ISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 3, September 2013

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1 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 The Blaiu and Saiadi Flow in a Nanoluid through a Porou Medium in the Preence Thermal adiation under a Convective Surace Boundary Condition F. M. Hady 1, Mohamed. Eid *, M.. Abd-Elalam 3, Motaa A. Ahmed 3 1 Department o Mathematic, Faculty o Science, Aiut Univerity, Aiut 71516, Egypt.) Department o Science and Mathematic, Faculty o Education, Aiut Univerity, The New Valley 7111, Egypt. 3 Department o Mathematic, Faculty o Science, Sohag Univerity, Sohag, Egypt Abtract The poroity eect on the low and heat traner characteritic o the Blaiu and Saiadi low in a nanoluid in the preence o thermal radiation. The reulting ytem o nonlinear partial dierential equation i olved numerically uing an eicient numerical hooting technique with a ourth-order unge Kutta cheme. The olution or the low and heat traner characteritic are evaluated numerically or variou value o the governing parameter, namely the nanoparticle volume raction and the poroity parameter. Three dierent type o nanoparticle are conidered, namely Cu, Al 3 and Ti. The variation o dimenionle urace temperature a well a low and heat-traner characteritic with the governing dimenionle parameter o the problem, which include the nanoparticle volume raction, the thermal radiation parameter N and the poroity are graphed and tabulated. eult o ome earlier worer have been deduced a pecial cae. Ecellent validation o the preent numerical reult ha been achieved with the earlier Blaiu and Saiadi low problem o lanrewaju et al. [37] or local Nuelt number without taing the eect o nanoparticle and poroity. Keyword: Nanoluid, poroity, Blaiu and Saiadi, Thermal radiation, convective urace boundary condition. Nomenclature a C c p Ec K * m N the convective parameter Sin riction coeicient Speciic heat Ecert number Dimenionle tream unction Thermal conductivity Permeability o the porou medium Mean aborption coeicient Surace temperature parameter adiation parameter Nu Nuelt number Pr Prandtl number q T r adiative heat lu Temperature u, v Velocity component along - and y-direction, repectively, y Carteian coordinate along the plate and normal to it, repectively Gree ymbol Thermal diuivity Similarity variable Poroity parameter Dimenionle temperature Eective vicoity Kinematic vicoity Denity * Stean Boltzmann contant Heat capacitance o the nanoluid C p n C p Heat capacity o the luid C p Eective heat capacity o the nanoparticle material Nanoparticle volume raction Subcript Fluid raction n w Nanoluid raction Solid raction Condition at the wall Stream unction condition at the ininity I. INTDUCTIN Studie related to nanoluid have attracted a great deal o interet in recent time due to their enormou enhanced perormance propertie, particularly with repect to heat traner. Nanoluid have novel propertie that mae them potentially ueul in many application in heat traner, including microelectronic, uel cell, pharmaceutical 5

2 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 procee, and hybrid-powered engine. Nanoparticle i o great cientiic interet a it i an eectively bridge between bul material and atomic or molecular tructure. Invetigation o boundary layer low and heat traner o vicou luid over a lat heet are important in many manuacturing procee, uch a polymer etruion, drawing o copper wire, continuou tretching o platic ilm and artiicial iber, hot rolling, wire drawing, gla-iber, metal etruion, and metal pinning. For intance, in their eperimental tudy o drug nanoparticle by antiolvent precipitation, Matteucci et al. [1] revealed that an adequate nowledge o nanoparticle volume raction i beneicial or deigning miing ytem and uractant tabilizer or orming nanoparticle o poorly water oluble drug with the potential or high diolution rate. Nanoluid are engineered colloid made o a bae luid and nanoparticle. Nanoluid are olid-liquid compoite material coniting o olid nanoparticle or nanoiber, with ize typically on the order o nm, upended in a liquid. Since the pioneering eperimental wor o Choi [] on nanoluid, numerou model have been propoed by dierent author to tudy convective low o nanoluid and we mention here the paper in e. [3 8]. A comprehenive urvey o convective tranport in nanoluid wa made by Buongiorno [9], who revealed that a atiactory eplanation or the abnormal increae in the thermal conductivity and vicoity wa yet to be ound. Moreover, the boundary layer low over a moving urace ha attracted coniderable attention in recent year due to it crucial role in numerou indutrial and engineering application. Very recently, Kuznetov and Nield [8] have eamined the inluence o nanoparticle on natural convection boundary-layer low pat a vertical plate, uing a model in which Brownian motion and thermophorei are accounted or. The author have aumed the implet poible boundary condition, namely thoe in which both the temperature and the nanoparticle raction are contant along the wall. Further, Nield and Kuznetov [10] have tudied the Cheng and Minowycz [11] problem o natural convection pat a vertical plate, in a porou medium aturated by a nanoluid. The analytical and eperimental reult or the low and temperature ield in the boundary layer regime were conirmed by Mainde [1] invetigated the ree-convection low with thermal radiation and ma traner pat a moving vertical porou plate. Saiadi [13] initiated the tudy o the boundary layer low over a tretched urace moving with a contant velocity and ormulated a boundary-layer equation or two-dimenional and aiymmetric low. Tou et al. [14] analyzed the eect o heat traner in the boundary layer on a continuou moving urace with a contant velocity and eperimentally conirmed the numerical reult o Saiadi [13]. Ericon et al. [15] etended the wor o Saiadi [13] to include blowing or uction at the tretched heet urace on a continuou olid urace under contant peed and invetigated it eect on the heat and ma traner in the boundary layer. The related problem o a tretched heet with a linear velocity and dierent thermal boundary condition in Newtonian luid have been tudied, theoretically, numerically and eperimentally, by many reearcher, uch a Crane [16], Fang [17, 18], Fang and Lee [19]. The claical problem (i.e., luid low along a horizontal, tationary urace located in a uniorm ree tream) wa olved or the irt time in 1908 by Blaiu [0]; it i till a ubject o current reearch [1, ] and, moreover, urther tudy regarding thi ubject can be een in mot recent paper [3, 4]. A tudy on boundary layer low o a nanoluid pat a tretching heet with a convective boundary condition wa conducted by Mainde and Aziz [5]. ecently, Ahmad et al. [6] preented a numerical tudy on the Blaiu and Saiadi problem in nanoluid under iothermal condition. Their reult revealed that the olid volume raction aect the luid low and heat traner characteritic o nanoluid. Moreover, their theoretical tudie o nanoluid relied on the aumption that the combined eect o both the vicou diipation and Newtonian heating on the low ytem are negligible. In reality, thi may not be the cae, ince vicou heating o the bae luid i enhanced by the addition o nanoparticle, and the convective heat traner may alo tae place at the heated plate urace. The ecluion o vicou diipation and Newtonian heating in the analyi may aect the outcome o their invetigation. To the bet o our nowledge, no attempt ha been made in the literature to highlight the combined eect o vicou diipation and Newtonian heating on the thermal boundary layer o nanoluid. Mainde [7] invetigate the combined eect o vicou diipation and Newtonian heating on the boundary layer low o water-baed nanoluid containing two type o nanoparticle uch a copper (Cu) and titanium (Ti ) over a moving urace. The natural convection boundary-layer low pat a vertical cone embedded in a porou medium illed with a non- Newtonian nanoluid in the preence o heat generation or aborption i preented in Hady et al. [8]. A imilarity olution o the teady boundary layer low near the tagnation-point low on a permeable tretching heet in a porou medium aturated with a nanoluid and in the preence o internal heat generation/aborption i theoretically tudied by Hamad and Pop [9]. Convective low in porou media ha been widely tudied in the recent year due to it wide application in engineering a pot accidental heat removal in nuclear reactor, olar collector, drying procee, heat echanger, geothermal and oil recovery, building contruction (Nield and Bejan [30], Ingham and Pop [31], Vaai [3] and Vadaz [33], etc.). It i well nown that conventional heat traner luid, including oil, water, and ethylene glycol miture are poor heat traner luid, ince the thermal conductivity o thee luid play an important role on the heat traner coeicient between the heat traner medium and the heat traner urace. An innovative technique or improving heat traner by uing ultra ine olid particle in the luid ha been ued etenively during the lat everal 6

3 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 vicoity, year. The derivation o the empirical equation which govern the low and heat traner in a porou medium ha been dicued in Mahdy and Hady [34], Ibrahim et al. [35], Abdel-Gaied and Eid [36]. The principal aim o thi paper i thereore to etend the wor o lanrewaju et al. [37] to report the eect o thermal radiation and Ecert number a well a Prandtl number Pr and convective parameter a on both Blaiu and Saiadi thermal boundary layer under a convective boundary condition. The ocu o thi paper i to eamine the eect o nanoparticle volume raction and poroity parameter or Blaiu and Saiadi low in a nanoluid. Three dierent type o nanoparticle are conidered, namely Cu, Al 3 and Ti, when the bae luid i H. II. PBLEM FMULATIN The governing equation o motion and heat traner or the claical Blaiu and Saiadi lat-plate low problem can be ummarized by the ollowing boundary value problem a lanrewaju et al. [37]. Taing into account the poroity term in the momentum equation or nanoluid. The thermo-phyical propertie o the nanoluid are tabled in Table 1 (ee ztop and Abu-Nada [4]). u v y 0, - n u u u u v, n u y y K n n 1 qr p n p n p n T T T u u v. (3) y ( c ) y ( c ) y ( c ) y The boundary condition or the velocity ield or the Blaiu lat-plate low problem are : u v 0; at y 0; u U at 0 u U a y And or the claical Saiadi lat-plate low problem : u U, v 0 at y 0; w u 0 a y, The boundary condition at the plate urace and ar into the cold luid may be written a T (,0) h [ T T (,0)], y T (, ). T where u and v are the velocity component o the nanoluid in the - and y-direction, repectively. Property n and n are the denity and eective vicoity o the nanoluid, (6) (1) () (4) (5) n and n are the thermal diuivity and the inematic the thermal conductivity o the nanoluid, K n i the permeability o the porou medium, U i the contant ree tream velocity, U w i the plate velocity and T i the temperature o the nanoluid inide the thermal boundary layer. which are deined a (ee Khanaer et al. [38]): n n 1 ; n ; ;. 5 n 1 C p C p 1 C p C ; n p n. Here i the olid volume raction, where n (7) i the vicoity o the baic luid, and are the denitie o the pure luid and nanoparticle, repectively, and c p c p are the peciic heat parameter o the bae luid and nanoparticle, repectively, and are the thermal conductivitie o the bae luid and nanoparticle, repectively. Uing the oeland approimation or radiation, the radiative heat lu i impliied a: q r 4 * 3 T y * 4, * * where and are the Stean Boltzmann contant and the mean aborption coeicient, repectively. We aume that the temperature dierence within the low uch a the term 4 T may be epreed a a linear unction o temperature. 4 Hence, epanding T in a Taylor erie about a ree tream temperature T and neglecting higher-order term we get: T 4T T 3T. (9) In view o Eq. (8) and (9) with Eq. (3): * 3 T T 16 T T n n u u v n, * (10) y 3( c p ) n y n y n where n (c ) i the thermal diuivity o a nanoluid. Eq. (10) become: p n T T n T n n u u v y 0 y n y * 3N n Where 0 ; N * 3 3N 4 T 4. (8) (11) a the radiation parameter. It i worth citing here that the claical olution or energy equation, Eq. (11) without thermal radiation and vicou diipation inluence can be obtained rom the above equation which reduce to 7

4 T T u v y ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 o a in Eq. (17). Thi condition can be met i the heat T a N (i.e 1). traner coeicient h i proportional to n y 0 Introducing a imilarity variable, a dimenionle tream unction ( ) and the non- dimenional temperature ( ) a: U y y e, u U ( ), 1 U T T v ( ) ( ), ( ). Tw T (1) where prime denote dierentiation with repect to η and U e i the local eynold number. Note that in Eq. (1); U U repreent Blaiu low, wherea U Uw indicate Saiadi low, repectively. We alo aume the bottom urace o the plate i heated by convection rom a hot luid at uniorm temperature which provide a heat traner coeicient h.the equation o continuity i atiied identically. We ubtitute Eq. (1) into Eq. () and (11) we have: n Ec 1 p.5 1 0, Pr 0 1 c p T c Where Ec (13) (14) Pr i the Prandtl number, c p T w T u e U K i the Ecert number. and poroity parameter, and the correponding boundary condition become: (0) 0, (0) 0, (0) a[1 (0)], ( ) 1, ( ) 0. For the Blaiu lat-plate low problem, and (0) 0, (0) 1, (0) a[1 (0)], ( ) 0, ( ) 0. or the Saiadi cae, repectively. Where h a U (15) (16) (17) For the momentum and energy equation to have a imilarity olution, the parameter a mut be a contant and not unction We thereore aume h c 1/ 1/ (18) Where c i contant. Putting Eq. (18) into Eq. (17), we have c a U (19) Here, a i deined by Eq. (19), the olution o Eq. (13)-(16) yield the imilarity olution, however, the olution generated are the local imilarity olution whenever a i deined a in Eq. (17). The quantitie o practical interet in thi tudy are the in riction coeicient C and the local Nuelt number C n Nu which are deined a: u u w y y0, Nu n T T y w y0 T Uing Eq. (1), quantitie (0) can be epreed a: 1 e 1/ C (0). 5 1 e 1/ n (0) (1) Nu () III. ESULTS AND DISCUSSIN (0) In order to get the phyical inight into the low problem, comprehenive numerical computation are conducted or variou value o the parameter that decribe the low characteritic and the reult are illutrated graphically. The ytem o non-linear ordinary dierential equation (13) and (14) with the boundary condition (15) and (16) are integrated numerically by mean o the eicient numerical hooting technique with a ourth-order unge Kutta cheme (MATLAB pacage). The tep ize i ued while obtaining the numerical olution with 5. ma We conider three dierent type o nanoparticle, namely, copper (Cu), alumina (Al 3 ) and titanium oide (Ti ) with H a the bae luid. Table 1 how the thermo-phyical propertie o H and the element Cu, Al 3 and Ti. The Prandtl number o the bae luid H i ept contant at 6.. It i worth mentioning that thi tudy reduce to thoe o a vicou or regular luid when 0. In order to veriy the accuracy o the preent method, we have compared our reult with thoe o lanrewaju et al. [37] or temperature proile in the abence o the (0) Blaiu and (0) Saiadi nanoparticle 0 and =0 or dierent value o a without thermal radiation ( ( i.e. 0 1) ) and N vicou diipation term and with thermal radiation 8

5 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 parameter. The comparion in all the above cae are ound to be in ecellent agreement, a hown in Table and Table 3. Table 4 depict the in riction at the urace (0) and the rate o heat traner (0) or variou value o Pr 6., poroity parameter with 0. 1, Ec.0, a =1.0 and N 5. 0 or dierent type o nanoparticle when the bae luid i H (Saiadi low). It i clear that a the poroity parameter increae, the in riction (0) increae, the rate o heat traner (0) increae and the Cu nanoparticle are the highet in riction than the other ollow by Ti and net Al 3 a hown in Table 4. Figure 1 1 depict the inluence o dierent parameter on the velocity and the temperature proile a well a the local in riction coeicient and the Nuelt number. A elected et o graphical reult preented in igure 1 1 will give a good undertanding o the inluence o dierent parameter on the velocity and the temperature proile a well a the in riction coeicient and the Nuelt number. Figure 1 and how the eect o nanoparticle volume raction on the nanoluid velocity and temperature proile, repectively, in the cae o nanoparticle are Cu and the bae luid i H ( Pr 6. ) when Ec.,a =1.0, 0,0.05,0.1,0.15, 0. with and N 5. It i clear that the nanoparticle volume raction increae, the nanoluid velocity increae and the temperature increae or the Blaiu low but a the nanoparticle volume raction increae, the nanoluid velocity decreae and the temperature increae or the Saiadi low. Thee igure illutrate thi agreement with the phyical behavior. When the volume o nanoparticle increae the thermal conductivity increae and then the thermal boundary layer thicne increae. The nanoluid velocity proile i the highet at the moving plate urace and decreae gradually to the ree tream zero value atiying the ar ield boundary condition. Figure 3 and 4 preent the dimenionle temperature and velocity proile or when 0.0,0.1,0.5,1.0,1.5,.0 Ec.0, Pr 6.,a =1.0, 0.1 and N 5.The thermal boundary layer thicne increae with the increae o the poroity parameter, while the velocity proile decreae with the increae o the poroity parameter, or both Blaiu and Saiadi low. Figure 5-8 how the variation o the hear tre in term o the in-riction coeicient and the rate o heat traner in term o the reduced Nuelt number or dierent value o nanoparticle volume raction,with Ec. 0, 6. Pr, a =1.0, 0.0 and N 5,or dierent type o nanoparticle,( Cu- H, Al 3 - H and Ti - H ) or both Blaiu and Saiadi low. Figure 5 illutrate the eect o parameter variation on the local in riction coeicient in cae o Blaiu low. The local in riction coeicient increae with the increae in the nanoparticle volume raction in cae o (Cu- H ) while it increae near the plate and then decreae at ome ditance rom the plate in cae o (Al 3 - H and Ti - H ). It i intereting to note that the Cu- H nanoluid produce i highet in riction coeicient than the Ti - H nanoluid and Al 3 - H nanoluid. A imilar trend i noticed in igure 6 in cae o Saiadi low. Figure 7 and 8 illutrate the eect o variou parameter on the heat traner rate at the moving plate urace or both Blaiu and Saiadi low. A the value o the nanoparticle volume raction increae, an increae in the Nuelt number i oberved. Generally, the heat traner rate at the moving plate urace or the Cu- H nanoluid are highet than the Ti - H nanoluid and Al 3 - H nanoluid a the woring nanoluid. Figure 9 and 10 illutrate the in riction at the urace (0) or variou value o poroity parameter with 0. 1, Pr 6., Ec.0, a=1.0 and 5. 0 N or dierent type o nanoparticle when the bae luid i H. It can be noticed that the numerical value o (0) decreae with an increae in the poroity parameter or dierent ind o nanoluid in cae o the Blaiu low a hown in igure 9, while it increae in cae o the Saiadi low, a hown in igure 10 and Table 4. In cae o the Blaiu low, It i ound that the rate o heat traner (0) decreae with the increae on poroity parameter ( 0.5 ). n the other hand ( 0.5 ) the rate o heat traner (0) increae with the increae on,a hown in igure 11 or dierent type o Pr 6., Ec. 0, a=1.0 nanoparticle with 0. 1, and N Finally, We oberve the remarable eect o poroity parameter on the rate o heat traner (0), i.e. the rate o heat traner (0) increae with the increae o poroity parameter or dierent type o Pr 6., Ec. 0, a=1.0 nanoparticle with 0. 1, and N 5. 0 in a cae o the Saiadi low a hown a igure 1 and Table 4. Table 1: Thermo-phyical propertie o luid and nanoparticle (ztop and Abu-Nada [4]): Phyical propertie Fluid phae (water) Cu Al 3 Ti C p ( J / gk ) ( g/ m 3 ) ( W / mk )

6 () ' () ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September ( K 1 ) Table :Value o (0) Blaiu with φ=0 and =0 or dierent value o a without thermal radiation and vicou diipation term. Parenthei indicate reult rom e. [37]. A Pr = 0.7 Pr = 10 Pr = ( ) (0.4035) ( ) (0.7718) ( ) ( ) ( ) ( ) ( ) ( ) (0.9317) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Table 4:Value related to the in riction and dierent value o with and ' (0) or φ =0.10,Pr=6., Ec=.0, a=1.0 N =5. ''(0) Saiadi '(0) Saiadi Al Cu 3 Al Ti Cu 3 Ti Table 3: Value o (0) Blaiu and (0) Saiadi with φ=0 and =0 or dierent value o a, Pr, and N in the abent o vicou diipation parameter. Parenthei indicate reult rom e. [37]. a Pr N (0) Blaiu (0) Saiadi ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =0.0,0.05,0.1,0.15,0. Cu- H Blaiu low... Saiadi low Pr=6. a=1.0 N Ec=.0 = Figure 1 Eect o nanoparticle volume raction on velocity ditribution ' () in the cae o Cu- H Cu- H Blaiu low... Saiadi low =0.0,0.05,0.1,0.15,0. Pr=6. a=1.0 N Ec=.0 = Figure Eect o nanoparticle volume raction on temperature proile () in the cae o Cu- H 30

7 '' (0) () ' () - '' (0) ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September Blaiu low... Saiadi low Cu- H =0.0,0.1,0.5,1.0,1.5,.0 Pr=6. a=1.0 N Ec=.0 = Figure 3 Eect o poroity parameter on velocity ditribution ' () in the cae o Cu- H Pr=6. a=1.0 N Ec=.0 = Cu Al 3 Ti Figure 6 Eect o nanoparticle volume raction on in riction coeicient '' () or dierent type o nanoparticle (Saiadi low) Cu- H Blaiu low... Saiadi low Pr=6. N Ec=.0 a=1.0 = Pr=6. a=1.0 N Ec=.0 =0.0 Cu Al =0.5,1.0,1.5,.0 - ' (0) Ti Figure 4 Eect o poroity parameter on temperature proile () in the cae o Cu- H Figure 6 Eect o nanoparticle volume raction on heat traner rate - ' (0) or dierent type o nanoparticle (Blaiu low) Pr=6. a=1.0 N Ec=.0 =0.0 Cu Al 3 Ti - ' (0) Pr=6. a=1.0 N Ec=.0 =0.0 Cu Al Ti Figure 5 Eect o nanoparticle volume raction on in riction coeicient '' () or dierent type o nanoparticle (Blaiu low) Figure 8 Eect o nanoparticle volume raction on heat traner rate - ' (0) or dierent type o nanoparticle (Saiadi low) 31

8 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 IV. CNCLUSIN The poroity eect on the low and heat traner characteritic o the Blaiu and Saiadi low in a nanoluid in the preence o thermal radiation. The reulting ytem o nonlinear partial dierential equation i olved numerically uing an eicient numerical hooting technique with a ourth-order unge Kutta cheme (MATLAB pacage). The olution or the low and heat traner characteritic are evaluated numerically or variou value o the governing parameter, namely the nanoparticle volume raction and the poroity parameter. Three dierent type o nanoparticle are conidered, namely Cu, Al 3 and Ti. The variation o dimenionle urace temperature a well a low and heat-traner characteritic with the governing dimenionle parameter o the problem, which include the nanoparticle volume raction, the thermal radiation parameter N and the poroity parameter are graphed and tabulated. In the cae o Blaiu low the velocity proile increae while it decreae in the cae o Saiadi low when the olid volume raction increae. The rie o the olid volume raction lead to increae o the temperature ditribution in both cae. An increment in the poroity parameter yield a decreaing in the velocity proile and an increment in the temperature ditribution in both cae, thi lead to a rapid reduction in the heat traner rate. The in riction coeicient increae a the nanoparticle volume raction increae when the nanoparticle are Cu, but decreae when the nanoparticle are Al3 and Ti in Blaiu and Saiadi low. 3

9 ISSN: IS 9001:008 Certiied International Journal o Engineering and Innovative Technology (IJEIT) Volume 3, Iue 3, September 013 The in riction coeicient i at decreae a the poroity parameter increae in the cae o Blaiu low. n the contrary o Saiadi low. The heat traner rate i decreae a the poroity parameter increae in the cae o Blaiu low. In contrat o Saiadi low a we epected. EFEENCES [1] M. E. Matteucci, M. A. Hotze, K. P. Johnton and.. William, III. Drug nanoparticle by antiolvent precipitation: miing energy veru uractant tabilization, Langmuir, vol., no. 1, pp , 006. [] S. U. S. Choi, Enhancing thermal conductivity o luid with nanoparticle, Proceeding o ASME International Mechanical Engineering Congre and Epoition, San Francico, pp , [3] D. Wen, and Y. Ding, Eperimental invetigation into the pool boiling heat traner o aqueou baed -alumina nanoluid. Journal o Nanoparticle eearch, vol. 7, no., pp.65 74, 005. [4] H. F. ztop, and E. 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