model for the effective thermal conductivity of nanofluids effect of interfacial layer and non-uniform size distribution of nanoparticles

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1 mme.modares.ac.ir : * - - moghiman@um.ac.ir * : 393 : : modelfortheeffectivethermalconductivityofnanofluids effectof interfaciallayerandnon-uniformsizedistributionofnanoparticles ZohrehShams *,MohammadMoghiman -DepartmentofMechanicalEngineering,FerdowsiUniversityofMashhad,Mashhad,Iran -DepartmentofMechanicalEngineering,FerdowsiUniversityofMashhad,Mashhad,Iran *P.O.B ,Mashhad,Iran,moghiman@um.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received3September04 Accepted4October04 AvailableOnlineNovember04 Keywords: Nanofluid Nanoparticle Effectivethermalconductivity,Non-uniform size Interfaciallayer Thisworkpresentsmodelforcalculatingtheeffectivethermalconductivityofnanofluids.Inthis method, the effect of non-uniform sizes of nanoparticles and interfacial layer is investigated simultaneously. The developed model for the thermal conductivity of nanofluids takes into accounttheeffectsofthermalconductivityofbasefluids,thermalconductivity,volumefraction and the sizeof nanoparticles,theinterfaciallayer,non-uniform sizesofnanoparticles,brownian motion and temperature. Hence, this model has the capability of offering both analytical and numericalpredictions.theaccuracyoftheproposedmodelfortheeffectivethermalconductivity of water-al O ethylene glycol-al O water-cuo ethylene glycol-cuoethylene glycol-al, water- TiO isinvestigated.theeffectoftemperature,sizeofnanoparticlesandvolumefractionof nanoparticles are determined. Results show that the interfacial layer at the nanoparticle-liquid interfaceandnon-uniformsizesofnonparticlesarethemostimportantparametersforcalculating the thermal conductivity of nanofluids. Comparison between the result and available experimental data of several types of nanofluids indicates that the proposed model provides accurateresultswithmaximumerrorof5% [4].[ [5. -.[] Pleasecitethisarticleusing: : Z.Shams,M.Moghiman,modelfortheeffectivethermalconductivityofnanofluids effectofinterfaciallayerandnon-uniformsizedistributionofnanoparticles,modares MechanicalEngineeringVol.5,No.,pp.9-98,05(InPersian)

2 : :[7 = + + ( ) + ( ). () -- = [ +]+ + ( ) + + [ + ]. =+ :[3 () =+ -3-.[4]. 3 0/5 0/4 - /9 80 0/5 [6] 4/9 0/74.. [7] [8]. [9] -. [0] [] [] [3]. [4].. [5] [6] [7] [8] 3 [9].. - [0] - -Brownianmotion -Cluster 3-Fractallow 9

3 - - - :.[8] 5 (5) = / 4 3 = ( k k [ + ] + k + k (k k ) + k k + k k k [ + ]. DLVO (3) (6) + sin ( sin ) = 0 = p, lr, f 6 7 (7) ( 0) =, ( ) = (8) =, = = 9 (9) =, = = + [3] -0 = 3 + = + + / + = (0) () (). cos :[3] 3 () () ( ( - 4- = :[0] "". -3.() Derjaguin-Landau-Verwey-Overbeck -Interfaciallayer 3-Complexnanoparticle(cp) (4)

4 : = 3.5, = + (0) = / [87. -) ( = [0] ( ) () = ln () ln( ) [0] 3 = = (3) / < < [8]..[0 0 () = 4 (4) =,,3, < <...3 (3) = =,, ( ) (,, ). = 4,,,, ( +, +, ( + ),, (4). =+ =+, =, ( ) = = 5-5) -5) ( - 5) =, -5) --3. " :[4 6 (6). = ",,, - =.5 8 ", (7) :[4] 8 (8) 9 7 = (9).5,

5 : = ().4.5 (5) =,,3,,. 4 - [3] / [4] [0]. [] [3] /03. x / ( 5)

6 : [4] [3] [] % [] [4] [3] /45 0/75 [3]. [4] [3]. / [3]

7 4 5.[ 4/3 9/ [3] -. : T( C) o [43] /0 /74 /00 0/65 3/00 /7 5/00 /8 / d dp(nm) p [] /50 8/0 4/5 7/88 8/60 9/6 5/70 /35 / Al O (8nm)/W Al O (33nm)/W Al O (80nm)/W Al O (9nm) /EG Al O (38nm) /EG Al O (60.4nm) /EG CuO(nm)/EG CuO(9nm)/EG CuO(35nm)/EG T( T( C) o

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