

120588 (119906120597119906

120597119909+ V

120597119906

120597119910) = minus

120597119901

120597119909+ 120583(

1205972119906

1205971199092+1205972119906

1205971199102)

120588 (119906120597V

120597119909+ V

120597V

120597119910) = minus

120597119901

120597119910+ 120583(

1205972V

1205971199092+1205972V

1205971199102)

120588(119906120597119879

120597119909+ V

120597119879

120597119910) =prop (

1205972119879

1205971199092+1205972119879

1205971199102)

(1)

Mathematical Problems in Engineering 3

0 02 04 06 08 1 12 14 160

1400

2800

4200

5600

7000

8400

9800

11200

12600

14000

X (m)

Nu x

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 160

2100

4200

6300

8400

10500

12600

14700

16800

18900

21000

X (m)N

u xRe = 30000

Re = 50000

Re = 80000Re = 100000

(b)

Re = 30000

Re = 50000

Re = 80000

Re = 100000

0 02 04 06 08 1 12 14 160

4800

9600

14400

19200

24000

28800

33600

38400

43200

48000

X (m)

Nu x

(c)

Figure 3 (a) Distribution of local Nusselt number for case 1 with 119879 = 313K and different Reynolds number (b) Distribution of local Nusseltnumber for case 2 with 119879 = 313K and different Reynolds number (c) Distribution of local Nusselt number for case 3 with 119879 = 313K anddifferent Reynolds number

Table 1 Cases and dimensions of geometries

Cases 119867 (cm) ℎ1 = 119867 minus 1198671 ℎ2 = 1198671 minus 1198672 119886 (cm) 119887 (cm) 119888 (cm)1 10 2 2 100 20 402 10 4 2 100 20 403 10 6 2 100 20 40


0 02 04 06 08 1 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Nu x

T = 313KT = 323K

T = 333KT = 343K

X (m)

(a)

0 02 04 06 08 1 12 14 160

2000400060008000

100001200014000160001800020000220002400026000280003000032000

X (m)N

u x

T = 313KT = 323K

T = 333KT = 343K

(b)

040008000

120001600020000240002800032000360004000044000480005200056000600006400068000

0 02 04 06 08 1 12 14 16X (m)

Nu x

T = 313KT = 323K

T = 333KT = 343K

(c)

Figure 4 (a) Local Nusselt number distribution for case 1 with Re = 100000 and different temperatures (b) Local Nusselt numberdistribution for case 2 Re = 100000 and different temperatures (c) Local Nusselt number distribution for case 3 with Re = 100000 anddifferent temperatures


0 02 04 06 08 1 12 14 160

5000

10000

15000

20000

25000

30000

35000

40000

45000

Case 1Case 2Case 3

X (m)

Nu x

Figure 5 Effect step height on local Nusselt number for cases 1 2and 3 at Re = 100000 and 119879 = 313K

Table 2 Value of the constants in transport equations

Value of constants1198621120576 1441198622120576 1921198623120576 009120590119896

10120590120576 13Pr 701

Table 3 Computational conditions

Computational conditionsFluid WaterPressure-velocity coupling(Scheme) Simple

Density 9982 gm3

Viscosity 0001 kgmsdotsPressure 101325 PaViscous model 119896 and 120576Reynolds number(Re = 120588119880119867120583)

30000 50000 80000 100000

Temperature 313 323 333 343K

The standard 119896-120576 turbulence model was employed for turbu-lence flow modeling [24] In FLUENT near-wall treatmentbased on standard wall functions was selected for highaccuracy results where it was suggested by Chung and Jia[25] for predication separation flow and heat transfer insudden expansion The transport equations were applied to

determine the turbulence kinetic energy 119896 (2) and dissipationrate 120576 (3)

120597

120597119909(120588119896119906) =

120597

120597119910([(120583 +

120583119905

120590119896

)120597119896

120597119910]) + 119866119896 minus 120588120576 (2)

120597

120597119909(120588120576119906) =

120597

120597119910([(120583 +

120583119905

120590120576

)120597120576

120597119910])

+ 1198621120576

120576

119896(119866119896 + 1198623120576119866119887) minus 1198622120576120588

1205762

119896

(3)

where 119866119896 describes the generation of turbulence kineticenergy by the turbulent viscosity and velocity gradients andis computed using

119866119896 = minus1205881205921015840119906120597120592

120597119909 (4)

120583119905 is calculated using

120583119905 = 120588119862119901

1198962

120576 (5)

The values of the constants employed in the simulationsare shown in Table 2

To enhance the accuracy of the simulations the second-order upwind scheme was used Additionally after eachiteration the residual sumwas computed and stored for everyconserved variable The required scaled residual for the con-vergence criterion was less than 10minus8 for the continuity andsmaller than 10minus7 for the energy and momentum equations

3 Numerical Procedure and Code Validation

Simulations were carried out using ANSYS FLUENT 14(CFD)The ICEMwas used formeshing and the 119896-120576 standardmodel in Fluent was used to analyze the water flow and heattransfer over the double forward-facing step in the turbulentregion The computational conditions used in the numericalsimulation are shown in Table 3 Grid independence wasverified by increasing the grid size step wise which yieldedsimilar results Independent verification was performed forRe = 30000 case 1 and initial grid sizes of 9099 37397 and67117 The difference in the Nusselt number relative to thatof the selected grid was less than 1 as shown Figure 2 Thegeometric dimensions were based on those reported by [19]

4 Results and Discussion

Numerical simulations were performed for heat transfer andturbulent water flow over a double forward-facing stepThreecases with different step heights at Reynolds numbers of30000 50000 80000 and 100000 and temperatures of 313323 333 and 343K were studied

41 Nusselt Number Figures 3(a) 3(b) and 3(c) show thevariation in the local Nusselt number for cases 1 2 and 3at 119879 = 343K and different Reynolds numbers In all casesthe Nusselt number increased with the Reynolds number


0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)

Figure 6 (a) Velocity of streamline for case 1 with Re = 30000 and 119879 = 313K (1) First step (2) Second step (b) Velocity of streamline forcase 1 with Re = 50000 and 119879 = 313K (1) First step (2) Second step (c) Velocity of streamline for case 1 with Re = 80000 and 119879 = 313K(1) First step (2) Second step (d) Velocity of streamline for case 1 with Re = 100000 and 119879 = 313K (1) First step (2) Second step


0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)

Figure 7 Effect step height on recirculation region for Re = 100000 and 119879 = 313K (a) Case 1 at first step (b) Case 2 at first step (c) Case 3at first step

and a sudden increase in the Nusselt number was observedat the first and second steps due to recirculation vortices Ahigher Nusselt number occurred at the second step for case3 compared to the Nusselt numbers observed in other casesThe effect of temperature on the local Nusselt number forcases 1 2 and 3 is illustrated in Figures 4(a) 4(b) and 4(c)As shown the trends of theNusselt number are similar beforethe first and second steps and the Nusselt number decreasessharply at the same Reynolds number for all cases A decreasein temperature leads to a decrease in the Nusselt number Forall temperatures the maximum value of the Nusselt numberwas observed at the first and second steps for all cases in case3 however a higher Nusselt number occurred at the secondstep compared with the numbers observed in the other casesas shown in Figure 5

42 Flow Visualization Figures 6(a) 6(b) 6(c) and 6(d)present the contour maps of the velocity field for case 1 at119879 = 313K and various Reynolds numbers Generally therecirculation zone is found before and after the first andsecond step with the recirculation zone around the first stepbeing larger than that around the second step for a givenReynolds number and temperature The recirculation zonealso increased with Reynolds number for case 1 at 119879 = 313KThe effect of the step height on the recirculation zone isillustrated in Figures 7(a) 7(b) 7(c) 8(a) 8(b) and 8(c) forcases 1 2 and 3 Re = 100000 and 119879 = 313K Increasing the

step height increased the recirculation flow and the largestrecirculation zone was found at the first step for case 3Re = 100000 and 119879 = 313K relative to that observed in case1 and 2

43 Pressure Coefficient Figure 9(a) shows the pressure coef-ficient along the 119909-axis for case 1 at 119879 = 313K and differentReynolds numbers Increasing the Reynolds number led to anincrease in the pressure coefficients particularly at the firstand second step which in turn increased the recirculationflow and enhanced the heat transfer rate Figure 9(b) presentsthe pressure coefficients at 119879 = 313K and Re = 100000 forcases 1 2 and 3 Case 3 shows the highest pressure coefficientand thus the largest increase in the Nusselt number

Figure 10 compares the Nusselt number for case 1 withRe = 30000 and 119879 = 313K with the values reported by [1820] An acceptable agreement between the trends especiallyat the step region justifies the use of this computationalapproach For more validation compare the local Nusseltnumber for case 2 at Reynolds number of 30000 and119879 = 313K with case 10 of [19] presented in Figure 11

5 Conclusion

Turbulent forced convection and heat transfer over a doubleforward-facing step was studied Three cases correspond-ing to three different step heights were investigated at


0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)

Figure 8 Effect step height on recirculation region for Re = 100000 and 119879 = 313K (a) Case 1 at second step (b) Case 2 at second step (c)Case 3 at second step

0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)

Figure 9 (a) Variation of pressure coefficient for case 1 with 119879 = 313K and different Reynolds number (b) Effect step height on pressurecoefficient at Re = 100000 and 119879 = 313K


Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]

Figure 10 Comparison of trend of Nusselt number with [18 20] forcase 1 Re = 30000 and 119879 = 313K

0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x

Yilmaz and Oztop [19]

Figure 11 Comparison of trend of Nusselt number for case 2Re = 30000 and 119879 = 313K with case 10 of [19]

four Reynolds numbers and four temperatures The resultsshow that increasing the Reynolds number and temperatureincreased the Nusselt number for all cases The enhancementof the Nusselt number occurred at the first and second stepsdue to separation flow and the highest augmentation wasobserved at the second step for case 3 relative to the valuesobserved in cases 1 and 2 The effect of step height on the

recirculation zone increased the separation length at thesame Reynolds number and temperature which increases theNusselt number In addition the obtained results indicate anincrease in the pressure coefficient with increasing Reynoldsnumber and step height

Nomenclature

119886 Length of bottom wall before thefirst step

119887 Length of bottom wall after thefirst step

119888 Length of bottom wall after thesecond step

1198621120576 1198622120576 1198623120576 120590119896 120590120576 Model constants119862119901 Specific heat119867 Width of channel before the steps1198671 Width of channel after first step1198672 Width of channel after second stepℎ1 Height of first stepℎ2 Height of second step119871 Total length of channel119870 Turbulent energyNu Nusselt number119875 PressurePr Prandtl numberRe Reynolds number119879 Temperature119880 Mean velocity119906 V Axial velocity119883 119910 Cartesian coordinates

Greek Symbols

120588 Water density120576 Turbulent dissipation120583 Dynamic viscosity120583119905 Turbulent viscosity

Acknowledgments

The authors gratefully acknowledge Grant UMRG RP012D-13AET Tuqa Abdularazzaq (UPM) and the University ofMalaya Malaysia for support in conducting this research

References

[1] R A Seban A Emery and A Levy ldquoHeat transfer to separatedand reattached subsonic turbulent flows obtained downstreamof a surface steprdquo International Journal of Aerospace Sciencesvol 2 pp 809ndash814 1959

[2] R A Seban ldquoThe effect of suction and injection on the heattransfer and flow in a turbulent separated air flowrdquo Journal ofHeat Transfer vol 88 no 3 pp 276ndash282 1966

[3] I Mabuchi T Murata and M Kumada ldquoEffect of free-streamturbulence on heat transfer characteristics in the reattachmentregion on the bottom surface of a backward-facing step (for


different angles of separation)rdquoTransactions of the Japan Societyof Mechanical Engineers B vol 52 no 479 pp 2619ndash2625 1986

[4] Y Mori Y Uchida and K Sakai ldquoA study of the time andspatial micro-structure of heat transfer performance near thereattaching point of separated flowsrdquo Transactions of the JapanSociety ofMechanical Engineers B vol 52 no 481 pp 3353ndash33611986

[5] T Kawamura A Yamamori J Mimatsu and M KumadaldquoTime and spatial characteristics of heat transfer at the reat-tachment region of a two-dimensional backward-facing steprdquoin Proceedings of the ASME-JSME Thermal Engineering JointConference vol 3 pp 197ndash204 1991

[6] T Kawamura S Tanaka I Mabuchi and M Kumada ldquoTem-poral and spatial characteristics of heat transfer at the reat-tachment region of a backward-facing steprdquo Experimental HeatTransfer vol 1 no 4 pp 299ndash313 1987

[7] K Oyakawa T Taira and E Yamazato ldquoStudies of heat transfercontrol by jet discharge at reattachment region downstream ofa backward-facing steprdquo Transactions of the Japan Society ofMechanical Engineers B vol 60 no 569 pp 248ndash254 1994

[8] K Oyakawa T Saitoh I Teruya and I Mabuchi ldquoHeat transferenhancement using slat at reattachment region downstreamof backward-facing steprdquo Transactions of the Japan Society ofMechanical Engineers B vol 61 no 592 pp 4426ndash4431 1995

[9] V I Terekhov N I Yarygina and R F Zhdanov ldquoHeat transferin turbulent separated flows in the presence of high free-streamturbulencerdquo International Journal of Heat and Mass Transfervol 46 no 23 pp 4535ndash4551 2003

[10] V E Alemasov G A Glebov and A P Kozlov Thermo-Anemometric Methods for Studying Flows with Separation vol178 KazanrsquoBranch of the USSR Academy of Sciences KazanRussia 1989

[11] W Aung ldquoAn experimental study of laminar heat transferdownstream of backsteprdquo Journal of Heat Transfer vol 105 no4 pp 823ndash829 1983

[12] J C Vogel and J K Eaton ldquoCombined heat transfer andfluid dynamicmeasurements downstream of a backward-facingsteprdquo Journal of Heat Transfer vol 107 no 4 pp 922ndash929 1985

[13] E M Sparrow and W Chuck ldquoPC solutions for the heattransfer and fluid flow downstream of an abrupt asymmetricenlargement in a channelrdquo Numerical Heat Transfer vol 12 no1 pp 19ndash40 1987

[14] Y T Chen J H Nie B F Armaly and H T Hsieh ldquoTurbulentseparated convection flow adjacent to backward-facing step-effects of step heightrdquo International Journal of Heat and MassTransfer vol 49 no 19-20 pp 3670ndash3680 2006

[15] S I S Masatoshi and S Kenichiro ldquoControl of turbulentchannel flow over a backward-facing step by suctionrdquo Journalof Fluid Science and Technology vol 4 no 1 pp 188ndash199 2009

[16] K Khanafer B Al-Azmi A Al-Shammari and I Pop ldquoMixedconvection analysis of laminar pulsating flow and heat transferover a backward-facing steprdquo International Journal of Heat andMass Transfer vol 51 no 25-26 pp 5785ndash5793 2008

[17] H I Abu-Mulaweh ldquoTurbulent mixed convection flow over aforward-facing stepmdashthe effect of step heightsrdquo InternationalJournal of Thermal Sciences vol 44 no 2 pp 155ndash162 2005

[18] S A G Nassab R Moosavi and S M H Sarvari ldquoTurbulentforced convection flow adjacent to inclined forward step in aductrdquo International Journal of Thermal Sciences vol 48 no 7pp 1319ndash1326 2009

[19] I Yilmaz and H F Oztop ldquoTurbulence forced convection heattransfer over double forward facing step flowrdquo InternationalCommunications in Heat and Mass Transfer vol 33 no 4 pp508ndash517 2006

[20] H F Oztop K SMushatet and I Yılmaz ldquoAnalysis of turbulentflow and heat transfer over a double forward facing step withobstaclesrdquo International Communications in Heat and MassTransfer vol 39 no 9 pp 1395ndash1403 2012

[21] A H Mahmoudi M Shahi and F Talebi ldquoEntropy generationdue to natural convection in a partially open cavity with a thinheat source subjected to a nanofluidrdquo Numerical Heat TransferA vol 61 no 4 pp 283ndash305 2012

[22] M Rahgoshay A A Ranjbar and A Ramiar ldquoLaminar pulsat-ing flow of nanofluids in a circular tube with isothermal wallrdquoInternational Communications in Heat and Mass Transfer vol39 no 3 pp 463ndash469 2012

[23] S V Patankar and D B Spalding ldquoA calculation procedurefor heat mass and momentum transfer in three-dimensionalparabolic flowsrdquo International Journal of Heat and Mass Trans-fer vol 15 no 10 pp 1787ndash1806 1972

[24] B E Launder and D B Spalding ldquoThe numerical computationof turbulent flowsrdquoComputerMethods inAppliedMechanics andEngineering vol 3 no 2 pp 269ndash289 1974

[25] B T F Chung and S Jia ldquoA turbulent near-wall model onconvective heat transfer from an abrupt expansion tuberdquo Heatand Mass Transfer vol 31 no 1-2 pp 33ndash40 1995

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with the results reported by Alemasov et al [10] Aung [11]Vogel and Eaton [12] Sparrow and Chuck [13] Chen et al[14] Masatoshi and Kenichiro [15] and Khanafer et al [16]conducted numerical and experimental studies on the airflowover a horizontal backward-facing step with uniform heatflux or uniform temperatureThe authors observed a decreasein the Nusselt number and recirculation zone with increasingbuoyancy force and noted that themaximumNusselt numberwas observed at the reattachment point Abu-Mulaweh [17]experimentally studied the turbulent fluid flow and heattransfer of a mixed convection boundary-layer of air flowingover a vertical forward-facing step The effect of the stepheight on the local Nusselt number distribution namelythe increase in the local Nusselt number with increasingstep height reached a maximum value at the reattachmentpoint Both the inclination angle and step height affected heattransfer and flow behavior for the single forward-facing stepstudied numerically by Nassab et al [18]

An early study on turbulent heat transfer and airflow overa double forward-facing step was reported by Yilmaz andOztop [19] The top of the wall and steps were insulated andthe bottom of the wall was heated The authors used 119870-120576model and found that the step ratio affected the heat transferand flow more strongly than the length ratio Later Oztopet al [20] presented a numerical study of heat transfer andturbulent airflow over a double forward-facing step with anobstacle The bottom of the wall and steps were heated andthe top of the wall was insulated The results showed that theobstacle aspect ratio (Ar) affected the heat transfer with themaximum Nusselt number corresponding to Ar = 1

The objective of this paper is to contribute new dataregarding water flow over double forward-facing steps toimprove the design of heat exchangers

To the best of the authorsrsquo knowledge turbulent waterflow and heat transfer over double forward-facing steps havenot been reported in the literature thus this work is the firstsuch study

2 Numerical Model

21 Physical Model A schematic diagram of the doubleforward-facing step and the flow shape employed in this studyis presented in Figure 1The bottoms of the wall and the stepswere heated to a given temperature (119879ℎ) while the top of thewall was adiabaticThe first step height (ℎ1)was varied from 2to 6 cmwhereas the second step height (ℎ2)was fixed at 2 cmThe entrance width (119867) was 10 cm while the exit width (1198672)

was 6 4 and 2 cm according to the first step height Threecases corresponding to three step heightswere investigated asshown Table 1 In addition the Reynolds number was variedfrom 30000 to 100000 and calculated based on entrancewidth (119867) and four different temperatures from 313 to 343Kwere adopted

22 Governing Equations The SIMPLE algorithm couplesvelocity and pressure [21 22] and links the momentum andmass conservation equations using pressure corrections [23]Therefore in this study the SIMPLE algorithmwas combined

Insulated

H1 H2H

a b c

Water flow

L

Heated Th

Figure 1 Physical model

0 02 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

Grid 1Grid 2Grid 3

Nu x

X (m)

Figure 2 Comparison of Nusselt number case 1 with Re = 30000and 119879 = 313K for grid independent

with the finite volume method to discretize continuity119883119884 momentum and energy equations in the computa-tional domain The conservation equations (1) assuming twodimensions steady flowand aNewtonian fluid can bewrittenas follows Yilmaz and Oztop [19]

120597119906

120597119909+120597V

120597119910= 0

120588 (119906120597119906

120597119909+ V

120597119906

120597119910) = minus

120597119901

120597119909+ 120583(

1205972119906

1205971199092+1205972119906

1205971199102)

120588 (119906120597V

120597119909+ V

120597V

120597119910) = minus

120597119901

120597119910+ 120583(

1205972V

1205971199092+1205972V

1205971199102)

120588(119906120597119879

120597119909+ V

120597119879

120597119910) =prop (

1205972119879

1205971199092+1205972119879

1205971199102)

(1)


0 02 04 06 08 1 12 14 160

1400

2800

4200

5600

7000

8400

9800

11200

12600

14000

X (m)

Nu x

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 160

2100

4200

6300

8400

10500

12600

14700

16800

18900

21000

X (m)N

u xRe = 30000

Re = 50000

Re = 80000Re = 100000

(b)

Re = 30000

Re = 50000

Re = 80000

Re = 100000

0 02 04 06 08 1 12 14 160

4800

9600

14400

19200

24000

28800

33600

38400

43200

48000

X (m)

Nu x

(c)





0 02 04 06 08 1 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Nu x

T = 313KT = 323K

T = 333KT = 343K

X (m)

(a)

0 02 04 06 08 1 12 14 160

2000400060008000

100001200014000160001800020000220002400026000280003000032000

X (m)N

u x

T = 313KT = 323K

T = 333KT = 343K

(b)

040008000

120001600020000240002800032000360004000044000480005200056000600006400068000

0 02 04 06 08 1 12 14 16X (m)

Nu x

T = 313KT = 323K

T = 333KT = 343K

(c)



0 02 04 06 08 1 12 14 160

5000

10000

15000

20000

25000

30000

35000

40000

45000

Case 1Case 2Case 3

X (m)

Nu x




10120590120576 13Pr 701



Density 9982 gm3


30000 50000 80000 100000




120597

120597119909(120588119896119906) =

120597

120597119910([(120583 +

120583119905

120590119896

)120597119896

120597119910]) + 119866119896 minus 120588120576 (2)

120597

120597119909(120588120576119906) =

120597

120597119910([(120583 +

120583119905

120590120576

)120597120576

120597119910])

+ 1198621120576

120576

119896(119866119896 + 1198623120576119866119887) minus 1198622120576120588

1205762

119896

(3)


119866119896 = minus1205881205921015840119906120597120592

120597119909 (4)


120583119905 = 120588119862119901

1198962

120576 (5)









0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 02 04 06 08 1 12 14 160

1400

2800

4200

5600

7000

8400

9800

11200

12600

14000

X (m)

Nu x

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 160

2100

4200

6300

8400

10500

12600

14700

16800

18900

21000

X (m)N

u xRe = 30000

Re = 50000

Re = 80000Re = 100000

(b)

Re = 30000

Re = 50000

Re = 80000

Re = 100000

0 02 04 06 08 1 12 14 160

4800

9600

14400

19200

24000

28800

33600

38400

43200

48000

X (m)

Nu x

(c)





0 02 04 06 08 1 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Nu x

T = 313KT = 323K

T = 333KT = 343K

X (m)

(a)

0 02 04 06 08 1 12 14 160

2000400060008000

100001200014000160001800020000220002400026000280003000032000

X (m)N

u x

T = 313KT = 323K

T = 333KT = 343K

(b)

040008000

120001600020000240002800032000360004000044000480005200056000600006400068000

0 02 04 06 08 1 12 14 16X (m)

Nu x

T = 313KT = 323K

T = 333KT = 343K

(c)



0 02 04 06 08 1 12 14 160

5000

10000

15000

20000

25000

30000

35000

40000

45000

Case 1Case 2Case 3

X (m)

Nu x




10120590120576 13Pr 701



Density 9982 gm3


30000 50000 80000 100000




120597

120597119909(120588119896119906) =

120597

120597119910([(120583 +

120583119905

120590119896

)120597119896

120597119910]) + 119866119896 minus 120588120576 (2)

120597

120597119909(120588120576119906) =

120597

120597119910([(120583 +

120583119905

120590120576

)120597120576

120597119910])

+ 1198621120576

120576

119896(119866119896 + 1198623120576119866119887) minus 1198622120576120588

1205762

119896

(3)


119866119896 = minus1205881205921015840119906120597120592

120597119909 (4)


120583119905 = 120588119862119901

1198962

120576 (5)









0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 02 04 06 08 1 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Nu x

T = 313KT = 323K

T = 333KT = 343K

X (m)

(a)

0 02 04 06 08 1 12 14 160

2000400060008000

100001200014000160001800020000220002400026000280003000032000

X (m)N

u x

T = 313KT = 323K

T = 333KT = 343K

(b)

040008000

120001600020000240002800032000360004000044000480005200056000600006400068000

0 02 04 06 08 1 12 14 16X (m)

Nu x

T = 313KT = 323K

T = 333KT = 343K

(c)



0 02 04 06 08 1 12 14 160

5000

10000

15000

20000

25000

30000

35000

40000

45000

Case 1Case 2Case 3

X (m)

Nu x




10120590120576 13Pr 701



Density 9982 gm3


30000 50000 80000 100000




120597

120597119909(120588119896119906) =

120597

120597119910([(120583 +

120583119905

120590119896

)120597119896

120597119910]) + 119866119896 minus 120588120576 (2)

120597

120597119909(120588120576119906) =

120597

120597119910([(120583 +

120583119905

120590120576

)120597120576

120597119910])

+ 1198621120576

120576

119896(119866119896 + 1198623120576119866119887) minus 1198622120576120588

1205762

119896

(3)


119866119896 = minus1205881205921015840119906120597120592

120597119909 (4)


120583119905 = 120588119862119901

1198962

120576 (5)









0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 02 04 06 08 1 12 14 160

5000

10000

15000

20000

25000

30000

35000

40000

45000

Case 1Case 2Case 3

X (m)

Nu x




10120590120576 13Pr 701



Density 9982 gm3


30000 50000 80000 100000




120597

120597119909(120588119896119906) =

120597

120597119910([(120583 +

120583119905

120590119896

)120597119896

120597119910]) + 119866119896 minus 120588120576 (2)

120597

120597119909(120588120576119906) =

120597

120597119910([(120583 +

120583119905

120590120576

)120597120576

120597119910])

+ 1198621120576

120576

119896(119866119896 + 1198623120576119866119887) minus 1198622120576120588

1205762

119896

(3)


119866119896 = minus1205881205921015840119906120597120592

120597119909 (4)


120583119905 = 120588119862119901

1198962

120576 (5)









0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 000

50

010

015

002

(m)0 0

005

001

001

50

02

(m)

X

Y

ZX

Y

Z

(a)

X

Y

ZX

Y

Z0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

(b)

0 000

50

010

015

002

(m)

0 000

50

010

015

002

(m)

X

Y

ZX

Y

Z

(c)

X

Y

ZX

Y

Z0 000

75

001

5

002

25

003

(m)

0 000

75

001

5

002

25

003

(m)

(d)



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 001

25

002

5

003

75

005

X

Y

Z

(m)

(b)

0 001

25

002

5

003

75

005

(m)

X

Y

Z

(c)







5 Conclusion



0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 000

75

001

5

002

25

003

(m)

X

Y

Z

(a)

0 000

50

010

015

002

(m)

X

Y

Z

(b)

0 000

5

001

001

5

002

(m)

X

Y

Z

(c)


0 02 04 06 08 1 12 14 16X (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

Cp

Re = 30000Re = 50000

Re = 80000

Re = 100000

(a)

0 02 04 06 08 1 12 14 16

Case 1Case 2Case 3

X (m)

minus30000

minus20000

minus10000

0

10000

20000

30000

40000

Cp

(b)



Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Present study

02

Nassab et al [18]

0 04 06 08 1 12 14 160

500

1000

1500

2000

2500

3000

3500

4000

4500

X (m)

Nu x

Oztop et al [20]


0 04 08 12 160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

Present studyX (m)

Nu x





Nomenclature





Greek Symbols


Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article CFD Simulation of Heat Transfer and ...Simulations were carried out using ANSYS...

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Transcript of Research Article CFD Simulation of Heat Transfer and ...Simulations were carried out using ANSYS...