lect - 10 external forced convection.pptx

8/17/2019 Lect - 10 External Forced convection.pptx

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External Forced ConvectionDr. Senthilmurugan S. Department of Chemical Engineering IIT Guwahati - Part 10


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Objectives

Distinguish bet een internal and external !loDevelo" an intuitive understanding o! !riction drag and"ressure drag# and evaluate the average drag andconvection coe!!icients in external !loEvaluate the drag and heat trans!er associated ith !lo

over a !lat "late !or both la$inar and turbulent !loCalculate the drag !orce exerted on c%linders during cross!lo # and the average heat trans!er coe!!icientDeter$ine the "ressure dro" and the average heat trans!ercoe!!icient associated ith !lo across a tube ban& !or bothin'line and staggered con!igurations


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Drag and )eat *rans!er +n External Flo

Fluid !lo over solid bodies !re,uentl% occursin "ractice such as the drag force acting onthe auto$obiles# "o er lines# trees# andunder ater "i"elines- the lift develo"ed b%air"lane ings- upward draft o! rain# sno #hail# and dust "articles in high inds- and the

cooling o! $etal or "lastic sheets# stea$ andhot ater "i"es# and extruded ires.Free-stream elocit!" *he velocit% o! the!luid relative to an i$$ersed solid bod%su!!icientl% !ar !ro$ the bod%.+t is usuall% ta&en to be e,ual to the

upstream elocit! V approach elocit! 0hich is the velocit% o! the a""roaching !luid!ar ahead o! the bod%.*he !luid velocit% ranges !ro$ ero at thesur!ace the no'sli" condition0 to the !ree'strea$ value a a% !ro$ the sur!ace.

Flow over bodies iscommonly encountered inpractice.


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5/12/16 | Slide

Friction and 3ressure Drag

Drag" *he !orce a !lo ing !luid exerts ona bod% in the !lo direction.*he co$"onents o! the "ressure and

all shear !orces in the normal directionto !lo tend to $ove the bod% in that

direction# and their su$ is called lift .4oth the s&in !riction all shear0 and"ressure contribute to the drag and theli!t.

Schematic for measuring the dragforce acting on a car in a windtunnel.

Drag force acting on a at plate parallel to

the ow depends on wall shear only

Drag forceacting on a

at platenormal to the

ow


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*he drag !orce F D de"ends on the densit%o! the !luid# the u"strea$ velocit% V # andthe si e# sha"e# and orientation o! thebod%# a$ong other things.*he drag characteristics o! a bod% is

re"resented b% the di$ensionless dragcoe!!icient C D de!ined asDrag coefficient:

*he "art o! drag that is due directl% toall shear stress τ w is called the s&in

!riction drag or just friction drag 0 since itis caused b% !rictional e!!ects# and the"art that is due directl% to "ressure P iscalled the "ressure drag.

Flat 3lat

For parallel ow over a at plate, thepressure drag is zero, and thus the dragcoe cient is equal to the frictioncoe cient and the drag force is equal tothe friction force.

For parallel ow over a at plate


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t lo e%nolds nu$bers # $ost drag is due to!riction drag .*he !riction drag is "ro"ortional to the sur!acearea.*he "ressure drag is "ro"ortional to the !rontalarea and to the difference bet een the

"ressures acting on the !ront and bac& o! thei$$ersed bod%.*he "ressure drag is usuall% do$inant !or bluntbodies and negligible !or strea$lined bodies .7hen a !luid se"arates !ro$ a bod%# it !or$s ase"arated region bet een the bod% and the!luid strea$.Separate# region" *he lo '"ressure regionbehind the bod% here recirculating andbac&!lo s occur.*he larger the se"arated region# the larger the"ressure drag.

7a&e8 *he region o! !lo trailing thebod% here the e!!ects o! the bod% onvelocit% are !elt.9iscous and rotational e!!ects are the$ost signi!icant in the boundar% la%er#

the se"arated region# and the a&e.

Separation during ow over atennis ball and the wa e

region


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Convection )eat *rans!er

;ocal and average


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5/12/16 | Slide =

3arallel !lo over !lat "lates

*he transition !ro$ la$inar to turbulent!lo de"ends on the surface geometry ,surface roughness , upstream velocity ,surface temperature , and the type offluid , a$ong other things# and is best

characteri ed b% the e%nolds nu$ber.*he e%nolds nu$ber at a distance x!ro$ the leading edge o! a !lat "late isex"ressed as

generall% acce"ted value !or theCritical e%nold nu$ber

*he actual value o! the engineeringcritical e%nolds nu$ber !or a !lat "late$a% var% so$e hat !ro$ 1> 5 to ( × 1> 6#de"ending on the sur!ace roughness#the turbulence level# and the variation o!

"ressure along the sur!ace.

!aminar and turbulent regionsof the boundary layer during

ow over a at plate


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5/12/16 | Slide ?

Friction Coe!!icient

4ased on anal%sis# the boundar% la%erthic&ness and the local !rictioncoe!!icient at location x !or la$inar !loover a !lat "late ere deter$ined

Fro$ ex"eri$ents the corres"ondingrelations !or turbulent !lo are

Co$bined ;a$inar @ *urbulent !lo 8

*he average !riction coe!!icient over theentire "late

Fro$ ex"eri$ents the corres"ondingrelations !or turbulent !lo are

3arallel !lo over !lat "lates


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5/12/16 | Slide 1>

Friction Coe!!icient

For la$inar !lo # the !riction coe!!icientde"ends on onl% the e%nolds nu$ber#and the sur!ace roughness has noe!!ect.For turbulent !lo # ho ever# sur!ace

roughness causes the !riction coe!!icientto increase several !old# to the "oint thatin !ull% turbulent regi$e the !rictioncoe!!icient is a !unction o! sur!aceroughness alone# and inde"endent o!the e%nolds nu$ber

curve !it o! ex"eri$ental data !or theaverage !riction coe!!icient in this regi$eis given b% Schlichting 1?:?0 as

3arallel !lo over !lat "lates ' ough Sur!ace

where ε is the surface roughness,and L is the length of the plate inthe ow direction. "n the absenceof a better relation, the relationabove can be used for turbulent

ow on rough surfaces for #e $ l% &,

especially when ε ' L $ (%)*

.


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)eat *rans!er Coe!!icient

*he local


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)eat *rans!er Coe!!icient variation3arallel !lo over !lat "lates

+he variation of the local

friction and heat transfercoe cients for ow over a

at plate.

raphical representation of the

average heat transfer coe cientfor a at plate with combinedlaminar and turbulent ow


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verage


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verage


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Flat 3late ith nheated Starting ;ength

%ocal &eat transfer coefficient For ;a$inar !lo conditions

For *urbulent !lo conditions

' erage heat transfer coefficientFor ;a$inar !lo conditions

For *urbulent !lo conditions Flow over a at plate with anunheatedstarting length


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Flat "lat ith uni!or$ heat !lux

7hen a !lat "late is subjected to uniform heat flux instead o! uni!or$ te$"erature#the local


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Flo across c%linders and s"heres

Flo across c%linders and s"heres is !re,uentl% encountered in "ractice.For exa$"le# the tubes in a shell'and'tube heat exchanger involve both internal !lothrough the tubes and external !lo over the tubes# and both !lo s $ust beconsidered in the anal%sis o! the heat exchanger.

lso# $an% s"orts such as soccer# tennis# and gol! involve !lo over s"herical balls.

*he characteristic length !or a circular c%linder or s"here is ta&en to be the externaldia$eter D.*hus# the e%nolds nu$ber is de!ined as e e D 9D/ ν

here 9 is the uni!or$ velocit% o! the !luid as it a""roaches the c%linder or s"here.*he critical e%nolds nu$ber !or !lo across a circular c%linder or s"here is about

e cr ≅ 2x1>5

.*hat is# the boundar% la%er re$ains la$inar !or about e 2x1> 5 and beco$esturbulent !or e 2x1> 5.


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Flo across c%linders

!aminar boundary layer separationwith a turbulent wa e- ow over acircular cylinder at #e /%%%

t ver% lo velocities# the !luid co$"letel%ra"s around the c%linder. Flo in thea&e region is characteri ed b% "eriodic

vortex !or$ation and lo "ressures.


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Flo across s"heres

Flow visualization of ow over a

smooth sphere at #e (0,%%% witha trip wire.

Flow visualization of ow over a

smooth sphere at #e 1%,%%%with a trip wire.Flow separation occurs at about θ ≅ 2%, when the boundary layer is laminar

and at about θ ≅ (*% ° when it is turbulent


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Ex"eri$ental drag coe!!icient !or s"here and c%linder

For !lo over c%linder or s"here# boththe friction drag and the pressure drag can be signi!icant.*he high "ressure in the vicinit% o! thestagnation "oint and the lo "ressure on

the o""osite side in the a&e "roduce anet !orce on the bod% in the direction o!!lo . *he drag !orce is "ri$aril% due to !rictiondrag at lo e%nolds nu$bers eG1>0and to "ressure drag at high e%nolds

nu$bers eH5>>>0.4oth e!!ects are signi!icant atinter$ediate e%nolds nu$bers.

verage drag coe!!icient !orcross!lo over a s$ooth circularc%linder and a s$ooth s"here.


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E!!ect o! Sur!ace oughness

+n general# increases the drag coe!!icientin turbulent !loSur!ace roughness# in general#increases the drag coe!!icient inturbulent !lo .

*his is es"eciall% the case !orstrea$lined bodies.For blunt bodies such as a circularc%linder or s"here# ho ever# an increasein the sur!ace roughness $a% increaseor decrease the drag coe!!icientde"ending on e%nolds nu$ber.

*he e!!ect o! sur!ace roughness on thedrag coe!!icient o! a s"here.

Surface roughness may increase or decreasethe drag coe cient of a spherical ob3ect,depending on the value of the #eynoldsnumber.


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Flo s across c%linders and s"heres# ingeneral# involve flow separation , hichis di!!icult to handle anal%ticall%.Flo across c%linders and s"heres hasbeen studied ex"eri$entall% b%

nu$erous investigators# and severale$"irical correlations have beendevelo"ed !or the heat trans!ercoe!!icient.*he value o!


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Several relations are available in the literature !or the average


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eneral E,uation !or average


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Flo across tube ban&s


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Flo across tube ban&s

Cross'!lo over tube ban&s is co$$onl% encountered in "ractice in heat trans!ere,ui"$ent# e.g.# heat exchangers .+n such e,ui"$ent# one !luid $oves through the tubes hile the other $oves overthe tubes in a "er"endicular direction.Flo through the tubes can be anal% ed b% considering !lo through a single tube#

and $ulti"l%ing the results b% the nu$ber o! tubes.For !lo over the tubes the tubes a!!ect the !lo "attern and turbulence leveldo nstrea$# and thus heat trans!er to or !ro$ the$ are altered.*%"ical arrange$ent8 in'line or staggered*he outer tube dia$eter D is the characteristic length.*he arrange$ent o! the tubes are characteri ed b% the transverse pitch S ,longitudinal pitch S ! , and the diagonal pitch S D bet een tube centers .


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5/12/16 | Slide 2:

Flo "atterns !or in'line and staggered tube ban&s.

in'linestaggered


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Di$ensions o! inline and staggered arrange$ents

Staggered"n)line

;rrangement of the tubes in in)line and staggered tube ban s 9 A ( , A T ,

and AD

are ow areas at indicated locations, and L is the length ofthe tubes


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5/12/16 | Slide 2?

Jaxi$u$ 9elocit% Calculation

+n tube ban&s# the !lo characteristicsare do$inated b% the $axi$u$ velocit%V $ax that occurs ithin the tube ban&rather than the a""roach velocit% V .*here!ore# the e%nolds nu$ber is

de!ined on the basis o! $axi$u$velocit% as

*he $axi$u$ velocit% is deter$ined!ro$ the conservation o! $assre,uire$ent !or stead% inco$"ressible!lo

For in"line arrange$ent# the $axi$u$velocit% occurs at the $ini$u$ !lo areabet een the tubes# and the conservationo! $ass can be ex"ressed as

+nstaggered arrange$ent# i!

+!


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)eat trans!er coe!!icient correlations

Several correlations# all based onex"eri$ental data# have been "ro"osed !orthe average


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)eat trans!er coe!!icient correlations

Correction !actor is introduced hen # ! %16 "rovided that the% are $odi!ied as

here F is a correction factor For e D H 1>>># the correction !actor is inde"endent o! e%nolds nu$ber.

*ube ban&s # ! %16


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3ressure Dro" Calculations

nother ,uantit% o! interest associatedith tube ban&s is the pressure drop ∆P #hich is the irreversible "ressure loss

bet een the inlet and the exit o! the tubeban&. +t is a $easure o! the resistancethe tubes o!!er to !lo over the$# and isex"ressed as

*ube ban&s


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Su$$ar%

Drag and )eat *rans!er in External FloFriction and "ressure drag)eat trans!er

3arallel Flo Over Flat 3latesFriction coe!!icient)eat trans!er coe!!icientFlat "late ith unheated starting length

ni!or$ )eat FluxFlo cross C%linders and S"heres

E!!ect o! sur!ace roughness)eat trans!er coe!!icient

Flo across *ube 4an&s3ressure dro"


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FO CED CO !lo s over the u""er sur!ace o! a 5'$'long !lat "late

hose te$"erature is 2> ith a velocit% o! 2 $/s !ig:.10 Deter$inethe total drag !orce and the rate o! heat trans!er "er unit idth o! theentire "late.

Exa$"le :'1 Lunus 0

Fig :'10


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Solution8 Exa$"le :.1SO; *+O< 8 Engine oil !lo s over a !lat "late. *he total drag !orce and the rateo! heat trans!er "er unit idth o! the "late are to be deter$ined.

SS J3*+O@6>0/2 > °C

M =:6 &g/$ ( 3r 2?62

& >.1 7/ $.N0 2. =5 x1> ' $ 2/s

< ;LS+S8


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5/12/16 | Slide (6

Cont . hich is less than the critical e%nolds nu$ber. *hus e have laminar flow

over the entire "late# and the average !riction coe!!icient is

1.(( 1.(( x .>2 x1> 0 '.5 >.>>66(


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5/12/16 | Slide (:

Cont . >.66 >.66 .>2 x1> 0 '.5 x 1?1(

*hen#

h x 1?1( 55.25 7/$ 2.N

h s

' 0 55.25 x 5x1 $ 20x 6>'2>0 11>5> 7


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5/12/16 | Slide (=

Exa$"le :'(*he !or$ing section o! a "lastics "lant "uts out a continuous sheet o! "lasticthat is !t ide and >.> in thic& at a velocit% o! (> !t/$in. *he te$"eratureo! the "lastic sheet is 2>> oF hen it is ex"osed to the surrounding air# and

a 2'!t'long section o! the "lastic sheet is subjected to air !lo at =>o

F at avelocit% o! 1> !t/s on both sides along its sur!aces nor$al to the direction o! $otion o! the sheet# as sho n in Fig.

Deter$ine

*he rate o! heat trans!er !ro$ the "lastic sheet to air b% !orced convectionand radiation.

Calculate the te$"erature o! the "lastic sheet at the end o! the coolingsection.

Data

Densit% :5lb$/!t (

S"eci!ic heat >. 4tu/ lb$. oF0

E$issivit% o! "lastic sheet >.?


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Sche$atic o! Cooling o! 3lastic Sheet.


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Cont .SO; *+O< " 3lastic sheets are cooled as the% leave the !or$ing section o! a"lastics "lant. *he rate o! heat loss !ro$ the "lastic sheet b% convection andradiation and the exit te$"erature o! the "lastic sheet are to be deter$ined.

SS J3*+O.:2>2& >.>162( 4tu/ h.!t.o

F0 >.2> x 1> '( !t2/s


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5/12/16 | Slide 1

;=;!@S"S 9a : Ae e6pect the temperature of the plastic sheet to dropsomewhat as it ows through the /)ft)long cooling section, but at thispoint we do not now the magnitude of that drop. +herefore, weassume the plastic sheet to be isothermal at /%% oF to get started. Aewill repeat the calculations if necessary to account for thetemperature drop of the plastic sheet.

Cont .


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C


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5/12/16 | Slide (

Cont . +herefore, the rate of cooling of the plastic sheet by combinedconvection and radiation is

@/%0* B /020 4639 Btu/h

9b : +o Cnd the temperature of the plastic sheet at the end of thecooling section,we need to now the mass of the plastic rolling out per unit time 9orthe mass ow rate:, which is determined from

!t20 (>/6>!t/s0 >.5lb$/s

+hen, an energy balance on the cooled section of the plastic sheetyields


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5/12/16 | Slide

C " ' 0* 2 * 1@

=oting that Q is a negative quantity 9heat loss: for the plastic sheet andsubstituting,the temperature of the plastic sheet as it leaves the coolingsectionis determined to be

* 2 2>> oF@ 1?(.6oF


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lect - 10 external forced convection.pptx

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