Prediction of batch heat transfer coefficients for pseudoplastic fluids ...

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72 (3-77 Substituting these terms in equations 3-75 ru~d 3-73 ~nd placing the Prandtl number in the nu..merator, as for Ne1oJtonian (3-78 or C YRe" -;;;;;; -; A?~ (~- ( ~ nv K"J1I Dei ( / -2~ I- cZ ) / K) J? /[J ) C d (3-79 Equation 3-79 then characterizes heat transfer to pmver law fluids being agitated by geometrically similar marine propellers. This characterization is based on a model which is believed to represent the flo1.J patterns fairly accurately. If the impeller geometry changes; that is, if the vertical "VJill increase and thus a higher Nusselt number will result. Equation 3-79 may be expanded to correct for geometrically unsimilar impellers by adding a sixth di!l1ensionless term, WalDa' where \-1 a is the impeller 1rddth .. AI. - c NJ~:;: f~/" iI.(f)i~V CjNjci e AI U - Re /Vp-1. K'w (Ii (;;- -1V (3-80 at Other geometry effects could be taken into account by adding more dimensionless groups such as found in the dimensional analysis for Newtonian fluids as presented in equation 2-35. 4i
73 Semi-Empirical Correlation i .., .. ' in Metzner has show~ that the shear rate in an agitated vessel is related to the agitation rate of the bnpeller v a = (11 .. 5 N) (2-20 as discussed in Chapter 2 and thus the apparent viscosity could be defined. (2-25 It was felt that using this apparent viscosity in place of the Nelvtonian viscosity in the Reynolds and Prandtl ntunbers of the l'lfeHtonian fluid correlation would yield a correlation suitable fol'" power-law fluids.. The Reynolds and Prandtl nurabers evaluated using this apparent viscosity are designated as NR~ and Np~ respectively_ The correlation Has expressed as (3-81
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Copyright Warning & Restrictions Th
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PREDICTION OF BATCH HEAT TRANSFER C
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while the latter has five to seven
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ACKNOWLEDGEMENTS The auther ex~ress
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Chapter 1: Chapter 2: Introducticm
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LIST OF FIGURES page 2-1 FlGW Behav
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CHAPTER I INTRODUCTION BATCH HEAT T
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3 as pseudoplasticso Pseudoplastic
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5 ~n addition to studying the effec
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7 A B SLOPE = /'n- .( 10 ~y FIG 2-1
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15.5, 183, 185).. Most of their eff
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va:ry withl. the slaear I'Rte.. 11.
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13 RHEOLOGIC_~ INVESTIGATION OFPO~~
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IS In(s) (2-8 (2-9 where Re is the
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'7 ft~ easier method of calibrating
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19 of' thixotropic breakdown l'Ji t
Page 33 and 34: 21 complicated by a variable viscos
Page 35 and 36: 2J Schultz-GrQnow (174) used a dime
Page 37 and 38: 2S The results shm-red that equatio
Page 39 and 40: Su.bstituti011 of equati 2-22 gives
Page 41 and 42: 29 In both Newtonian and non-Newton
Page 43 and 44: 31 for viscous pseudoplas tics at 1
Page 45 and 46: 33 (2-29 when both the distances ar
Page 47 and 48: JS Thermometers or thermocouples ar
Page 49 and 50: .37 2: a in in heat cQ@tent of the
Page 51 and 52: J9 cooling mediu..:m side, the heat
Page 53 and 54: 41 ports a value of 3/4-.. He then
Page 55 and 56: 43 find the effects of one or two o
Page 57 and 58: 45 The group to the left of the equ
Page 59 and 60: 47 the highest heat tra...nsfer coe
Page 61 and 62: 49 A pitched blade turbine gave coe
Page 63 and 64: SI done on the correlation of heat
Page 65 and 66: 5J evaluated at the wall temperatur
Page 67 and 68: ss to (2-46 where ill is the consis
Page 69 and 70: CHAPTER .2 DEVELOPMENT OF CORRELATI
Page 71 and 72: momentum" mass" and energy may be ~
Page 73 and 74: 61 Vr;> Jt.- ,,"Ii'\... ..", ::: (V
Page 75 and 76: 63 Substitution of these dimensionl
Page 77 and 78: l/(R + 1) and was able t@ elim.iE.a
Page 79 and 80: 67 All of the variables and differe
Page 81 and 82: 69 The average heat transfer coeffi
Page 83: N"v = C Iv''' (;';~-"')&'i'~ (%t-n,
Page 87 and 88: 75 7I1C1?/lfOCOUPLc .JuNe T/ON IMBE
Page 89 and 90: 77 _I"---- / SCALE I ~~, .5 j t /Z.
Page 91 and 92: also cop~ected to the pipes leading
Page 93 and 94: 81 Ve8sel :J all th:l c]me 8 8 .) '
Page 95 and 96: 83 potentiometer for varing the mot
Page 97 and 98: 85 MATERIAL 7:0 STAIIJLESS STEEL /
Page 99 and 100: 11 Wa.ll (Mi€1dl~) Same as #5 81
Page 101 and 102: 89 shea.r ra.tes, tl?1ey a.re unaff
Page 103: and if' lO"V'l$' a sm.all amount of
Page 106 and 107: 94- was about 40-45 ndmutes .. Tke
Page 108 and 109: 96 vThere N is in rev./sec .. and S
Page 110 and 111: 88 ql\fETI A = 6 T \--T -s L/kw (1+
Page 112 and 113: I {)D The generalized Reynolds n~mb
Page 114 and 115: 02. CHAPTER !2. RESUI,TS Many heat
Page 116 and 117: 01 TABLE 5-2 sutn~U{Y OF ADDITIONAL
Page 118 and 119: 108 the batch than the other ticJO
Page 120 and 121: 108 optimum impeller heights were u
Page 122 and 123: 10 I r "'" , •• ,'., "",' """",
Page 124 and 125: 112 correlations for the prediction
Page 126 and 127: TABLE 5 - 4 Correlation Constants A
Page 128 and 129: 1/6 Table 5-5 and 5-6. A measure of
Page 130 and 131: TABLE S - 6 IMPELLER Correlation Co
Page 132 and 133: 120 greater than 2.0. In this case
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12.2
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TABLE 5 - 9 CORRELATION E t (a/n +1
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TABLE 5 - 10 IMPELLER Correlation C
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TABLE 5 - 11 CORRELATION G (1.30/61
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1.30 of the substantial improvement
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1.3 2. The probable error in the ca
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134 .,;' : :: :::: : ~ !~. , " . .'
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T." ••••••• ,_ .....
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38 the cooling of nitration liquors
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140 The average deviation of the me
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42 tween 0.25 and 0.58. L~~l had re
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144 transfer coefficients to non-Ne
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16 of fit and it may t...herefore b
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148 'tvas insufficient data to eval
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50 A ::: Apr ... B ::: C p ::: CPr
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52. Q ::. Average heat transfer rat
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Xc = Function of Reynolds nL:l.m.be
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IS6 G REE:>{ ALPHABET 0 ::: Value o
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158 coefficient. Thus, for the wate
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160 , ., I .. : I :. '. • • !.
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162 I , . I . "I '1 I i I 1 I 1· '
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64 ncr --~iIluto e torque of the in
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166 rive different temperatures; ab
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168 TABLE A-4. SLOPE OF "LOG SHEAR
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TABLE 11.-5 RHEOLOGICAL DATA FOR CA
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TABLE A-5 (eollt. ) /12 o . 24;;& C
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'11 The flow behavior index and flu
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i .f.C ·F s o 6 1 6 I
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· . . . " , · . :::11" ': "'" ~ .
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180 Tke thermal e€l1'!ciluetlvity
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182 Heat capacity data for 100% gly
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IB4- wkiek ex~resses the aensity e
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186 Ts - Torque X :: Peree~t 0~ ful
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Phase I Calcu13tiJ~ of Slope of !oG
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3 REAL). N. ti •• D 4 cN=N E'I'
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~~-- ~---- --~--~ ~~~--------------
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Phase IV Correlation of Flow Behavi
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96 HEAT TRANSFER DATA FOR WA'fER US
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DATA /98 Batch \'ieight '" 94 •.
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zoo Run Center Dia!!1ec;er Ri'M Are
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DATA 20l. WATER - TUHBINSS Batch We
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204- HEAT T'rtANSFEH DATA USED IN C
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DATA ANCHor;: 206 Batch :'Ieight =
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2.08 Run Diameter RP!'1 Area Dynamo
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DAT_': 210 "i'ADDI,ES 9:5.7'10 GLYC
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212 DATA PADDLES 0.15 PEHC:::N'r CA
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211- D!~ 'I'l\. PA-:JDLES 0.20 PERC
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~;:. 'I'A 3.16 P.;'DDLES 0.24 PEHCE
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2/8 DATA PROPELL:SH3 0.15 P:~RCEN'l
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DATA DISK & VANE 'l'URBINE \'iATER
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2.22 DATA Tu.'i:SINES 0.15 PERCENT
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CALCULATION OF HEAT TRANSFER AND PR
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________________ ~parent viscosity
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------------------------ -_._------
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~--~, ~ ---- ---- -----------~-----
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232 NOMEliCLATURE FOR BEAT TRANSFER
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2.34- CALCULATED RSSULTS WATER Run
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2,36 Run Center Diameter h NNu Npo
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2.38 CALCULAT'ED ~E~:UL'rS ?!ATER P
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CALCULA'rED 1-{E8iiLlJ. 1 S \.;!\.'
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CALC:_:LA'i'ED _12:-)ULTS 24c. ANCH
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CALCULATEDR3SULTS PADDLE - CENTER H
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CALCULATED HESULTS 216 PADDLES - CE
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248 CALCULATED RESULTS PADDLES - CE
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CALCULATED RE:>ULTS 2. So PADDLf~S
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PADDLES - CALCULATED RE6ULTS CENTSH
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255 CALCULATED !tESULTS PROPELLERS
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CALCULA'rED RELmL'l'S PROPELLr~RS -
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CALCULATED HESULTS DISK AND VANE ;r
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DISK AND VAI'E .rU~1BINES CALCULATE
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DISK AND VANE '.i.'UR13HiES - CEl'i
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26S RESULT,:; U:3ED FOR REGRESSION
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of a least squares line can be calc
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269 (0-9 where y "" log NNu xl = lo
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-------------- -.Basi.c "Progr.a.rr
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-----------~---------- -~----------
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--~-------------- ------ ~~ -------
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Modi fi cati onB-foT' ev:alnatj ng-
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constants forco~~~latjQn F --------
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.------~.~~-- ---------------------
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28.J ENGLISH ALPHABET . - ¢,'"'~-=
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References 2.8S 1. ') L. 3. Lt- •
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287 56. 57. 58. C:;o ./ / . 60. 61.
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289 119. 120. 121. 122. 123. 12L~
Page 303 and 304:
176. 177. 178. 179. 1(30. 181. 182.
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Prediction of batch heat transfer coefficients for pseudoplastic fluids ...

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