Fn lmn compaon o ransn dsspa dobl ds magnoconc nanold lo rom a roang rcal poros srac n poros mda Bg O hmma and Shr SR hp://dx.do.org/.77/977977856 l hors p URL Fn lmn compaon o ransn dsspa dobl ds magno conc nanold lo rom a roang rcal poros srac n poros mda Bg O hmma and Shr SR rcl Pblshd Da 7 hs rson s aalabl a: hp://sr.salord.ac./66/ USIR s a dgal collcon o h rsarch op o h Unrs o Salord. Whr coprgh prms ll x maral hld n h rposor s mad rl aalabl onln and can b rad donloadd and copd or non commrcal pra sd or rsarch prposs. Plas chc h manscrp or an rhr coprgh rsrcons. For mor normaon ncldng or polc and sbmsson procdr plas conac h Rposor am a: sr@salord.ac..
Procdngs o h Inson o chancal Engnrs- Par N: Jornal o Nanomarals Nanongnrng and Nanossms ISSN: 9779 ISSN: 9779 PUBLISHER: SGE PUBLISHING EPED RH 6 H 7 FINIE ELEEN OPUION OF RNSIEN DISSIPIVE DOUBLE DIFFUSIVE GNEO-ONVEIVE NNOFLUID FLOW FRO ROING VERIL POROUS SURFE IN POROUS EDI. hrpah hmma * O. nar Bég and Sa Rdd Shr Dparmn o ahmacs B V Ra Ins o chnolog da 5 langana Inda. Fld chancs Spra Rsarch Grop Prolm/Gas Engnrng Dson Non Bldg. Unrs o Salord anchsr 5W U. Dparmn o ahmacs Gandh Ins o chnolog/anagmn Unrs Hdrabad Inda. *orrspondng ahor-emal: hrpah.hmma@gmal.com Rnnng had: FINIE ELEEN RNSIEN DISSIPIVE GNEO-ONVEIVE NNOFLUID FLOW bsrac: hs papr amd o nsga h ransn dsspa HD dobl ds r conc bondar lar lo o lcrcall-condcng nanolds rom a saonar or mong rcal poros srac n a roang hgh prmabl poros mdm consdrng boanc hrmal radaon and rs ordr chmcal racon. hrmo-dson Sor and dso-hrmal Dor cs ar also consdrd. Darc s la s mplod. h mahmacal modl s ormlad b consdrng ar-basd nanolds conanng mallc nano-parcls or boh saonar and mong pla cass. hr nanolds ar xamnd naml coppr almnm oxd or anm oxd n ar. h ransormd non-lnar copld dmnsonlss paral drnal qaons dscrbng h lo ar sold h phscall appropra bondar condons b sng Galrn ghd rsdal schm. For prscrbd prmabl nmrcal rsls ar prsnd graphcall or h nlnc o a nmbr o mrgng paramrs. Valdaon o n lmn solons or sn rcon and Nssl nmbr s achd a comparson h h prosl pblshd or as spcal cass o h prsn nsgaon and r good corrlaon oband. Incrasng roaonal paramr s obsrd o rdc boh prmar and scondar loc componns. Prmar and scondar locs ar conssnl lad h ncrasng Sor Dor hrmal Grasho and solal Grasho nmbrs. Incrasng Schmd nmbr chmcal racon and scon paramr boh spprss nano - parcl concnraon hras h conrs bhaor s compd h ncrasng Sor nmbr. h sd s rlan o hgh mprar roang chmcal ngnrng ssms xplong magnzd nanolds and also lcromagnc nanomaral manacrng procsss. ords: Dobl ds concon; Nanold; Roang ld; Boanc; hmcal racon; Radaon.
Inrodcon agnc nanolds ar mrgng as a n branch o possbl orng lds h ponal n or xampl lcrcal ransormr chnologs mdcal ngnrng and son por ssms. hs lds ar manacrd b dsprsng magnc nanoparcls n bas lds.g. ar and ar rspons o h applcaon o magnc lds. o smla h manacr o sch marals magnohdrodnamcs prods an xclln plaorm. ddonall man sabl magnc nanolds ar snhszd a hgh mprars and hs nos hrmal rada ha ransr Zad al. []; Srgs al. []. Rcnl h sd lamnar dmnsonal concon lo o l O -ar bo-nanolds n a crclar b ndr consan all mprar condons as smlad h FV Fn Volm hod b Bg al. [] as ll as lo pas n a channl b adopng conrol olm approach nsgad b Rashd al. []. allc nanoparcls ha bn shon o hold xclln ars or radaon absorpon d o h plasmon rsonanc absorpon band n h sbl and nar IR spcrm ha can b nd b ngnrs o opmz proprs. Ohr cs ma also ars.g. chmcal racon and roaon o ssms Borbah al. [5]. In nclar ngnrng mplmnaon o magnc nanolds man o hs cs can also ars smlanosl. Frhrmor h dplomn o magnc nano-parcls n drg dlr ma also bn rom nsgaons o chmcall rac magnc nanolds h roaonal bod orcs. I s hror o bn o mprong sch dsgns and opmzng prormanc ha connos dlopmn n mahmacal and compaonal modls s ssand and rnd. hs moas h prsn nmrcal nsgaon. In rcn ars a nmbr o nsgaons o magnohdrodnamc nanold concon los ha bn rpord. hs sds ha xndd h ponrng or no coolans o ho a rgonn Naonal Laboraor n h Und Sas n h md-99s ho [6]; ho al. [7] cond h rm nanold o dscrb lds ngnrd b sspndng small olmrc nanoparcls l l O O S SN ln h arag szs lss han nm n connonal ha ransr lds H O H 6O and also ohr bas lds l ngn ol mnral ol bo-lds and poor ha ransr lds. h hrmal-nhancng proprs o magnc nanolds ha aracd ncrasng nrs n r-drsng lds sch as lcroncs opcal dcs maral snhss hgh por x-ras lasrs and bomdcal scncs. os sds o magnc nanold ranspor ha lzd h Lornz magnc bod orc ormlaon. Ozop al. [8] sdd h hdromagnc naral concon n an nclosr rom o sm-crclar hars on h boom all. hamha and l [9] rpord on magnc r conc lo o a nanold h ha sn/sorc cs. Ellah [] sdd h HD lo o non-nonan nanold n a pp. Rcnl h orh ordr Rng- a Shoong chnq s mplod o nsga h nsad HD lamnar conc nanold lo or prmabl acclrad srchng rcal srac b Frdoonmhr al. []. Shholslam al. [] nsgad magnc ld cs on nanold lo and ha ransr n a sm-annls nclosr b consdrng h cs o hrmophorss and Bronan moon and alad h gradn o nanoparcls olm racon. Roang los o nanolds ha also garnrd consdrabl anon. Sch sds no orols bod orc rms d o h roaon o h nanold. ahaan and rora [] consdrd conc nsabl n a hn lar o a roang magnc nanold consdrng Bronan dson hrmophorss and magnophorss cs. Usng a hbsh psdo
spcral nmrcal mhod and consdrng drn bondar condons h ond ha or ar and sr basd magnc nanolds h magnc ld domnas h boanc mchansm n ld lars abo mm hc. Nadm and Salm [] nsgad h a homoop analss mhod H h ransn mxd magnohdrodnamc roang nanold concon on a roang con h magnc ld and consdrd hr drn cass hr h ld s roang and h con s a rs h ld and h con ar roang h qal anglar loc n h sam drcon and hr onl h con s n roaon. h shod ha magnc ld dprsss loc magnds and ha loc ld s modd sgncanl dpndng on h roaon cas mplod. Bg al. [5] analzd h ransn sagnaon-pon bondar lar lo o nanolds rom a spnnng sphr sng boh homoop and doman dcomposon mhods. h shod ha h ncrasng roaonal paramr.. srongr srl c proporonal o h roaonal loc o h sphr prmar loc s nhancd hras scondar loc s rdcd and also mprars and nano-parcl concnraon magnds dcrasd. Rana al. [6] sdd h a araonal n lmn algorhm h ransn magno-hdrodnamc bondar lar lo and ha ransr n an ncomprssbl roang nanold or a srchng connos sh shong ha boh prmar and scondar loc ar srongl rardd h ncrasng Harmann magnc nmbr hras mprar and nanoparcl concnraon ar nhancd. h also ond ha grar roaonal paramr dclras boh prmar and scondar loc and rdcs mprar and nanoparcl concnraon. Shholslam al. [7] sd a orh-ordr Rng a mhod o sd magnohdrodnamc HD nanold lo and ha ransr n a roang paralll pla channl ssm consdrng coppr slr almna and anm oxd nano-parcls sspndd n ar. h shod ha Nssl nmbr s a maxmm or h anm oxd-ar nanold cas hras s srongl rdcd h ncrasng magnc paramr. Hamad and Pop [8] also xamnd roang hdromagnc nanold concon rom a prmabl pla nong ha h ncrasng roaon and ha sorc paramrs h sn rcon s rdcd as s h mprar and hrmal bondar lar hcnss. hmcal racon and hrmal rada cs n nanold los ar as laborad arlr also o nrs n parclar drng hgh-mprar snhss o nano-parcl sspnsons. Usall a rs ordr chmcal racon modl s mplod alhogh racons ma b mor complx. h can b homognos or hrognos and also ma b o scond or hghr ordr. Inrsng sds o chmcall-racng nanold los h magnohdrodnamcs ha appard q rcnl n h lrar. Ramzan and Blal [9] mplod a homoop mhod H o oban por srs solons or hrdmnsonal lo o scolasc condcng nanold along a bdrconal srchng sh h spcs dson and chmcal racon shong ha chmcal racon xrs a srong nlnc on mprar and nano-parcl concnraon ransr ra Shrood nmbr. h also nod ha mprar s lad hras nano-parcl concnraon rdcd h ncrasng Bronan moon paramr hras prmar and scondar loc ar boh spprssd h grar scolasc o h nanold. Uddn al. [] sdd drn ordr chmcal racon cs on naral concon nanold bondar lars sng apl nmrcal soar. h dmonsrad ha locs and mprars ar nhancd hras nanoparcl olm racon s rdcd h ncrasng ordr o chmcal racon. Rcnl Rashd al. [] sdd o dmnsonal lamnar r conc bondar lar lo o an Osald-d Wal Por-la nanold ndcd b a sadl roang nn ds o a nondarcan ld pas an pard acng chmcall racng horzonal pla sarad n a poros mdm b mplong OH Opmal Homoop nalss hod.
hrmal radaon s radonall smlad n bondar lar los h Rossland s dson lx modl hch approxmas h rada ha ransr as an algbrac lx modl. Sral nsgaors ha addrssd rada cs on nanold ranspor. rlmazogl and Pop [] drd analcal solons sng h Rossland lx modl or rada hang cs on ransn r concon nanold bondar lar los or coppr anm slr almnm oxd nanolds. Saa Naraana al. [] drd prrbaon solons or rada magnc roang nanold lo h ha gnraon n a poros mdm shong ha grar rada conrbon sgncanl ncrass nanold mprars. Vr rcnl Sa Rdd and hrpah [] nsgad ha and mass ransr cs on naral concon lo n h prsnc o olm racon or coppr-ar nanold. Uddn al. [5] nsgad radaon lx and hdrodnamc hrmal and solal slp cs on nanold xndng/conracng sh lo h l grop mhods and shoong qadrar nong ha ha ransr ras ar srongl nlncd b rada ha ransr as ar nanoparcl mass ransr ras. Frhr sds consdrng hrmal radaon n nanold concon los ha bn rpord b Ibanz al. [6] ho consdrd nrop gnraon n HD rada nanold slp lo n mcro-channls. h combnd nlnc o Sor and Dor dsonal phnomna ar also a sgncan ara o nrs n marals procssng ssms. Sch cs bcom promnn hn spcs ar nrodcd a a srac n a ld doman. h rlaons bn h drng ponals and lxs ar o a hghl nrca nar. h nrg and mass lxs ar gnrad a composon and mprar gradns rspcl. hs lxs ar also rmd dsonhrmo Dor and hrmal-dson Sor cs. Whn boh cs occr oghr sch los ar dnd as dobl-ds concon los. h sd o dobl ds naral concon n poros mda nds nmros applcaons n rado-ncld sorag and ranspor n gologcal marals chromaograph bo-chmcal conamnan ranspor n aqrs lraon chnologs marals abrcaon c. Exns horcal and nmrcal sds o dobl ds concon n boh xrnal bondar lar los and nrnal los or drn gomrcal congraons ha bn commncad. hs ncld ranspor rom a prmabl sphr El-abr al. [7] mcropolar concon rom a sphr Bg al. [8] ha and mass ransr n nclnd sqar cas handrashar and shan [9] magnohdrodnamc lo ha and mass dson rom a srchng sh n poros mda Bg al. [] and bondar lar lo rom a concal gomr n poros mda rom rncad con Rashad and hamha []. Sor and Dor cs r shon n hs sds o xr a mard nlnc on loc mprar and concnraon lds. h abo nsgaons gnrall dd no consdr h collc cs o hrmal radaon scos dsspaon spcs and hrmal boanc or chmcal racon or roang nanold los. In ralsc snhss opraons hs cs ar mporan. anacrng o magnc nanolds nols rqnl hgh mprar and dsrc chmcal racon cs as hghlghd b Vnasarl and Naraana [7]. Frhrmor roaonal bod orc and poros mda lraon mda can b xplod o br conrol bondar lar procsss n sch lds hch lad o mor homognos dsrbons o nanoparcls. cal lo procsss ar also nsad.. m-dpndn n manacrng ssms as laborad b Borbah al. [5]. In ssms h dsng spcs nano-parcls cross-dson cs can also ars. In h prsn arcl s hror consdr ransn magnohdrodnamc HD dobl-ds r conc bondar lar lo o nanolds rom a saonar/mong rcal poros pla n roang poros mda. Wall scon laral mass lx and scos
5 hang cs ar also ncorporad. n amp s mad o nsga comprhnsl h nlnc o prnn paramrs on prmar and scondar loc dsrbons or boh h saonar pla and mong pla cass as ll as mprar and concnraon dsrbons or hr drn ar-basd nanolds: H O and l O H O and O H O. Gnrall o modls ar poplar or smlang nanolds naml h Bongorno [] Bongorno modl hch nclds man mchansms b hch mphaszs h conrbon o Bronan dson and hrmophorss or ha ransr nhancmn and h ar-das ormlaon ar and Das [] hch ars a nano-parcl olm racon. Vr rcnl Garoos al. [] sd n olm dscrzaon mhod o sd h naral concon ha ransr o nanold n a odmnsonal sqar ca conanng sral pars o hars and coolrs Hs sng Bongorno modl. h lar mplmn n h prsn sd. h ransormd bondar lar qaons hch gorns h lo and ha and mass ransr o nanolds ar srongl nonlnar n nar and a nmrcal mhod s rqrd or solon o h ransormd bondar al problm. h n lmn mhod FE s mplod. In scon h mahmacal modl s dlopd. In scon nmrcal solons ar dscrbd h aldaon and grd-ndpndnc. Scon conans h dscsson and alaon o h nmrcal rsls. Fnall h mporan obsraons ar smmarzd n h scon 5 onclsons. h crrn sd s rlan o hgh-mprar magnohdrodnamc HD nanold marals procssng ssms mplong roaonal bod orcs. ahmacal ormlaon o h problm h schmac modl o h coordna ssm and h phscal problm ndr nsgaon ar dpcd n Fgr. h arsan coordna ssm s slcd sch ha h x axs s along h drcon o h pla hrogh hch ld lo n h pard drcon s consdrd axs s prpndclar o h pla and z axs s normal o h x plan.. ransrs o h plan o h pla. No consdr h magnohdrodnamc r concon lo h ha and mass ransr spcs dson o an lcrcall-condcng nanold rom h sm-nn rcal poros pla adacn o a homognos soropc poros mdm n h prsnc o norm scon n a roang ram o rrnc. Darc s modl s mplod or poros mdm drag cs. h pla s assmd o b n rgd bod roaon h consan anglar loc abo h axs. norm magnc ld o srngh B s mposd ransrsl o h lo.. along h axs.
6 Fgr. Phscal modl and coordna ssm or h problm. h pla s mong h h loc bng a consan. I s assmd ha lo s drn b h moon o h pla hch oscllas h consan rqnc n n m so ha pla mprar oscllas o cos n. n-drconal rada lx acs normal o h pla srac. h nanold hch saras h poros mdm s dsspa and s absorbng mng and gra b no scarng. Hall crrn and axll dsplacmn crrn cs ar nglcd. Inall a m boh h pla and ld ar manand a norm mprar and norm nano-parcl concnraon. Onc h pla sars mong.. hn along x axs drcon agans graaonal ld h mprar s rasd o hch s hghr han h ambn mprar and h spcs nano-parcl concnraon a h srac s manand norml a. Snc h pla s assmd o b o nn xn along xand drcons hn all h phscal qans ar dpndn soll on and. In comparson h h xrnal magnc ld appld s assmd ha ndcd magnc ld s nglgbl snc h magnc Rnolds nmbr o lo s an o b r small Lron and Wlhlm [5]. hs hs assmpon s sd snc h magnc Rnolds nmbr s r small or mallc lqds and parall onzd lds. Fnall s also assmd ha hr s no appld olag hn hr s no xrnal lcrc ld s appld so ha h polarzaon o h ld s nglgbl ramr and Pa [6] h bas ld and sspndd nano parcls ar n hrmal qlbrm sa h nanoparcls ar assmd o ha a norm shap sz and pla s lcrcall non- condcng and h racon s assmd o a plac nrl n h sram. B consdrng h aormnond assmpons h gornng bondar lar qaons o consraon o mass momnm nrg and concnraon qaons b ollong Vnasarl and Saa Naraana [7] or nsad r conc lo ndr h Bossnsq approxmaon ar gn b:
7 B g g n n n n n B n n n c c D q c p s m n r n n p 5 D D m m r m h nal rms on h rgh hand sd o qaons and rprsn h Darcan lnar drag orcs or h prmar and scondar lo rspcl. h corrspondng nal and bondar condons Ishga [8]; Ganapah [9]; Das al. [] on h rcal srac and n h rsram can dnd as: 6 cos { n or or Hr ar loc componns along z and x drcons rspcl and dnos h drcon o moon o h pla. Whn h pla s sad o b n saonar sa and hn hs corrsponds o h cas hr h pla s mong rcall pards. I s orh mnonng hr ha nomnclar s prsnd n ppndx. h nanold proprs Ozop and b-nada [] ar gn b: 7 a c c c s s n n s p p n p s n h c hrmal condc o h nanold s adopd rom Brnman [] modl as 7.5 b n h c hrmal condc o h nanold s gn b axll-garns modl ollod b Ozop and b-nada [] 7 c s s s s n h conn qaon. q lads o h rdcd mass consraon qaon. On ngrang hs rsls hr consan s h normal scon loc a h pla
8 and q s consan. For an opcall hc phoon man r pah s r small ld n addon o msson hr s also sl-absorpon and sall h absorpon cocn s alngh dpndn so hs h n rada ha lx rm Brsr [] s hn approxmad sng h Rossland dson modl as: 8 q r Hr and ar h Rossland man absorpon cocn and San-Bolzmann consan 5.6697* -8 Wm - - rspcl. hs modl has bn appld n a drs rang o boh magnc and non-magnc ha and mass ransr problms and has bn shon o b q accra or opcall-dns rgms as laborad b Bg al. [-7]. I s assmd ha h mprar drnc hn h lo ar scnl small sch ha ma b xprssd as a lnar ncon o h mprar b xpandng n a alor srs abo as... 6 and b nglcng h hghr ordr rms gs: 9 Hnc rom Eq. 8 sng Eq. 9 h rslan s: 6 q r Procdng h h analss a s o non-dmnsonal arabls dnd as ollos: Pr 6 c c D D D Sr g Gc g Gr c E c R B D Sc r S n n p s m m m o p o p o m o o r o o o o o o o Sbsng nanold proprs and h abo dmnsonlss arabls.. qaons 7a- 7c and no qaons lds h ollong ssm o nsad copld non-dmnsonal nonlnar paral drnal qaons. Gc Gr S S D Ec S 5 Sr r Sc S
9 Whr c p n.5 n n R. c Pr n n hs xprssons conan nano-parcl olm racon and ohr propr conrbons. h appropra nal and bondar condons n non-dmnsonal orm a h orm: n p n or or { a as cos n 6 Fn lmn compaonal solons and aldaon h ransormd ssm o non-lnar copld and non-homognos dmnsonlss paral drnal qaons - 5 ndr h bondar condons qaon 6 ar sold nmrcall b sng h xnsl-aldad and robs n lmn mhod h a Galrn ghd rsdal schm. hs mhod comprss ndamnal sps naml dscrzaon o h doman draon o h lmn qaons assmbl o lmn qaons mposon o bondar condons and nall ra solon o h assmbld qaons h a robs mhod.g. hols dcomposon Gassan lmnaon c. Dals o h n lmn approxmaons ar prodd n h ppndx. n xclln dscrpon o hs sps ar prsnd n h x boos o Rdd [8] and Frhr dals o hs mhodolog as appld o nanolds ar gn n Rana al. [9]. Dmnsonlss prmar loc scondar loc mprar and nano-parcl concnraon ar compd. h grd ndpndnc s condcd b ddng h nr doman no sccssl szd grds o msh dns 55and7 7. h bondar condons or a ar rplacd b a scnl larg al hr h loc mprar and concnraon prols approach zro. h PLE-basd FE cod s ran hn h scon paramr S. 5 or drn sp szs and r good agrmn bn h rsls or all h prols s achd as prsnd n abl. r man rals or compaonal lxbl 8 s mposd hr max max.. xrnal o h momnm nrg and concnraon bondar lars and hr adopd or all h compaons 5 nrals o qal sp sz.5. ach nod or ncons ar o b alad so ha ollong assmbl o lmns a s o 6 non-lnar qaons ar ormd. hror an ra schm s adopd and b nrodcng bondar condons h ssm o qaons ar sold ssmacall. h solon s assmd o b conrgd hn h solon drnc sass h dsrd accrac -7. n xclln conrgnc or all h rsls s achd. hrmo-phscal proprs o H O g l O and O -ar nanolds ar adopd rom Ozop and b-nada [] and docmnd n abl. Frhrmor s mporan o calcla h ngnrng qans o nrs. hs ncld h sn-rcon srac all shar srss ncon hch s oband as n. h ra o h ha ransr a h pla s dnd as a Nssl nmbr
and gn b N n. h ra o mass ransr o nano-parcls a h all s compd sng h Shrood nmbr hch s gn b Sh n. In ordr o alda h accrac o h nmrcal rsls oband hrogh h PLE-basd n lmn cod h prsn rsls ar compard or sn rcon and Nssl nmbr h h rsls oband hrogh arlr analcal sds. h crrn modl rdcs o ha o Hamad and Pop [8] n h absnc o hrmal radaon ha gnraon and mass ransr.. nglcng h spcs dson qaon and assocad rms. h comparson s docmnd n abl shong r good corrlaon. Frhrmor comparsons o h prsn n lmn solons h Vnasarl and Saa Naraana [7] ha also bn condcd or h cas o consan srac mprar and oscllaor pla loc ho ha gnraon rms and hs ar shon n abl. h comparsons conrms ha h prsn rsls ar ndd ald and n agrmn h h pblshd lrar. hror hs aorabl comparsons s condnc n h n lmn cod mplod hch can b sd hror n prsnng rhr rsls qanal and graphcall. Rsls and dscsson Exns nmrcal compaons ha bn prormd h h n lmn cod. Hr hs arcl addrss h nlnc o Sr D Gr Gc Ec R Pr Sc and r on h nanold loc mprar and spcs concnraon dsrbons. Solons ar dpcd graphcall n Fgrs o 6. Nmrcal solons ar llsrad n hs grs b xng h als n n /.. 9 and. 5 m s hror no xplcl sdd n h Fgrs o 6. h PU oo. sconds or 5 nodal pons h h Inl cor procssor ndr ndos plaorm hch s compd b sng h apl command m or compaon o loc mprar and concnraon prols. h ollong dal als r adopd o rprsn phscall ralsc los or n lmn compaon as ollos: S.. Sr. D.5 Gr 5 Gc Ec.. R.5 Pr 6. Sc. 5 and r. 5. I s nod ha h nlnc o som paramrs on phscal qans ar no prsnd graphcall or brnss and ar nod n ohr sds o nanold bondar lars. paramrc nsgaon s no ndran o lcda h hrmo-phscal characrscs o h lo. In all plos h asmpoc prols or larg conrm ha an adqal larg bondar condon s mposd n h rsram and ha solons ar ndd corrcl conrgd. Fgrs o 5 dpc h prmar and scondar loc or and cass mprar and concnraon prol dsrbons or hr drn ar-basd nanolds H O coppr ar l O H O lmnm oxd-ar and O H O anm oxd-ar. Fgr dmonsras ha boh prmar and scondar loc prols or h saonar pla scnaro ar nall zro h pla s sagnan and h progrss dsanc along h pla n h -drcon als gro as h bondar lar gros. h pa magnds n boh cass ar aand rlal clos o h ladng dg and hrar dcrasd o zro a a scnl larg al o. hs sbsanall largr magnds o boh prmar and scondar loc ar obsrd or H O nanold. Progrssl
lor als corrspond o h l O H O and O H O nanolds. Sgncan lo acclraon s hror achd h H O nanold hras srong dclraon s assocad h h l O H O and O H O nanolds. Fgr shos ha a r drn rspons n h prmar and scondar loc prols s compd or h mong pla scnaro. For hs cas prmar loc commncs h h acal mong pla loc and progrssl dcrass o zro asmpocall n h rsram. Prmar loc xhbs monoonc dca or all nanold ps. Hor scondar loc rals a smlar parn as obsrd n h saonar pla cas n ha magnd o h scondar loc prols gros rom h ladng dg pas som dsanc rom h ladng dg and hn dcas asmpocall o zro n accordanc h h rsram bondar condons. Gnrall sgncanl grar magnds o scondar loc ar ssand compard h prmar loc h dsanc along h pla. Hghr als o prmar loc ar compd or h saonar pla a nrmda dsancs rom h ladng dg hras or h mong pla scnaro h al a h all s maxmzd. I s also nrsng o no ha a slgh dsplacmn n pa scondar loc occrs hn h nanold s changd rom H O o l O H Oand hn o O H O. s h h saonar pla scnaro anm oxd-ar nanold aans los prmar and scondar loc magnds hras h coppr-ar nanold conssnl aans hghs magnds. Fgrs and 5 dmonsra ha mprar and concnraon prols or H O ar mardl hghr as compard h h l O H O and O H O nanolds. hs s arbabl o h hgh hrmal condc o rla o l O and O hch manss n an nhancmn o h hrmal and spcs dson n h bondar lar rgm. s a rsl h hrmal and concnraon bondar lar hcnsss or H O nanold ar grar han or l O and O nanolds. h prols or mprar and concnraon ar alas monoonc dcas rom h ladng dg o h rsram. grar modcaon n magnds s achd or mprars compard h concnraons. Fgrs 6 and 7 prsn h rspons n prmar and scondar cross lo loc prols agan or boh cass o a saonar and a mong pla or drn als o roaonal paramr and h hr drn nanold sspnsons. h roaonal paramr ars n h orols bod orc rms arsng n boh h dmnsonlss prmar momnm qaon and h dmnsonlss scondar momnm qaon. hs rms ar rspcl and rspcl. h rm / s drcl proporonal o h anglar loc o h roang pla. s s ncrasd h orols orc s also nhancd.. h roaon o h pla s mor nns b h bod orc hch s nga or prmar lo bcoms srongr also and hs lads o a sgncan dclraon n h prmar and scondar lo no h pla s saonar onl n h sns ha s no mong rcall pards or n Fgr 6. lhogh h scondar roaonal bod orc s ncrasd h domnan c s ha o h prmar roaonal bod orc orols orc hch lads o a concrrn dclraon also n h scondar lo.. dampng o h lo loc. hs obsraons ar also conssn h classcal Nonan roang pla lo sds docmnd n Grnspan [8]. h rnds compd n Fgr 6 ar also n gnral agrmn h h ndngs o Vnasarl and Saa Naraana [7] or roang pla nanold dnamcs. In Fgr 6 s obsrd ha h prmar and scondar loc magnds ar consdrabl grar or H O nanold compard h l O H O
nanold. lhogh rardaon o h lo s promnn lo rrsal s nr obsrd.. magnds o boh prmar and scondar loc rman pos or all als o rrspc o h magnd o or h nanold cas. In Fgr 7 or h rcall pard mong pla scnaro agan h prmar and scondar loc prols ar mardl drn. hr s a gradal dca n prmar loc rom h ladng dg h dsanc o anshng loc n h rsram. Hor h scondar loc prol s smlar o h cas n Fgr 6 or h saonar pla scnaro h zro magnd a h ladng dg ollod b a pa shorl hrar and hn a progrss dca o h rsram. Boh loc componns hor dcras as n Fgr 6 h grar als o h roaonal paramr and agan hghs magnds corrspond o h H O nanold hras los magnds ar assoca h l O H O nanold. Fgrs 8 and 9 dpc h prmar and scond loc prol rspons o a chang n magnc ld paramr. h prmar and scondar momnm qaons.. Eqs. and ach ar a Lornzan magnohdrodnamc bod orc componn spccall and. Boh prmar and scondar loc lds ar hror drcl nlncd b h magnc ld c. h paramr s rlad drcl o h appld magnc ld srngh Bo. Incrasng magnc ld srngh hror las h Lornzan drag orc hch nhbs boh prmar and scondar los or boh saonar and mong pla cass. Ecl h applcaon o ransrs magnc ld o h lcrcall-condcng nanold gnras a rss p orc hch acs agans h moon o h nanold. Whn h magnc bod orc s qal o h scos hdrodnamc orc. For h magnc orc s domnan. h dclraon rardaon n h bondar lar lo rsls n an ncras n momnm bondar lar hcnss. For h saonar pla cas Fgr 8 pa loc arss som dsanc rom h ladng dg and as nod n arlr graphs dcas asmpocall o zro a h dg o hdrodnamc bondar lar. For h mong pla scnaro Fgr 9 agan prmar loc s a maxmm a h ladng dg and drops gradall o ansh n h rsram hras h scondar loc assms a smlar bhaor o h saonar pla scnaro and agan pas clos o h ladng dg.. xhbs a parabolc prol. For boh pla cass H O nanold achs grar acclraon han l O H O nanold. gan s apparn ha dsp h srong magnc ld als consdrd lo rrsal baclo s nr ndcd n hr h prmar or scondar los. Hor h applcaon o a magnc ld achs xclln lo conrol n h rgm and prods a smpl b c mchansm or rglang nanomaral s procssng opraons. Fgrs o dspla nlnc o hrmo-ds Sor nmbr Sr and dso-hrmo Dor nmbr D on h prmar and scondar loc or boh h cass o saonar and mong plas. Sor nmbr arss n h rm Sr n h concnraon consraon qaon 5. hs rm rprsns h nlnc o mprar gradn on h concnraon ld. I s hror on o o cross-dson rms h ohr bng D hch arss n h mprar qaon ars h Dor nmbr and sgns h nlnc o concnraon gradn on h mprar ld. In Fgrs and
an ncras n Sor nmbr Sr s ond o gnrall nhanc h prmar and scondar loc magnds or all als o h coordna. h magnds o prmar loc ar hor sgncanl grar or h saonar pla cas Fgr. For h mong pla cas Fgr agan hghr als o prmar loc ars a h ladng dg b lshr h scondar loc s ond o b grar. Incrasng Sor nmbr hror dnl ads n momnm dlopmn and acclras boh prmar and scondar lo componn locs. gan coppr-ar nanold achs conssnl grar magnds o boh prmar and scondar loc compard h almnm oxd nanold. Fgrs and sho ha ncrasng Dor nmbr xrs a smlar nlnc o Sor nmbr.. nhancs boh prmar and scondar locs. Orall hror h conrbon o boh cross dson gradns s asss o h prmar and scondar lo lds. Fgrs and 5 prsn h rspons n prmar and scondar loc o aros hrmal Grasho nmbrs Gr. hrmal Grasho nmbrs sgns h rla magnd o h hrmal boanc orc and h opposng rconal orc scos hdrodnamc orc acng on h ar- basd nanolds. Phscall Gr Gr Gr rprsn coolng o h pla hang o h pla and absnc o r concon crrns rspcl hs las cas corrsponds o orcd hrmal concon hr Gr. lmnas h hrmal boanc orc rm Gr n h prmar momnm qaon. h hrmal boanc rm hror copls h prmar momnm qaon h h nrg consraon qaon. Snc h non-zro als spcd or Gr ar 5 or -5 h hrmal boanc orc domnas or h scos orc onl hn Gr ar boh orcs o qaln magnd. For h saonar pla cas Fgr nga Grasho nmbr clarl ndcs a dclraon n h prmar lo hras pos Grasho nmbr acclras h lo. sss hrmal boanc coolng o h pla hror ads n momnm dlopmn hras opposng hrmal boanc hang o h pla dsros momnm. h conrs c s compd or h scondar lo ld hor hr coolng o h pla Gr 5. s obsrd o acclra h lo lss nga als o scondar loc hras hang o h pla Gr 5. ndcs srong dclraon grar nga als o scondar loc. h scondar lo or h saonar pla cas s alas rrsd snc als o ar alas nga. Onl pos als o prmar loc ar compd ndcang ha baclo dos no ars n h prmar lo ld. I s dn rom Fgr ha h shap o h prmar loc and magnd o h scondar loc or h cas o saonar pla ar h sam b n oppos drcons.. h prmar and scondar loc componns dmonsra a smmr abo h ln. hrmal boanc hor dos no ar n h scondar momnm qaon mplng ha h mpac on scondar loc s ndrcl xprncd a coplng h h prmar momnm qaon. Gnrall H O nanold ndcs srong acclraon n boh h prmar and scondar lo compard h l O H O nanold. Prols or boh prmar and scondar lo or h mong pla scnaro Fgr 5 da sgncanl rom h saonar pla scnaro Fgr. In boh lo lds rrsal o lo s nr obsrd. Prmar loc dcas as nod n arlr plos rom a maxmm a h ladng dg o a mnmm n h rsram hras scondar loc ascnds rom zro a h ladng dg o pa a shor dsanc rom hs pon and hn dcas smoohl o zro. gan H O nanold rsls n mch grar prmar and scondar loc als han l O H O nanold. h mong pla scnaro also achs gnrall a mor sabl lo parn or boh prmar and scondar componns snc baclo s compll lmnad n hs cas.
Fgrs 6 and 7 dpc h olon n prmar and scondar lo locs or boh cass o saonar and mong plas rspcl h araon n solal Grasho nmbr Gc. h solal nano-parcl spcs boanc orc also arss soll n h prmar momnm qaon a h rm Gc. hs rm cl copls h prmar momnm qaon drcl o h nano-parcl spcs concnraon consraon qaon. Onl als o Gc ar consdrd... and. or hch h spcs boanc orc sgncanl xcds h scos orc n h rgm. Rrs lo s nr compd n hr Fgr 6 and 7 snc onl asss spcs boanc orcs ar prsn Gc. In Fgr 6 saonar pla lo cas h prmar loc and scondar loc ar boh nhancd h grar Gc als and H O nanold achs mardl grar magnds han h l O H O nanold. In Fgr mong pla scnaro h csomar rspons n prmar and scondar loc dsrbons s obsrd. Prmar loc pas a and dscnds o ansh or larg. Scondar loc clmbs rom zro a and hrar xhbs a parabolc prol h ncrasng als. Incrasng spcs Grasho nmbr Gc clarl ndcs a srong acclraon n boh h prmar and scondar lo. s bor h magnds ar lor hor or l O H O nanold compard h H O nanold a characrsc agan probabl casd b h grar hrmal condc o h coppr nano-parcls. Fgrs o 7 srongl mphasz ha boh hrmal and spcs boanc xr a non-ral nlnc on loc componns n h nanold bondar lar lo rgm. Fgrs 8 and 9 llsra h modcaon n prmar and scondar loc componns or h saonar and mong pla cass h drn als o h nano-parcl olm racon. s olm racon ncrass h hrmal condc o nanold s lad. hror hrmal dson s asssd n h rgm. Prmar and scondar loc magnds ar hor srongl dcrasd h ncrasng als as sn n Fgr 8 or h saonar pla cas. lhogh prmar loc s grar nall han scondar loc h progrss dsanc along h pla.. grar als hs rnd s rrsd and scondar loc al xcds prmar loc ar rom h ladng dg.. closr o h rsram. Hr H O nanold agan achs conssnl grar magnds o boh prmar and scondar loc as compard h l O H O nanold. Hor rhr no ha h prmar loc magnds n h l O H O nanold ar dsncl grar han h scondar loc als h H O nanold. Fgr 9 shos ha or h mong pla cas a sgncan dclraon s also compd n boh prmar and scondar loc componns h grar nanoparcl olm racon. h nlnc on prmar loc s conssn hor or all als o h coordna along h pla hras s onl ssand or a n dsanc or h scondar loc and h rrs c s obsrd nar h rsram as n Fgr 8. Sgncanl lor magnds o h prmar loc ar compd n Fgr 9 as compard h Fgr 8. Hor h domnanc o H O nanold or l O H O nanold s manand n n h mong pla scnaro.. coppr ar nanold achs br prormanc. Fgr llsras h c o Rossland hrmal radaon paramr R on mprar dsrbons or H O and l O H O nanolds. I s dn ha h grar R
5 als mprars ar mardl nhancd hrogho h bondar lar along h pla. hrmal radaon arss n h agmnd hrmal dson rm n h nrg consraon 6 qaon.. hr n R and R rlas h rla c Pr p n rol o hrmal rada ha ransr o hrmal condcon ha ransr. Whn R boh mods conrb qall. Whn R hrmal condcon domnas and hn R hrmal radaon domnas. For h als o R xamnd n Fgr...... h conrbon o hrmal radaon s progrssl grar. hs nnss h ha ransr and nrgzs h nanold bondar lar hch manss n an laon n mprars. oppr ar nanold agan rsponds mor sccssll han almnm oxd ar nanold o a chang n rada lx snc conssnl aans hghr mprars. h c o hrmal radaon s hror r sgncan on h araon o mprar. I s smd ha mprar ncrass rapdl n an ncras n h hcnss o hrmal bondar lar. Nanold maral proprs ma hror b srongl manplad a h mposon o a rlal a rada lx n manacrng opraons. Fgr dpcs h nlnc o Dor nmbr on mprar dsrbons. h conrbon o concnraon gradns o hrmal nrg lx n h lo rgm s masrd h h Dor nmbr D. From h graph s nocd ha mprar ncrass srongl h an ncras n Dor nmbr D and hs rsls n an laon n hrmal bondar lar hcnss. hs s d o ncras n conc ha xchang a h pla srac. h cross dson rm D hch arss n h mprar qaon hror xrs a promnn c on mprars n h bondar lar. gan s nod ha H O aans sbsanall grar mprars or all als o h -coordna as compard h l O H O nanold. Fgr prsns h araons n h mprar prols or drn als o Prandl nmbr Pr. Prandl nmbr rrs o h rla conrbon o momnm dson o hrmal dson n h bondar lar rgm. Frhrmor an ncras o Prandl nmbr rsls n a dcras n mprar dsrbon n hrmal bondar lar. h phscal rason s ha smallr als o Prandl nmbr ar assocad h grar hrmal condc and hror ha s abl o ds aa rom h had srac mor rapdl han a hghr als o Prandl nmbr.. h nrg dson ra s grar han h momnm dson ra or Pr hras h conrs s dn or Pr. For Pr boh h nrg and momnm dson ras ar qaln and h momnm and hrmal bondar lar hcnsss h sam. Ecl h ra o ha ransr s rdcd and an ncras n Pr ndcs a rdcon n hcnss o h hrmal bondar lar. Sgncanl grar mprars ar hor compd h coppr ar nanold rla o almnm oxd ar nanold a an Prandl nmbr ndcang ha hrmal condc o nano-parcls has a domnan nlnc n nanold bondar lar ranspor phnomna. Fgr prsns h olon n mprar prols h araon n Ecr nmbr Ec. hs paramr s assocad h h scos hang c and s sall r small or ncomprssbl los as sdd hr and rhr laborad n Gbhar al. [5]. I xprsss h rlaonshp bn h nc nrg n h lo and h bondar lar
6 nhalp drnc. I hror rprsns h qan o conrson o nc nrg no nrnal nrg b or don agans h scos ld srsss. n ncras n Ecr nmbr a dsspaon o mchancal nrg casd b nrnal rcon bn molcls o h nanold no hrmal nrg ha ll nhanc h mprar o h ar-basd nanolds n h poros rgm as obsrd n Fgr. h classcal loc orshoo obsrd n man sds s also compd n Fgr and arss nar h pla ladng dg. Smooh dca o mprars ollong hs pa ar compd no h rsram. hrmal bondar lar hcnss s gnrall nhancd h grar Ecr nmbr and agan h c s mor promnn n coppr ar nanolds han n almnm oxd ar nanolds. Fgrs o 6 rprsn h nlnc o Schmd nmbr Sc Sor nmbr Sr and chmcal racon paramr r on nano-parcl concnraon prols rspcl. Fgr rals ha hr s a ssand rdcon n concnraon magnds o nano-parcl spcs h ncrasng Schmd nmbr. h Schmd nmbr rprsns h rao o h momnm ds o h mass nano-parcl spcs ds.. rlas h hcnss o h hdrodnamc bondar lar o ha o h concnraon bondar lar. I also rlas h momnm scos dson ra o h molclar nano-parcl dson ra. For Sc momnm dson s domnad b molclar dson. For Sc boh dson ras ar h sam. For Sc momnm dson ra xcds molclar dson ra. s Sc s ncrasd h nano-parcl molclar ds s rdcd. hs rsls n dcrasng spcs dson ras and a lorng n nano-parcl concnraon magnds hrogho h bondar lar. Phscall hs also manss n a dcras n h nano-parcl concnraon bondar lar hcnss h ncrasng Schmd nmbr. Irrspc hor o h Schmd nmbr h coppr-ar nanold agan achs hghr concnraon als han h almnm oxd ar nanold. In Fgr 5 s obsrd ha an ncras n Sor nmbr Sr ndcs a sgncan nhancmn n concnraon prols hch n rn ncras h hcnss o spcs concnraon bondar lar. Nar h pla srac spcs concnraon srongl xcds ha n h rsram. h rm Sr n h concnraon consraon qaon 5 hror booss concnraon magnds srongl. Hnc mprar gradns xr a sgncan nlnc on h nano-parcl spcs dson n h bondar lar. Grar concnraon bondar lar hcnss s achd h copprar nanold compard h almnm oxd ar nanold. Fnall Fgr 6 shos ha h ncrasng chmcal racon paramr r magnds o concnraon ar mardl rdcd. h rm r n qaon 5 ndcas a dsrc chmcal racon n hch nano-parcl spcs s dcrasd n h rgm or r. hs rsls n dplon also n nano-parcl concnraon bondar lar hcnss. In boh Fgrs 5 and 6 s obsrd agan ha H O nanold narabl aans mch grar nano-parcl concnraon magnds or all als o h -coordna as compard h l O H O nanold. Hghr concnraon bondar lar hcnss ll hror also b assocad h H O nanold.
7 onclsons mahmacal modl has bn prsnd or h ransn ncomprssbl HD dobl ds r conc bondar lar lo o nanolds rom a roang rcal poros pla consdrng boanc hrmal radaon scos hang and chmcal racon cs. h non-dmnsonalzd paral drnal qaons or prmar and scondar momnm nrg and spcs consraon hch gorn h lo problm ha bn sold nmrcall b sng robs n lmn mhod. Valdaon o solons h arlr pblshd rsls has bn ncldd. sh-ndpndnc sd has also bn condcd. Boh cass o an pardl mong pla and a saonar pla ha bn consdrd. Rsls ha bn compd and dpcd graphcall or nlnc o Sr D Gr Gc Ec R Pr Sc and r on h nanold loc mprar and spcs concnraon dsrbons. Frhrmor a ar o ar basd nanolds.. H O l O H O and O H O nanolds ha bn consdrd. h nmrcal solons ha bn prsnd a a slcd m nral. h prncpal ndngs o h crrn nsgaon ar smmarzd blo. h prmar and scondar lo ar boh acclrad h ncrasng als o Sr D Gr and Gc hl h ar dclrad h ncrasng als o and or boh saonar and mong pla cass. H O nanold loc dsrbons aans zro loc asmpocall asr han h l O H Onanold n ncras n R Ec and Dnds o la mprars and hror ncrass hcnss o h hrmal bondar lar. onrsl an ncras n h paramrs Pr dcrass mprars and rdc h hcnss o hrmal bondar lar. h nano-parcl concnraon magnds and hror spcs concnraon bondar lar ncrass h an ncras o Sr hl ncrasng paramrs Sc and r manss n a rdcon n nano-parcl concnraons and concnraon bondar lar hcnss. Grar hcnss o hrmal and concnraon bondar lars s achd or H O nanold rla o l O H Onanold. Boh Sor and Dor nmbr xr a h hrmal-dson and dson-hrmo crosslo gradn cs a sgncan nlnc on ha and mass ransr characrscs o ar basd nanolds. Fr scop h prsn analss has bn connd o Nonan nanolds. Fr sds ll addrss non-nonan nanold modls sch as Erngn s mcropolar hor La al. [5] and ll b commncad soon. cnoldgmns h ahors ar gral o boh rrs or hr nsghl commns hch ha srd o mpro h prsn or. Rrncs
. Zad Z Sad H Sadr R amalsarsan and Rahm N. Rada proprs o nanolds. In. omm. Ha ass ransr ; 6: 7 8.. Srgs Barr and Hardalpas Y. Ponal or mpromn n hgh ha lx hpr aporon lmn prormanc sng nanolds. Proc. h IE FE San Dgo US.. Bg O Rashd bar and Hossn. compara nmrcal sd o snglphas and o-phas modls or Bo-nanold ranspor phnomna. Jornal o ch. In dcn and Bolog ; :5 pags.. Rashd Hossn Pop I mar S and Frdoonmhr N. ompara nmrcal sd o sngl and o-phas modls o nanold ha ransr n a channl. ppl. ah. ch.-eng. Ed. ; 57: 8-88. 5. Borbáh Bca D Poncz I Vas L Borbah I and Boros. agnc nanolds and magnc compos lds n roang sal ssms. IOP onrnc Srs: Earh and Enronmnal Scnc ; : -. 6. ho S. Enhancng hrmal condc o lds h nanoparcls n Dlopmns and pplcaons o non-nonan los. Sgnr D Wang HP dors SE 995; 66: 99-5. 7. ho SUS Zhang ZG Y W Locood FE and Grl E. nomalosl hrmal condc nhancmn n nanob sspnsons. ppl. Phs. L ; 79: 5. 8. Ozop HF Rahman hsan Hasanzzaman Sadr R and l-salm H al. HD naral concon n an nclosr rom o sm-crclar hars on h boom all. In. J Ha ass ransr ; 55: 8 5. 9. hamha J and l. HD r concon lo o a nanold pas a rcal pla n h prsnc o ha gnraon or absorpon cs. hm. Eng. omm. ; 98: 5-.. Ellah R. h cs o HD and mprar dpndn scos on h lo o non- Nonan nanold n a pp: analcal solons. ppl. ah. odl ; 7: 5 67.. Frdoonmhr N Rashd and Shohl D. Unsad HD r conc lo pas a prmabl srchng rcal srac n a nanold. In. J. hrmal Sc. 5; 87: 6-5.. Shholslam Gor-Bandp Gan DD Rana P and Solman S. agnohdrodnamc r concon o lo-ar nanold consdrng hrmophorss and Bronan moon cs. omprs & Flds ; 9: 7 6.. ahaan and rora. oncon n roang magnc nanolds. ppld ahmacs and ompaon ; 9: 68 696.. Nadm S and Salm S. Unsad mxd concon lo o nanold on a roang con h magnc ld. ppl. Nanoscnc ; : 5-. 5. Bg O abood F and Nazrl Islam. Homoop smlaon o nonlnar nsad roang nanold lo rom a spnnng bod. Inrnaonal Jornal o Engnrng ahmacs 5; rcl ID 779 5 pags hp://dx.do.org /.55/5/779. 6. Rana P Bhargaa R and Bg O.. Fn lmn smlaon o nsad magnohdrodnamc ranspor phnomna on a srchng sh n a roang nanold. Proc. I ch. E- Par N: J. Nano marals Nanongnrng and Nanossms ; 7: 77 99. 7. Shholslam Haam and Gan DD. Nanold lo and ha ransr n a roang ssm n h prsnc o a magnc ld. J. olclar Lqds ; 9:. 8
8. Hamad and Pop I. Unsad HD r concon lo pas a rcal prmabl la pla n a roang ram o rrnc h consan ha sorc n a nanold. Ha and ass ransr ; 7: 57 5. 9. Ramzan and Blal. hr-dmnsonal lo o an lasco-scos nanold h chmcal racon and magnc ld cs. J. olclar Lqds 6; :.. Uddn J Bg O. and Ismal I. Rada conc nanold lo pas a srchng/shrnng sh h slp cs. I Jornal o hrmo phscs and Ha ransr 5; 9: 5-5.. Rashd omona E Frdos and Basr P. L-grop solon or r conc lo o nanold pas a chmcall racng horzonal pla n a poros mda. ahmacal Problms n Eng. ; rcl ID: 98 pags.. rlmazogl and Pop I. Ha and mass ransr o nsad naral concon lo o som nanolds pas a rcal nn la pla h radaon c. In. J. Ha and ass ransr ; 59: 67 7.. Saa Naraana PV Vnasarl B and Vnaaramana S. hrmal radaon and ha sorc cs on a HD nanold pas a rcal pla n a roang ssm h poros mdm. Ha rans san Rs. 5; : -9.. Sa Rdd S and hrpah. Ha and ass ransr cs on naral concon lo n h prsnc o olm racon or coppr-ar nanold. J. Nanolds 6; 5: -. 5. Uddn J Bg O.. zz and Ismal I d. Grop analss o r concon lo o a magnc nanold h chmcal racon. ahmacal Problms n Engnrng 5; 5 rcl ID 65 pags hp://dx.do.org/.55/5/65. 6. Ibanz G Lopz Panoa J and orra J. Enrop gnraon analss o a nanold lo n HD poros mcrochannl h hdrodnamc slp and hrmal radaon. In. J. Ha and ass ransr 6; : 89 97. 7. El-abr S hamha J Rashad and l-dha HF. Sor and Dor cs on ha and mass ransr b Non-Darc concon rom a prmabl sphr mbddd n a hgh poros mdm h chmcall rac spcs. In. J. o Enrg and ch. ; : -. 8. Bg O.. Prasad VR Vas B Bhasar rdd N L Q and Bhargaa R. Fr concon ha and mass ransr rom an sohrmal sphr o a mcropolar rgm h Sor/Dor cs. In. J Ha and ass ransr ; 5: 9-8. 9. handrashar B and shan N. Sor and Dor cs on r conc ha and sol ransr n ld sarad nclnd poros ca. Eng. Sc. and ch. In. J. 5; 8: 5-55.. Bg O. Bar Y and Prasad VR. Nmrcal sd o r concon magnohdrodnamc ha and mass ransr rom a srchng srac o a sarad poros mdm h Sor and Dor cs. ompaonal arals Scnc 9; 6: 57-65.. Rashad and hamha J. Ha and mass ransr b naral concon lo abo rncad con n poros mda h Sor and Dor. In. J. Nmrcal hods or Ha & Fld Flo ; : 595-6.. Bongorno J. onc ranspor n nanolds. SE J Ha ransr 6; 8: 5.. ar R and Das. Ha ransr agmnaon n a o-sdd ld-drn drnall had sqar ca lzng nanolds. In. J Ha ass ransr 7; 5: 8. 9
. Garoos F Jahanshaloo L Rashd Badahsh and l E. Nmrcal smlaon o naral concon o h nanold n ha xchangrs sng a Bongorno modl. ppl. ah. nd omp. 5; 5: 8-. 5. Lron N and Wlhlm HE. Ingraon o h magnohdrodnamc bondar lar qaon b sn s mhod. J. ppl. ah. ch. Z 97; 5: 7-7. 6. ramr R and Pa SI. agnold dnamcs or ngnrs and appld phscss. cgra-hll; N Yor 97. 7. Vnasarl B and Saa Naraana PV. hmcal racon and radaon absorpon cs on h lo and ha ransr o a nanold n a roang ssm. ppl. Nanoscnc 5; 5: 5-6. 8. Ishga H. Prodc bondar lar nar a o-dmnsonal sagnaon pon. J. Fld ch. 97; : 77 86. 9. Ganapah R. no on oscllaor o lo n a roang ssm. SE J. ppl. ch. 99; 6: 8 9.. Das S Jana RN and hamha J. agnohdrodnamc r conc bondar lar lo o nanolds pas poros pla n a roang ram. J. Nanolds 5; : 76-85.. Ozop HF and b-nada E. Nmrcal sd o naral concon n parall had rcanglar nclosrs lld h nanolds. In. J. Ha ass ransr 8; 9: 6-6.. Brnman H. Vscos o concnrad sspnson and solon. J. hm. Phs. 95; : 57-58.. Brsr Q. hrmal rada ransr proprs. Wl: N Yor 97.. Bg O Zco J ahar HS Bg and Sad. ransn non-lnar opcall-hc rada-conc dobl-ds bondar lars n a darcan poros mdm adacn o an mplsl sard srac: nor smlaon solons. omm. Nonlnar Scnc and Nmrcal Smlaon. 9; : 856-866. 5. Bg O Zco J Bg ahar HS and aha E. NS analss o m-dpndn nonlnar boanc-drn dobl-ds rada concon lo n non-darc gologcal poros mda. ca chanca 9; : 8-. 6. Bg O Ghosh S and Narahar and Bg. ahmacal modllng o hrmal radaon cs on ransn gra-drn opcall-hc gra concon lo along an nclnd pla h prssr gradn. hmcal Eng. omm. ; 98: -5. 7. Bg O Zco J Ghosh S and Hdar. Unsad magnohdrodnamc ha ransr n a sm-nn poros mdm h hrmal radaon lx: analcal and nmrcal sd. dancs n Nmrcal nalss: rcl ID pp. -7 DOI:.55/ /. 8. Rdd JN. n nrodcon o h n lmn mhod. rd d. cgra-hll Boo ompan: N Yor 6. 9. Rana P Bhargaa R and Bg O. Fn lmn modlng o conga mxd concon lo o lo-ar nanold rom an nclnd slndr hollo clndr. Phsca Scrpa ; 88:5. 5. Grnspan HP. h hor o roang lds. ambrdg Un. Prss: U. 5. Gbhar B. Boanc-ndcd los and ranspor. Hmsphr: Washngon US 988. 5. La N Uddn J Bg O and Ismal I. Unsad orcd bo concon slp lo o a mcropolar nanold rom a srchng/shrnng sh. Proc. IEHE- Par N: J. Nanongnrng and Nanossms 5; -. DOI:.77/7995687.
BLES abl. Grd ndpndnc sd or drn grd szs hn S. 5 :scondar loc :prmar loc : mprar :oncnraon Grd szs 5 7 5 7 5 7 5 7.8.8.8.78.78.78.9655.9655.9655.967.967.967.96.96.96.5.5.5.9.9.9.95.95.95.69.69.69.78.78.78.9.9.9.97.97.97....8.8.8.869.869.869.87.87.87.86.86.86.789.789.789.89.89.89.8.8.8.85.85.85.5.5.5.85.85.85.85.85.85.67.67.67.5965.5965.5965.787.787.787.786.786.786.5.5.5.65.65.65.7558.7558.7558.7589.7589.7589.58.58.58.688.688.688.7.7.7.7.7.7 abl. hrmo-phscal proprs o ar and nanoparcls Phscal proprs H O g l O O p/g 79 85 5 765 686. ρg/m 997. 89 5 97 5 W/m.6 9 8.958 β X -5 /.67.89.85.9 σ S/m 5.5x -6 59.6x 6 6.x 6 5x 6.6x 6 abl. omparson o Sn rcon and Nssl nmbr or aros als o Pr R Ec Gc Sr D Pr Pros rsls [8] N Prsn rsls.5. 5.967. 5.9675..58 6.6.5899 6.696.5.96 6.5.969 6.57.. 6.6.5 6.656 abl. omparson o Sn rcon and Nssl nmbr or aros als o Pr Gc Ec Sr D N
Pr Pros rsls [7] N Prsn rsls.5.5978 5.967.598 5.967..5675 6.6.5676 6.6.5.97895 6.59.977 6.59..768 6.66.765 6.665 N Fgr. Vloc prols or drn nanolds. Fgr. mprar prols or drn nanolds. Fgr. Vloc prols or drn nanolds.
Fgr 5. oncnraon prols or drn nanolds. Fgr 6. Vloc prols agans or aros als o Roaon paramr. Fgr 9. Vloc prols agans or aros als o agnc ld paramr. Fgr 7. Vloc prols agans or aros als o Roaon paramr. Fgr. Vloc prols agans or aros als o Sor nmbr. Fgr 8. Vloc prols agans or aros als o agnc ld paramr. Fgr. Vloc prols agans or aros als o Sor nmbr.
Fgr. Vloc prols agans or aros als o Dor nmbr. Fgr 5. Vloc prols agans or aros als o hrmal Grasho nmbr. Fgr. Vloc prols agans or aros als o Dor nmbr. Fgr 6. Vloc prols agans or aros als o solal Grasho nmbr. Fgr. Vloc prols agans or aros als o hrmal Grasho nmbr. Fgr 7. Vloc prols agans or aros als o solal Grasho nmbr.
5 Fgr 8. Vloc prols agans or aros als o olm racon paramr. Fgr. mprar prols agans or aros als o Dor nmbr. Fgr 9. Vloc prols agans or aros als o olm racon paramr. Fgr. mprar prols agans or aros als o Prandl nmbr. Fgr. mprar prols agans or aros als o radaon paramr. Fgr. mprar prols agans or aros als o Ecr nmbr.
6 Fgr. oncnraon prols agans or aros als o Schmd nmbr. Fgr 5. oncnraon prols agans or aros als o Sor nmbr. Fgr 6. oncnraon prols agans or aros als o chmcal racon paramr.
7 PPENDIX Nomnclar x z arsan coordnas x z axs ms - Vlocs along Dmnsonlss locs along x z n onsan rqnc and m n onsan rqnc and m haracrsc loc g cclraon d o gra ms - Prmabl o poros mdm * an absorpon cocn c s c p oncnraon sscpbl Spcc ha a consan prssr Jg - - axs Roaonal paramr Dmnsonlss magnc ld paramr R hrmal radaon paramr Pr Prandl nmbr Sr Sor nmbr Ec Ecr nmbr D Dor nmbr Gr hrmal Grasho nmbr Gc Solal Grasho nmbr Non-dmnsonal concnraon Sc Schmd nmbr r hmcal racon paramr Dm ocn o mass ds m s - hrmal dson rao m an ld mprar B onsan appld magnc ld s hrmal condc o h sold Wm - - hrmal condc o h ld Wm - - hrmal condc o h nanold n Wm - - Local mprar o h ld Wall mprar o h ld mbn mprar o h ld N Nssl nmbr Sn rcon cocn Sh Shrood nmbr Prmabl paramr S Scon paramr Gr smbols onsan anglar loc ms - onsan = or hrmal xpanson cocn - s ocn o hrmal xpanson o h ld - ocn o hrmal xpanson o h sold - Dns o h ld rcon gm - Dns o h sold rcon gm - s n Dns o h nanold gm - nmac scos m s - nmac scos o h ld m s - Dnamc scos Nsm - Dnamc scos o h ld Nsm - n Vscos o h nanold Nsm - Elcrcal condc Sm - s Elcrcal condc o h sold Sm - Elcrcal condc o h ld Sm - n Elcrcal condc o h nanold Sm - * San Bolzmann consan paramr Ha capacanc o h nanold Jm - - p p n Ha capacanc o h ld Jm- - Volm racon paramr Small consan qan Non-dmnsonal mprar Sbscrps s Fld Sold n Nanold ondon a h all ondon a rsram
8 Dmnsonal concnraon gm - oncnraon a h srac gm - oncnraon a rsram gm- Normal loc ms - PPENDIX Varaonal ormlaon h araonal ormlaon assocad h Eqs. - 5 or a pcal o-nod lnar lmn s gn b 7 d Gc Gr S 8 d S 9 d D S d Sr r Sc S Whr and ar arbrar s ncons and ma b d as h araons n and rspcl. r rdcng h ordr o ngraon and non-lnar arr a h ollong ssm o qaons. d Gc Gr S d S D d D S Sr d Sr r Sc S
9 Fn Elmn ormlaon h n lmn modl ma b oband rom Eqs. 7 - b sbsng n lmn approxmaons o h orm: and 5 Wh hr and ar h loc n h drcon o x-axs -axs and mprar rspcl a h h nod o pcal h lmn and ar h shap ncons or hs lmn and ar an as: and 6 h n lmn modl o h qaons or h lmn hs ormd s gn b. 7 b b b b Whr mn mn and m b and n m r h marcs o ordr and rspcl and prm ndcas. hs marcs ar dnd as ollos: d d Gc d Gr d d d d S d d d d d S
d d D d d S d d r d Sc d S d Sr Sr b D b b b