Numerical Study of Transient Forced Convection Heat Transfer in Square Duct with Nanofluid

Transcription

1 ISSN: International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 merical Study o Transient Forced Convection Heat Transer in Square Duct wit Nanoluid Amed. H. Ali 1 and Taseen.A.Al-Hattab Department o Automotive, Tecnical College o Naja, Naja, Iraq 1 Department o Electrocemical Engineering, niversity o Babylon, Babylon, Iraq ABSTRACT: In te present paper, te problem o transient laminar orced convection low o nanoluids in orizontal square duct as been torougly investigated using a single pase approac. Te water is adopted as base luid,wile te(al O 3 ) and(cuo) are a solid nanoparticles. Computations are validated wit experimental data available in te literature, good agreements are obtained. Te results sowed tat Convective eat transer coeicient or nanoluids is greater tan tat o te base liquid. Heat transer enancement increases wit te particle volume concentration increase, but it is accompanied by increasing wall sear stress values. Te isoterms are presented or various void ractions and Reynolds numbers. Also, te relation between te sselt number, and riction actor wit Time are introduced or various Reynolds numbers and volume raction o nanoparticles. KE ORDS: TRANSIENT FORCED CONECTION, SQARE DCT, LAMINAR FLO, NANOFLID, CONSTANT HEAT FL I. INTRODCTION Te augment o eat transer rate is one o te most important tecnical aims or industry and researces. Also, te decrease in te pressure drop or systems tat generate ig luid pressure drop is very noticeable. Te eat convection can passively be enanced by canging low geometry, boundary conditions or by enancing luid termopysical properties. Nanoluids are liquids tat containing nanopowders wit dimensions smaller tan 100 nm and are suspended in base luid suc as water, oil or etylene glycol. II. RELATED ORKS Nanoluids are best or applications in wic luid lows troug small passages because nanoparticles are small enoug to beave similarly to liquid molecules. uan and Roetzel[1] were sowed tat te termal conductivity o te suspensions can increase by more tan 0% causing increase in eat transer rate. Maı ga et al.[] developed numerical simulation or te ydrodynamic and termal caracteristics o a laminar orced convection low. Results sowed tat eat transer enancement tat appears to be more pronounced wit te increase o te particle volume concentration is accompanied. Later, Abarinia and Bezadmer[3] Fully developed laminar mixed convection o a nanoluid numerically. tey estimated water and Al O 3 in 3-D orizontal curved tubes. Tey concluded tat Te nanoparticles volume raction does not ave a direct eect on te secondary low, axial velocity and te sin riction coeicient. Abari et al.[4] oered merical investigation o ully developed laminar mixed convection wit single pase model used(water+ Al O 3 ). Te results illustrate tat te nanoparticles concentration does not ave signiicant eect on te secondary low, axial velocity proile and also on te periperally average sin riction coeicient. Izadi et al.[5] studied Heat transer mecanisms in annulus wit Laminar orced convection o a nanoluid numerically. Tey ound tat te dimensionless axial velocity proile does not signiicantly cange wit te nanoparticle volume raction. But, te temperature proiles are aected by te nanoparticle concentration. He et al.[6] perormed merical simulations using a single and combined Eulerian and Lagrangian metod on te convective eat transer o aqueous γ-al O 3 nanoluids lowing troug a straigt tube under te laminar low conditions. Loti et al[7] submitted Forced convective o a nanoluid tat consists o water and Al O 3 in orizontal tubes. Autors reported tat "It is clear rom te results tat te rate o termal enancement decreases wit te increase o nanoparticles volume concentration". Mansour et al.[8] were studied mixed convection lows in a square lid-driven cavity DOI: /IJIRSET

2 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: partially eated. various volume ractions o (Cu, Ag, Al O 3 and TiO ) and results reer to adding alumina will provide igest sselt number. And in te same time, using TiO will reduce eat transer enancement to lest. Farad Talebi [9] were designed model to simulate numerically a laminar mixed convection lows troug a copper water nanoluid in a square lid-driven cavity. Tey seem tat solid concentration as a positive eect on eat transer enancement. Experimental studies on convective eat transer o Cu/ater,CuO/ater and Al O 3 /ater nanoluids are reported by einali et al.[10,11]. Te experimental set-up consisted o a one-meter annular tube, wic was constructed o 6 mm diameter inner cupper tube 0.5 mm tic, and 3 mm diameter outer stainless steel tube. Te nanoluid lows inside te inner tube wile saturated steam entered te annular section, wic created constant wall temperature condition. Also, Nassan et al. [1], presented a single-pase model to study te laminar low and eat transer caracteristics o nanoluids in a square duct experimentally in steady state condition. indicate tat a considerable eat transer enancement as been acieved by bot nanoluids compared wit base luid. However, CuO/water nanoluid sows better eat transer intensiication compared wit Al O 3 /water nanoluid troug square cross-section duct. Sundar and Sarma[13] were studied Te single pase turbulent convective eat transer o Al O 3 nanoluid in a circular tube wit dierent aspect ratios o longitudinal strip inserts. an eective increasing (reaces to 30.3%) wen compared to water at 0.5% concentration and maximum Reynolds number used. Te main endeavor o tis study is numerically investigation o te transient beavior o laminar low orced convection wit various concentrations o nanoparticles and given Reynolds number on te eat transer enancement. PROBLEM CONFIGRATION AND BONDAR CONDITIONS Fig.(1)sows te geometrical coiguration under consideration. It consists o a tube wit a lengt (L) in te - direction, wile Te eigt and widt o duct is (H).Te nanoluid considered is composed o water and Al O 3 or CuO particles. Te luid enters wit uniorm temperature and axial velocity proiles at te inlet section. Te duct as appropriate lengt in order to obtain ully developed proiles(velocity and termal) at te outlet section. H y,v x,u L Flow z,w H Fig. (1) Te geometry o te duct and te coordinate axis. DOI: /IJIRSET Te no 15717

3 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: slip conditions are written as -Inlet Condition u(0,y,z)=u in, v(0,y,z)=w(0,y,z)=0, T(0,y,z)=T in (1) -Outlet Condition u i T 0, 0 () x x xl -wall condition ( i) 0, u i T z y0 xl T z yh T y zo T y zh q - Initial Condition u(0,y,z,0)=u in,v(0,y,z,0)=w(0,y,z,0)=0, T, y, z,0 Tin III. MATHEMATICAL MODELING 0 (4) Te low is assumed to be Newtonian, tree-dimensional and incompressible. It is also assumed tat te base luid and te nanoparticles are in termodynamic equilibrium and tat tey low at te same velocity. Te viscous dissipation terms and termal radiation are assumed to be negligible. Te governing equations or 3-D transient laminar wit orced convection o constant properties are modeled as Continuity Equation (3) u i x i 0 (5) Momentum equations: ui ui p u j ui u j (6) t x j xi xi xi x j Energy equation: T T T Cp ui. (7) t xi xi to solve above-mentioned equations, te Termo pysical parameters o nanoluid suc as density, viscosity, eat capacity, and termal conductivity must be evaluated. Tese parameters are deined as: -Density p 1 (8) -Heat Capacity C P C P C P p -iscosity (9) -Termal Conductivity p p introducing te ollowing dimensionless variables or square duct x y z u v,,,,, D D D u u Re uin D, Pr Cp in p in, Cp p (10) (11) w u in, T Tin q D, p P u, t in t u D DOI: /IJIRSET

4 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 DOI: /IJIRSET ISSN: Cp Cp Cp K,,,, Te above governing partial dierential equation are re-written in dimensionless orm according to above dimensionless variables as: 0. (1) Re 1 P (13) Re 1 P (14) Re 1 P (15) Pe (16) I. COMPTATIONAL PROCEDRE Te governing equations wit boundary and initial conditions are solved numerically by using commercial sotware COMSOL 3.5 wic depends on inite element tecnique. Te validation o te computational results is acieved by comparison wit tat o Nassan et al.[1] or experimental nanoluids in square cross-section duct as sown in igure (). Te Termo pysical properties o water, Alumina and Copper oxide are listed in table (1). material Density (Kg/m 3 ) iscosity (pas) Heat capacity (J/g.K) Termal conductivity. (/m.k) water x AL o CuO Table( 1): Properties o pure water, Al O 3 and CuO particles at T = 93 K. Te grid independence study was conducted by altering te cell size and number inside te computational domain. Several meses were tested to ensure tat te solution was independent o te mes. Tis tests indicated in table () No. o element at t=0.01 at t=0. 1 at t=ss Time o solution(sec) Table () o sow values o sselt mber in dierent time at Re=1000,ϕ=0.5% Based on tis observation, cells were considered or te inal simulation. In order to estimate te eat transer enancement, we ave calculated Te eat transer coeicient as[14] w b w T T z T (17) ere, T b is a bul temperature and deine as [14]

5 T b International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 u CpTdA ucpda (18) Besides, local and average sselt number or te ot walls as: 1 1 L and dx (19) x x L 0 ISSN: ]1Nassan [ present wor Re Fig.()Comparison o sselt number versus Reynolds mber at SS And, a dimensionless sselt number ratio ( r ) is deine as r (0) w Te riction coeicient is deined by P D L u m. RESLTS AND DISCSSION Ater determination te properties o nanoluid, discretization te domain and coupled governing equations, and assigning te initial, inal and step or dimensionless times as 0.001, 0.01, 0.1 and at Steady State respectively. (1) DOI: /IJIRSET

6 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: (A) (B) (C) (D) Fig.()ariation o temperature distribution or Re=1000 and (ϕ)=0.05% en (A) t=0.001 (B) t=0.01 (C) t=0.1 (D) t=ss (A) (B) (C) (D) Fig.(3) ariation o temperature distribution or Re=1000 and (ϕ)=0.1% wen (A)t=0.001 (B) t=0.01 (C) t=0.1 (D) t=ss DOI: /IJIRSET

7 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: Figures ( troug 4) sow te temperatures beavior wit time or dierent values o (ϕ), axial distance at time period. Te increase o temperature wit increasing o time can be sowed obviously. tere are some ottest regions inside duct especially at corners were tat reer to low velocity compared wit oters regions, since te luid taes enoug time to transer te eat rom eac oter and rom te wall. And as time travelled, temperature o bul luid increase gradually and tis raising eep on until reacing steady state condition. it is observed tat te regions o isoterms are mostly symmetric wit respect to te center o te duct. Moreover, above igures provide a proo tat increasing (ϕ) only wit ixing te rest o te parameters causes reduction in bul temperature. Te ig termal conductivity and Reynolds number is te main reason to accelerate transient state as te volume raction increases. (A) (B) (C) (D) Fig.(4) ariation o temperature distribution or Re=1000 and (ϕ)=0.5% wen (A)t=0.001 (B) t=0.01 (C) t=0.1 (D) t=ss Local sselt mber variation wit duct lengt at a dierent values o Reynolds mber, time and given volume construction are demonstrates in Figs.(5-6).it is clear tat increasing o volume construction cause an active increase in sselt mber at speciied Re. te penomena o increasing sselt mber reerred to increase o termal conductivity o nanoluid compared o bul luid. At te beginning o low, tere are immense dierence in temperature variation between wall and bul nanoluid led to maximum value o. Anoter reason tat little boundary layer ticness at te inlet o te entry region, causing ig Local, and as te ticness o te termal B.L. increases, te local decreases and ten, reaces to small variation in its value as te termal B.L. ead to te center o te cannel. DOI: /IJIRSET

8 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: OAl0.05%psi= CuO0.05% psi= 3OAl0.1%psi= CuO0.1%psi= (A) OAl0.05%psi= CuO0.05% psi= 3OAl0.1%psi= (B) OAl0.05% psi= CuO0.05% psi= 3OAl0.1% psi= CuO0.1%psi= 3OAl0.5% psi= CuO0.5%psi= (C) OAl0.05%psi= CuO0.05% psi= 3OAl0.1%psi= (D) Fig.(5) ariation o sselt mber or dierent value and types o (ϕ) at Re=1000 wen (A) t =0.001 (b) t=0.01 (C) t=0.1 (D) t=ss Fig. (7) sow te average variation o sselt mber versus time as a unction o loaded particles, or all implemented Reynolds numbers. It can be seen tat te eat transe rate increases wit nanoparticles concentration. Also, a comparison between (A) and (B) in Figure(7) sows tat o CuO nanoluid is larger tan o Al O 3 nanoluid, at speciied Re and (ϕ) in te same time, according to mentioned igures, average sselt ratio decrease wit time passing because in te beginning o low, te presence o te nanoparticles canges and enances te temperature distribution maing it more uniorm wic means more energy transers troug te luid comparison wit te same time period o tat o base luid. DOI: /IJIRSET

9 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: OAL0.05% psi= CuO0.05%psi= 3OAL0.1%psi= CuO0.1%psi= One sould note ere tat te deinition o includes 75 3OAl0.05% psi= 70 CuO0.05% psi= 3OAl0.1% psi= CuO0.1%psi= CuO0.5%psi= 3OAl0.5% psi= OAl0.05% psi= CuO0.05% psi= 3OAl0.1% psi= CuO0.1%psi= 3OAl0.5% psi= CuO0.5%psi= OAl0.05%psi= CuO0.05% psi= 3OAl0.1%psi= CuO0.1%psi= Fig.(6) ariation o sselt mber or dierent value and types o (ϕ) at Re=000 wen (A) t=0.001 (b) t=0.01 (C) t=0.1 (D) t=ss, wic also increases appreciably wit an augmentation o te particle concentration. It is interesting to study te low representation along wit te termal representation, tereore, we investigate te bot low and termal presentations wit tree dierent concentrations levels o nanoluid loadings. Te riction actor in Fig.(8) is associated wit te pressure drop and we observed tat te is tiny dierence in pressure drop or all concentrations levels. As a result, we can ier te riction actor as no eective cange. Pysically, te nanoparticles are ultraine and te concentrations are relatively small. DOI: /IJIRSET

10 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: ) 3O(Al0.001 t= )(CuO0.001 t= ) 3O(Al0.01 t= )(CuO0.01 t= ) 3O(Al0.1 t= )(CuO0.1 t= ) 3Ot=ss (Al ) t=ss (CuO )3O(Al0.001 t= )(CuO0.001 t= )3O(Al0.01 t= )(CuO0.01 t= )3O(Al0.1 t= r (A) r (B) (ϕ %) (ϕ %) Fig.(7) ariation o sselt mber wit (ϕ) or dierent value o dimensionless time or (A) Re=1000 & (B) Re=000 II. CONCLSION Te model was applied to simulate te transient orced convection lows o Alumina water and Copper oxide-warer nanoluid in a orizontal square duct or dierent Reynolds numbers and void ractions o nanoparticles. Te results sowed at a given Reynolds number, solid concentration as appositive eect on eat transer enancement. Also, tere is an enancement in eat transer eatures were times or converting to steady state is lower tan tat o base luid. In t= 0.001t= 0.01t= t=ss (ϕ%) t= 0.001t= 0.01t= t=ss (ϕ%) Fig.(8) ariation o riction actor wit (ϕ) or dierent value o dimensionless time or (A) Re=1000 & (B) Re=000 DOI: /IJIRSET

11 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: addition, te average sselt number is igly dependence on te void raction. Tis point is also observed in te computation o te dimensionless temperature. Nomenclature Gree symbols A Area α termal diusivity C p Speciic eat at constant pressure solid volume raction D Hydraulic diameter μ dynamic viscosity Heat transer coeicient θ dimensionless temperature Termal conductivity ρ density L Duct lengt τ dimensionless time H Square side lengt sselt number Subscripts p Pressure b Bul luid P Dimensionless pressure w all Pe Peclet number in Inlet Re Reynolds number Nanoluid Pr Prandtle number p particles T Temperature Superscripts t Time Properties dimensionless sign,, Dimensionless velocity components u, v,w elocity components Abbreviations x, y,z Cartesian coordinates CHF Constant Heat Flux,, Dimensionless coordinates SS Steady State REFRENCES [1] imin uana, and ilried Roetzel, Conceptions or eat transer correlation o nanoluids, International Journal o Heat and Mass Transer, ol.43, pp , 000. [] Sidi El Be caye Maı ga, Samy Josep Palm, Cong Tam Nguyen, Gilles Roy, and Nicolas Galanis, Heat transer enancement by using nanoluids in orced convection lows, International Journal o Heat and Fluid Flow, ol.6, pp , 005. [3] Abarinia, A., and Bezadmer, A., merical study o laminar mixed convection o a nanoluid in orizontal curved tubes, Applied Termal Engineering ol.7, pp , 007. [4] Abari, M., Galanis N., and Bezadmer, A., Comparative analysis o single and two-pase models or CFD studies o nanoluid eat transer, International Journal o Termal Sciences, ol.50, pp , 011. [5] Izadi, M., Bezadmer, A., and Jalali-aida, D., merical study o developing laminar orced convection o a nanoluid in an Annulus, International Journal o Termal Sciences, ol.48, pp , 009. [6] urong He, ubin Mena, unua ao, Huilin Lu, and ulong Ding, merical investigation into te convective eat transer o TiO nanoluids lowing troug a straigt tube under te laminar low conditions, Applied Termal Engineering, ol.9, pp , 009. [7] Loti, R., Sabooi,., and Rasidi, A.M., merical study o orced convective eat transer o Nanoluids: Comparison o dierent approaces, International Communications in Heat and Mass Transer, ol.37, pp.74 78, 010. [8] Mansour, M.A., Moamed, R.A., Abd-Elaziz, M.M., and Amed, S.E., merical simulation o mixed convection lows in a square lid-driven cavity partially eated rom below using nanoluid, International Communications in Heat and Mass Transer, ol.37, pp , 010. [9] Farad Talebi, Amir Housang Mamoudi, and Mina Sai, merical study o mixed convection lows in a square lid-driven cavity utilizing nanoluid, International Communications in Heat and Mass Transer, ol.37, pp.79 90, 010. [10] einaliheris, S., Etemad, SG., Nasr Esaany, M. Experimental investigation o oxide nanoluid laminar low convective eat transer in circular tube, International Communication in Heat and Mass Transer, ol.33, pp , 006. [11] einaliheris, S., Nasr Esaany, M., Etemad, SG., Experimental investigation o convective eat transer o Al O 3/ater nanoluid in circular tube, International Journal o Heat and Fluid Flow, ol.8, pp.03 10, 007 DOI: /IJIRSET

12 International Journal o Innovative Researc in Science, (An ISO 397: 007 Certiied Organization) ol. 3, Issue 8, August 014 ISSN: [1] Nassan, T.H., einali Heris, S., and Noie, S.H., A comparison o experimental eat transer caracteristics or Al O 3/water and CuO/water nanoluids in square cross-section duct, International Communications in Heat and Mass Transer ol.37, pp.94-98, 010. [13] Syam Sundar, L., and Sarma, K.., Heat transer enancements o low volume concentration Al O 3 nanoluid and wit longitudinal strip inserts in a circular tube, International Communications in Heat and Mass Transer ol.53, pp , 010. [14] ite, F. M., iscous Fluid Flow (3 rd Ed.), McGraw Hill, New or, DOI: /IJIRSET