International Journal of Heat and Fluid Flow

Transcription

1 Interntionl Journl of Het nd Fluid Flow 29 (28) Contents lists ville t ScienceDirect Interntionl Journl of Het nd Fluid Flow journl homepge: Numericl study of nturl convection in prtilly heted rectngulr enclosures filled with nnofluids Hkn F. Oztop, Eiyd Au-Nd, * Deprtment of Mechnicl Engineering, Fırt University, Elzig TR-23119, Turkey Deprtment of Mechnicl Engineering, Hshemite University, Zrq 1311, Jordn rticle info strct Article history: Received 8 Jnury 28 Received in revised form 22 April 28 Accepted 28 April 28 Aville online 18 June 28 Keywords: Nnofluids Het trnsfer Nturl convection Enclosure Het trnsfer nd fluid flow due to uoyncy forces in prtilly heted enclosure using nnofluids is crried out using different types of nnoprticles. The flush mounted heter is locted to the left verticl wll with finite length. The temperture of the right verticl wll is lower thn tht of heter while other wlls re insulted. The finite volume technique is used to solve the governing equtions. Clcultions were performed for Ryleigh numer (1 3 6 R 6 1 ), height of heter (.1 6 h 6.7), loction of heter (.2 6 y p 6.7), spect rtio (. 6 A 6 2) nd volume frction of nnoprticles ( 6 u 6.2). Different types of nnoprticles were tested. An increse in men Nusselt numer ws found with the volume frction of nnoprticles for the whole rnge of Ryleigh numer. Het trnsfer lso increses with incresing of height of heter. It ws found tht the heter loction ffects the flow nd temperture fields when using nnofluids. It ws found tht the het trnsfer enhncement, using nnofluids, is more pronounced t low spect rtio thn t high spect rtio. Ó 28 Elsevier Inc. All rights reserved. 1. Introduction Buoyncy induced flow nd het trnsfer is n importnt phenomenon in engineering systems due to its wide pplictions in electronic cooling, het exchngers, doule pne windows etc. These pplictions re reviewed y Ostrch (1988). Enhncement of het trnsfer in these systems is n essentil topic from n energy sving perspective. The low therml conductivity of convectionl het trnsfer fluids such s wter nd oils is primry limittion in enhncing the performnce nd the compctness of such systems. An innovtive technique to improve het trnsfer is y using nno-scle prticles in the se fluid (Choi, 199). Nnotechnology hs een widely used in industry since mterils with sizes of nnometers possess unique physicl nd chemicl properties. Nno-scle prticle dded fluids re clled s nnofluid which is firstly utilized y Choi (199). Some numericl nd experimentl studies on nnofluids include therml conductivity (Kng et l. 26), convective het trnsfer (Mig et l, 2; Au-Nd, 28), oiling het trnsfer nd nturl convection (Xun nd Li, 2). Detiled review studies re pulished y Putr et l. (23), Wng et l. (26), Xun nd Li (2), Trisksri nd Wongwises (27), Dungthongsuk nd Wongwises (27), nd Wng nd Mujumdr (27). * Corresponding uthor. Tel.: ; fx: E-mil ddress: eiyd@hu.edu.jo (E. Au-Nd). Studies on nturl convection using nnofluids re very limited nd they re relted with differentilly heted enclosures. Hwng et l. (27) investigted the uoyncy-driven het trnsfer of wter-sed Al 2 O 3 nnofluids in rectngulr cvity. They showed tht the rtio of het trnsfer coefficient of nnofluids to tht of se fluid is decresed s the size of nnoprticles increses, or the verge temperture of nnofluids is decresed. Khnfer et l. (23) investigted the het trnsfer enhncement in two-dimensionl enclosure utilizing nnofluids for vrious pertinent prmeters. They tested different models for nnofluid density, viscosity, nd therml expnsion coefficients. It ws found tht the suspended nnoprticles sustntilly increse the het trnsfer rte ny given Grshof numer. Jou nd Tzeng (26) used nnofluids to enhnce nturl convection het trnsfer in rectngulr enclosure. They conducted numericl study using Khnfer s model. They indicted tht volume frction of nnofluids cuse n increse in the verge het trnsfer coefficient. Jng nd Choi (24) investigted the Benrd regime in nnofluid filled rectngulr enclosures. Wng et l. (26) conducted study on nturl convection in nnofluid filled verticl nd horizontl enclosures. Also, recent study y Polidori et l. (27) nlyzed the het trnsfer enhncement in nturl convection using nnofluids. Nturl convection het trnsfer in prtilly heted enclosure is n importnt issue due to wide pplictions in uildings or cooling of flush mounted electronic heters. Chu et l. (1976) conducted n experimentl nd numericl study to nlyze the effects X/$ - see front mtter Ó 28 Elsevier Inc. All rights reserved. doi:1.116/j.ijhetfluidflow

2 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) Nomenclture A spect rtio (W/H) C p specific het t constnt pressure (kj kg 1 K 1 ) g grvittionl ccelertion (m s 2 ) H height of the enclosure (m) h locl het trnsfer coefficient (W m 2 K 1 ) h dimensionless length of prtil heter, h /H h length of heter, (m) k therml conductivity (W m 1 K 1 ) Nu Nusselt numer, Nu = hh/k Nu vg verge Nusselt numer Pr Prndtl numer q w het flux, (W m 2 ) R Ryleigh numer T dimensionl temperture (K) u, v dimensionl x nd v components of velocity (m s 1 ) U, V dimensionless x nd v components of velocity W length of the enclosure (m) x, y dimensionless coordintes y p dimensionless center of heter center of loction of heter (m) y p Greek symols fluid therml diffusivity (m 2 s 1 ) therml expnsion coefficient (K 1 ) e numericl tolernce u nnoprticle volume frction / trnsport quntity m kinemtic viscosity (m 2 s 1 ) h dimensionless temperture W dimensionless strem function w dimensionl strem function (m 2 s 1 ) X dimensionless vorticity x dimensionl vorticity (s 1 ) q density (kg m 3 ) l dynmic viscosity (N s m 2 ) Suscripts vg verge nf nnofluid f fluid H hot L cold s solid w wll p prticle of heter size, loction, spect rtio nd oundry conditions on nturl convection in rectngulr ir filled enclosure. They indicted tht heter size nd loction re importnt prmeters on flow nd temperture field nd het trnsfer. The prolem of temperture nd flow field in prtilly heted enclosure for different conditions in ir or wter filled enclosure hs een studied extensively in the lst three decdes (Frouk nd Fusegi, 1989; Koc et l. 27; Vrol et l., 26; Ishihr et l. 22; Nsr et l. 26; Aydin nd Yng, 2; Turkoglu nd Yucel, 199; Ahmed nd Yovnovich, 1992; Hsnoui et l., 1992; Cho et l., 1983). The min im of this study is to exmine the nturl convection het trnsfer in prtilly heted rectngulr enclosure filled with nnofluids. Three different nnofluids s Cu, Al 2 O 3 nd TiO 2 re tested to investigte the effect of nnoprticles on nturl convection flow nd temperture fields. The mentioned literture survey indictes tht there is no study on nturl convection in prtilly heted enclosure filled with nnofluid. h' y T H Heter g H y' p W Fig. 1. Sketch of prolem geometry nd coordintes. T L x 2. Governing equtions nd prolem formultion Fig. 1 shows schemtic digrm of the prtilly heted enclosure. The fluid in the enclosure is wter sed nnofluid contining different type of nnoprticles: Cu, Al 2 O 3, nd TiO 2. The nnofluid is ssumed incompressile nd the flow is ssumed to e lminr. It is ssumed tht the se fluid (i.e. wter) nd the nnoprticles re in therml equilirium nd no slip occurs etween them. The thermo physicl properties of the nnofluid re given in Tle 1. The left wll is mintined t constnt temperture (T H ) higher thn the right wll (T L ). The thermo-physicl properties of the nnofluid re ssumed to e constnt except for the density vrition, which is pproximted y the Boussinesq model. The governing equtions for the lminr nd stedy stte nturl convection in terms of the strem function-vorticity formultion re o ox Vorticity x ow oy ¼ l nf q nf Energy o T ow ox oy o oy ox ox þ ox2 oy 2 Kinemtics o oy o 2 w ox þ o2 w ¼ x 2 oy ð3þ 2 k eff nf ¼ ðqc p Þ nf x ow ox T ow ox þ ðuq s s þð1 uþq f f Þ g ot q nf ox ¼ o ox ot nf ox þ o oy ot nf oy ð1þ ð2þ ð4þ

3 1328 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) The effective density of the nnofluid is given s q nf ¼ð1 uþq f þ uq s The het cpcitnce of the nnofluid is expressed s (Au-Ndu, 27; Khnfer et l. (23)): ðqc p Þ nf ¼ð1 uþðqc p Þ f þ uðqc p Þ s The effective therml conductivity of the nnofluid is pproximted y the Mxwell Grnetts model k nf k f ¼ k s þ 2k f 2uðk f k s Þ k s þ 2k f þ uðk f k s Þ The use of this eqution is restricted to sphericl nnoprticles where it does not ccount for other shpes of nnoprticles. This model is found to e pproprite for studying het trnsfer enhncement using nnofluids (Akrini nd Behzdmehr, 27; Au-Nd, 28; Plm et l., 26; Mig et l., 2).The viscosity of the nnofluid cn e pproximted s viscosity of se fluid l f contining dilute suspension of fine sphericl prticles nd is given y Brinkmn (192): l f l nf ¼ ð1 uþ 2: The rdil nd tngentil velocities re given y the following reltions respectively, u ¼ ow oy ; v ¼ ow ox : The following dimensionless groups re introduced x ¼ x H ; U ¼ uh f ; y ¼ y H ; X xh 2 ; W ¼ w ; V ¼ vh ; ¼ f f f h ¼ T T L T H T L : ðþ ð6þ ð7þ ð8þ ð9þ ð1þ ð11þ By using the dimensionless prmeters the equtions re written s 2 3 o ox XoW o oy oy XoW Pr ¼ 4 ox ox ð1 uþ :2 ð1 uþþu q s ox þ ox 2 oy 2 q f " # 1 þ RPr s 1 ot ð1 uþ q þ f u q u q þ 1 f ð12þ f s ð1 uþ q þ 1 ox s o ox how o oy oy how ¼ o ox ox koh þ o ox oy koh ð13þ oy o 2 W ox þ o2 W 2 oy ¼ X 2 k ¼ k nf k f ð1 uþþu ðqcpþ s ðqc pþ f R ¼ gh3 ðt H T L Þ m ð14þ ð1þ ð16þ The dimensionless rdil nd tngentil velocities re given s, respectively: U ¼ ow oy ; ð17þ V ¼ ow ox : ð18þ The dimensionless oundry conditions re written s 9 1 On the left wllðheterþi:e:;x ¼ ; W ¼ ;X ¼ o2 W ; h ¼ 1: ox 2 2 On the left wllðno heterþi:e:;x ¼ ; W ¼ ;X ¼ o2 W ; oh ¼ : >= ox 2 ox 3 On the right wll i:e:;x ¼ 1; W ¼ ;X ¼ o2 W ; h ¼ : ox 2 4 On the top nd ottom wlls : W ¼ ; X ¼ o2 W ; oh ¼ : >; oy 2 oy ð19þ WW Nu W w Present Work N n P s Fig. 2. Typicl control volume. Khnfer et l. (23) Brkos nd Mitsoulis (1994) Mrktos nd Pericleous (1984) De Vhl Dvis (1983) Fusegi et l. (1991) S 1.E+3 1.E+4 1.E+ 1.E+6 R Fig. 3. Nusselt numer versus R numer nd comprison with other pulished works. (See ove-mentioned references for further informtion.) θ x e E Present Work Krne nd Jesse (1983) Khnfer et l. (23) Fig. 4. Comprison etween present work nd other pulished dt for the temperture distriution on the left wll (R =1, Pr =.7). EE

4 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) Numericl implementtion Eqs. (12) (14) with corresponding oundry conditions given in Eq. (19) re solved using the finite volume pproch (Ptnkr (198), Versteeg nd Mllseker (199)). The diffusion term in the vorticity nd energy equtions is pproximted y second-order centrl difference scheme which gives stle solution. Furthermore, second order upwind differencing scheme is dopted for the convective terms. The lgeric finite volume equtions for the vorticity nd energy equtions re written into the following form: P / P ¼ E / E þ W / W þ N / N þ S / S þ ð2þ where P, W, E, N, S denote cell loction, west fce of the control volume, est fce of the control volume, north fce of the control volume nd south fce of the control volume respectively (see Fig. 2). Similr expression is lso used for the kinemtics eqution where only centrl difference is used for the discritiztion t the cell P of the control volume. The resulted lgeric equtions re solved using successive over/under relxtion method. Successive under relxtion ws used due to the non-liner nture of the governing equtions especilly for the vorticity eqution t high Ryleigh numers. The convergence criterion is defined y the following expression: e ¼ P j¼m P i¼n j¼1 P j¼m j¼1 i¼1 j/nþ1 / n j P i¼n < 1 6 ð21þ i¼1 j/nþ1 j where e is the tolernce; M nd N re the numer of grid points in the x nd y directions, respectively. c Fig.. Stremlines (on the left) nd Isotherms (on the right) for Cu-wter nnofluids (---), pure fluid ( ), h =., A =1, y p =., u =.1, () R =1 4, () R =1, (c) R = 1.

5 133 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) Fig. 6. Stremlines (on the left) nd isotherms (on the right) for Cu-wter nnofluids, R =1, y p =., A =1,h =.1, () u =.2, () u =.1. An ccurte representtion of vorticity t the surfce is the most criticl step in the strem function vorticity formultion. A second order ccurte formul is used for the vorticity oundry condition. For exmple, the vorticity t the ottom wll is expressed s: X ¼ ð8w 1;j W 2;j Þ 2ðDyÞ 2 ð22þ Similr expressions re written for other wlls. After solving W, X, nd T, further useful quntities re otined. For exmple, the Nusselt numer cn e expressed s Nu ¼ hh k f The het trnsfer coefficient is expressed s q w h ¼ T H T L The therml conductivity is expressed s q w k nf ¼ ot=ox ð23þ ð24þ ð2þ By sustituting Eqs. (24), (2), nd (7) into Eq. (23), nd using the dimensionless quntities, the Nusselt numer on the left wll is written s: Nu ¼ k nf ot ð26þ k f ox The verge Nusselt numer is defined s Nu vg ¼ Z 1 NuðyÞdy A 1/3rd Simpson s rule of integrtion is used to evlute Eq. (27). ð27þ 4. Grid testing nd code vlidtion An extensive mesh testing procedure ws conducted to gurntee grid independent solution. Seven different mesh comintions were used for the cse of R =1 nd Pr =.7. The present code ws tested for grid independence y clculting the verge Nusselt numer on the left wll. It is found tht grid size of 1 1 ensures grid independent solution. The converged vlue (Nu = 4.644) ws compred to other known vlues reported y other reserchers s shown in Fig. 3. Therefore, the converged vlue compres very well with other vlues otined in literture. The present numericl solution is further vlidted y compring the present code results for R =1 nd Pr =.7 ginst the experiment of Krne nd Jessee (1983) nd numericl simultion of Khnfer et l. (23). It is cler tht the present code is in good greement with other work reported in literture s shown in Fig. 4.. Results nd discussion Numericl nlysis of uoyncy induced flow in prtilly heted rectngulr enclosure filled with nnofluid hs een performed using the MG model. The effect of volume frction of nnofluid, spect rtio, type of nnoprticles, length of the heter, loction of the heter nd Ryleigh numer re nlyzed. The se cse ws tken s A = 1 (squre cvity), R =1, h =., y p =. nd u =.1. Prndtl numer is tken s Pr = 6.2. Fig. () (c) shows comprison etween Cu-wter nnofluid (plotted y dshed lines) nd pure fluid (plotted y solid lines) on stremlines (on the left) nd isotherms (on the right) using different vlues of Ryleigh numer. The figure demonstrtes tht single circultion cell is formed in the clockwise direction for ll

6 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) c d -9.4 Fig. 7. Stremlines (on the left) nd isotherms (on the right) for R =1, h =., A = 1, () u =.1, y p =.2, () u =.2, y p =.2, (c) u =.1, y p =.7, (d) u =.2, y p =.7. vlues of Ryleigh numers. Fig. () presents the cse of R =1 4 where circulr shped cell is formed with w min = The corresponding isotherms exhiit the chrcteristics of conduction dominted regime since they re distriuted pproximtely prl-

7 1332 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) lel to the verticl wlls. As the Ryleigh numer increses, the length cell increses nd egg shped cell is oserved s shown in Fig. (). By incresing the vlue of Ryleigh numer the flow strength increses nd the oundry lyers ecome more distinguished. Isotherms show tht temperture grdients ner the heter nd cold wll ecome more severe. For R = 1, the stremlines elongte prllel to the horizontl wll for pure fluid. Also, n ovl shped circultion cell ws oserved ner the right verticl wll s seen from Fig. (c). Volume frction of nnoprticles is key prmeter for studying the effect of nnoprticles on flow fields nd temperture distriutions. Thus, Fig. 6() nd () re prepred to present the effect of volume frction of nnoprticles. The figure includes stremlines (on the left) nd isotherms (on the right) for R =1, y p =., h =.1. As shown from the figure, n egg shped circultion cell is formed for the cse of u =.2 with w = However, it moves towrds to the heter for u =.1. The comprison indictes tht more fluid is heted for higher vlues of volume frction of nnoprticles s shown from the isotherms. Flow strength lso increses with incresing of volume frction of nnoprticles. Fig. 7 is presented to show the effects of oth heter loction nd volume frction of nnoprticles on flow fields nd temperture distriution. Fig. 7() illustrtes the stremline (on the left) nd isotherm (on the right) for u =.1, h =. nd y p =.2. For this cse, ovl shped circultion cell is formed with w min = due to cvity heted from the ottom corner. When volume frction of nnoprticles increses from.1 to.2, length of the circultion cell ecomes smller nd flow strength increses, s seen from Fig. 7(). When the heter is plced on the upper hlf prt of the enclosure, i.e., y p =.7, n egg-shped recircultion cell is oserved with w min = 8.43 for u =.1 (Fig. 7(c)) nd w min = 9.4 Tle 1 Thermophysicl properties of fluid nd nnoprticles Physicl properties Fluid phse (wter) Cu Al 2 O 3 TiO 3 C p (J/kgK) q (kg/m 3 ) K (W/mK) (m 2 /s) (1/K) for u =.2 (Fig. 7(d)). When the heter is locted in the upper hlf, the flow strength decreses compred with the loction in the lower hlf. This is due to impingement of hot fluid to the top insulted wll. In this cse, the fluid t right ottom corner ecomes motionless due to impingement of circulted fluid to the middle of the left verticl wll. Also, the hlf ottom of the cvity ecomes cooler thn the upper hlf prt. Overll oservtion of Fig. 7 shows tht s the volume frction increses, movements of prticles ecome irregulr nd rndom due to incresing of energy exchnge rtes in the fluid. Fig. 8 compres the stremlines nd isotherms using different nno-fluids s TiO 2 -wter nd Al 2 O 3 -wter nd using different Ryleigh numer s R =1 4 (Fig. 8()) nd R =1 (Fig. 8()). For oth nnofluids, single circultion cell ws oserved in the clockwise directions. For lower vlues of Ryleigh numer, the flow strength is higher for Al 2 O 3 thn tht of TiO 2. On the contrry, the flow strength ecomes smller for Al 2 O 3 t R =1. Isotherms show lmost sme distriution for these two nnofluids due to closer vlue of therml conductivity of Al 2 O 3 nd TiO 2 which is given in Tle 1. Fig. 8. Stremlines (on the left) nd isotherms (on the right) h =., A =1,y p =.2 () R =1 4, () R =1 (----) TiO 2 (w min =.391 for R =1 4 nd w min = for R =1 ), Al 2 O 3 ( ), (w min = for R =1 4 nd w min = for R =1 ).

8 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) Fig. 9 shows the stremlines nd isotherms using different spect rtios. It is cler tht the flow strength nd the temperture isotherms re influenced y the presence of nnoprticles. The ehvior is similr to the trend encountered t A = 1. Fig. 1() (c) presents the vrition of men Nusselt numer with volume frction using different nnoprticles nd different vlues of Ryleigh numer. Results re presented for the se cse, i.e., h =. nd y p =.. The figure shows tht the het trnsfer increses lmost monotoniclly with incresing the volume frction for ll Ryleigh numers nd nnofluids. For R =1 3 (Fig. 9()), the lowest het trnsfer ws otined for TiO 2 due to domintion of conduction mode of het trnsfer since TiO 2 hs the lowest vlue of therml conductivity compred to Cu nd Al 2 O 3. However, the difference in the vlues of Al 2 O 3 nd Cu is negligile. The therml conductivity of Al 2 O 3 is pproximtely one tenth of Cu, s given in Tle 1. However, unique property of Al 2 O 3 is its low therml diffusivity, Tle 1. The reduced vlue of therml diffusivity leds to higher temperture grdients nd, therefore, higher enhncements in het trnsfer. The Cu nnoprticles hve high vlues of therml diffusivity nd, therefore, this reduces temperture grdients which will ffect the performnce of Cu nnoprticles. As volume frction of nnoprticles increses, difference for men Nusselt numer ecomes lrger especilly t higher Ryleigh numers due to incresing of domintion of convection mode of het trnsfer. The highest het trnsfer is recorded when using Cu-nnofluids for u =.2 nd R =1. Fig. 11 presents the verticl velocity profiles long the mid-section (middle plne) of the squre enclosure using different nnofluids nd R =1, u =.1, h =. nd y p =.. Due to uoynt flow inside the enclosure, the velocity shows prolic vrition ner the isotherml wlls. The verticl velocity is not sensitive to the type of nnoprticles where three types of nnoprticles show similr verticl velocity. This is explined y looking t Eq. (8) where the Brinkmn formul shows tht the viscosity of the nnofluid is only sensitive to the volume frction of prticles nd not influenced y the type of nnoprticles. However, the verticl velocity c d Fig. 9. Stremlines (on the left) nd isotherms (on the right) for R =1, h =., y p =., () A =2,u =.1, () A =2,u =.2, (c) A =., u =.1, (d) A =., u =.2.

9 1334 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) of nnofluid is lower thn tht of pure fluid t the hot side nd higher t the cold side. It mens tht prticle suspension ffects the flow field. The flow velocity is lmost zero round the center of the cvity. The profile lso gives ide on flow rottion direction. Using the sme prmeters given in Fig. 11, the vrition of locl Nusselt numer is illustrted long the prtil heter in Fig. 12 using different nnoprticles. Vlues of locl Nusselt numer hve higher vlues t onset of heting nd end point of the heter due to high temperture difference. As shown from the figure, lmost U- shped vrition is otined. Agin, the highest locl Nusselt numer vlues were formed for Cu nd the lowest one for pure fluid. Vrition of locl Nusselt numer using different volume frction of nnoprticles for different spect rtios is given in Fig. 13 for h =., y p =., R =1 nd Cu-wter nnofluid. As shown from the figure, the het trnsfer increses when incresing the volume frction of nnoprticles. Thus, more prticles re suspended nd therml conductivity of nnofluid increses. This result is supported y Khnfer et l. (23). Also, the figure shows tht s the spect rtio increses the vlue of the Nusselt numer decreses ecuse of the decrese in temperture grdients. The three spect rtios, s depicted in Fig. 13() (c), show similr trend in the vrition of the Nusselt numer. However, t the lower edge of the heter (i.e., y =.2) the vlue of the Nusselt numer, V pure X Cu, Al 2 O 3, TiO 2 Fig. 11. Velocity profiles t the middle of the enclosure for different nno-prticles R =1, R =1, h =., A = 1 nd y p = Cu 33 Nu TiO3 Al2O Nuy 18 Cu Nu c Nu ϕ Cu TiO3 Al2O ϕ Cu TiO3 Al2O ϕ Fig. 1. Vrition of men Nusselt numers with volume frction for different nno-prticles t R =1, h =. nd y p =., () R =1 3, () R =1 4, (c) R = pure TiO 2 Al 2 O Y Fig. 12. Vrition of locl Nusselt numer long the heted wll for different nnoprticles t R =1, h =., A = 1 nd y p =.. for A =., is more sensitive to the presence of nnoprticles compred to A = 2. For exmple, t this edge, the enhncement in the Nusselt numer when the volume frction of nnoprticles is incresed from to.2, using A =., is pproximtely 4% wheres the enhncement is round 2% for A = 2. This finding is further supported in Fig. 14. The figure shows the vrition of the men Nusselt numer using different spect rtios. The enhncement in the men Nusselt numer when the volume frction of nnoprticles is incresed from to.2, using A =., is pproximtely 26% wheres the enhncement is round 14% for A = 2. This tells tht, for rectngulr enclosures, the enhncement in het trnsfer, due to the presence of nnoprticles, is more pronounced t low spect rtio thn t high spect rtio. Finlly, the effect of dimensionless heter length (h /H) on het trnsfer is shown in Fig. 1 for h =., y p =., R =1 nd u =.1 using different nnofluids. The figure shows tht het trnsfer increses with heter size s expected due to incresing of heting surfce. This grph is lso supported y Chu et l. (1976) for pure fluid. An interesting result tht the difference for het trnsfer

10 H.F. Oztop, E. Au-Nd / Interntionl Journl of Het nd Fluid Flow 29 (28) Nuy Nuy c Nuy ϕ=.2 2 ϕ=.1 1 ϕ= Y ϕ= ϕ=.1 ϕ = ϕ=.2 ϕ=.1 ϕ= vlue ecomes higher for higher heter size due convection mode of het trnsfer ecomes dominnt. For lower heter size, vlues re lmost equl for Cu nd Al 2 O 3. This figure lso indictes tht Y Y Fig. 13. Vrition of locl Nusselt numer long the heted wll for different volume frction t R =1, h =. nd y p =. for Cu-wter nnofluid, () A =., () A = 1, (c) A =2. Nuy A=. A=1 A= ϕ Fig. 14. Vrition of men Nusselt numer for volume frction for different spect rtio, Cu-wter nnofluid h =., y p =., R =1. Nu using of nnofluid enhnces the nturl convection het trnsfer nd Cu-nnofluid hs the highest het trnsfer enhncement. 6. Conclusions A numericl study hs een performed to investigte the effect of using different nnofluids on nturl convection flow field nd temperture distriutions in prtilly heted squre enclosure from the left verticl wll using MG model. Some importnt points cn e drwn from the otined results such s () Both incresing the vlue of Ryleigh numer nd heter size enhnces the het trnsfer nd flow strength keeping other prmeters fixed. () The type of nnofluid is key fctor for het trnsfer enhncement. The highest vlues re otined when using Cu nnoprticles. (c) The difference in het trnsfer, using different nnofluids, increses with incresing the vlue of volume frction of nnoprticles. (d) When incresing the heter size, the difference in het trnsfer vlues is incresed nd depends minly on the type of nnofluid used. (e) For rectngulr enclosures, the enhncement of het trnsfer, due to the presence of nnoprticles, is more pronounced t low spect rtio thn t high spect rtio. In the future, the study cn e extended for higher Ryleigh numers, different types of nnofluids. An optimiztion study my e necessry for this study ut it is not gol of the present study. References Cu Al 2 O 3 TiO h/h Fig. 1. Vrition of men Nusselt numer for different length rtio of the heter nd h =., y p =., R =1, u =.1, A = 1, (). Au-Nd, E., 28. Appliction of nnofluids for het trnsfer enhncement of seprted flows encountered in ckwrd fcing step. Int. J. Het Fluid Flow 29, Ahmed, G.R., Yovnovich, M.M., Numericl study of nturl convection from discrete het source in verticl squre enclosure. J. Thermophys. 6, Akrini, A., Behzdmehr, A., 27. Numericl study of lminr mixed convection of nnofluid in horizontl curved tues. Appl. Therm. Eng. 27, Aydın, O., Yng, W.J., 2. Nturl convection in enclosures with loclized heting from elow nd symmetricl cooling from sides. Int. J. Num. Meth. Het Fluid Flow 1, Brkos, G., Mitsoulis, E., Nturl convection flow in squre cvity revisited: lminr nd turulent models with wll functions. Int. J. Num. Meth. Fluids 18, Brinkmn, H.C., 192. The viscosity of concentrted suspensions nd solutions. J. Chem. Phys. 2,

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