;:“.:;..>:-c I.'.’:?" 534:5’
`5-fiii
`St. Louis San Francusco Auckland
`New Yofk
`Bogoh Hamburg
`Johannesburg London
`Madrid MEXICO Montrea% New Delhu
`Panama Pans Séo Pauio Smgapore
`Sydney Tokyo Toronto
`
`UTC-2001.001
`
`GE v. UTC
`
`Trial IPR20l6—01304
`
`

`
`PRINCIPL ES OF
`
`CONVECTION
`
`I 51
`
`the |1lcL‘l1;II11\m anal C;llClllLll.l0l1 of
`The prccciling cliziptcn haw «.'un~.iilci‘cLl
`C()lI(l1lL'll0Il
`l1L‘Ll'l 1r;inxlL-i, (funxccimn \\'.l\ ;'i!l1\ltlUI'§‘\l Ulll\
`ii1ml';iI".i\ iI rclnlcd
`i.Ull]Cl1\!LIIlLl:1l'_\
`\.'0l1{llll0l1\lll1[M\\CLl 0l‘l.lk.'l‘llLlllL'l|\5ll r\ml1|<:nL We mm \\I\l1 Eu
`cmniinc the methods nl'c:i|cu|;iiing mm cuiiuii liciil ir-.mx1‘cr ‘mil. in PJllIlL‘l|l‘.li'.
`the \\:1}'\ ml" prcLlii.‘Iing_' ihc \illllL‘ ml Ihc {L\ll\L‘L‘l]l1ll
`l1c;it—li';ir1xtL'r uncllicicnl /1,
`The xtlhiccl oli i.'un\cc[iim hr:'.il
`lr;m~lL'r' i'cquiI'c\ an L'llL'l'3.L_\
`l‘;il‘.mca.'
`.ilun-__‘ with
`an unulysix ul' lhc fluid \l_\n;imii.'\ nli llll.‘ pml\li.~1n\ unm'uI'i\cil, Hui‘ \_ll\;_‘|_|\\lnn
`in this clmplcr u ill lirxl miisiulcr \i1l'1‘lL' nlihc \|lI!["lL' r'c|;m'nnx ml" lluid «J; ngiimcs
`and l7Ull|"l*.lill'_\‘-li!7\L'l‘.ll1;il\\l.5 \\l1JL'l1 arc iinpi=i'I;mI I'm" 1‘
`lmwic lIl}LlL'l'\!i|l]Ll|ll:_' 0|"
`i:(_)i1\'ccIioi1lic;il t:':ir1st‘ci'.
`."~lc\1. uc xhiill ll11DL1\L‘l1llL'[lL‘l'{J)
`lV.i|.inucm1 tln: Iluu
`aj.'\li:in and ilclcrminc the ll1lllJL‘l‘l\.'Q ml‘ lhc llmx on lhc lcmpcr'.imi‘c ;_'t‘::ilicn1s
`in thy lllllll.
`l‘|l1Ltll_\.
`lizuing Ul"ldlllL‘Ll Ll L\l](1\\|L‘\|¥L‘
`.11‘ mg lL’lll[')L‘r‘2IllJl'L‘ kll\ll'l-
`buliun.
`lhL'
`licul-tI‘uI1xl'ci‘ lulu limn .1
`l1L‘1llL‘tl
`\iLi'l'.auc In .1 Eluiil
`xx l1].'l‘1 ix l‘nr'ccil
`over it m;i_\ he dclci’n1ii1cd_
`l\
`lllltl
`in i.'llL!l'ilu'lL‘r
`Uur klL'\-L'lU[')H'lL'I'll
`in tliix gliuplcr ix pI'im.1ril} illl.ll}llL';|l
`cnnccrncil only \\l1ll liUI'L'L‘tl-C0l1\ CCl.lUll llim x._\ «turn» .5LIl‘l\L'L]llClll ;'l1;l[‘lC['\ xx ill
`present cnipiricul l'L‘l;ll|lH1\ for \.‘§llCLll1l1|l1l_.! l'nI'~:cdr..'oi1\cciiun hc.il uum»l'cI' and
`will ulm Ircul Ilic \Lll“_lL‘L’l\ 0l'i1.iIuiuil gurixcuiimi .md lmiliiig and \.'0l1|.lc‘l1\‘.lIlU!'l
`llcul Ii';inxl'ci'.
`
`.‘.iv-,'?
`
`=5
`
`1.'t.:";
`
`:'
`
`llcginning .l[
`.‘—l and 5-3.
`('ui1xiilcrtl1cllim mcr .| rlut p|.iic \l‘ ~l1n\\:‘sm I I3“
`the lcziding edge nl‘ thc pl.iIe. :i rcgiun dcxclupx \\ licrc the iiillucmc nl' \ mmiis
`furccx ix I1-ll.
`'l‘hcxc \iu:oia.~ l'ui\.'c~ use ilc~«.‘i:hcil
`in terms nli El
`\l1::ar \iI‘€\\
`.-
`heluccn the lluid lii\s.'i'\,
`ll'
`ll1i~ \'ll'L‘\\
`ix Ll\\lllllL‘Ll In EM; propui‘liun;il In ihc
`nnrm.il iclncru ;_'i'uLlici11. wc lmxc [hc ilclinm-_.' cqimiion for the \l\L'U\|l}.
`
`UTC-2001.002
`
`UTC-2001.002
`
`

`
`\\ hurt
`
`“fix p
`!HL'l1\ll
`
`-\lr!
`lukcn ;
`»1Iu:m'«
`"ltuhu
`lmmit
`the flu
`Ham \ \
`or mu:
`
`Rc_\nn
`mm 11-
`Ngaill.
`The
`..rc Ind
`{hr In:
`I hia Ii:
`.cr_\ cl
`:‘.:||wr
`Thc
`micr H
`‘MCI’.
`.;U,__“
`-I fun
`"1: \ E\
`The
`’;'.i‘ .11
`
`I-
`
`'.sin
`'
`1[\
`
`r
`
`1
`
`(541
`
`1_\ p1«_".¢I xci
`,u1~ cafllcxl Il1cJ\m.‘mu ..w. nun, _-\
`]'h¢g.m~t;lr1IuI pmpm'tmr1;1!i1‘_\
`ml’ umlx |\l1L'\\-[OI]-\CCt‘rl'|L1\[‘L‘l'\L1UL1lL' Im-Kcr: hmxcxm m.m_\ sch at umis arc
`uwd 101 the \i.\cU~|lj..;:E1L1;':\IL‘ muxthcl.:kuI11u~c|m‘I ThuDI-\p::I'gI'ul£1“»\hiUh
`MN hc ..'\\lW\I\IL‘!U mm lhc h!|HllH.1liUl‘. ki[ hum’
`luuhn-_.' cd‘__'«: ml‘ the plum In
`HIL‘
`rug_'Inn ml" flsm which dL‘\cluI‘~ EIHIH Lin:
`umuh ihc c1't'cL'1~ u1'\i\\.'n\:l} arc nbxcl uni I~ Lallcd Tho: hmnd;u'\
`|;u_\cI, Swine:
`;u"r'wi1mIj\ point
`|‘~
`ll\L'd In x|c-[§4rLxir
`the = pmnlsnn \\i1cI<.'
`thc hnumimx i;1_\c1‘
`cmlxzllmp-»II1I l\ll\li£lH\ \.'hcMc11.1~ihr'. LUUI\|II1.|IL"~\|1\:TL‘1h<: \ c|x\cII}'hccuI11c\
`‘N prn.‘cn'I of lhc l‘I‘cc-\Irc.xr11 \.Llu::.
`|;smm.u. hm :11 mrnc \.1:Ii..';:|
`1»
`[Il|Il1l”\.
`Ihc fmumiuljx-l.1_\ci' Li{‘\L'i€’[‘7T1L’!1[
`dixlnllcc fmnl the ic.:L1In_: cdg’,xicg‘-.‘I1diI1:nI1lhclimk I1;-M.1m1I'l\m:prupcrlicx.
`»m.zH LlI~1uI'l\xm'=;~ m Ch: Hun Iwgm l\-
`twpmm-
`.lH'l[“inL’L1. and .1 Imrmllun
`[‘|0\.'L’\\I;1i\L‘\ p|‘.uccur:t|lH1:.' Ham l‘L'xU!'[1L‘\ tn: hulcm lhc ILLJ'hL1|cI1I-I1:-\\
`I'c;_‘iun
`nu} he pictnlrcd .:~ ‘1
`r_mdm1~. glm|n|I1;_'u..‘1:un x-.11h uhunkx ul' fluid mu\im__~ to
`and {In 111.1]! d:lucIm|1~ "I he tsxmaulinn hum |.umn.u' In '=,LH‘f*LI|cm Hum uccurs
`xx hcn
`
`UTC-2001.003
`
`UTC-2001.003
`
`

`
`3"5§iEt‘E.' ii, : fI'C€-\II'L‘Lt1‘l1 xelocitt
`.\' = Liifilitllcli from leading edge
`V = ,ufp : i\lllL‘I1T.LllL‘ Vixeoxity
`itnd i.x di-
`'§'5I1ix piirtietiltii' grouping of terms ix called the Re_\nol«.lx number.
`ansiitinlexx if it \,‘0l'Ii.\txh:nl xei of unitx is taxed for ll“ the propertiex:
`H,.\'
`—-
`1.
`
`tr-"5
`_
`
`Re
`
`:
`
`_
`
`l|';|I1\lliL\ll on 1.‘ thit phite ix Ll\Llilii_\
`Although the critical. Re} noldx nunihei l‘oi
`‘I:
`It!‘ for moxt iin;il_\tic;il ptirpoxex. the criticiil \‘i,lil|L‘
`in ti pnictictil
`_
`_ nation is xtrongly dependent on the .xtii‘li;ice-toughnexx conditions" and the
`rbulence le\el" of the free Slrciittt. The l1U|'m‘di
`rtini__'e for the heginning of
`-+- sition is between 5
`HI‘ Llfid Hi". With \ei'_\
`iLll'l_.'C ilixtitrh;ince~. present in
`flow.
`train.-.ition rn;i_\ begin with Re_\no|tlx nuniherx Li.x low in ll)‘. iind for
`$1\L'S which :ii'e \‘L’l‘_\ free front tltictiiiitioiix. it niu_\ not xttirt until Re - 2
`-
`10"
`at more.
`In i‘etilit_\'.
`the I1".ll1\iIIOE‘I procexx ix one which coxerx zi
`i‘;ii‘i-__'c of
`7 §.t‘to|d.~. ntimherx. with H'it|"l\'|Ii\‘vH heing complete .ind with dexeloped ttirhiiient
`inn" l]f~ill2lii_\' Oh!'\L‘l'\€Li
`Lil Re_\nol-Jx numhcrx twice the \;1il.|L‘ ill which ti':in.xition
`The i'el:iti\'e xhatpex for the \'e|ocit_\ prolilex in luniintir and turbulent flow
`indicated in Fig‘ 5-1. The Itimintir protile ix'.t[Wpt‘t‘i\in1'.tlei). puruholic. while
`turbulent prolile htix ii portion l1C2.tE' the will which is xery ne.irl_\
`linear.
`is linear portion ix Hlllti to he due to ‘it I;iinin;ir xtihltit er which htigx the xtitllice
`‘cry closely. (}lilI\ltiL‘ thix xiihhi_\-'ei' the \Ci0\.'l1_\ profile ix |'L‘i.llli\‘Ci_\
`tliit
`in com-
`jtarison with the i1ll'l1ifli.tt' protile.
`ix. one 0Iit11t\l‘[‘l€n[llm exchange. Con-
`The ph_\'.~;ic-.il mech:ini.~.m of vi~.co~.ii_\
`r the liimin;ii'~fiow xittititioii. Moiectiles m:i_\ rnoxe from one i‘d'|T1ll”i‘i| to im-
`r. carrying with thent zi momenttim correxponding to the telocity of the
`' w. There is it net momentum transport from I'C5_.'ittn\' ofhii:-h \‘elocit_\ to rei_;ion5
`low velocity. thux ci'e;itiiig ti force in the direction of the how. Thix force ix
`fie viseotis-xhe'.ii' 3xlt‘-csx which ix ciilciihited with EL].
`i_<—t t.
`The rate zit which the momenttini tr'.inxl'ei‘ tiikex pltice ix depentlent on the
`eztt which the nioleciilex tTtn\‘Cl1L'['0.xx the Iluitll:i_\er.x. In ;i giix. the inoleculiex
`tltiivuld lTIO\C 1ihUL1l with xome '.o.er-.i_ue speed proportionzil to the \qLl'.l1'C root of
`tihxoltite lL‘I11P§.‘1'illlll'L‘ xince.
`in the kinetic li‘ICt\l'_\ ol‘ g-.ixex_ we identit'_\
`“kmperaittire with the l11L’L|['l kinetic energ_-_\ of Lt molecule. The tiixtei‘ the mo!-
`acitules mot e. the more ntomeiitiim the) will ll'ilI7\[‘t\l'li Hence we xhotilil expect
`the viscoxit} of L‘ git». to he L|['1p|'0\if‘I1‘.llCi_\ proportioitiil to the xqiiiire root of
`;kmper2ittii'e.
`iintl
`ihix C\['|€L.‘I‘.lIiL\t1
`ix corroboiiitetl t";iii‘l_\ well hi experiment.
`The viseoxitiex of some l)Di.\.'&li thiitlx tire git en in Appendix A.
`- In the ttti'hu|ent-How region dixtinct fiuitl ];i).erx are no longei‘ ohxer\ ed. zintl
`e are forced to xeel-t
`Ll xomewhtit
`t|it‘t‘erent concept for xiscoux iiction. A
`iflualitzitive picture of the ttirhulent~tlow pro-cexx in;i_\ he t\i"l‘il1|1\ILi
`I-at
`iimigining
`ztcroscopic chunl-.x of lliiitl
`'l1';ll"t\|‘tl'l'iiI1g energy and nionienttint
`|l]\lt.‘LtLi ot
`
`UTC-2001.004
`
`UTC-2001.004
`
`

`
`.‘\‘;nm:';:|I_\. \\c mould
`n1ic:'uscnpi\.' 1r;m~puH on my mm mi undmdml n1.nJcc£J\c~.
`s.'\pw:\.'1l}1c |‘.lI;_'cI'
`.'n.1~\ u1".?.1L' In.n.w'n\u[m cl;-mcx1'.~«\l'fl'.mi Iu1I'.mspnI’l morc
`cncr-__'_\ and l1IUl'I1c'H[l|m1h..1:Shy Lmhxuhml i11I|lL‘(lI[L'\,.:I'lt! uc~hnL1l\|.x|~mc\pccl
`Ll l.:r'gcr \ |xuuu~~~hc;u I1-r..u in !url*=.:lL-HI mm than m i.:Inm;u'J1m\ mud ‘.1
`l;u'_1:cI‘
`lhcrnm| cum1ucl|\n_\ m xu-H1
`Jh:~ u\pc¢I.::um |~ xcmicxl by L-\pcJ'1mcm..u1d
`I1 I\ lhh l:!l"__'L'l
`\i\\.'UU\_1c1m|1 tn mrlmlcnl flmk \\h|.'!1«.';:LI~c~ Ihc 11:11
`\<.'|w.'i1}.
`pmlflc uuilczalcd in Hg 5%
`(‘umider Ihc mm iI1;llLH‘c;i\ \!‘lL\\\ n in Hg. 53 .-\ hu|mI;u \ i.x_\L‘I' dc\L'|Up\
`at the cmI';n1cc..:\ \hL\\\H, }-\c:mm|i_\ I!1u1‘uumi'.u'\
`l.y\c[ lillx Ihc cmirc Iuhc.
`and the Hm» :~ mid Iu he tulh duxcinpcd 1!
`lhc Huh 1» Lmnn:u'.
`:1 pumlmhs.‘
`\c1m;H_\ profile ix c\pcz‘1cmcd .:\ whnmn in My, 534:,
`\\hL'|I Lhc Hum is mr—
`lmlcm. ‘.1
`\Ul11L'\\h.|l hlumcl prntilc l\1\l"\L’|'\L‘d. .\\H1 111;. 5-Eb. 1n:nHJl\'.lhc
`Reynolds number xx ;Lg.uin used §1\
`;: cr'1::*I'iuH mr L¢mm.:I' .md Iurhulcnl Hun.
`IIUI
`
`Ru
`
`"N
`
`lint!
`
`the {km 1» uxuuily u}‘~cr\cd lnhc:u:'lm\cI1I
`_‘v__'.:in. u mngc u!'Rx.'_\I1u|d~ num!\'i~ 10:’ llullxillun m..\ be uh»;-rxcnl. dc-
`pcmhng on Ihc pipc ln\LJ§_'hflL'\\ MR1 xmuntlmcxx or
`the Hun. H1: gcncr::|I_x'
`;u.'«.'cpIs.-xl Hinge lur I|';:r1\i‘:inn ix
`
`IUIMI
`
`V Re‘
`
`-IHHH
`
`UTC-2001.005
`
`UTC-2001.005
`
`

`
`uincd up to RC} i111l1l~ lH!!1'lbL'i‘\ ut‘ 25.111!”
`111‘ H1111 h1l\ been 111111111
`ough lnmitt
`;1l111'1. 1:11111hti1111~.
`ulhstl 1111101‘
`carefully conlr
`1111.11 Hum 111
`lL’lt|[i\\n for o11e-di111c11~.i
`The c11n1111ui11
`H1
`’
`i11t,,,.-31
`
`.1 tube ix
`
`re 1151 4
`“m
`
`l111\'.
`l11'1|\\ rule 111'
`mean xclocitt
`A =2 C[‘0\.\-\L‘CliUIT.ti
`
`‘.111:;1
`
`e define the 111;1~x \cl111.‘it_\
`
`-.1x
`
`Manx \ ch.11.'it1
`
`1 that the Rc§.11u!1!\ n11111l1c1' 111111
`
`‘.tl\U he \\|'i1t1.‘n
`(lit!
`Re“,
`
`,U.
`
`Equation (5-61 1.» \0m1:1
`
`hues 111111‘:
`
`:11n\‘1:11ici1t
`
`tn use thtm liq. |5—‘~I.
`
`iN\.,-"t“S‘¥3CEJ S-7%.’
`
`in 1111111: LI'l\1'.\nL'L'\ the 1111111 111111 he It'et1t1:d
`ix iT1\t\Cid.
`hough n11 r1:;1l fluid
`ut' the L‘qll:tli1‘In\ which ;1ppl_\
`in
`111 hilc 111 prcxcnt mnw
`such. and it
`ix 11 nrtl
`se ci1'c1I111st:1ncea. For L‘\{\lT1P1\3.
`in the H:1t—p|.1tc 'DT‘t\i‘iCl'11 KHNCKINNCK1 ;1hme_
`flow ill
`11
`\ulT11."1e11t1_\
`large kh\l1lI'lL'L‘ 3111111 the plate \\iH behme :1\ 11 n11t1\i\—
`-, s flow systeni. The 1‘e‘.1~1.1t1 I111‘ lhix ‘he-11-.1\i111' i\ that the \'el1.1uit_\ g!'Lt1.liL‘l1l\
`al to the 111111 dire
`1.
`.1n1l hence the 1 i\1.'UU\~\hL".1t‘ t\\n.‘c\
`cti1111.1rc 1er_\‘ \ll]ill
`small,
`I
`111‘
`lI1\.'U[‘I1[\l't.‘\\lNL‘ fittid 111111
`1111
`ex ix 11111111‘
`.111 elcinen 11m 111‘ the fluid -:|c111ent. the
`t‘111'c
`‘‘ If :1 bailunce 111'
`1 to the L-h;1i1;_~c 111 111111111-111
`Se forcex 211’: \1:l cquu
`l11ni_v21 ~lt'c;:mh11e 1‘1;~11lta:
`rnoulli cqtititiuii for 111111
`
`-.1
`
`CONN
`
`. in dilTere11ti-.1| tksrin.
`
`11
`
`in Him
`
`here p : thiid dC11\it_\
`,1:
`prc~.\u1'e tit p111‘tic11h11' puii
`Y 2 \1:lucii_\ of Hm-.
`111 that point
`1111~i1lc1'ed 1111 energy cqt111ti11n bCL'1ll.|\'C
`The Ber11n111li cq11;1ti1111 ix \0l111.‘[Il11L‘\ c
`;1111l the Pl'L‘\\ll['L‘ 1’c'p1‘1.'~i:11t~ putu11ti;1l
`‘file 't'31'3‘u‘ term rcp1'cs1:11tx ki11eliL' e11c1'1::3
`th.1t thexc l1.‘l'[11\
`;11'c durixcd 1111 the
`energy: h0\\1:\cr. it 11111~t he 1'ei11er11het'c1J
`
`UTC-2001.006
`
`UTC-2001.006