notes4 - Convecfi‘g’x Coeffra'cnl' £3 Laminar Ejgy In...

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Unformatted text preview: Convecfi‘g’x Coeffra'cnl' £3 Laminar Ejgy In Circuhr Tube, m “:Derzvable ‘ffieord-tcafij, J‘usf as we. derived TTie {rial-«bin Coeffrorml‘ f: 64 /fi€3 ‘ swam; - Use approprc'ab Gobi-rot volume, . energy balanoz and. .New'l-an': Law 038 coab'njmr Four-car’s Law of comma-1 an. Assam on: : - HF‘DC = v=0 ; u=u(n)=2um(l-)(i:‘ bl .TFoc: j Ts—T )1: 0 fax Ts‘Tm ' ° Low-speed .Flow =7 Work. << heal- afield frdckon oInmeroes£bl¢ {laid => meswmfim (’F=(v. , - Sfcad'd slab,- Na aemahafi 0 energy. 4f (DerWaJ-ion : 3 60"!an Propu- es. Cowl-ml vaLume : Ting 012 ‘H‘H'otnessdr at». u u Eat-de EnergL’ Balance 3W0: - m _ ewngcpw 2 % (Kg; 222494 ...n’LL_B_T = o< 106%) “3‘2? 1 - - Q P J. .‘ L9) 2’ v 3* ' €13“ _ r26; me??? n, -, +62 06%) = éizump—iflflgfl ..(e.w RH: Indeperdwl‘ 4X ,'.LH$ indepench 0,6 x. SoLuJHon _ L 4 1-01.): 29—07 _ i ]+ affix, +61 0‘ alx 4 16):; 305: A’: i=0: T (5 jelmlz’ q :0. Ab nun» , ‘r = 13 L " T ‘ 2.9.“ éflm 310‘) ' CZ - 5 0L ( *)(,—/ : T __ 2“ In," Tm ‘ 3 J- ‘f— A 2. Ta) 3 jg % 1.754%; 77(1)] ---(8.50) Lb) Ts : Gmskant' Q]: = B‘L)EIL whore TmCX) Is expmenJ-mtg BX R—Tm dbwyf/y‘ H? X. £30.54) 3 3T = 2.9.. flm —l—_):3 12:: --8.51) 2:. 520621) (am dx)L at] T,-T ( Sow-ion possible , W 7701‘ 51mm by Simple, express/an. Knowma T099; 3&3 Tm 0‘) '- Consx'der 'ermal energy flow rah), acres: c.s. mm? Wm quM'Hé’ I and. local. guanh'h'a. ’10 gum m," chm : £gu 2/610!” gr no LT", =__2_ Jude/c 74min," 0 Subsklu)‘; 3e” ’2). and T and. Inl‘¢gr¢l’¢;4o 8017 For g : Comer". Tm :_ T, -— .LL u... 2:3“ ale) 1+? 0c 37 = Q" 2117:» _._. 7:2"10 I n W/ __3 5,9 CF gunjf/z : +Ts _ .LL 1‘0 2Q: n 48’ C (X z 2% [’5’ argumlza = _ "m -_- K :21; 13 fins; .22:— a 43%) ,1: :.T —T = -_u. z; T = -_‘Z_§ by N-K-afaolc m 5 I48 K. i, hj NH :9 112 = fl : “‘3‘ 3’ K, H "(353) Lb) T5 3 (ans): Table 8.4 Summary of convection correlations for internal flow“ " CORRELATION CONDITIONS \ f = 64/ReD (8.19) Laminar. fully developed \ NuD = 4.36 (8.53) Laminar. full_vdeve10ped. constant qg‘,m , \' .VuD = 3.66 (8.55) Lammar. full} developed. constant TD P, 2 0‘6 — \ \‘UD = 0-066“ D/L ) RFD PF Laminar. thermal entry length (Pr >> 10, an 1 - 0‘04[(D/1_)Ren p,]3/3 unheated starting length). constant 7; (8.56) or. a , Laminar, combined entry length _. 1 Re Pr 'V p. R P L/D 1/3 014 2 2‘ Nun =1sei ” ) (—) (3.57) l( 90 ’/ ) (ti/u.) ] L/D constant T3. 0.48 < Pr < 16.700. 00044 < (pt/pi) < 9.75 —‘ f = 0.316Reh"4 (8.20)‘ Turbulent. full) developed, R0,, 5 2 X 10‘ f= 0.18-4Rvj,I ’5 (8.21)‘ Turbulent. full) developed. R01) 2 2 ><‘ 10‘ Nu!) = 0.023Rt-7,'/5l’r" (8.60)"" Turbulent. fully developed. 06 s Pr 5 160, Rep 210.000.L/D 210.n - 0.4 for T, > Tm and n - 0.3 for T. < T,,, or. U l4 V OOVR 4,5,) In 1-1 ) 861 t” Turbulent. lull) developed. 07 .<_ Pr 5: 16.700. '“n‘ "‘ ‘1’ ’ u“ “ ’ Rep 2 10.000. L/Dz to \‘u,, = 4.82 -— 0.0185t R0,,Pr)m:7 (8.65) Liquid metals. turbulent. fully developed. constant q,". 3.6 x 103 < Rep < 9.05 x 105. 102 < Pep < 10‘ .VuD = 5.0 — 0025( Rep Pr )” h (8.66) Liquid metals. turbulent. full) developed. constant 7;. Pen >100 __——-’ “Properties in Equations 8 53. 8 55. 8.60. 8.61. 8.65. and 8.66 are based on Tm: properties in Equations 819. 8 20. and 8.21 are based on T, -=— (7'I + Tm)/2; properties in Equation 8.56 and 8 57 are based on TM 5 (TR, e Two.) 3 [Rep E Dnum l'l D,1 E 4,-1‘,,'P;um — I‘ll/0A(. (Equations 8:0 and 8.21 pertain to smooth tubes. For rough tubes the leton-Colbum analcgv. Equation 8.58. should be used Wllh the results of Figure 8.3. _ “As a first approxrmation. Equation 8.60 or 8.61 maybe used to evaluate the average Nusselt number A'uD 0Ver the entire tube length. if ( L/D) 2 10. The properties should then be evaluated at the average of the mean temperature. T," 5 (Tm, - 7,,1 OJ/Z. 'lmpr0ved accuracy is prOvided by Equations (8.62) and (8.63). ...
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This note was uploaded on 10/13/2010 for the course MECH 414 taught by Professor Ghia during the Winter '06 term at University of Cincinnati.

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notes4 - Convecfi‘g’x Coeffra'cnl' £3 Laminar Ejgy In...

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