Конспект лекций по теломассообмену Михатулин Д. С. Чирков А. Ю. МВТУ 2009 (1014135), страница 2

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5.1.D/T~ Le ,Le–D/a(5.2).,.-,(xy),:vxvx. 5.1).(,vxxvyvyc p vxvyxTxvxypxvypyyc pvyvxxTyxgyyvx,yvyxTxxvyvxx0,– 43 –y(5.3)vyxyTy,y,(5.4)(5.5)(5.6).,Cxvx.CyvyxD,, 2009CxC.yDy(5.7),-.(5.3)–(5.7)-,x.vyvx,xxx,TCD,,xxxx,,,,-..,p(x),.(.(5.4)-).vx / y 2 .,,|Tw–T |T ,.T –,.M > 0,25.:vxvxxc p vxvxvxyvyTxc pvyvxxvyCxyvyCypxTyyTyy0,vx,y(5.8)vxy2,(5.9)(5.10)yDC.y– 44 –(5.11).,., 2009yTv1xx0>TT1. 5.2.,(5.8)–(5.11).-,Re xv x/Re .3,2 10 5:Re xRe10 6 .Re(..

5.2).,(5.8)–(5.11),T,T, D( T, T, DT), ,DDT ..10(),,.10.,-vxvxxvxTx:.vyvxyTyvyvxy2,(5.12)2aTy2,.,:21 px(5.13)., 2003.– 45 –-.,vyvxxPr, 20090,yCxvx.(5.14)2CyvyDC(5.15)0p/ x 0a D ),Le Sc 1 (,..y2,.vxvTTTwTww,(5.16)w« »,«w» –;,-..St TSt DCf /2,St Tqwv c p (TSt DJwv (C2Cf–(5.17)Tw )Cw ),(5.18),(5.19)w2(5.20)v,,; qw, Jww–,-,5.2..,,,– 46 –-.,.vxv, 2009p.x(5.21)(5.8)(5.10).,,,.(5.8)(5.21).x( v x2 )y( vx v y )vxvvx.yy(5.22)(5.22)vx .,,vxvxxvyvxy.vxx( vx ) vxy( vy )x( v x2 )y( vx v y ) .(5.23)v ,,v-x,x( vx v )(5.22)0xv x (vy( vyv )vxv.x(5.24)(5.24)v x ) dy0yv y (vv x ) dy(vvx )00– 47 –yvdyxvxdy .

(5.25)x.,v y (vy0.v x ) dy, 2009v y (vvx )0 , vyvx,= 0; v xw vw v0v(5.25)yvxdyxy1vvxxv(vw ,=w.wyv2(5.27)0v x )dyvxvdy ,vxv11001**(5.26).0*,v x (vv x ) dy00(5.28)(5.28)vxvdy .(5.29),(,(((5.29).-)–)).yx,,11xpxp1vvx2MvM21vv,x(5.30)(5.25)d **dxf (2HM2)wv2– 48 –w vwv,(5.31).,., 2009; fM –,* / ** –; Hcpx( v xT *)yv x2T * (Pr 1),y2c pyv x2–2c p(5.32)T* TcpT*( v yT *)( * * / v )(dv / dx ) –.(5.9)-(5.32).11,x( v xT * ) c py( v yT * ) 0 ,(5.33)v2–2c pT,.:cp0xv x (T * T * ) dycp0yv y (T * T * ) dy0011yv y (T * T * ) dyyv x2T * (Pr 1)dy .y2c pw v w (Tw,,T*) ,(5.34)(5.35)cp– 49 –TT*..,y0y.T * (Pr 1), 2009v x2dy2c pTyqw .0(vxv**T01TwT*TwT*(5.36))dy ,(5.37),yx,ddxT-**TvqwcpTwv wT,(5.38)Tw T * .(5.38):1d(v T dx**Tv1 ddx(5.39)d T**dx**TT)d T**dx1p1 d TT dx**T1dpdxM2(5.40)1 d TT dxSt1 dvv dx1 ddx1 dv.v dx, (5.39)(5.40)(5.38)(1 M 2 )q w /(c p1 dvv dxvM<<1– 50 –T).Stw vwv,(5.41)(5.42).-.,., 2009,:Cf0d Re* *dXf Re L (2 H )d Re TdXRe T d TT dXRe L St 0 (d Re DdXRe D d CC dXRe L St D 0 (Re Lb) ,bD ) ,DT(5.44)/;2w vwCf0Sv;-Cf0 /2;; bTSt/St 0 –;v St D 0/»,wvwD;–; bDvRe DCf /Cf 0 –Re ;b(5.45),«**(5.43)bT ) ,SvRe* *v * * / ; ReTC Cw C ; X x / L ; L –; Re Lv L / ; Cf0, St0, StD0 –(2Dw vwv St 0–-St D / St D 0 ––..-,(5.43)–(5.45),,Cf, St, StD,,.Cf, St, StD...-.,.(dp/dx=0),.– 51 –.,., 20095.3.vyp/ x 0.y= v x v , v y0;:y=0 v x0,/ x.-0.(x, y),/ y , vy: vxxy v /( x) (y),vyvx–/ v x.(5.12),f( )-,2f0.ff(5.46):vxyvyfyf' 0(5.47)v( fx12xv f ,f ).=0; f ' 1= .(5.46).(5.48)(5.49).,.w ( x)12.:.vxyf ,-vw/.f, f12vxvf ' ' (0) 0,332 v., 1997.– 52 –..x...:(5.50).,., 2009,bllb0,664bvw ( x) dxlv .(5.51)0,x/v .5(5.52)x/v .* 1,73* * 0,664(5.53)x/v .(5.54)0,(5.55)(5.13)d2d(TTw ) /(TPr df2 d2Tw ).(5.55):0;=0=1.(5.56)d .(5.57)(5.55)f ( )0d /f ( )Pr0Pr = 1(T(TPrTw )Tw )(5.57)f ( )f ( )vx,v(5.58)-.()-– 53 –x(TwT ).,.Tyv, 2009vxy 0f (0)Prf ( )Prx0.

(5.59)d0(0,332xx dxx)0.0,6643PrvL.(5.61)0,3323 Pr Re x ,, Re Ld ReTd Re xSt 0vL/(5.62)(5.63).Nu xRe x Pr0,332Re x Pr 2 / 3.(5.64)d ReT / d Re x ,,St 0,0,22Re T Pr4/30,3323 Pr ,(5.60)0,6643 Pr Re L ,Nux/v0Nu xvPrL1LRe x3/-..(5.65)«– 54 –», –.-.,., 2009., Cf0 /2,-0,22 / Re* * .,,.5.4.,-().v y ( y 0) vw 0.vx,vyx.vx / x 0const vw .,vw2vxyvxy2,(5.66):y = 0 vx0;y=(5.66)vxvxv .(5.67)(5.67 )vvw y1 exp.,***(5.68),vw,2v w-(5.69),– 55 –(5.70).,.vxyw, 2009vw v ,(5.71)w2 vwCf.(5.72)-,,xvvw4v2.(5.73).T/ x0vw2Pr y 2yTT,TwTw;Pr vw y1Tyqw(5.74).qwv c p (TStw(5.75)Tw ),-:Stvw.v(5.76)-,.– 56 –.,vxvTT.expvwexpvwy, 20091,(5.77)1vwyavexp w TaexpTwTw1,(5.78)1:CfStw vwwv22vw p v w(TTw )1v c p(TTw )vexp wa*10**0vxdyvvwvxvx1dyvvexp1vw,(5.79)1w vw1Texp1vw2v wexp1vexp wav.T,(5.80)1(5.81)11vw.(5.82)15.5.,(M > 0,25),(5.55)vx / y 2 .– 57 –-.,d2d.Pr v 2( f )2 .c p (TTw )Pr df2 d2, 2009(5.83)(5.83),,.-Tw.TTw T..

5.3).(y-T*88TT*TTw*q w <0q w =0Twq w >0 x. 5.3.(M < 1)-TwTrrv22c pr (Pr)T1 rk 1 2M ,2Tw* TwT*(5.85)T–,M –– 58 –(5.84).,., 2009, T* –,k–-.r( 0,6Pr6 ),Pr– r4k /(9k 5) .3Pr .Pr-.13xNu xB0,564 Pr1 / 2PrxNu w,xB Re 0x,5 ,(5.86)0,33 Pr1 / 30, B,80,029 Re 0w,xPrw0 ,43wTwPr0 ,4Tw*TTw*0,6 .0 ,110,1 Tw /Tw* 1,613.:/...., 2004.10M..– 59 –.(5.87)2,5..M.:4,5.,., 20096..,.xr–,-,dp/dx<0,.,1 d dv xrr dr dr1 dp.dx,(6.1). vx0r=d/2,.v x (r ) v0 1v0r2r02d–(6.1)-,1 dp–4 dx(6.2), r0=d/2.vRe v d /,-0,5v0 .Re.2300...10 4 .Re.(6.1 ).,..x,.,..,(6.2).– 60 –.-.,., 20092r0rv0x02vx1l)rTw=const2r0Tw <T0xTv0T0 0TwTwT0lT0 TwT<T0).

6.1.. 6.2.( )( )Tw,T-– 61 –.,., 2009():,,-,.x,(.. 6.1 ).(.. 6.2).(.,. 6.1)..l/d0,055Peqwconst ,(6.3)l/d0,07 PeTwconst ,(6.4)-llPr .qw(TwT)const,Tw / xT / x.(c p vx.. 6.2).Tx1(r r,dTdx2q wp v r0dTdR2q w v x Rr0 ,)r-T.rconst ,(6.5)r0d /2,(6.5)d(dRRT )Rr / r0 .(6.6)– 62 –(6.6).,., 20092R1Nu dd(Tw T )qw ddNu d0(104811T4,363,65Nu d(v x / v x ) RdR1qwTwdR ./ )R(6.7)const ,(6.8)const .(6.9)Nu d0,021 Re 0,8 Pr 0,43 (Pr f Prw ) 0,25(6.10)Nu d0,021 Re 0,8 Pr 0,43 ((6.11)fw)0,14.,,.,d,–4F /.,F–,(,)-.(.. 6.3),-.,(.),,.(),.– 63 –.,., 2009Rd-A. 6.3.T w > T0v0T0. 6.4.,(..

6.4)-.,(),.(),-,.,,(.. 6.5).,.– 64 –-.,., 2009. 6.5.. 6.6.( )( ),:Nu fd0,5 Re 0fd,5 Pr 0,38(Pr f / Prw ) 0,25fRe fd5...10 3 ,(6.12)Nu fd0,25 Re 0fd,6 Pr 0,43(Pr f / Prw ) 0,25fRe fd10 3...2 105 ,(6.13)0,023Re 0fd,8 Pr 0,37(Pr f / Prw ) 0,25fRe fd2 105...2 10 6 . (6.14)Nu fd30°< <90°,,,1 0,54cos 2 .(6.12) (6.14)-(.. 6.6).,.– 65 –,.,., 20097.7.1.,,().,,,-,,.),Ts.,-,,.,-,(,).,,.,.-..,,.-90.180,..,,,,.,-.:.,,.().,–– 66 –.,., 2009..,,.5–10,.,.-,,,,.,,.,),,–-(...Nu 3,2 10Nu 5 10Nu:KR(Ts64Re* 0,84Re* 1,571,16 1 / 3K Pr1,16 1 / 3K Pr(7.1)R(7.2)2 Ts,r (Ts)w21d2Ts–;dTr 2 2w)28 104Re*3,3 103Re* 1,8 10Re*(Tsr3,3 10w) ,32, (7.1).(7.2)Pr,-;( , , r, )-s.7.2..

7.1.-,.– 67 –.,.. 7.1., 2009:qw –,Ts –Tw –. 7.2.,,–.(.).,,-,.,.(,),-.. 7.2,Oz,.2Ty20.– 68 –(7.3).,., 2009vxy2g,(7.4),vxOx,2vz0vy0.px,0,,.,(7.3), (7.4)TTw , v xTTs –d vxdyTs ,y 0,0d vxdyy0(7.5),(7.6).,0-.(7.3)(7.5), (7.6)dTdyqTsTw(dT / dy )qTsTw.(7.7)(7.7).(7.8),,–– 69 –.,., 2009q(Ts(7.8)Tw ) .(7.9)(7.9),/ ,(7.10)..xgvxy 2 C1 y C2 .2(7.11),C2g0 , C1-.(gvx2(2 yy2 ) ...

7.2)(7.12)lz 1 )lz (v xlz ,G1vx(7.13)v x dy .(7.14)y 0(7.12),vxg22ydy2y 0– 70 –y dyy 0g32(7.15).,.gG, 20092 3lz3.(7.16)dxdGg2 2lzd .(7.17).,(TsTw )l z dxr–rdG ,.(7.17)(7.18)x(Ts Tw )rg2 2TTsTwgr 2 44 (Ts Tw )x 0Cd.dx(TsgrTw )2(7.10),– 71 –x(7.19)constC.(7.20)0,-0.4,(7.18)14(7.21).,., 2009142 3gr4 (TsTw ) x.(7.22)( TsTwconst ):1hxh –x 0 ).hdx ,(7.23)0,(4gr3 4 (Ts(7.22),142 32 30,943Tw )h(7.24),gr(Ts Tw )hPr/-, Ga gh3 /r–c p (Ts Tw )–, K–:2(7.25)–,-.,(Ts(7.25)T-Tw ) const .(7.19)q(7.24)0,943(Ga Pr K )1/ 4 ,, cp –T,.Nuh/14h(7.27)Nu-q = const,.-const ,xg2 3r3 q– 72 –C.(7.26).,x., 200900,-= 0.33 qxg2.(7.27)r(7.10),2g r3 qx23213g r3 qh,(7.28)13.(7.29)ReqTconst13%,const .,..K,,51 Pr 100.,K<5100.(,) Ts ),,14.:.,,-,,.T(yPr >-),(T ( yPr <1,,-,) Ts .14.,.,..:– 73 –., 2003..,., 2009-Nu T wave .Nu –;,(T(7.30)s/w )(w/1/ 83s)-–,(sw,0,04(Re /4) –; Re4),v/);wave; v ––=(.Re-,,.(x)r vTx ,(3.31)Th.r(3.32)Re4Re,Re> 10–20,20 < ReRe > 1600< 1600,..Re4Re,h–489 0,024(Prs / Prw )Th, ZrsAr1 / 3ssr,T0, 25, ArsPrs0,25 ( Zgh3 (s2s s2300)),43,–w,(Ts– 74 –(3.33)Tw).-.,., 20097.3.,.g()(7.7)ggxg cos .4(7.34)os .(7.35)-,.,-.d0 –,<< d0,,dxd0d .2(7.36)-:0,725gr(s(7.37)2 3w )d 0,– 75 –14.(7.37)-.,.Nu, 20090,725(Ga Pr K ) 0,25,(7.25)(7.37) (7.38)(7.24) (7.25).(,(7.38).-),...,T.,,-.,K>5Pr > 1.,d0,20 /( g )0, 5.,.7.4..-.,.,,.,,..–.-..-,,,,.– 76 –-.,., 2009....,5–10,-.15–40.,,()15–30.,(.).,..NuRe 4G /(.,,0,023 Pr 0, 4 Re 0,8 1 ( / " 1) X ,d0 ) , G –,X–,(7.39)–.– 77 –.,., 20098.8.1..,,,.-..,Ts.«».-,-..(,-,)..–.,,..,,,,.,-),.,-,,..:()Tw > TsTs,..T Tw– 78 –-Ts ,.,., 2009(.) qw.-qwT,..

8.1.,,-.(qw ~ T 4 / 3 ,ABRa 10 9 (~ T 1/ 3), q w ~ T 5 / 4 ,).~ T 1/ 4. 8.1).-Ra 10 9 (-. 8.1.-–-..T,BC(. 8.1).,T =5° ..,,– 79 –--.,., 2009.-.n=,,qw ~ T n ,.3–3,3.,.(),. 8.1)..,F).-(25 °9 1052.,FG(CD. 8.1).«»-.,,...-.q1(qw < q2F. 8.1)..q 2–q:.,21,qeq,q(G)q 2.-qeq < qw < q 1< qw < qeq.,0,1–10q 1/qeq 4–6..– 80 –.,.q4kr1, 2009g(),(8.1)k = 0,13–0,15, r –,,–,––-.. 8.2.()qq 1.q 1/q2,20–50.2,.q,q.. 8.222,-.,–.,,((-).),-...– 81 –.,., 2009,,,-..8.2.,.,.,,-(T > Ts),()..,-,.-,.(–; M (4 / 3) R 34 R2–4 R2 ,)M;(8.2)––;; R –,.,.,;..R .,2R(max)4 2R3.,(8.3)(8.4)-– 82 –.,., 2009max..-,,pppp2 /R ,p –(8.5).,Ts,–pTwpTsdpdTrTs (,),TTwTs(8.5).(8.6)(8.6),-2 Ts.r R(8.7)(8.7),.,.-,.,.15,15.:1.:,.2.3.....;...,.,..:...,..:, 1997;.4./.

2..,. .:.,.:, 1979;., 2003;., 2000.:– 83 –.-.,:., 2009T 2, 3 .const.-,.2/320,075 1 10Ts–1/3q w2 / 3 ,(8.8),-,.8.3.,,,,,,,.,-.... 8.3.,x ( v v x ),-.g()dy 2v 0y 0,v v ,y, v–d 2v–.– 84 –0.(8.9)(8.10),(8.11)-.,., 2009. 8.3.-v vyg()2( yy2 ) .(8.12)v,,,,vg() 2 /( 2 ) , v,,(d v / dy )(8.11)= ).: 1)0 ; 2)vy0 ( dv / dy 0g()2(2 yy2 ) .-d 2T / dy 2qwTTwT,(8.13)Ts .,– 85 –0,.,., 2009(8.13),/ .x(8.14)(qw = const)qw xTcp wrTs2vdy .(8.15)0,.,:12 q w xr g()3 qw xr g()x1/ 4v(8.16)1/ 4(d v / dy )0,463r g(qw x)0,69r g(qw x)x0,0,(8.17)0,(8.18)1/ 4v1/ 4(d v / dy )0,(8.19)1 c p T / 2r .hL1L0x dx32x L.-(8.20):R.– 86 –(8.21).,., 2009TRTsconst :1/ 4x( )3 r g ()0,5)xT (1x( )3 r g ()0,705)xT (1/Twv0,(8.22)1/ 4(d v / dy )0,(8.23)x.20 %,h,D0.v,v v y/.r vxxqw = const,2q w xT (1(8.24)1/ 4r v0,5,-qw = const,)x(8.25)-..,,LCgL3 ()( )Lqw26r (6)g 21,4 10 ; C = 0,01, n = 0,57n2.(8.26)2 10 4; C = 0,28, n = 1/31,4 106gL3 (( )– 87 –)2gL3 (1,5 10 7 .( )2).,., 20098.4.(.),,TTs.,..,,.,-.-.,,.-../01 (0/20)0,5,–,–-.,.1).,(2)–.,,.,«.–3)».,-,4))...,.– 88 –.,., 2009–.5).-.6).,,.-...

8.4): I –(), II –().III –I III.II2,5-3,4..-.,,... 8.4.– 89 –.,., 2009. 8.5.:1–, 2–,.,,,I-.,,.(.-,. 8.5).,.,.– 90 –..,., 20099.9.1.,..(),,.. 9.1.(.. 9.1),Q0,QAQR,QDQ0QRQAQD .(9.1),,:RQR,Q0(9.2)AQA,Q0(9.3)DQD.Q0(9.4)– 91 –.,., 2009,(R=1),(D=1),-––(A=1).– R 0, A+D 1.D 0, A+R 1;.-,().,.. 9.2.(),()-.,,,-.(9.2).,..).,,(,,,,–,.,().I-dE ,2)dd– 92 –.,., 2009IdE.d(9.5)IdE.d(9.6)d(EI d0())2I d .(9.7)0()I,I0(9.8)I0 –.E,E0E0 –(9.9),.9.2.,,I0C1C2e T5,1– 93 –(9.10).,C12 c2h-2310–3,74 10.16, C2, 2009hck, h = 6,625 10-34.0,01438/c –())– 94 ––, k = 1,38. 9.3.. 9.4., = 2,998 108.,., 2009. 9.3max Tmax–T.2,9 103.-,(9.11),I0-I0E0I0 d ,0T4,E0= 5,67 10-8 /(,(),( .2(9.12)4)–..= .. 9.4)().,-2E,T–ET 4;ET5,67100(9.13)4,(9.14)..-,0T40T4(9.15)T,– 95 –.,., 2009T /4 .T-,.TT-T,I5C11,C2TexpT5C1T.C2TexpC2.(9.16),,T,(9.17)T,1T1Tln (C 2 (1,TT ,C22)1112)T,.T-(9.17)T .-.A.(qE,E.AE 0 .q(9.18).

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