Ready to use formula for the calculation of Heat Transfer Coefficient for Jacket

1. 622 Modeling of Chemical Kinetics and Reactor DesignTable7-14
Equationsforcalculatinginsidefilmcoefficients(hi)ofjacketedagitatedvessels
Reynolds
AgitatortypeBaffled?number(NRE)Nusseltnumber(NNu)Remarks
PaddleYes/No20<NRE<4,0000.415(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Vesselgeometryisdiscussedby
HollandandChapman[4]
PaddleYes/No>4,0000.36(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Vesselgeometryisdiscussedby
HollandandChapman[4]
FlatbladeturbineYes/No<4000.54(NRE)0.67
(NPr)0.33
(μb/μw)0.14
DA/DT=1/3,H/DT=1.0.Six-
bladedturbine.Standardgeometry.
FlatbladeturbineYes>4000.74(NRE)0.67
(NPr)0.33
(μb/μw)0.14
DA/DT=1/3,H/DT=1.0.Six-
bladedturbine.Standardgeometry.
FlatbladeturbineYes2,000<NRE<700,0001.10(NRE)0.62
(NPr)0.33
(μb/μw)0.14
PropellerYes>5,0000.64(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Threeblades
PropellerYesNolimitation0.54(NRE)0.67
(NPr)0.25
(μb/μw)0.14
45°pitched,four-bladeimpeller.
Equationisbasedonlimiteddata
withregardtopropellerpitchand
vesselbaffling.Dividehiobtained
withthisequationbyafactorof
about1.3.
RetreatingbladeYesNolimitation0.33(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Glassed-steelimpeller.Three
turbineretreatingblades.Thelower
constant(0.33)fortheglassed-steel
impellerisattributedtogreater
slippagearounditscurvedsurfaces
thanaroundthesharpcornersof
thealloy-steelimpeller.

2. Fluid Mixing in Reactors 623
RetreatingbladeYesNolimitation0.37(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Alloy-steelimpeller.Threeretreat-
turbineingblades.
RetreatingbladeNoNolimitation0.68(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Sixretreatingblades.
turbine
PropellerYesNolimitation0.54(NRE)0.67
(NPr)0.25
(μb/μw)0.14
45°pitchedfourbladedimpeller.
Equationisbasedonlimiteddata
withregardtopropellerpitchand
vesselbaffling.Dividehiobtained
withthisequationbyafactorof
about1.3.
AnchorNo30<NRE<3001.0(NRE)0.67
(NPr)0.33
(μb/μw)0.18
Theoverallheattransfercoefficient
U,variesinverselywiththeanchor-
to-wallclearance.Anchortowall
clearanceislessthan1in.
AnchorNo300<NRE<4,0000.38(NRE)0.67
(NPr)0.33
(μb/μw)0.18
Similarconditionasbefore.
AnchorNo4,000<NRE<37,0000.55(NRE)0.67
(NPr)0.25
(μb/μw)0.14
Anchortowallclearanceof1to
5.125in.Vesselgeometryisillu-
stratedbyHollandandChapman[4]
HelicalribbonNo<1300.248(NRE)0.5
(NPr)0.33
(μb/μw)0.14
×(e/DA)–0.22
(i/D)–0.28
e=clearance,(DT–DA)/2,ft
DA=impellerdiameter,ft
i=agitator-ribbonpitch,ft
HelicalribbonNo>1300.248(NRE)0.67
(NPr)0.33
(μb/μw)0.14
Sameasabove.
×(i/D)–0.25

3. 624 Modeling of Chemical Kinetics and Reactor Design
Table7-15
Equationsforcalculatingoutsidefilmcoefficients(hO)ofjacketedagitatedvessels
Reynolds
Jackettypenumber(NRe)Nusseltnumber(NNu)Remarks
Annularjacketwith>10,0000.027(NRe)0.8
(NPr)0.33
(μb/μw)0.14
(1+3.5De/Dc)Thisjacketisconsideredaspecial
spiralbafflingcaseofahelicalcoilifcertain
factorsareincorporatedintoequations
forcalculatingoutside-filmcoeffi-
cients.Intheequationsatleftand
below,theequivalentheattransfer
diameterDe,forarectangularcross-
sectionisequaltofourtimesthe
widthoftheannularspace,wand
Dcisthemeanorcenterlinediameter
ofthecoilhelix.Velocitiesare
calculatedfromtheactualcross-
sectionoftheflowarea,pw,where
pisthepitchofthespiralbaffle,
andfromtheeffectivemassflowrate,
W',throughthepassage.Theleakage
aroundspiralbafflesisconsiderable,
amountingto35–50%ofthetotal
massflowrate.Theeffectivemass
flowrateisabout60%ofthetotal
massflowratetothejacket:W′=
0.6W.TheNNuforthisequation
shouldbeexpressedintermsof
De(NNu=hjDe/k)asshouldthe
Reynoldsnumber(NRe=Devρ/μ),k
beingthermalconductivity,vbeing
velocity,andρbeingdensity.

4. Fluid Mixing in Reactors 625
Annularjacketwith<2,1001.86(NRe)0.33
(NPr)0.33
(De/L)0.33
(μb/μw)0.14
Sameastheabove.Lislengthof
spiralbafflingcoilorjacketpassage,ft
Annularjacketwith2,100<NRe<10,000Usetheaboveequationsdepending
spiralbafflingonthevalueofNRe
Annularjacket,Laminarflow1.02(NRe)0.45
(NPr)0.33
(μb/μw)0.14
(De/L)0.4
DjiandDjoaretheinsideandout-
nobaffles×(Djo/Dji)0.8
(NGr)0.05
sidediametersofthejacketrespec-
tively.Forthisequation,De=Djo
–Dji.TheGrashofnumberNGr=
De
3
ρgβΔtG/μ2
wereDeisequivalent
diameter,gisaccelerationdueto
gravity,βiscoefficientofvolumet-
ricexpansion,μisviscosity,ρis
density,andΔtGisthedifference
betweenthetemperatureatthewall
andthatinthebulkfluid.NGrmust
becalculatedfromfluidproperties
atthebulktemperature.
Annularjacketwith<2,1001.86(NRe)0.33
(NPr)0.33
(De/L)0.33
(μb/μw)0.14
TheNusseltandReynoldsnumbers
spiralbafflingmustbecalculatedwithDeasthe
diameterterm.
Annularjacket,Turbulent0.027(NRe)0.8
(NPr)0.33
(μb/μw)0.14
Fortheequivalentheattransfer
nobaffles×(1+3.5De/Dc)diameterforturbulentflow,use
De=[(Djo)2
–(Dji)2
]/Dji,whereDji
andDjoaretheinsideandoutside
diametersofthejacketrespectively.
Thecross-sectionalflowarea,Ax=
π[(Djo)2
–(Dji)2
]/4

5. 626 Modeling of Chemical Kinetics and Reactor Design
Annularjacketwith210<NRe<10,000Usetheaboveequationsdepending
spiralbafflingonthevalueofNRe.
Half-pipecoiljacketLaminarflow18.6(NRe)0.33
(NPr)0.33
(De/L)0.33
(μb/μw)0.14
Whenpipecoilsaremadewitha
semicircularcross-section,De=
πdci/2,wheredciistheinner
diameterofthepipe,infeet.For
calculatingthevelocity,thecross-
sectionalflowareaequalsπd2
ci/8.
Whenpipecoilsaremadewitha
120°centralangle,De=0.0708dci
andthecross-sectionalareaequals
0.154(dci)2
.
Half-pipecoiljacketTurbulentflow0.027(NRe)0.2
(NPr)0.33
(μb/μw)0.14
×(1+3.5De/Dc)Dcisthemeandiameterofthecoil.
Half-pipecoiljacketTransitionflowUsetheaboveequationsdepending
ofthevalueofNRe.
DimplejacketLaminarflow1.86(NRe)0.33
(NPr)0.33
(De/L)0.33
(μb/μw)0.14
TheequivalentdiameterDe,ina
dimpledjacketequals0.66in.the
cross-sectionalflowareaequals1.98
in.2
perfootofvesselcircumference.
Table7-15
(continued)
Reynolds
Jackettypenumber(NRe)Nusseltnumber(NNu)Remarks

6. Fluid Mixing in Reactors 627
Reynoldsnumber,NRe=
μ
=
μ
ρρVDNDA
2
whereρ=density
V=velocity
D=diameter
DA=impellerdiameter
N=rotationalspeedofthe
agitator
μ=viscosity
Viscositynumber,μb/μw
whereμb=viscosityatthebulkfluid
temperature
μw=viscosityatthewall
surfacetemperature
(μb/μw)0.14
≅1.0forwater
Prandtlnumber,NPr=
μC
k
P
whereCP=specificheat
μ=viscosity
k=thermalconductivity
Grashofnumber,NGr=
Δ
μ
DgteG
32
2
ρβ
whereDe=equivalentdiameter
ρ=density
g=accelerationduetogravity
β=coefficientofvolumetric
expansion
ΔtG=differencebetweenthe
temperatureatthewall
andthatinthebulkfluid
Nusseltnumber,NNu=
hD
k
whereh=heattransfercoefficient
D=diameter
k=thermalconductivity
DimplejacketTurbulentflow0.27(NRe)0.8
(NPr)0.33
(μb/μw)0.14
Thecoefficientsarenotvery
accurateduetoturbulencecreated
bythedimplesintheflowsteam.
DimplejacketTransitionflowDetermineNNufromtheaboveequa-
tionsdependingonthevalueofNRe.
Thedimensionlessparameters: