Effect of thermal radiation on unsteady convective heat transfer flow of a rotating nano-fluid past a vertical plate
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1 alabl onln a.plagararchlbrary.co Plaga arch Lbrary anc n ppl cnc arch 7:8-9 IN: 97-8 CODEN : FC Ec o hral raaon on nay conc ha ranr lo o a roang nano-l pa a rcal pla K. r anga an an D... aaa ao Dparn o ahac r ahya a In o Hghr Larnng nanapr Dparn o ahac r Krhna Daraya nry nanapr C In h papr nga h c o hral raaon an ocllaory prar on nay conc ha ranr lo o a nanol pa a rcal pla n h prnc o ha gnrang orc. nalycal clo or olon ar oban or boh h on an h nrgy qaon ng h rglar prrbaon ho. Graph ar o llra h gncanc o y parar on h nanol locy an prar rbon. Kyor: hral aaon Ha ranr Nanol rcal Pla INODCION Nano l ar ol-lq copo aral conng o ol nanoparcl or nanobr h ypcally on h orr o n pn n a lq. Nano l ar characr by an nrchn o a ba l l ar oln hyln glycol or ol h nanoparcl n ary o yp l al Ox Carb Carbon Nr c. oay nanol ar ogh o ha rang o applcaon n cal applcaon bocal nry rgncy por gnraon n nclar racor an or pccally n any ha roal nol nral applcaon. h ongong rarch r nc hn ha xn o laon o nano-l n crolcronc l cll pharaccal proc hybr-por ngn ngn coolng hcl hral anagn oc rrgraor chllr ha xchangr nclar racor coolan grnng achnng pac chnology n an hp an bolr l ga prar rcon []. Inpably h nano l ar or abl an ha accpabl coy an br ng prang an pron propr on a ol rac [ 7]. ral r [ ] on nano l h rpc o hral an rhologcal propr ha bn rpor. h nano l ha an apl collcon o ponal applcaon n lcronc pharaccal proc hybr-por ngn aoo an nclar applcaon hr nhanc ha ranr or rorcl ha paon rqr. In o h Kbln al. [] gg or pobl xplanaon or h anoalo ncra n h hral concy o nano l. h ar nanoparcl clrng ronan oon o h parcl olclar ll layrng o h lq/parcl nrac an ballc ha ranr n h nanoparcl. Dp a a aon o lrar on h lo o nanol ol propo by ongorno [] ar rrrng o a rcn [9] n h arcl. Hor ar ollong h nanol ol propo by ar an Da [] hch bng by any crrn rarchr [788] on aro lo l. Plaga arch Lbrary 8
2 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 h y o HD lo an ha ranr o h c o a agnc l n a roang ra o rrnc ha arac h nr o any ngaor n o applcaon n any nral arophycal alng h h npo lopn h olar cycl an h rcr o a roang agnc ar chnologcal an ngnrng applcaon HD gnraor on proplon HD pp c. an any ohr praccal applcaon ch a n bochancal probl.g. bloo lo n h plonary alolar h. any ahor ha h lo an ha ranr n a roang y h aro gorcal aon []. Haa [9] nga h c o a ranr agnc l on r concon lo o a nanol pa a rcal nn la pla. cnly aya Narayana al. [] h Hall crrn an raaon aborpon c on HD cropolar l n a roang y. o ohr rla or can alo b on n rcn papr [ ]. hral raaon poran n o applcaon bca o h annr n hch raan on pn on prar an nanoparcl ol racon. h hral raaon c on x concon ha ranr n poro a ha any poran applcaon ch a h nbl ha orag b h nclar racor coolng y pac chnology an nrgron nclar a poal. o h b o h ahor nolg ro h lrar no ha bn conca h ar h rgar o h y o lo an ha ranr ncn o a nanol pa a rcal pla h hral raaon n a roang ra o rrnc. cnly ayanarayana al [] ha h c o raaon on h conc ha ranr lo o a roang nanol pa a poro rcal pla h ocllaory locy. In h papr nga h c o hral raaon on nay conc ha ranr lo o a nanol pa a rcal pla n h prnc o ha gnrang orc. nalycal clo or olon ar oban or boh h on an h nrgy qaon ng h rglar prrbaon ho. Graph ar o llra h gncanc o y parar on h nanol locy an prar rbon. Nonclar : conan appl agnc l C : n rcon cocn Gr ybol α: hral y α : hral y o h l E: appl lcrc l α n : hral y o h nanol F: ha raaon parar : hral xpanon cocn g: acclraon o gray : cocn o hral xpanon o h l K: prably parar : cocn o hral xpanon o h ol : prably o poro : ny o h l rcon : an aborpon cocn : ny o h ol rcon : nonl agnc l parar n : ny o h nanol N: local Nl nbr n: nac coy Nr: rc Nl nbr n :nac coy o h l : anl nbr µ: ynac coy : nonal ha orc parar µ n : coy o h nanol H : nonal ha orc : lcrcal concy o h l q r : raa ha lx * : an olann conan parar q : ha lx ro h pla C n : ha capacanc o h nanol : nonal roaonal parar : all conan qany x : local ynol nbr χ: coplx ncon : con parar : non-nonal prar : local prar o h nanol bcrp : all prar o h l : l : ol n: nanol : prar o h abn nanol : characrc locy : conon a h all : noral locy : conon a r ra x y : Caran coorna :locy coponn along x an y ax Plaga arch Lbrary 8
3 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 x Ω y FOLION OF HE POLE W analy a rann hr nonal lo o a nanol conng o a ba l an all nanoparcl or a -nn poro rcal pla h hral raaon. nor agnc l o rngh H appl noral o h pla. I a ha hr no appl olag hch pl h abnc o an lcrc l. h lo a o b n h x-rcon hch an along h plan n an par rcon an -ax noral o h pla. lo a ha h hol y roang h a conan anglar locy cor Ω abo h -ax. h l a o b gray aborbng ng b no carng. h raa ha lx n h x-rcon conr nglgbl n coparon h ha n h -rcon. D o a -nn pla rac apon h lo arabl ar ncon o an only. Fgr. ho h probl nr conraon an h co-orna y. In h prn probl h ollong apon ha bn a: h pla ha an ocllaory on on an rqncy n h locy hch gn by Co n. Inally < h l a ll a h pla ar a r b or h hol y allo o roa h a conan locy Ω abo h -ax. I a ha h hr no appl olag hch pl ha an lcrc l abn. In a phycally ralc aon canno nr prc nlaon n any xprnal -p. hr ll alay b o lcaon n h prar. h pla prar a o ary haroncally h. I ar ro a ar ro o π /.nc all h pla prar ar only lghly ro h an al.h abn prar ha h conan al. h conraon qaon o crrn ny. J g J conan. nr h abo non apon h qaon o on an hral nrgy rpcly can b rn n nonal or a : Ω µ n g H n µ n o n Ω µ n µ H n o n n C P n h bonary conon ar: q r H C P n Plaga arch Lbrary 8
4 K. r anga an an D... aaa ao. ppl. c.. 7: Plaga arch Lbrary or o any an or h propr o h Nano l ar n a ollo n n n C P C P n C p n n C p n n n α µ µ. / W conr h olon o qaon a - 7 h raaon ha r by ng h olan approxaon gn by q r q 8 W nroc h ollong nonl arabl: F o H H n n ν ν ν µ ν ν ν Ω 9 Eqaon- n h non-nonal or ar P r Whr. P C P C F n
5 K. r anga an an D... aaa ao. ppl. c.. 7: Plaga arch Lbrary h bonary conon rc o or any an or In o h l locy n h coponn or: h qaon an rc o h bonary conon rc o a or any or EHOD OF OLION Eqaon an ar copl non-lnar paral rnal qaon an h can no b ol n clo or. Hor h qaon can b rc o a o ornary rnal qaon hch can b ol analycally. h can b on rprnng h locy an prar o h l n h nghborhoo o h pla a: Z 7 bng h abo xpanon & 7n qaon an an qang h haronc an nonharonc r an nglcng h hghr orr r o O. W oban h ollong o qaon: ZEOH ODE EION 8 9 FI ODE EION:
6 K. r anga an an D... aaa ao. ppl. c.. 7: Plaga arch Lbrary ECOND OEDE EION h corrponng ranor bonary conon ar a a olng qaon 9- h h bonary conon oban h xpron or h locy an prar a: xp xp o xp xp o hr xp xp xp xp xp xp xp xp xp h phycal qan o nr ar n rcon an Nl nbr hch ar rpcly n a: o C τ xq N Whr τ an q ar h all har an h all ha lx ro h pla rpcly hch ar gn by n n q an µ τ xp xp. C xp xp n n N Whr
7 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 EL ND DICION ahacal an or h analycal olon o h probl pror an h oco ar llra graphcally n Fgr - 8. hy xplan h acnang ar o poran parar on h nanol locy prar n rcon an Nl nbr rbon n a roang y or hr rn yp o ar ba nano l. W a h al o h nanol ol racon n h rang o.8. Hor hallan ha conr or h conc lo n a l rn cay h al o h nanol ol racon n h rang.8. I h concnraon xc h ax ll o.8 naon col a plac. W ha chon hr n n π /.. hl F ar ar or a rang hch ar l n h gr lgn. Fg. rprn h c o agnc l on h nanol locy prol. I on ha h nanol locy l rc h ncra o agnc l parar along h rac. h c ar ch gncan nar h rac o h pla. h ho ha h l locy rc by ncrang h agnc l an conr h ac ha h applcaon o h agnc l o an lcrcally concng l proc a ragln orc hch ca a raraon n h l locy. W alo n ha h nano l locy n h ca o CO ar nanol rlaly grar han ha o l O -ar nanol. h phnonon ha goo agrn h h phycal ral. Fg. rprn h nanol locy prol or rn al o roaonal parar. h rl play ha h nanol locy rc h an ncra n a no n rrnc []. Frhr n ha h l O -ar nanol xhb lor locy han h lo a copar o h C-ar nanol. Fg. & 8 ho ha h nanol locy an prar h con parar n h ca o C an l O nanoparcl rpcly. I can b n ro h prol o nanol locy ha rc or hghr hch nca ha h con abl h bonary groh. h r concon c alo apparn n h gr. For a x h nanol locy on o ncra an rach a ax al n a rgon clo o h lang g o h pla an hn graally cra o ro. h c o on h nanol locy h rr n h ca o Haa al []. h o h ona rol o h raaon n h l l. h rl ar clarly ppor ro h phycal pon o. W alo noc ha l O -ar nanol ha lr locy prol han h C-ar nanol. lar bhaor noc n h ca o prar prol xcp ha h prar prol or ln-ar nanol rlaly hghr han ha o coppr-ar nanol.fg. & 9 rprn h bhaor o nanol locy an prar or rn al o ha gnraon parar. h gr clarly ho a crang nncy n h locy an prar h an ncra n. h o h ac ha hn ha aborb h boyancy orc cra hch rar h lo ra an hr by g r o a cra n h locy an prar prol. Fg. & rprn h araon o nanol locy an prar h rn al o anl nbr. I on ha an ncra n h anl nbr rc h locy an nhanc h prar n h lo l n h ca o C-ar nanol hl n h ca o l O ar nanol an ncra n nhanc h locy an rc h prar. lo l O -ar xhb rlaly lor al n coparon o C-ar nanol. Fg. & play h c o nanoparcl ol racon on h nanol locy an prar prol rpcly. I on ha a h nanoparcl ol racon ncra h nanol locy an prar ncra. h gr llra h agrn h h phycal bhaor. Whn h ol o h nanoparcl ncra h hral concy an h hral bonary layr hcn ncra. W alo noc ha h nanol locy n h ca o l O ar nanol rlaly lor han ha o Car nanol. Fg.7 & xhb h nanol locy an prar or aro al o raaon Plaga arch Lbrary 89
8 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 parar F. n ncra n F la o an nhancn n h locy an prar rbon acro h bonary layr. h c o hral raaon o nhanc ha ranr bca o h ac ha hral bonary layr hcn ncra h an ncra n h hral raaon. h pon o ha h raaon hol b n o ha h coolng proc proc a a ar ra. W alo n ha nanol locy an prar n h ca o l O -ar nanol coparaly l han ha o C-ar nanol. h occrrnc ha a pror agrn h h phycal rla. abl. play h bhaor o local n rcon coponn τ x an τ y an Nl nbr N a h pla y. I on ha an ncra n h Harann nbr rc τ x an τ y hl an ncra n h roaon parar rc τ x an nhanc τ y a y. lo τ x an τ y nhanc h ncra n h con parar an h raaon parar F an rc h ncra n h rngh o h ha gnrang orc or C-ar an l O -ar nanol. n ncra n h nanoparcl ol racon nhanc τ x an τ y or C-ar nanol an rc or l O -ar nanol. h local Nl nbr N a y on o nhanc h ncra n or or boh C-ar an l O ar nanol. n ncra n F or nhanc N a y or C-ar nanol an rc n h ca o l O ar nanol. n rcon an Nl nbr a y. abl : hro-phycal propr o ar an nanoparcl Phycal propr War/ba l C Coppr l O lna O n C p J/g K g/ K W/ K / ɸ X - /K X X X X -..9 abl : Coparon o n rcon an Nl nbr o h prn ca h ho o Haa al [8].... n Frcon Nl Nbr. F.. n F... n ayanarayana al [] Haa al [8] n ayanarayana al [] Haa al [8] abl F. ϕ....8 CO l O τ x τ y N τ x τ y N Plaga arch Lbrary 9
9 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 Plaga arch Lbrary 9
10 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 Plaga arch Lbrary 9
11 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 CONCLION h nanol locy rc or hghr hch nca ha h con abl h bonary groh. W alo noc ha l O -ar nanol ha lr locy prol han h C-ar nanol. lar bhaor noc n h ca o prar prol xcp ha h prar prol or ln-ar nanol rlaly hghr han ha o coppr-ar nanol. hr a crang nncy n h locy an prar h an ncra n ha gnraon parar. n ncra n h anl nbr rc h locy an nhanc h prar n h lo l n h ca o C-ar nanol hl n h ca o l O ar nanol an ncra n nhanc h locy an rc h prar. h nanoparcl ol racon ϕ ncra h nanol locy an prar ncra. n ncra n h raaon parar F la o an nhancn n h nanol locy an prar rbon acro h bonary layr. EFEENCE []..garal.. haar P.G. hhar P. []..barna.bolah.lar ppl hral Engnrng. []. la.a.haya Co. Nonlnar c. Nbr laon7. []. J.ongorno E J Ha ran 8. []..Gha.ar H..C.laar In. J Ha a ran []..Hajpor..Dhor In. J hr. c.. [7].... Haa. Fro ppl ah cheng E [8].... Haa I.Pop Ha a ran [9].... Haa In. Co. Ha a ran []. K.C.D.Hcan97InEngCh []. H P.H.obr9oPhy [].P.K. Kaaran. Narayana P. bana PN rhy In. J Ha a ran [].D.Ch. Kaaah P..aya Narayana.naaraana In. J ppl. ah ch [].P.Kbln..Phllpo... Cho J..Eaan In.J. Haa ranol.8-8. [].I..ahbbl.ar..alna In. J Ha a ran []...ar 99 E J pplch 8 7. [7]. C.. Ngyn G.oy C.Gahr N.Galan 7 ppl. hro Eng 7. [8].. Norah I. nar P.Ioan cach n 8. Plaga arch Lbrary 9
12 K. r anga an an D... aaa ao. ppl. c.. 7: 8-9 [9].P. ana.hargaa Co. Nonlnar c. Nbr laon7. [].. h Kar.araj In. J o Ha a ran [].P..ayanarayana.naarl an.naaraanaha ranr-an arch DOI:./hj.. [].P.. ayanarayana.naarl.naaraana n-ha Engnrng Jornal hp://x.o.org/./j.aj... [].. rna.braanya y.. aaohan In. J Ha a ran 8. []..K.ar.K.Da7 In. J Ha a ran : 8. Plaga arch Lbrary 9
Engineering Circuit Analysis 8th Edition Chapter Nine Exercise Solutions
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