Turbulent entry length. 7.3 Turbulent pipe flow. Turbulent entry length. Illustrative experiment. The Reynolds analogy and heat transfer
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1 Turulet etry legt 7.3 Turulet ie l Etry legts x e ad x et are geerally srter turulet l ta lamar l Termal etry legts, x et /, r a case it q cst imsed a ydrdyamically ully develed l 7.3 Turulet ie l ill e mre ta 5% e its ully develed value turulet l Fr liquid metal x et is very lg ad strgly deed Re ad Pr Fr gases ad metallic liquid, x et is t strgly sesitive t Re, Fr metallic liquid, Pr>, δ t < δ, δ t is very t, x et a e Turulet etry legt Sae te let ad uirm l ill legte x et Batti ad Sa crrelati (L/>3, Pr 0.7 C + ( L / 7.3 Turulet ie l ully develed value te sselt umer Cstats r te gas-l simultaeus etry legt crrelati, r varius let ciguratis. Illustrative exerimet Kreit exerimetal data (Re, Pr, x/ (Re, Pr Te data als relect etry legt Lamar l 3.66 at Re 750 ~ 0 Trasiti rage, greatly, at Re 0 ~ Turulet ie l T cst Turulet regi Re, r R e > 5000 Heat traser t air l a l I.., 60. lg ie 3 4 Recall: lat surace turulet udary layer C ( x/ St x Pr ρcu +.8[Pr ] C ( x / Fr ully develed ie l q u u C ( x C cst T T Nt valid at very l Pr Valid eiter q cst r T cst Valid ly t smt all 7.3 Turulet ie l 7.3 Turulet ie l arcy-weisac ricti actr ead lss Δ ie legt ρu L ρu Wall stress ricti rce luid Δ[( π / 4 ] Δ surace area ie π L 4L S Δ Δ 4C C L ρu ρu ρu ρu / 4L 4 4 Fr ully develed l ( /8Re Pr [Pr ] / 8 5 6
2 Pie ricti actrs 7.3 Turulet ie l ε ( Δδ Histrical rmulatis C /3 /3 /3 St Pr Pr r Re Pr ( / 8 8 Fr smt ie( 4 < Re < /3 C 0.03Re Pr 0. 4 Re Prerties are evaluated at mea T mea (T +T / 7.3 Turulet ie l We (T T is large eug t cause serius cage μ μ /3 0.03Re Pr μ 0.4 Fr liquid Maximum errr +5% ~ -40% 0.67 Pr Mder rmulatis Fully develed l smt ie, Petuv (950 eq. ( /8Re Pr / [Pr ] / 8 Caracteristic Temerature T ricti actr (.8lg Re.64 Trasiti l, Gielsi /3.7[Pr ] /8 7.3 Turulet ie l 4 6 < Re < < Pr < 00 r 6% accuracy 00 Pr < 000 r % accuracy ( / 8(Re 00 Pr Re 5 + Rug-alled ies Rugess a ie all disrut te viscus ad termal sulayer Tyical all rugess cmmercial ies e e Recall: ticess te sulayer δsulayer 30 ere u ricti velcity u ρ ee: rugess Reylds umer Re ε u ε /8 Reε Re Re u u ε ε ρu ε u u ρ Turulet ie l 9 Variatis ysical rerties Variati is accuted y viscsity rati r temerature rati Fr liquid (e 0.5 μ /μ.5 μ 0. r T > T ere μ 0.5 r T < T (7 μ / μ / 6 r T > T K ere K T 0.4 ( μ / μ r T < T Fr gases (e 0.7 T /T Turulet ie l T 0.47 r T > T ere T 0.36 r T < T m T 0.5 r T > T ere m T 0.38 r T < T Hydraulically smt Re ε < 5 Trasitial rug 5 Re ε 70 Fully rug 70 < Re ε Fr ully rug regime, Batti ad Sa 4 ( /8Re Pr Re (4.5Reε Pr 8.48 / Pr Were 0.00 ε / ε /.8lg + Re 3.7 At te same Re, rug > smt, rug > smt 7.3 Turulet ie l
3 7.3 Turulet ie l Heat traser t ully develed ls tues Velcity ad temerature riles durg ully develed turulet l a ie. We Pr <<, liquid metal, δ <δ t, T is t lueced y sulayer, vais rm uctial equati (Pe Pr α We Pr >>, il, δ > δ t, T is lueced y sulayer, is very imrtat ully develed liquid-metal ls tues liquid metals eated lg tues it q cst q Fr T cst: Fr q cst: Pe Pe 7.3 Turulet ie l raly ( Te metal did t et te er surace ( Imurities te metal Treerece ( T + Tut / L/ > 60 Pe u/ α > Heat traser surace vieed Ojectives A ie it T cst, 7.4 Heat traser surace vieed is, t d Q A( T T??? 7.4 Heat traser surace vieed as a eat excager Suc a secti ie ca e vieed it verall eat traser ceiciet U Q ( mc ( T T A( LMT ut Were ( T T ( ut T T LMT T T ut l T T T dx T T ut 5 6 Heat traser surace vieed I T, T ut, T, ad is, t d A mc( T T ut A ( ( LMT I T, T, ad is, t d T ut, Q qpdx P( T T dx mc dt By tegrati 0 L P T ut dt ( T dx Were mc T ( T T 7.4 Heat traser surace vieed L dx L 0 PL T T T T ut ut PL l ex mc T T T T mc Valid t lamar ad turulet ls ducts ay crss secti H t d T ut i q cst??? Examle 7.5 Fully termally develed air l T 0 C, cm, u 0.7m/s, T 60 C T d T x0.5? sluti u Re 4 Lamar l W/m T T ut PL π L ex ex T T mc /4 ρuc π T 0.698( T -T + T 47.9 C ut 7.4 Heat traser surace vieed 7 8
4 Hydraulic diameter Hydraulic diameter 4A c Factr 4 t esure r circular duct P r circular ducts i a 4a a a+ a+ π πi 4( 4 4 π ( + i i e a >> 9 0 Turulet l circular ducts All qualitative ideas develed r circular ducts still valid r circular duct Use lace t calculate ad T turulet l it te rmula circular duct lace t calculate ad m ad u must e ased true crss secti area Examle 7.6 Air l square duct, T 7 C, u m/s, utside te duct T 37 C, utside 5W/m K T d T ut Sluti 4a a a+ 5m u Re 90 > 300 Turulet l T evaluate T ut T T 4 ut U L ex T T ρu c Examle 7.6 T d y eq.(7.43 ad eq. (7.4 ( / 8(Re 00 Pr + /3.7[Pr ] / W/m U +.33W/m side utside T T 4 ut U L ex T T ρu c (.8lg Re.64 Lamar l circular ducts Fl etee arallel late u 3 y 4 u Lamar, ully develed sselt umers ased ydraulic diameters T ut 3.3 C errr 0% ~ % 3 4
5 7.6 Heat traser durg crss l ver cylders Hmer
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