Heat Transfer and Turbulent Nanofluid Flow over a Double Forward- Facing Step

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1 Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs Avalable onlne at ISSN (Prnt): , ISSN (Onlne): , ISSN (CD-ROM): AIJRSTEM s a refereed, ndexed, peer-revewed, multdscplnary and open access ournal publshed by Internatonal Assocaton of Scentfc Innovaton and Research (IASIR), USA (An Assocaton Unfyng the Scences, Engneerng, and Appled Research) Heat Transfer and Turbulent Nanoflud Flow over a Double Forward- Facng Step Mohammed Saad Kamel Department of Mechancal Technques/ Al- Nassryah Techncal Insttute Southern Techncal Unversty Dh Qar/ Al-Nassryah/Baghdad street IRAQ Abstract: Heat transfer and turbulent nanofluds flow over a double forward-facng step were nvestgated numercally. The fnte volume method was used to solve the contnuty, momentum, and energy equatons usng the k- model. Four cases, correspondng to dfferent nanofluds at constant step heght, were nvestgated for Reynolds numbers rangng from 3, to 8,. The bottom of the wall was heated at constant temperature 333K. Whereas the top wall was nsulated. The results show that the surface Nusselt number ncreased wth the Reynolds number. The maxmum Nusselt number was observed for water/ ZnO nanofluds, wth a Reynolds number of 5,.The behavor of the Nusselt number was smlar for all cases at a gven Reynolds number and temperature. The results ndcate also, that the pressure drop ncreased wth ncreasng Reynolds number for all cases and the pressure drop n water/ CuO was hgher that other at. FLUENT software was employed to run ths smulaton. Keywords: Nanofluds; Heat transfer; Double forward-facng step; Nusselt number. I. Introducton The purpose of ths study s to nvestgate two-dmensonal double forward-facng step flows, and the results of numercal computatons for dfferent nanofluds types, and Reynolds numbers at constant bottom wall temperature are presented heren. Numerous studes have been performed on sngle forward- and backward facng steps; however, the lterature on double forward and backward-facng steps s very lmted, and the physcal bass of flow separaton and vortex creaton remans unclear. Flud flow over a backward- or forwardfacng step generates recrculaton zones and subsequent reattachment regons, due to sudden contracton or expanson n flow passages. Many practcal engneerng applcatons, such as the coolng of electronc devces, open channels, power generatng equpment, heat exchangers, combuston chambers, and buldng aerodynamcs, nvolve separatng flows [1]. The frst attempts to study heat transfer and flud flow over forward- or backward-facng steps were made n the 195's. Later, researchers were able to analyze complex flows n three dmensons due to the development of CFD software. Seban et al. [2] and Seban [3] poneered the study of flud flow over backward- and forward-facng steps froma heat transfer perspectve. The authors dscovered that the maxmum heat transfer coeffcents occur at the reattachment pont and decrease toward the outlet. The effect of stream turbulence on the heat transfer rate n the reattachment regon on the bottom surface of a backward-facng step was demonstrated by Mabuch et al. [4]. Improvements n devce capabltes have allowed researchers to measure reattachment ponts and heat transfer characterstcs; Mor et al. [5] used a thermal Tuft probe, Kawamura et al. [6, 7] obtaned the temporal and spatal parameters of heat transfer n the reattachment regon usng a new heat flux probe, and Oyakawa et al. [8, 9] employed et dscharge. The hydrodynamc characterstcs of gas flows past a rb and a downward step n feature separaton flow regons were studed by Terekhov et al. [1]. An early study on turbulent heat transfer and arflow over a double forward-facng step was reported by Ylmaz and Oztop [11]. The top of the wall and steps were nsulated, and the bottom of the wall was heated. The authors used k- model and found that the step rato affected the heat transfer and flow more strongly than the length rato. Later, Oztop et al. [12] presented a numercal study of heat transfer and turbulent arflow over a double forward-facng step wth an obstacle. The bottom of the wall and steps were heated, and the top of the wall was nsulated. The results showed that the obstacle aspect rato (Ar) affected the heat transfer, wth the maxmum Nusselt number correspondng to Ar = 1. AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 39

2 Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), More recently, the maorty of studes have been utlzng nanoflud because of ts hgher thermal conductvty compared to normal flud [13]. Abu Nada [14] s a poneer n research on lamnar nanoflud flow over a backward-facng step wth Cu, Ag, Al2O3, CuO, and TO2 nanoflud, volume fractons between.5 and.2 and Reynolds numbers rangng from 2 to 6. An nvestgaton of fndngs sgnfes that the Nusselt number ncreased wth the volume fracton and Reynolds number. Later, Kherbeet et al. [15] presented a numercal nvestgaton of heat transfer and lamnar nanoflud flow over a mcro-scale backward-facng step. The Reynolds numbers ranged from.1 to.5, nanopartcle types comprsed Al2O3, CuO, SO2, and ZnO, and the expanson rato was 2. An ncreasng Reynolds number and volume fracton seemed to lead to an ncreasng Nusselt number; the hghest Nusselt number value was obtaned wth SO2. The obectve of ths paper s to contrbute new data regardng water and nanofluds flow over double forwardfacng steps to mprove the desgn of heat exchangers. II. Model descrpton A. Physcal Model A schematc dagram of the double forward-facng step and the flow shape employed n ths study s presented n Fgure 1.The bottoms of the wall and the steps were heated to a gven temperature (T h ), whle the top of the wall was adabatc. The frst and second step heghts (h1, h2) was fxed at 2mm. The entrance wdth (H) was 1 mm. The Reynolds number was vared from 3, to 8, and calculated based on entrance wdth (H), and The temperature of heated wall was 313. Fgure 1: Schematc dagram of physcal model. B. Governng equaton The two-dmensonal nstantaneous governng equaton of mass, momentum and energy equatons for study ncompressble n fully developed flow can be wrtten n conservaton form expressed n Cartesan coordnates as follows [19]:- u ( uu ) ut p k cp T ( ) u [ ( The Reynolds stress tensor u u u ) u u ] can be determned accordng to the Boussnesq assumpton as (1) (2) (3) u u u u = 2 t ( ) k 3 -Where μt s the turbulent eddy vscosty and s estmated by the (k-ε) two equatons turbulent model. (4) AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 31

3 Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), μt= cμρk2/ε (5) The dfferental equaton of k and ε are gven as ( u k) t k [( ) ] Gk k 2 ( u ) t [( ) ] C1G C 2 k k u -Where Gk u u ( ) s the turbulent producton term. (6) (7) The remanng coeffcents that appeared n the above equaton are as quoted by[19] : Cμ=.9,Cε1=1.44, Cε 2 =1.92, σ k =1 and σε=1.3 The Reynolds number s computed based on nlet channel heght (H).. (8) Where (L) s the length of the heated wall. (9) C. Numercal Procedure and grd dependence Smulatons were carred out usng FLUENT The gambt was used for meshng, and the k- standard model n Fluent was used to analyze the water and nanofluds flow and heat transfer over the double forward-facng step n the turbulent regon. Grd ndependence was verfed by ncreasng the grd sze step wse, whch yelded smlar results. Independent verfcaton was performed for Re=3, and water used as workng flud the ntal grd szes of (6522, 13765, 22647, 3478, 89228, and ). The dfference n the Nusselt number relatve to that of the selected grds was less than.5% and grd number 6 was adopted as shown Fgure 2. III. Fgure 2: Grd dependence test Thermo-physcal propertes of nanofluds Thermophyscal propertes of the base flud and the nanopartcles used n ths study shown n table.1. The effectve propertes of nanofluds are defned as follow: Densty: (1) AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 311

4 Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), Heat capacty:.(11) The Eqs. (6) and (7) were ntroduced by [15]. The thermal conductvty: (12) Ths was ntroduced by [16]. Where (n) s a shape factor and equal to (3) for sphercal nanopartcles. The vscosty: The effectve vscosty can be obtaned by usng the followng mean emprcal correlaton [17]. (13) Where: (14) Where: M s the molecular weght of base flud, N s the Avogadro number = 6.22*123 mol -1, ρ bf s the mass densty of the base flud calculated at temperature T=3 K. the table 1. Show the thermo-physcal propertes of nanopartcles and workng fluds. IV. Results and Dscusson 4.1 Effect of the Reynolds number The effects of the Reynolds number on the local Nusselt number for the turbulent ranges are presented n Fgs.3 (A, B and C). Wth the ncrease of Reynolds number, the Nusselt number ncreased n the turbulent ranges for all nanofluds. Results ndcate that snce hgher Reynolds number leads to hgher velocty and temperature gradents at heated wall, consequently the local nusselt number s ncreased by ncreasng Reynolds number. 4.2 Effect of dfferent types of nanopartcles Dfferent types of nanopartcles such as Al2O3, CuO and ZnO and pure water as a base flud are used. The Nusselt number for dfferent nanofluds and dfferent values of Reynolds number are shown n Fg.3 (A, B, C and D). It can be clearly seen that ZnO nanoflud has the hghest average Nusselt number, followed by CuO, Al2O3 respectvely. Ths s because ZnO has the lowest thermal conductvty than other nanofluds, but hgher than water also, the heat capacty for ZnO s small compared wth other nanofluds that means the heat transfer n partcles move quckly and that let to get hgh temperature n t. 4.3 Pressure drop The pressure drop varaton wth axal dstance for water/ Al2O3 at dfferent Reynolds numbers and dfferent nanofluds at s presented n Fg.4 and Fg.5. Accordng to the results, the pressure drop ntensfed as the Reynolds number ncreased for water flow and also, the water/ CuO nanofluds has hgher drop than other nanofluds at constant volume fracton. Generally, the hghest pressure drop occurred at the downstream nlet regon due to recrculaton flow whch caused the mprovement of heat transfer. V. Concluson Turbulent nanofluds forced convecton and heat transfer over a double forward-facng step was studed. Four cases, correspondng to three dfferent nanofluds and base flud, were nvestgated at dfferent Reynolds numbers AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 312

5 surface nusselt number surface nusselt number surface nusselt number Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), and constant temperature. Recrculaton zone ncreased the separaton length at the same Reynolds number and temperature, whch ncreases the Nusselt number. The results show that ncreasng the Reynolds number and temperature ncreased the Nusselt number for all cases. The enhancement of the Nusselt number occurred at the water/ ZnO nanoflud at 5. Reynolds number compard wth other nanofluds. In addton, the obtaned results ndcate an ncrease n the pressure drop wth ncreasng Reynolds number for all cases poston X n (m) water Re water/al2o3 Re water/cuo Re water/ ZnO Re (A) poston X n (m) (B) water Re 5 water/ Al2o3 Re 5 water/ Cuo Re 5 water/ ZnO Re poston X n (m) (C) water Re 8 water/ Al2o3 water/ Cuo water/ ZnO AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 313

6 pressure drop (pa) statc pressure (pa) average nussult number Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), water water/al2o3 water/cuo water/zno Reynolds number (D) Fgure 3. (A) surface nusselt number at Re, (B) surface nusselt number at Re 5, (C) surface nusselt number at and (D) Average nusselt number at dfferent Reynolds number poston X n (m) water Re 8 water/ Al2O3 water/ CuO water/ ZnO Fgure 4: Pressure drop wth dfferent Nanofluds at poston X n (m) water/ Al2O3 Re water/ Al2O3 Re 5 water/ Al2O3 Fgure 5: Pressure drop wth dfferent Reynolds number for (Al2O3-water) AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 314

7 Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), Table 1. Thermophyscal propertes of the base flud and the nanopartcles used n ths study [16, 17, 18] property water Al2O3 CuO ZnO (kg.m-3) Cp (J/kg.k) K (w/m.k) (N.s/m2) VI. Nomenclature Cp specfc heat capacty (J kg-1 K-1) NuL surface Nusselt number Nuav average Nusselt number P Pressure (Pa) Pr Prandtl number Re Reynolds number Tw Heated Wall temperature (K) T Temperature (K) u velocty component (m s-1) x, y spatal coordnaton (m) L Length of the heated downstream wall (m) h1 Frst Step heght (m) h2 Second Step heght (m) H Heght of nlet channel (m) a Length of bottom wall before the frst step (m) b Length of bottom wall after the frst step (m) c Length of bottom wall after the second step (m) M molecular weght of baseflud Partcles dameter (nm) Baseflud dameter (nm) N Avogadro number Greek symbols K thermal conductvty (W m-1 K-1) µ dynamc vscosty (Pa s) ρ densty (kg m-3) ρbf Densty of baseflud (kg m-3) Volume frcton (%) Subscrpts nf p bf nanoflud Nano partcles baseflud VII. References [1] Hussen Togun, Ahmed Jassm Shkarah, S. N. Kaz,1 and A. Badarudn. "CFD Smulaton of Heat Transfer and Turbulent Flud Flow over a Double Forward-Facng Step", Hndaw Publshng Corporaton " Mathematcal Problems n Engneerng" Volume 213, Artcle ID , 1 pages. [2] R. A. Seban, A. Emery, and A. Levy, Heat transfer to separated and reattached subsonc turbulent flows obtaned downstream of a surface step, Internatonal Journal of Aerospace Scences, vol. 2, pp , [3] R. A. Seban, The effect of sucton and necton on the heat transfer and flow n a turbulent separated ar flow, Journal of Heat Transfer, vol. 88, no. 3, pp , [4] I. Mabuch, T. Murata, and M. Kumada, Effect of free-stream turbulence on heat transfer characterstcs n the reattachment regon on the bottom surface of a backward-facng step (for dfferent angles of separaton), Transactons of the Japan Socety of Mechancal Engneers B, vol. 52, no. 479, pp , [5] Y. Mor, Y. Uchda, and K. Saka, A study of the tme and spatal mcro structure of heat transfer performance near the reattachng pont of separated flows, Transactons of the Japan Socety of Mechancal Engneers B, vol. 52,no. 481, pp , [6] T. Kawamura, A. Yamamor, J. Mmatsu, and M. Kumada, Tme and spatal characterstcs of heat transfer at the reattachment regon of a two-dmensonal backward-facng step, n Proceedngs of the ASME-JSME Thermal Engneerng Jont Conference, vol. 3, pp , [7] T. Kawamura, S. Tanaka, I. Mabuch, and M. Kumada," Temporal and spatal characterstcs of heat transfer at the reattachment regon of a backward-facng step, Expermental Heat Transfer, vol. 1, no. 4, pp , [8] K. Oyakawa, T. Tara, and E. Yamazato, Studes of heat transfer control by et dscharge at reattachment regon downstream of a backward-facng step, Transactons of the Japan Socety of Mechancal Engneers B, vol. 6, no. 569, pp , AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 315

8 Mohammed Saad Kamel., Amercan Internatonal Journal of Research n Scence, Technology, Engneerng & Mathematcs, 9(3), [9] K. Oyakawa, T. Satoh, I. Teruya, and I.Mabuch, Heat transfer enhancement usng slat at reattachment regon downstream of backward-facng step, Transactons of the Japan Socety of Mechancal Engneers B, vol. 61, no. 592, pp , [1] V. I. Terekhov, N. I. Yarygna, and R. F. Zhdanov, Heat transfer n turbulent separated flows n the presence of hgh freestream turbulence, Internatonal Journal of Heat and Mass Transfer, vol. 46, no. 23, pp , 23. [11] I. Ylmaz and H. F. Oztop, Turbulence forced convecton heat transfer over double forward facng step flow, Internatonal Communcatons n Heat and Mass Transfer, vol. 33, no. 4, pp , 26. [12] H. F. Oztop, K. S.Mushatet, and I. Yılmaz, Analyss of turbulent flow and heat transfer over a double forward facng step wth obstacles, Internatonal Communcatons n Heat and Mass Transfer, vol. 39, no. 9, pp , 212. [13] M. Hassan, R. Sadr, G. Ahmad, M. Dahar, S. Kaz, M.R. Safae, E. Sadeghnezhad, Numercal study of entropy generaton n a flowng nanoflud used n mcro- and mnchannels, Entropy 15 (213) [14] E. Abu-Nada, Applcaton of nanofluds for heat transfer enhancement of separated flows encountered n a backward facng step, Int. J. Heat Flud Flow 29 (28) [15] A.S. Kherbeet, H.A. Mohammed, B.H. Salman, The effect of nanofluds flow on mxed convecton heat transfer over mcroscale backward-facng step, Int. J. Heat Mass Transfer 55 (212) [16] R. S. Vaha and D. K. Das, Expermental determnaton of thermal conductvty of three nanofluds and development of new correlatons, Internatonal Journal of Heat and Mass Transfer, vol. 52, no , pp , 29. [17] R. S.Vaha, D. K. Das, andd.p.kulkarn, Development of new correlatons for convectve heat transfer and frcton factor n turbulent regme for nanofluds, Internatonal Journal of Heat and Mass Transfer, vol. 53, no , pp , 21. [18] J. H. Lenhard and J. Lenhard, A Heat Transfer Textbook, Phlogston Press, Cambrdge, Mass, USA, 2. [19] Ferzgen, J. H. and Perc, M. "Computatonal methods for flud dynamc".2th edton, Sprnger. Berln, (1999). AIJRSTEM ; 215, AIJRSTEM All Rghts Reserved Page 316