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McGARW-HILL INTERNATAILO N SSeNia.:wnLof.OoVruaoKsrinc Ck .lO SOCM PANY Aucklnad eo801a Gua1emaa l �j.°'�.:S\urg Libson Loodo• Madrdi Mexico Monrteal NewD elhi ........ Paris SanJ uan S�;r.,:ioPaulo re Tokyo Toronto BruceF iAn.l ayson ProfesosfCo hre micEanlg ineerainndAg p pliMeadc henratks UniverosfiWtays hington, Seattle NONLINEARA NALYSIS INC HEMICAL ENGINEERING� CONTENTS Preface I lntCrlodaucslisono iEffiq cuaattiioonn s 1-1 2 AlgSebruEqauiacclS icou·nes b ssstiivteu tion 2-tN ewton-Raphson 8 2-2C omparison 11 2-3S tQuudeys tions 13 PBriobbllieomgsr aphy 111565 3 O3r-d1TiIn aQienrfyfrt ermeeanEqtirunQiaanptldui ooo ansll-dloanrigltaiPayirlto- obVulaelnrmsu e e 1177 3-2E xIpnltiMecegitrtha otdiso n 20 3-3I mIpnltiMecegitrtha otdiso n 25 3-4P rediacnRtduo nrg-MeCe-otrKhruoendcast 2o7 r 3-5E xtraaSnptdoe Clpoa-ntStiirozonel 28 3-6St abi!ity 32 37- HigehSr-c ohtrehadmSaretteasa nd bndolOo setc ill3a7t e 3-8Eq uSaotlivoenr s 45 39- 47 riC3Oi-l'fIlfERsPBCON T Se1rio Qfuombuedbplerylaise erotnmigicssroe oansnps h y 5llO,78 . l9 4 O44r--d2IiF MnaDieriDyff'ni eiriehnffEqltMouieaaelRedlir o etonesshf-nBiooWucnddcdealu ira yPca- rgVolablhesms t ed 6060 4-3R ePgeurltaurr bation " 44--54OD irfftaCuhnRosodelig alooEconnxtRc aaiealcost tnui -lotns 7703 4-4-4-4-44-44-411-1-I86-3412O9 7 IC QSGOA 1O L Po noutardrewQimual1atrFMeuCCptdsehphTtiMereDEooayiiortouenes-selll rlagkigrcifthUtceoflliiloivoDbhtohepioFDmnooosn-nennianreosopomiie rccMoeaV atfiE d feanpnffn aanaalalaifql rsnRoiuttt rt l onuuRe destssiiirunsedem iaei oozie si aetc onna c ocnitn tenttoi is isnoo o 1111111 n9879644432104n48 32663n Problems 166 Bibliography 167 References 170 171 S OPnaerS apbaoPtlaiDinaicilm aeDlnis ffieorne nlial Equati11.oands -Time 5555----3241S S OMFi eireenDopmtt ieTWioCfaihhVtcrrelTfo lrooaeeai lRaagdr nnglreot ishoisniaftctiaoboeayldnlrdt u em iasaol tnsi on1111l7l 988701 42 5SSSSS----·-&798I5O GC OF onwevralTcei rhrnltotFunoiDCkahgtivP hEioeloien om olffle gEo iuMrueuoMlnoqnseiFasneonto d nit tc dE niha liotseti meoe nn t ""2222 3321018 4 Compraoins 261 StduyQ uesontsi 265 Prbolmes 2'6 Bilbgiropayh 269 Rfeerneecs 110 CONTENTSi x 6 ParItiDnaitlff reroednEutqicuatalt iioionnnT sw oS pacDei mensions 271 6-1F inDiitffee rence 272 6-2O rtghoonCaoll location 276 6-3G alienrF kinEilteem Meentth od 286 6-4C omparison 291 6-5P roblems 307 Bibliography 312 References 331 314 AppendiCxo mputPerro grams 316 AuthIonr dex 359 SubjeIcntd ex 361 PREFACE Tefinbtonhoonn ngoiioblikstnaoins clnopne, ipdkforee pdnr oftaorrieotrefirbioffavh mnn lnsberisea igeta l rdo entth mneeellyiaoecs mnifu ent o sclrt tmou eleirefro,uoqoon sr sruandttettder u,hsahrincotc re,roanl rota imagtali inisanoceryeognoendn oy enpne f y aa ltnmt a lplog�ert powitdhlcadni �oiradeasplcdtTel oeiHasier rraoneb ori t?feriaennpu aelmln,gerrrt imat.y qobh te-n isubate�ytayailatoma rh l,estientyeoa .m aaiots Me rd snphneiati pdto­i nt sili hdny sese d useful trheacstau nbl edt esr ifvreodem a cmhe thoTdh.es amper obleamrssc o lved witdhi ffermeentth osdots h atth ree adcearna ssess mtehtehsoeid nsp ractaincda l simiclaasre Tsh.ee xamplaeres from autthheo orw'nse xperieflnucieftd: o w f,( iTnhcell peuovdoylemiftlen h rgbe sho )eo,aikt tsi r natnrsaorendrdcu, hac entmodtir hrcyteea,r al ec atmtoomirdes oen rlt.ii enngttoewda trhde non�saliEsvte.n s ot her eadiesri ntrodutcoet dh el atemsots,tp owerful tcehniquTehsec. o urissbe a seodn a s uccesgsrraudlu caoteu rastet heU nvieirtsy orW �ingtno,a ndm ostc hemiceanlg inetearksi ntgh ec oursaere e xper­i mavaSbyepeol�npi�rauvosphSti�o1tr�n�w airostv� Tcm.im�C:Ohan d.gnfe �ri c o :kepole,aarlc_ nctdroiddth_eeyewnale eirst slse o ph�Til.ianehga rdkcteilidssDto vlnr d aah ieygefnecnwDn t lt l aa h vdabsve.eeedosi i xe arsb1ppn l9eeidMi7rrn tio9wt tykg,ahlopCero_ opy hea ftb ae ad peyran hKs tcgyatcihat, rehc rh deatwu teFfiw npeelehi rhs. crcrnnot d�qehei t�u regtale e otndillnr l pwCarnhhodjToeitrec htlso-n tet aebmhe fawioa,iut tyhu t�lohhh figS r osaicp' resv:sa.;a.i Y l l1aeoa.l5rts � t d aha pn8 ; k syk/cu�gs:1h �:o .1 ortc g0l a;o�1o1c o.ftt s1nae_h h fatulr-e.:ammcelW .duhdtsyrd yi huif loptotr::pircisa'otna hmu srbgon:miep to dael p o kndokrecrrMt e otehahaaiungiriblnr, eskimolgCd m evno y aupnorktl dyoi .esv,gn ssa bttnhhl ide.ee Seatel l 1890 BrucAe. Fyiosnnl a CHAPTER ONE INTRODUCTION Theg oaolrt hibso oikst ob ritnhgre e adienrtc oo ntwaicttth h eeffi cient computtaotoitlohsna atr ea vailtaobdlateyo s oldvieff ereenqtuiaatli ons modelpihnygs pihceanlo mseuncaahsd, i ffusrieoanc,ht ieoatntr, a nasnfftdeu ri,d flowA.r tmears tetrhimena gt eriinta hlbi oso yko ush oublead b lteoa ppal y varioermt eyt hods-finite deilffeemrecenontlc,le o,c paefitrnitioutnre,b ation, etc.-alytohuwo iunlgolhb t e a ne xpeirnat n yo ft heWmh.e fna cweidta h probtlose oml yvoewu i klnlo wwh imceht haordsesu itaanbwdlh eai tn formation cabne e asdieltye rmbiynw ehdi cmhe thoTdh.ee mphaissoi nsn umerical methoudssi,an cgo mpuatletrh,o suogmhoe f t haep proaccahanel ssy oi eld powerrefsuulal ntasl ytTihceaa ultlhypo.hr i'lso siostp ouh sype r eprogrammed compuptaecrk awgheesan v ailbaebclaetu hseeay l ltohwre e adteosr a mple, �rusaen,ds oldvieffi cpurlotb lweimtlshe sesff orTth.er eadieshr,o wever, introtdotu hcteeh de aonrtdye chnuisqeiudnte hse csoem puptreorg rams. 1-C1 LASSIAFTIICOOFNE QUATIONS Eqautnismo odleipnhgy spihceanlo mheanvdaei ffecrheanrta ctdeerpiesntdiicnsg onh owt hemyo deevlo luitnti iomanen tdh ien flueonrbc oeu ndcaornyd ilions. Whnec ornorntweidtam h o deelx,p reisnts hreeod r omfa d iffereeqnutai,tta ihloe n adneelatsrynmtmeu itssdh mteee c twihdhtoeathd tayas rpto see reu qiut.aa tibistlo oebn es olvTehdac.th aracterization C��sidaec rl ossyesdt (einm.o ei .n tereco hrma answgsi tthhs eu rroundings) cannodcti3 a.mTn ght tehh rrcceehoeeem mnpcieoocncmataplsrno e nwa(ehcsnotwatcs hysoee tn nhc seeyn statirreisageml ti livuboemyncni ws1 ni· ,at� th·,e d Fiugrel·IR cacnosnysctm. ceslepoqicaticnugoet etnafhaniasrsss ga ot epfu n o icfin.rsvcoTien neothfedignitorrq i hftuce�cn�s iateyc t.Ti)sea shoa,eymdnytrn rs � se a ecsmhgit_ 0 t ose, �1e oi w atssnco p i t arnFier iokdetgnn1i h. o-cce w1aoat ,nnns a dtc hefdenui tonfforfceeftat aar hticleeioh n on tn i �== -+kk12cc1·2c3 df (1-1) �f ==kd3 Inittihcaeol nlcye ntorfca otmipoonntsew naotn sld h rac·_ieze e raon,td h ien itial concenotfcr oatmipoonon neinegst i vaescn0 • W et huwsi sthos olEvqes0 .- l) subtjotech iten ictoinadli tions (1-2) Notteht ahtce o ndiatpipoolnnysla ytt imzee rnoo.tt ol atteirmt e.T sh ree anc tio procienet dismi efw;e k nowwh erteos tawretc ani ntegtrhaeetq eu ations indefiTnhiietsve ollyu.pt rioopnye ireteylq dusa ttihoaantrsc e a lilneid1 ial-value potsrnyetoolsx_hbyntoti.i il efeo Iasn sem rnbt d md bhesciripadnesevsiEatv naeffqroiOd.r esy a(De air t1EtnlaeeIe- ati bqnd1Vr m1l.uot )P.eTee a ri h ,tdtu iiEhsondqaa nais(trs-rf.Ii e Iyf na ) ein ert(dqei1 u)na-apa tl2rrti-gesoiavo ibolavnln tleIdcesuhrbn etm,eeny i hsa re si. e s Consindeexdrti ffnu asnidro eactiinao pno romuesd i.uW me havae hp;�:re�ottc�dcvtd�rc��si1Tuu1o fusssgfs iyccbeosnou)nt(ceht, esfe motfirmwA l.ceaemi mi t adoees dwbnrsetiai lhtlpa aheolon rntacse vh eaysor ss slo tiwuuoehmmgfmtipehd htcl ipehhefro e fre uuoamsuscteisitisadnoa nau dnngnm (tr)J1t')_JJ , �sefflocer:;tira:idnd:v il:dtue��ff �· �hs 1r:n3;• i1.rt�:c <o�eocolnf f ir_ � 1i?.1rice·�\ 1_f� t;a wA ec �ie-pceontst r1Xeex-tiu h rrunp+o -"tne lrt-nc iiv eh1 opotol+lse,menl �us )tprJu eix: (�iio mnz s m+napnoe1 ofe R ef pt (culo r lh)nris vuev imdaies ot rmc i- veittJdioaloo.F Bnla riycu�ru c lmJ lskiue wb(ai1'tsd no3n-nseh it)g nh g INTl.ODUCTION 3 or J J,,= - D..�u. xcr= ·- D" O� y J,= - D..�u , (1-4) Thiesq uaalisosnue mqeusi mdoilfafr(u osinmoeon lo err cacd1iafnftiu nas neds onmeo loefp roducl oudtia)fn,fad ul tslhe mesi crosdceotpaoiiftcl h pseo rous mediaurmle u mpiendlt ohd ei ffusion coeftfiomc oideaens ltpeci .fi c Obviously physsiictaulat thdieio fnf ucsoieoffincm iuesnetti tbheem re asuorrde edd uced frosmi mislyasrt.W e (imtsh ) atphp (irso x )itmhea e(qt iuoa )bnte i coonm es aa;=cfuo o.. ax" ' +ayo o.. "ay ' +aza o.,"'az +R <c(>1- 5) or �=V·c+DR.,(Vc) Iboumpendaryrmea ble e=e1 - L FIJtinl-l Dilf111iD11inasl11b. �c1.iitcNe O�hxLnt'lt��ltkis�.!ulN;_e Enot.nAswne ns R eso;ttlx afgNedAehg e idyaiA s �s itlLs Y-cehStbvmtrtIt:se erSanI(are ts iNeeeitCu e a chgoHstaFi�_E,avotte M<!.-m_�ion iIe.iaC ofdAl t gai·LZn� - E()gJ�rrN�h s� ' ,J:tG.;aou lieNec rnseEoops E) uiRmn!la.clriInuo 5ptN cI.a0re o.fl ts it•s n yihhEniai s taeqp nwt (h.eto� to-ih yet li)u5te d at� msdhl1no eoe a1Tzd � nrbdu nhdeii sv. ta1,c1 vrm eriheisttmaeunz ofi.snn i e�1n tr.hs snooieiot lb itno ey hAs dcAnwroisnecgte ffa lt�eoiennetm �urd �aEq t1� oeoeq(ion(n.t� 0 hac �d1eo-�l6x ne) :�care5 dtegsaxwnot�+ foit i Rrdd nmooe�e (npp=pac Oeea )nn rodvdt ndaesoi irn nafitl.lfoa y etnbreoel�meqn eadnu psteretno)id{ndni( -oitrnaeatye)6tlh c�ovaio;raarl�l:nnd�.drliEe��nc� uryiiruaaq)��h swe�: e�.nbeu e-eIc(�filn1�noqe •o6xd�s t)e iti:a.r� dds·sttor � �e hnssoasceetat �io oay;htodnsrtstehftediidi wra.w ha -dTennbso t oeeehrgomdl t e uu aabhsnsbsitoesedt mhcu p a peonerreondocyycrrdafi hoymif n,nc� et�oy1e dooain nsoa1 naboeseartntHslten)n cr wtute a sdn-ioeosxa crasdon tt edhi eeehhr d x=O -Dd�e=� O (1-7] pbbcchdlT�bRreooa1hhpraoeeonuidmaebbrenaae�n�tdb ennr eteooeb eios adpe nnrhuinldiactEb-fcrefos r hibha stoenattpcrpsaqld e(ou bdwraeapsf c1imriO1tf6uhtctsel� toto,tcet-D )heo ef b h hetcoioe yaeds..msmEi teatnmltiToe,ipo( auto-1n tdr nnne-lisr h E efi esmmr- cBi ampm iqe.nsl aa,(sev-ia8l (VitnnoeIsd abeiar cn)uliPssuiii a t e tavsatnnesos spd-ofea. snsn xduc o-sH)d omoaih5enrl ltat per1kuifi bpryee) s,sc.resn m duloidl nn ooa e c0p-iuaixto, lts .eurcttlfnnnct mapddlh=dss ihhi la da es ri ei eeiauebeeeftoratnotofffd fdcinq yth wyrealwlbef fp hnu he sy,uoplrepur aga a t - t-oeerrsboe tntevfopisnmeoioqbidr acrootisnbwuuoloe olch in ut.tl-oxnanenan.tunn e iiheutd I nm aebsieitsoah(amtliiaC nup o q cena1lvhdsoinr aadta -vsi en sy 8en � -) g v alue Tidap�s�espeh1no1dinln1vr atn1Ti eohestu 1a.ew idvno hv,aroenpaoatdeeO mletonbner :ixre sinaanll rin.ofs.W t ;,ip 1�ee ·dfqe r,nT=11id e,,, hiiX c uf·i,q•.�eaveh n r u D .'aa� ea�larnfl.�i,,m cc1 �·l\ r t,tta.co1o+ ll�oavi fRtnt cu (hhcasvdc)se,oeueae ol � frt npl shdue cue notcd e tdndioehecoe nprxednenp eaad onecnn entscnetodanioo e n te(nntrr - c a1i � �ws)9hs T�ndt�'hIJceleocse�ed ne a\ pea �tucy.a�sa n�tlrtCdoew=1eoqt.tdutr he oenW �ntin tioeea fnav n b.cnicxidircn lu ilaaoaok oantnlolit ei•s'E 0bei �pleh in�a.ei v: .b. s �to�k?cstu '7o::c )'due�ma.or:� : n(l) dr.y::�aXn q(,e�:oic, -.1s8 rn·��e 0(��m-.p)duo-�svIp7g re=r)�( tr ft a Xoe�vo��e�o) i(a·bbl1a T l �rl-1a-sh euibe0nnte,aau)mtdse ie t ptt w rntphai comc huerobo ooerd aounlilenc ubloktstipcn br(aairns-irtrt-fea1a1eco ariel)m0tn ers i INTIODUCTION!! f"igurDeilff-uls ioninalonr.ca1alys1pellc1. Iwfe s olEvq.e int woort hrsepead ciem enwseia olnhssao v ape a rabolic pardtiirffeaenlt (ei-qla5ul)a twiiottnhh,I e v aribaebilenevg o lutainotdnh a.e'¥:r: .y ·'" anzd v aribaebilonerbgs o undartyy-pvIeant.l w duoie m enwseih oanvse (1-111 wei ncltuwsdope a dciem enbsuiatol nlsoo nwls yt eady-stattheet nhs ei tuations eIqru arteidountc oe s( ) ( ) �, 1o . �". '+aa; ;,,' fy'D' R(+c= )o (l-12) Theiqsau tiwoonu mlodd beolt dhi ffaunsrdie oanc itnaic oant aplayrstttih cialste vteyelopr foby oni ugndtn ahzrce dy oi nrdeicsttotii hooazan nvtrs,aD e ria irlaial1croniheweool ergnebd lsto i- u(gtnsidyFecbaipeo.1lrge n 3-ey d) Ti.oht rei ons thfier ksitn d t'=<s" (1-13) Neumann-eot rby opundcaornyd iotrti hosene sco knidn d -D,.riik ij-D"". ·Vnt•=- /• (1-14) andRo bnit-yopreb o udnarcyo nditionsk ionordrmt ihxceeo dnt dhiitrido ns -Da,;t. k= k.,()< '-ca (1-15)

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Nonlinear Analysis in Chemical Engineering PDF

369 Pages·1980·13.254 MB·English
by  Bruce A. Finlayson
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McGARW-HILL INTERNATAILO N SSeNia.:wnLof.OoVruaoKsrinc Ck .lO SOCM PANY Aucklnad eo801a Gua1emaa l �j.°'�.:S\urg Libson Loodo• Madrdi Mexico Monrteal NewD elhi ........ Paris SanJ uan S�;r.,:ioPaulo re Tokyo Toronto BruceF iAn.l ayson ProfesosfCo hre micEanlg ineerainndAg p pliMeadc henratks UniverosfiWtays hington, Seattle NONLINEARA NALYSIS INC HEMICAL ENGINEERING� CONTENTS Preface I lntCrlodaucslisono iEffiq cuaattiioonn s 1-1 2 AlgSebruEqauiacclS icou·nes b ssstiivteu tion 2-tN ewton-Raphson 8 2-2C omparison 11 2-3S tQuudeys tions 13 PBriobbllieomgsr aphy 111565 3 O3r-d1TiIn aQienrfyfrt ermeeanEqtirunQiaanptldui ooo ansll-dloanrigltaiPayirlto- obVulaelnrmsu e e 1177 3-2E xIpnltiMecegitrtha otdiso n 20 3-3I mIpnltiMecegitrtha otdiso n 25 3-4P rediacnRtduo nrg-MeCe-otrKhruoendcast 2o7 r 3-5E xtraaSnptdoe Clpoa-ntStiirozonel 28 3-6St abi!ity 32 37- HigehSr-c ohtrehadmSaretteasa nd bndolOo setc ill3a7t e 3-8Eq uSaotlivoenr s 45 39- 47 riC3Oi-l'fIlfERsPBCON T Se1rio Qfuombuedbplerylaise erotnmigicssroe oansnps h y 5llO,78 . l9 4 O44r--d2IiF MnaDieriDyff'ni eiriehnffEqltMouieaaelRedlir o etonesshf-nBiooWucnddcdealu ira yPca- rgVolablhesms t ed 6060 4-3R ePgeurltaurr bation " 44--54OD irfftaCuhnRosodelig alooEconnxtRc aaiealcost tnui -lotns 7703 4-4-4-4-44-44-411-1-I86-3412O9 7 IC QSGOA 1O L Po noutardrewQimual1atrFMeuCCptdsehphTtiMereDEooayiiortouenes-selll rlagkigrcifthUtceoflliiloivoDbhtohepioFDmnooosn-nennianreosopomiie rccMoeaV atfiE d feanpnffn aanaalalaifql rsnRoiuttt rt l onuuRe destssiiirunsedem iaei oozie si aetc onna c ocnitn tenttoi is isnoo o 1111111 n9879644432104n48 32663n Problems 166 Bibliography 167 References 170 171 S OPnaerS apbaoPtlaiDinaicilm aeDlnis ffieorne nlial Equati11.oands -Time 5555----3241S S OMFi eireenDopmtt ieTWioCfaihhVtcrrelTfo lrooaeeai lRaagdr nnglreot ishoisniaftctiaoboeayldnlrdt u em iasaol tnsi on1111l7l 988701 42 5SSSSS----·-&798I5O GC OF onwevralTcei rhrnltotFunoiDCkahgtivP hEioeloien om olffle gEo iuMrueuoMlnoqnseiFasneonto d nit tc dE niha liotseti meoe nn t ""2222 3321018 4 Compraoins 261 StduyQ uesontsi 265 Prbolmes 2'6 Bilbgiropayh 269 Rfeerneecs 110 CONTENTSi x 6 ParItiDnaitlff reroednEutqicuatalt iioionnnT sw oS pacDei mensions 271 6-1F inDiitffee rence 272 6-2O rtghoonCaoll location 276 6-3G alienrF kinEilteem Meentth od 286 6-4C omparison 291 6-5P roblems 307 Bibliography 312 References 331 314 AppendiCxo mputPerro grams 316 AuthIonr dex 359 SubjeIcntd ex 361 PREFACE Tefinbtonhoonn ngoiioblikstnaoins clnopne, ipdkforee pdnr oftaorrieotrefirbioffavh mnn lnsberisea igeta l rdo entth mneeellyiaoecs mnifu ent o sclrt tmou eleirefro,uoqoon sr sruandttettder u,hsahrincotc re,roanl rota imagtali inisanoceryeognoendn oy enpne f y aa ltnmt a lplog�ert powitdhlcadni �oiradeasplcdtTel oeiHasier rraoneb ori t?feriaennpu aelmln,gerrrt imat.y qobh te-n isubate�ytayailatoma rh l,estientyeoa .m aaiots Me rd snphneiati pdto­i nt sili hdny sese d useful trheacstau nbl edt esr ifvreodem a cmhe thoTdh.es amper obleamrssc o lved witdhi ffermeentth osdots h atth ree adcearna ssess mtehtehsoeid nsp ractaincda l simiclaasre Tsh.ee xamplaeres from autthheo orw'nse xperieflnucieftd: o w f,( iTnhcell peuovdoylemiftlen h rgbe sho )eo,aikt tsi r natnrsaorendrdcu, hac entmodtir hrcyteea,r al ec atmtoomirdes oen rlt.ii enngttoewda trhde non�saliEsvte.n s ot her eadiesri ntrodutcoet dh el atemsots,tp owerful tcehniquTehsec. o urissbe a seodn a s uccesgsrraudlu caoteu rastet heU nvieirtsy orW �ingtno,a ndm ostc hemiceanlg inetearksi ntgh ec oursaere e xper­i mavaSbyepeol�npi�rauvosphSti�o1tr�n�w airostv� Tcm.im�C:Ohan d.gnfe �ri c o :kepole,aarlc_ nctdroiddth_eeyewnale eirst slse o ph�Til.ianehga rdkcteilidssDto vlnr d aah ieygefnecnwDn t lt l aa h vdabsve.eeedosi i xe arsb1ppn l9eeidMi7rrn tio9wt tykg,ahlopCero_ opy hea ftb ae ad peyran hKs tcgyatcihat, rehc rh deatwu teFfiw npeelehi rhs. crcrnnot d�qehei t�u regtale e otndillnr l pwCarnhhodjToeitrec htlso-n tet aebmhe fawioa,iut tyhu t�lohhh figS r osaicp' resv:sa.;a.i Y l l1aeoa.l5rts � t d aha pn8 ; k syk/cu�gs:1h �:o .1 ortc g0l a;o�1o1c o.ftt s1nae_h h fatulr-e.:ammcelW .duhdtsyrd yi huif loptotr::pircisa'otna hmu srbgon:miep to dael p o kndokrecrrMt e otehahaaiungiriblnr, eskimolgCd m evno y aupnorktl dyoi .esv,gn ssa bttnhhl ide.ee Seatel l 1890 BrucAe. Fyiosnnl a CHAPTER ONE INTRODUCTION Theg oaolrt hibso oikst ob ritnhgre e adienrtc oo ntwaicttth h eeffi cient computtaotoitlohsna atr ea vailtaobdlateyo s oldvieff ereenqtuiaatli ons modelpihnygs pihceanlo mseuncaahsd, i ffusrieoanc,ht ieoatntr, a nasnfftdeu ri,d flowA.r tmears tetrhimena gt eriinta hlbi oso yko ush oublead b lteoa ppal y varioermt eyt hods-finite deilffeemrecenontlc,le o,c paefitrnitioutnre,b ation, etc.-alytohuwo iunlgolhb t e a ne xpeirnat n yo ft heWmh.e fna cweidta h probtlose oml yvoewu i klnlo wwh imceht haordsesu itaanbwdlh eai tn formation cabne e asdieltye rmbiynw ehdi cmhe thoTdh.ee mphaissoi nsn umerical methoudssi,an cgo mpuatletrh,o suogmhoe f t haep proaccahanel ssy oi eld powerrefsuulal ntasl ytTihceaa ultlhypo.hr i'lso siostp ouh sype r eprogrammed compuptaecrk awgheesan v ailbaebclaetu hseeay l ltohwre e adteosr a mple, �rusaen,ds oldvieffi cpurlotb lweimtlshe sesff orTth.er eadieshr,o wever, introtdotu hcteeh de aonrtdye chnuisqeiudnte hse csoem puptreorg rams. 1-C1 LASSIAFTIICOOFNE QUATIONS Eqautnismo odleipnhgy spihceanlo mheanvdaei ffecrheanrta ctdeerpiesntdiicnsg onh owt hemyo deevlo luitnti iomanen tdh ien flueonrbc oeu ndcaornyd ilions. Whnec ornorntweidtam h o deelx,p reisnts hreeod r omfa d iffereeqnutai,tta ihloe n adneelatsrynmtmeu itssdh mteee c twihdhtoeathd tayas rpto see reu qiut.aa tibistlo oebn es olvTehdac.th aracterization C��sidaec rl ossyesdt (einm.o ei .n tereco hrma answgsi tthhs eu rroundings) cannodcti3 a.mTn ght tehh rrcceehoeeem mnpcieoocncmataplsrno e nwa(ehcsnotwatcs hysoee tn nhc seeyn statirreisageml ti livuboemyncni ws1 ni· ,at� th·,e d Fiugrel·IR cacnosnysctm. ceslepoqicaticnugoet etnafhaniasrsss ga ot epfu n o icfin.rsvcoTien neothfedignitorrq i hftuce�cn�s iateyc t.Ti)sea shoa,eymdnytrn rs � se a ecsmhgit_ 0 t ose, �1e oi w atssnco p i t arnFier iokdetgnn1i h. o-cce w1aoat ,nnns a dtc hefdenui tonfforfceeftat aar hticleeioh n on tn i �== -+kk12cc1·2c3 df (1-1) �f ==kd3 Inittihcaeol nlcye ntorfca otmipoonntsew naotn sld h rac·_ieze e raon,td h ien itial concenotfcr oatmipoonon neinegst i vaescn0 • W et huwsi sthos olEvqes0 .- l) subtjotech iten ictoinadli tions (1-2) Notteht ahtce o ndiatpipoolnnysla ytt imzee rnoo.tt ol atteirmt e.T sh ree anc tio procienet dismi efw;e k nowwh erteos tawretc ani ntegtrhaeetq eu ations indefiTnhiietsve ollyu.pt rioopnye ireteylq dusa ttihoaantrsc e a lilneid1 ial-value potsrnyetoolsx_hbyntoti.i il efeo Iasn sem rnbt d md bhesciripadnesevsiEatv naeffqroiOd.r esy a(De air t1EtnlaeeIe- ati bqnd1Vr m1l.uot )P.eTee a ri h ,tdtu iiEhsondqaa nais(trs-rf.Ii e Iyf na ) ein ert(dqei1 u)na-apa tl2rrti-gesoiavo ibolavnln tleIdcesuhrbn etm,eeny i hsa re si. e s Consindeexdrti ffnu asnidro eactiinao pno romuesd i.uW me havae hp;�:re�ottc�dcvtd�rc��si1Tuu1o fusssgfs iyccbeosnou)nt(ceht, esfe motfirmwA l.ceaemi mi t adoees dwbnrsetiai lhtlpa aheolon rntacse vh eaysor ss slo tiwuuoehmmgfmtipehd htcl ipehhefro e fre uuoamsuscteisitisadnoa nau dnngnm (tr)J1t')_JJ , �sefflocer:;tira:idnd:v il:dtue��ff �· �hs 1r:n3;• i1.rt�:c <o�eocolnf f ir_ � 1i?.1rice·�\ 1_f� t;a wA ec �ie-pceontst r1Xeex-tiu h rrunp+o -"tne lrt-nc iiv eh1 opotol+lse,menl �us )tprJu eix: (�iio mnz s m+napnoe1 ofe R ef pt (culo r lh)nris vuev imdaies ot rmc i- veittJdioaloo.F Bnla riycu�ru c lmJ lskiue wb(ai1'tsd no3n-nseh it)g nh g INTl.ODUCTION 3 or J J,,= - D..�u. xcr= ·- D" O� y J,= - D..�u , (1-4) Thiesq uaalisosnue mqeusi mdoilfafr(u osinmoeon lo err cacd1iafnftiu nas neds onmeo loefp roducl oudtia)fn,fad ul tslhe mesi crosdceotpaoiiftcl h pseo rous mediaurmle u mpiendlt ohd ei ffusion coeftfiomc oideaens ltpeci .fi c Obviously physsiictaulat thdieio fnf ucsoieoffincm iuesnetti tbheem re asuorrde edd uced frosmi mislyasrt.W e (imtsh ) atphp (irso x )itmhea e(qt iuoa )bnte i coonm es aa;=cfuo o.. ax" ' +ayo o.. "ay ' +aza o.,"'az +R <c(>1- 5) or �=V·c+DR.,(Vc) Iboumpendaryrmea ble e=e1 - L FIJtinl-l Dilf111iD11inasl11b. �c1.iitcNe O�hxLnt'lt��ltkis�.!ulN;_e Enot.nAswne ns R eso;ttlx afgNedAehg e idyaiA s �s itlLs Y-cehStbvmtrtIt:se erSanI(are ts iNeeeitCu e a chgoHstaFi�_E,avotte M<!.-m_�ion iIe.iaC ofdAl t gai·LZn� - E()gJ�rrN�h s� ' ,J:tG.;aou lieNec rnseEoops E) uiRmn!la.clriInuo 5ptN cI.a0re o.fl ts it•s n yihhEniai s taeqp nwt (h.eto� to-ih yet li)u5te d at� msdhl1no eoe a1Tzd � nrbdu nhdeii sv. ta1,c1 vrm eriheisttmaeunz ofi.snn i e�1n tr.hs snooieiot lb itno ey hAs dcAnwroisnecgte ffa lt�eoiennetm �urd �aEq t1� oeoeq(ion(n.t� 0 hac �d1eo-�l6x ne) :�care5 dtegsaxwnot�+ foit i Rrdd nmooe�e (npp=pac Oeea )nn rodvdt ndaesoi irn nafitl.lfoa y etnbreoel�meqn eadnu psteretno)id{ndni( -oitrnaeatye)6tlh c�ovaio;raarl�l:nnd�.drliEe��nc� uryiiruaaq)��h swe�: e�.nbeu e-eIc(�filn1�noqe •o6xd�s t)e iti:a.r� dds·sttor � �e hnssoasceetat �io oay;htodnsrtstehftediidi wra.w ha -dTennbso t oeeehrgomdl t e uu aabhsnsbsitoesedt mhcu p a peonerreondocyycrrdafi hoymif n,nc� et�oy1e dooain nsoa1 naboeseartntHslten)n cr wtute a sdn-ioeosxa crasdon tt edhi eeehhr d x=O -Dd�e=� O (1-7] pbbcchdlT�bRreooa1hhpraoeeonuidmaebbrenaae�n�tdb ennr eteooeb eios adpe nnrhuinldiactEb-fcrefos r hibha stoenattpcrpsaqld e(ou bdwraeapsf c1imriO1tf6uhtctsel� toto,tcet-D )heo ef b h hetcoioe yaeds..msmEi teatnmltiToe,ipo( auto-1n tdr nnne-lisr h E efi esmmr- cBi ampm iqe.nsl aa,(sev-ia8l (VitnnoeIsd abeiar cn)uliPssuiii a t e tavsatnnesos spd-ofea. snsn xduc o-sH)d omoaih5enrl ltat per1kuifi bpryee) s,sc.resn m duloidl nn ooa e c0p-iuaixto, lts .eurcttlfnnnct mapddlh=dss ihhi la da es ri ei eeiauebeeeftoratnotofffd fdcinq yth wyrealwlbef fp hnu he sy,uoplrepur aga a t - t-oeerrsboe tntevfopisnmeoioqbidr acrootisnbwuuoloe olch in ut.tl-oxnanenan.tunn e iiheutd I nm aebsieitsoah(amtliiaC nup o q cena1lvhdsoinr aadta -vsi en sy 8en � -) g v alue Tidap�s�espeh1no1dinln1vr atn1Ti eohestu 1a.ew idvno hv,aroenpaoatdeeO mletonbner :ixre sinaanll rin.ofs.W t ;,ip 1�ee ·dfqe r,nT=11id e,,, hiiX c uf·i,q•.�eaveh n r u D .'aa� ea�larnfl.�i,,m cc1 �·l\ r t,tta.co1o+ ll�oavi fRtnt cu (hhcasvdc)se,oeueae ol � frt npl shdue cue notcd e tdndioehecoe nprxednenp eaad onecnn entscnetodanioo e n te(nntrr - c a1i � �ws)9hs T�ndt�'hIJceleocse�ed ne a\ pea �tucy.a�sa n�tlrtCdoew=1eoqt.tdutr he oenW �ntin tioeea fnav n b.cnicxidircn lu ilaaoaok oantnlolit ei•s'E 0bei �pleh in�a.ei v: .b. s �to�k?cstu '7o::c )'due�ma.or:� : n(l) dr.y::�aXn q(,e�:oic, -.1s8 rn·��e 0(��m-.p)duo-�svIp7g re=r)�( tr ft a Xoe�vo��e�o) i(a·bbl1a T l �rl-1a-sh euibe0nnte,aau)mtdse ie t ptt w rntphai comc huerobo ooerd aounlilenc ubloktstipcn br(aairns-irtrt-fea1a1eco ariel)m0tn ers i INTIODUCTION!! f"igurDeilff-uls ioninalonr.ca1alys1pellc1. Iwfe s olEvq.e int woort hrsepead ciem enwseia olnhssao v ape a rabolic pardtiirffeaenlt (ei-qla5ul)a twiiottnhh,I e v aribaebilenevg o lutainotdnh a.e'¥:r: .y ·'" anzd v aribaebilonerbgs o undartyy-pvIeant.l w duoie m enwseih oanvse (1-111 wei ncltuwsdope a dciem enbsuiatol nlsoo nwls yt eady-stattheet nhs ei tuations eIqru arteidountc oe s( ) ( ) �, 1o . �". '+aa; ;,,' fy'D' R(+c= )o (l-12) Theiqsau tiwoonu mlodd beolt dhi ffaunsrdie oanc itnaic oant aplayrstttih cialste vteyelopr foby oni ugndtn ahzrce dy oi nrdeicsttotii hooazan nvtrs,aD e ria irlaial1croniheweool ergnebd lsto i- u(gtnsidyFecbaipeo.1lrge n 3-ey d) Ti.oht rei ons thfier ksitn d t'=<s" (1-13) Neumann-eot rby opundcaornyd iotrti hosene sco knidn d -D,.riik ij-D"". ·Vnt•=- /• (1-14) andRo bnit-yopreb o udnarcyo nditionsk ionordrmt ihxceeo dnt dhiitrido ns -Da,;t. k= k.,()< '-ca (1-15)

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