seriince osm putational if?-� methoidnms c hanics• � � antdh ersmcaile ncesd}/ Numerical Heat. Trarn sfe and Fluid Fl SuhaV.s OW Patankar ' (Cot1ie11d1f uroimn sfirdoefn lta p) Numerical Ina dditsipoenct,io aplia crdsei scussed, includtiwnog-:d imepnasriaobnfoallloi wc; Heat three-dimpeanrsaibofonllaoiplwca ; r tially parabfolloiwacsn ;dt hfei nite-element Transfer method. Theb ooiksa ni mporrteafnet rfeonrc e andF luid engineperraicntgi tainodin see xrtsr,e mely usefausal t exitnc ourdseeasl wiintgh Flow computaotffi lounfli odwa ndh eat transfer. Heriesa s elf-consttarianiegdh,t forward treatomfet nhtpe r actdiectaaiJin lvso lved inc omputataicotnifavolinr tu ym erical heattr anasnfdefl uri fdl oawn alysis. Intenadsae ndi ntrodutcott hifeoi ne ld, thbeo oekm phaspihzyessis ciagJn ificance rathtehram na themamtainciapJu lation. Mosotf t hmea themautsietcdhs r oughout arlei mittoes di mpalJeg ebra. Theb oocka rrtihedese scriopftt hieo n numermiectahJto odt hpeo iwnhte re readcearbnse gtionw rictoem puptreor gramPsr.e paraantdti eosnt oifsn ugc phr o gramasrt eh oroudgehslcyr ibed. Beginwniitnchgo nsideorfha etaito n conductthiaeou nt,h doirs cutshsieen st er actioofcn o nvecatnidco onn duclteiaodn ABOUTT IIAEU TIIOR intgo a naloyfst ihspe r ocefdouflrru ei d SuhaV.sP ataniksaap rr ofeisnts hoer flocwa lculation. DepartomfeM netc hanEincgailn eaetr ing Probleenmdsi snogm ceh aptaerres desigtnoae idud n derstawnhdiiillnelg u,s thUen iverosfMi itnyn esHoeto ab.t ained trataipvpel icsaptoitolnsisog lhutto ifo n hiBsa chelaonrdM' ass tedre'gsri eneI sn dia, practcihcaaJll. e nges andr eceihviPeshd . fDr.o tmh Iem perial Thesaep pliciantcilounddseev :e loping ColleLgoen,d on. floiwna c urvpeidp ceo;m bicnoendv ection Befojroei ntihnUegn iverosfMi itnyn e ina h orizotnutbmaeel;l tairnogu anv de r sotfaa culDtrPy.a, t anhkealprdo sitions ticpailp teu;r buflleonawtn dh eattr ansfer att hIe ndiIanns tiotfTu etceh nology, ini nterfnianlnlteyud b easd ;e fletcutred KanputrhI;em perCioalll eLgoen,d oann;d bulejnetat h ;y permijxewitin tgh ai n thUen iverosfW iattye rClaonoa,.d a thrust-auegjmeecnattp oiernr;gi ofduilcl y Heh abse eanc tiivnt eh dee velopment develdoupceftdl oawn;dt hermal-hydraulico fn umermiectahlo adnsdc ompuptreor analoyfsa is st eagme ner.a tor gramfsop rr actsiictaula itnivoonlsfv liunigd (Co1e1dt0 11i i1n1s1bi1adcefk l ap) flowa ndh eattr ansfer. NUMERICAL HEATT RANSFER ANDF LUIFDL OW SeriinCe osm putaMteitohnoadls inM echaanniTdch se rSmcaile nces W.J .M inkowayncEdz. M .S parErdoiwt,o rs NUMERICAL HEAT TRANSFER AND FLUID FLOW Suhas V. Patankar Professor of Mechanical Engineering University of Minnesota , .. ,;:::�?-·,\ ___,, _u,·.�··• ...• .:' l i l?{l[§:1_¢:±J= I 0 HEMISPHERE PUBLISHING CORPORATION Washington New York London McGRAW-HILL BOOK COMPANY New York St. Louis San Francisco Auckland Bogota Hamburg Johannesburg London Madrid Mexico Montreal New Delhi Panama Paris Sao Paulo Singapore Sydney Tokyo Toronto ri 465829 NUMERIHCEAALTT R ANSFAENRDF LUIFDL OW Copyr©i g1h9bt8yH 0 e misPpuhbelrCieos rhpionrgAa lrtlii gorhnet.ss e rved. Priinntt ehUden iStteadot fAe mse rNiocp aa.or ftt h piusb limcaabyte i on reprosdtuocirenaedr d,e trsiyesvtoalert m r,a nsimnai ntfyto erodmrb, y anmye aenlse,c tronic, mecrheacnoirocdroai tlnh,ge ,rp whiosteo,c opying, withtohpuert iw orri tpteernm iosfts hipeou nb lisher. BCBC 89867543210 1 2 3 4 5 6 7 8 9 0 LibraoryfC ongrCaetsasl oiginPun bgl icDaatitoan PatanSk arV, Numecraihle tarta nasnflfedur i fldo w. (Seirnci oemsp utmaettihoionnmdae slc haannidc s thersmcaile nces) Biblpiho:ypg .r a Includes index. 1.Heat-Tra2n.sF mliudsiysdni aomni.c s. 3.N umeraincalaly IsT.ii st.Il IeS..e ries. QC320.P53376 '.729 -28286✓ ISBN0 -07-048740-S Thbioso wkas se itnP reRsosm abnyH emisPpuhbelrCieos rhpionrga tion. Theed iwteorrMesar yA .P hilalniEdpd sw aMr.Md i lltmhapenr ;o duction superwvaRises ebokraM hc Kinannetdyh t;ey pesweaStsat neFdr.rW aa tts. BookCrIan,fwc ta.epsrr isna,tn bedir n der. Tom yw ifRea jani CONTENTS Preface xi 1 INTRODUCTION 1.1S coopfte hBeo ok 1.2M ethoofdP sr ediction 3 1.2-E1x periImnevnetsatli gation 3 l.2T-h2e oreCtailccaull ation 3 1.2-A3d vanotfaa Tg heeso rCeatliccaull ation 4 1.2-D4i sadvoafna Tt haegoersCe atliccualla tion 5 1.2-C5h oiocfPe r ediMcettihoond 7 1.3O utloiftn heBe o ok 7 2 MATHEMATIDCEASLC RIPTION OFP HYSICPAHLE NOMENA 11 2.1G overDniifnfge rEeqnutaitailo ns 11 2.1-M1e anoifan D gi fferEeqnutaitailo n 1 I 2.1-C2o nserovfaa C thieomniS cpaelc ies 12 2.1-T3h Een erEgqyu ation 13 2.1-A4 M omentum Equation 14 2.1-T5h Tei me-AvEeqruaagtfeiodTor un rsb ulent F1l4o w 2.1-T6h Teu rbulence-KEiqnueattiico-nE nerg1y5 2.1-T7h Gee neDriaflf erEeqnutaitailo n 15 2.2N atuorfCe o ordinates 17 2.2-I1n depeVnadreinatb les 17 2.2-P2r opCehro iocfCe o ordinates 18 2.-23O ne-aWnaTydw o-WCaoyo rdinates 20 Problems 22 vii