Lecture Notes for Students(1)

8/14/2019 Lecture Notes for Students(1)

1/26

Thermodynamics 2: EG40JK

Dr Yakun Guo

[email protected], ! 2"#

$ourse arrangemen%: &ec%ures: e'ery Tuesday: (()(2*m: !2+ (2)(*m: -T4. Tu%oria /%o%a

" one)hour %u%oria: week 14 (15 October), week 16 (29 October), week 17 (5 November), week

18 (12 November), week 19 (19 November) and week 21 (3 December), all take place on !e"da#$rom 4 to 5pm at %N3&

1ssessmen%:

/( a %hree hour eamina%ion, 30, 5 6ues%ions a carry 20 marks

/2 7*en book cass %es%, (0

8e9erences:

(. 8ogers and -ayhe: Engineering Thermodynamics+ *ubished by ;ren%icencro*era and De?i%%: undamen%as o9


2/26

) !alidity of lumped capacitance method

4. $orced convecton

(?nat!ral convecton)*$l!d " $orced to $low b# e:ternal mean" (p!mp, wnd, etc)& Newton"law*+ < +eat tran"$er coe$$cent or $lm coe$$cent, dependn on t+e $l!d and t+e $low reme

2

)

""*+

)

"*+

d)

d"*+, 21&&&&&&

=

==

( )-w ""h+, =


3/26

3& adaton* all matter contn!o!"l# emt" electromanetc radaton !nle"" t" temperat!re "

ab"ol!te ero& No materal (med!m) " re!red $or +eat tran"$er&te$an.oltmann -aw *where . the emissivity of the surface and < 5&669:[email protected](te$an.oltmann

con"tant)

ompar"on between t+e mec+an"m"

ond!cton* ke# parameter* cond!ctvt# (k) . a propert# o$ t+e materal

onvecton* Ce# parameter* +eat tran"$er coe$$cent (+) . relatn to $l!d $low pattern

adaton* Ce# parameter* em""vt# . a propert# o$ t+e "!r$ace, radaton " proportonal to

4&

$onduc%ion

ond!cton* +eat tran"$er t+ro!+ a "nle.la#er wall%rom %o!rer" law*

Ae +ave

+en

R.)/#+0)


4/26

$ombina%ion o9 conduc%ion and con'ec%ion overall +eat tran"$er coe$$cent U$or $l!d $lm and

"old wall* !"n electrcal analo#*

'


5/26

Thermal resistance in a different form: !"n lo mean area or lo mean rad!" o$ t+e c#lnder*

w+ere+ln" lo mean area,rln" lo mean rad!"&+ere$ore +eat tran"$er t+ro!+ a c#lnder*

$onduc%ion %hrough cyindrica ayers B a compo"te "tr!ct!re0eat tran"$er t+ro!+ "teel ppe wt+ $o!ln = n"!laton *

$ombina%ion o9 conduc%ion and con'ec%ion overall +eat tran"$er coe$$cent U$or +eat tran"$ert+ro!+ c#lndrcal la#er* !"n electrcal analo#*

+oand+i are o!t and nner "!r$acearea of cylinder3 +w" lo mean area o$ t!be*

E " overall +eat tran"$er coe$$cent*

A+ere rw" t+e lo mean rad!" o$ t+e t!be*

5

ln

12

ln *+

rr

*+

rR

=

= ( ) lr

rr

rrl

++

+++ &&2

)Bln(

2

)Bln(ln

12

12

12

12ln

=

=

= )Bln( 12

12ln

rr

rrr

=

( )ln

2121

&B +*r

""

R

"",

=

=

1+++C1+

C1+

+*

rr

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rr

""

l*

rr

l*

rr

l*

rr

""

RRR

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ln,

23

ln,

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41

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++

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++

=

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ooww

w

ii

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oi

+h+*

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++=

++=

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11 oio

ow

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oio ""'+

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)

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++

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Bln

=


6/26

Dimensiona anaysis

Dmen"onal anal#"" can be !"ed to* (1) ed!ce n!mber o$ e:perment" needed "mpl$#

e:perment"> (2) :permental data pre"entaton> (3) roaden t+e !"e o$ e:permental re"!lt" to a

wde condton"> and (4) 0elp n !nder"tandn t+e p+#"c" o$ a problem& 0owever, dmen"onalanal#"" t"el$ can not completel# "olve t+e problem a" e:perment" are e""ental $or t+e

determnaton o$ emprcal con"tant"&

!ckn+am G t+eor#* $ r " t+e d"tnct re$erence mant!de" re!red to e:pre"" t+e dmen"onal

$orm!la o$ all n mant!de" drectl# a$$ectn a p+#"cal p+enomenon, t+en t+e"e n mant!de" ma#

be ro!ped nto (n.r) ndependent dmen"onle"" parameter" (o$ten re$erred a" ")

:ample* o $nd a "et o$ dmen"onle"" ro!p" $or t+e problem o$ t+e $low o$ an ncompre""ble

$l!d t+ro!+ a ppe&

()-"t relevant varable"*

' p < pre""!re drop

' D < ppe dameter

' Em < mean veloct#

' - < lent+ o$ ppe

' < v"co"t#

' < den"t#

() =""!me t+e $ollown relaton"+p*

() Arte t+e dmen"on o$ t+e varable"

Harable" Dmen"on Ent

Gre""!re (G) IB-2 Ga (NBm2)

Den"t# () IB-3 kBm3

H"co"t# () IB- k B" m

Heloct# (E) -B mB"

-ent+ (D, -) - m

(v) !b"tt!te t+e"e nto above e!aton #eld"*

(v)!atn ndce" #eld"*

%or I* 1 < a J b (1)%or -* .1 < .3a . b J c J d J e (2)

;

Am

6

edc

m

-a LDuconstp &&&&&)&( =

[ ] [ ]edca

LL"

L

L"

L

L"

=

32


7/26

%or * .2 < .b . c (3)

(v) olvn above e!aton" and !"n e:perment" #eld"

mm Dutcons

u

p

L

D

=

tan

2

+e"e de$ne $rcton coe$$cent and e#nold" n!mber

+en we +avef.f4#Re$, &e& $rcton coe$$cent " t+e $!ncton o$ e#nold" n!mber&

Dmen"onal anal#"" proced!re*1) -"t all t+e varable" :1, :2, K, :n,

2) =""!me a relaton"+p n term" o$ a prod!ct o$ power" o$ t+e varable"

3) E"e t+e prncple o$ dmen"onal +omoenet# to wrte down*4) !ate t+e power" o$ t+e $!ndamental dmen"on" on bot+ "de" o$ e!aton n "tep 3) and "olve

t+e e!aton obtaned, c+oo"n "ome o$ t+e power" a" nece""ar#>

5) !b"tt!te $or t+e power" nto t+e e!aton and +ence wrte # a" a $!ncton o$ t+e dmen"onalro!p"&

Note" on Dmen"onal =nal#""*

+e non.dmen"onal ro!p" are not !n!e& =lwa#" c+oo"e t+e commonl# !"ed one"

Non.dmen"onal ro!p" !"ed "+o!ld be ndependent

:ample* Dmen"onal anal#"" $or $orced convecton ($reeBnat!ral convecton " nelected)*

varable"* +eat tran"$er coe$$cent h3 $l!d v"co"t#5, den"t#6, t+ermal cond!ctvt# *, "pec$c +eatcapact# o$ $l!d cp, d$$erence between "!r$ace and $l!d7tand $l!d veloct# !, t+en we +ave

h.f(53 63 *3 cp,7t3 u3 l$.+ 5a6*ccp

d7teuflg

l" c+aracter"tc lnear dmen"on, = " con"tant& E"n dmen"onal anal#""*

=

'l

*

cf

*

hl p,

e#nold" n!mber*forceviscous

forceinertial'D'l

===

e

N!""elt n!mber**

hD

*

hl&u ==


8/26

d$$erence between two part" o$ $l!d den"t#64and68; &at!ral convecton depend" on !pt+r!"t* #64-68$g. 687tg; Dmen"onal anal#"" "+ow" t+at

&u.f#B=r4>) *&u.+#=r;8?Et!rb!lent

$low (4>=r$*&u.+#=r;B>& Groperte" taken at $lm temperat!re#"s 9 "a$/8

3& %ree convecton $rom +orontal $lat plate"

a) 0ot plate" $acn !pward" or cold plate" $acn downward"*&u.>;?B#=r;8?(4>?=r84>G)

&u.>;4B#=rG=r@4>4>)

b) 0ot plate" $acn downward" or cold plate" $acn !pward"

&u.>;8G#=r;8?(34>?=r4>4>)

w+ere* - < mean o$ plate lent+ breadt+,

< " . a (", a* plate "!r$ace ar temperat!re),

Groperte" at $lm temperat!re (" J a)B2

8


9/26

Mn man# ca"e" o$ nat!ral convecton, t " po""ble to !"e an appro:mate e!aton to eval!ate +eat

tran"$er coe$$cent, +& %or e:ample, $or nat!ral convecton $rom a +orontal ppe

h.4;@8#7t/d$4/Bwhen 4>B=r4>

h.4;8?7t4/@when 4>=r4>48

w+ere hn ABm2&C,7tn0and dn m&

Therma con'ec%ion correa%ions: 9orced con'ec%ion

1& %low n"de crc!lar t!be"

a) Dtt!".oelter e!aton ($or t!rb!lent $lowe ? 1@,@@@, @&7Gr1@@)*

&u.>;>8BRe>;;Bfor +eatn

&u.>;>8BRe>;;@for cooln

b) on"der e$$ect o$ varaton o$ $l!d properte"

c) -amnar $low

!o%e:ppe MD, mean veloct# and properte" at b!lk temperat!re are !"ed n t+e above e!aton"&

2& %low o!t"de t!be"Bc#lnder"

a& orrelaton $or $l!d" $lown o!t"de a "nle t!beBc#lnder normal to t*

&u.>;8BRe>I;@

b& %or ar and t+e common a"e", t+e above ma# be "mpl$ed to*

&u.>;8IRe>;I

Note*

a) +e lent+ term n N! e " t+e o!t"de dameter o$ t+e t!be>b) Groperte" are at t+e mean temperat!re m= s

&u

( ) ( ) ( ) )2@@@(eBBGre86&1 14&@3B13B1


10/26

2& Gre""!re drop n a non.crc!lar c+annel

Iet+od a)* $rcton coe$$cent can be obtaned $rom e:perment"

Iet+od b)* orrelaton" $or crc!lar t!be" are !"ed and D " replaced wt+ t+e 0#dra!lc (e!valent)Dameter (D+)

D+


11/26

!aton" (1) and (2) are e!valent $or c


12/26

En"tead# or tran"ent +eat tran"$er problem", ar"n w+en "#"tem bo!ndar# condton" c+ane, are

ver# d$$c!lt to "olve& = "mple approac+* t+e Lumped capacitance ethod, " !"ed w+en

temperat!re radent" wt+n t+e "#"tem are "mall&

:ample* +ot metal $orn&

Ietal " ntall# at !n$orm temperat!re & Mt " !enc+ed b# mmer"on n a l!d Yntall#Z at"Q"i at tme t


13/26


14/26

$or a "p+ereLc. r>/@; o mplement crteron n con"ervatve $a"+on,Lc" a""ocated wt+ t+e lent+

"cale corre"pondn to t+e ma:m!m "patal temperat!re d$$erence&

Pith Lc.!/+s, we +ave

T is thermal diffusivity; Fo" dmen"onle"" tme, w+c+, wt+ ot n!mber, c+aractere" t+e

tran"ent cond!cton problem&

+e l!mped capactance met+od can be !"ed to (1) anal#e t+e tme re!red $or t+e +eat tran"$erproce"" to reac+ "ome $nal temperat!re > (2) anal#e t+e $nal temperat!re re"!ltn $rom a tme

perod o$ t "econd" o$ a +eat tran"$er proce""&

Note:1oth the &usselt numer and the 1iot numer have the same form (hL/*)& 0owever, $or t+e

ot n!mber, t+e t+ermal cond!ctvt# k !"ed " t+at $or t+e "old> $or calc!latn N!""elt n!mber t+ek val!e a" t+at o$ t+e $l!d& +e ot n!mber " a mea"!re o$ t+e rato o$ t+e temperat!re drop n t+e

"old materal and t+e temperat!re drop between t+e "old and t+e $l!d& +e N!""elt n!mber " a

dmen"onle"" ver"on o$ t+e temperat!re radent at t+e "!r$ace between t+e $l!d and t+e "old, andt t+!" provde" a mea"!re o$ t+e convecton occ!rrn $rom t+e "!r$ace&

; No

totall# black bod# e:"t" n practce, b!t man# "!r$ace" appro:mate to t+e de$nton&

ner# radated $rom a bod# per !nt area per !nt tme " called t+e emmissive power

= black bod# " t+e be"t po""ble emtter a" well a" t+e be"t po""ble ab"orber&

+e em""vt# o$ a bod# " de$ned b#

14

&&

&&&&

\&

&&&&&&&&&&&&&&]&&

&

&

&&

&

&&

&&

2

22

num-erFouriertheL

tFwhere

F1c!t+hor

c

*-n

L

t

*

Lh

L

t

c

*

*

Lh

Lc

th

c!

t+h

c

o

oi

p

s

pc

c

cp

c

cpp

s

=

=

====

( )Fo1i""

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ii

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=

R%

-ody-lac*aofpoweremmisivethe

-odyaofpoweremmisivethe=


15/26

=b"orptvt# e!al" em""vt# w+en t+e two bode" are at t+e "ame temperat!re& +" " called

Crc+o$$" law* t+e em""vt# o$ a bod# radatn ener# at temperat!re, , " e!al to t+e

ab"orptvt# o$ t+e bod# w+en recevn ener# $rom a "o!rce at a temperat!re, &

The grey body

%or t+e maXort# o$ materal" t+e em""ve power per !nt wavelent+ " a $!ncton o$ t+at wavelent+

Yncl!dn black bode"Z& 0owever, t+ere are certan materal" $or w+c+ t+e em""vt# " vrt!all#con"tant over all wavelent+" and $or all temperat!re& !c+ an deal "!r$ace " called a re# bod#,

and T.U, at all temperat!re", w+ere ^ and _ are total ab"orptvt# and total em""vt# over all

wavelent+&

The C%e9an)o%mann &a

. law lnk" t+e em""ve power and t+e temperat!re o$ a bod#& +e law "tate" t+at t+e em""vepower or ener# emtted " proportonal to t+e 4t+power o$ t+e bod#" temperat!re, &e&

on"der bod# 1, o$ em""vt# U4at temperat!re "4, completel# "!rro!nded b# black "!rro!ndn" atlower temperat!re "8& +e ener# leavn bod# 1 " completel# ab"orbed b# t+e "!rro!ndn"& +en

t+e rate o$ +eat tran"$erred $rom t+e bod# to t" "!rro!ndn" per "!are meter o$ bod# "

w+c+ " t+e d$$erence between t+e ener# tran"mtted and ener# ab"orbed b# t+e bod#& M$ t+e

em""vt# o$ t+e bod# at 1 " "n$cantl# d$$erent $rom t+at o$ t+e bod# at 2 t+en t+e

appro:maton o$ a re# bod# ma# not be "!$$centl# acc!rate& Mn t+" ca"e, a ood appro:maton "to take t+e ab"orptvt# o$ bod# 1 w+en recevn radaton $rom a "o!rce at 2a" ben e!al to t+e

em""vt# o$ bod# 1 w+en emttn radaton at 2&

&amber%s a and %he geome%ric 9ac%or

%or mo"t "!r$ace" t+e reater part o$ t+e emtted radaton " normal to t+e "!r$ace& +!", t "

mportant to con"der +ow t+e radaton " d"trb!ted n t+e varo!" drecton" $rom two "!r$ace"& o

t+" end, t+e nten"t# o$ normal radaton, i, " de$ned $or

drecton" normal and "ome ot+er anle to t+e "!r$ace&i&" t+e nten"t# o$ normal radaton and de$ned a" t+e rate o$ ener# em""on $rom !nt "!r$ace

area, t+ro!+ !nt "old anle, alon a normal to t+e "!r$ace& +e nten"t# o$ radaton n an# ot+er

drecton at an# anle ` to t+e normal " denoted a" iV&

Note* a "!r$ace "!btend" a "old anle at a pont d"tance r $rom all pont" on t+e "!r$ace,

e!al to t+e "!r$ace area dvded b# r8& %or e:ample, t+e "!r$ace o$ a "p+ere " Br8and +ence t+e"old anle "!btended b# t+e "!r$ace at t" centre " B&

15

&,&&

)&(B1@67&5,,&

4R

4284R

odytheofemissivitytheiswhereodylac*nonafor"%and

0mPwhereodylac*afor"%1

=

==

( )424

11

R

& ""J =

4

2

4

1

R

&&&&21""J"hen "" =


16/26

%!re "+ow" t+e "c+ematc $or t+e "old anle&

&amber%s cosine a

+e varaton o$ nten"t# o$ radaton " ven b# &amber%s cosine a+e rate o$ ener# em""on $rom a "!r$ace o$ area d+ is then given y

on"der a "mall area d+, and t+e radaton $rom d+w+c+ pa""e" t+ro!+ a "mall element o$ t+e"!r$ace area o$ a +em"p+ere wt+ d+at t" centre ("ee $!re above)& +e element "!btend" an anle

` at t+e centre o$ t+e +em"p+ere and t+e "mall ncrea"e n anle over t+e wdt+ o$ t+e element "

t+en dV& +e wdt+ o$ t+e element " t+e lent+ o$ t+e arc, o$ t+e anle dV, and t+e rad!" r&(&e& = n t+e $!re), namel#* wdt+ o$ element, =


17/26

%or black bod#

4"% =

+!", d+id+" & &&&&&4

=

o, B&&4

"i& = t+e nten"t# o$ normal radaton or t+e rate o$ ener# em""on $rom !nt"!r$ace area t+ro!+ a "old anle&

+e "old anle

Note* =n area " "ad to "!btend n t+ree dmen"on" a "old anle at an o!t"de pont& +e "old anle" mea"!red b# t+e area "!btended (b# proXecton) on a "p+ere o$ !nt rad!" or b# t+e rato o$ t+e

area (=) ntercepted on a "p+ere o$ rad!" r to t+e "!are o$ t+e rad!" (=Br2)& +e !nt o$ "old anle

" t+e "teradan& +e "old anle completel# "!rro!ndn a pont " 4 "teradan"& M$ a "mall area (d=)" at a d"tance $rom a pont and t" normal make" an anle [ wt+ a lne drawn to t+e pont, t+e

"old anle $ormed b# t+e area and t+e pont " (d=&co"[)B2&

Geome%ric 9ac%or

on"der two "mall black "!r$ace" o$ area d+1and d+2 at temperat!re" 1and 2, a d"tance)apart,and nclned a" "+own n $!re& Net+er bod# receve" all t+e radaton $rom t+e ot+er&

-et "!r$ace d+2"!btend a "old anle dw1at t+e centre o$ "!r$ace d+1& +en*

1 2

x

dA1

atT

1

dA2

atT

2

17

2

4

121212

2

221

4

11112

4

1112

1

co"co"

co"&

co"

&&

co"1

)

"d+d+d+onincidentenergyofratethe+nd

)

d+dw

anglesolidtheofdefinitionthefromalso

"d+dwd+onincidentenergyofRate

"herefore

surfacelac*afor"i&ow

d+dwid+onincident

d+fromemissionofRate

&

&

=

=

=

=

=


18/26

+e eometrc $actor"F4-8andF8-4can be obtaned $rom do!ble nteraton o$ e!aton" 1,2 and 2,1,

anal#tcall# or rap+call#& %or a lare area, compo"ed o$ "mall area" d+4and d+8, averae eometrc

$actor" can be de$ned n a "mlar manner a" above&

8adian% in%erchange be%een grey bodies

ado"t#, , " de$ned a" t+e total radant ener# leavn a bod# per !nt area per !nt tme&

Mrradaton, , " de$ned a" t+e total radant ener# ncdent on a bod# per !nt area per !nt tme&

0ence

18

( )

( )

( )

( )424

121212

R

4

2

4

112121

R

4

2

4

12

212121

R

2

12112

2

22121

4

11

2

4

1212121

2.1

4

111

Fd

Fd

wrttenbecan+"

co"co"Fd

""!r$ace"ebetween t+enterc+anener#o$ratenett+e

)1,2&&&&&&&&(&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&co"co"

2,1&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&co"co"

co"co"&&

,%,$actorReometrcRt+ecalled"$r"tb# t+e

emttedener#t+ebod# to"econdon t+encdentener#t+eo$rato

&&&d="d=$romem""onener#totalo$ratet+eNow

""d+For

""d+F

"")

d+d+

"hen

)

d+F

Nimilarly

)

d+Ftherefore

"d+)

"d+d+Fei

"he

"

=

=

=

=

=

=

( )

( )

yreciprocitoftheoremiprelationshreciprocalthe+F+F

""+F,and

""+F,ei

=

=

=

&&&&&&&&&&&&&

"een t+atbecante!aton"t+e"e$romand

&&

212121

4

2

4

121212

R

4

2

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112121

R

R4

R

44R

RRR

&&

&

,

="Wei

surfacethefromreflectedenergy

offractiontheincludemustradiositythe-odygreyaFor

"Wand"%-ody-lac*aFor

surface-odytheofareatheis+where

+=W,-odyfromtransferheat&et

1

+=

==

=

( )

)&&&&&&(&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&F

"n

F&e&

2,bod#b#dntercepte"w+c+=radaton

o$$ractont+e",%$actor,eometrct+e,2and1bode"an# two%or

)&&&&&&(&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&1

1&&

1

1

&,1,

R

R

2121121R

122211

RR

2122121121

R

R

11

2.1

R4

R

4R

RRR

R

4R

R

R4

R

-WWF+

F+F+guand

WF+WF+

W

aW"+

,or

"W

W=W+,ei

"W=or

="W

"herefore

vitytransmissineglecting-odygreyafor+lso

=

==

=

==

=

+=

==

R

WR

=


19/26

=n electrcal analo# can be !"ed ba"ed on O+m" law> w+ere F " analoo!" to c!rrent, (4.) "analoo!" to potental d$$erence, re""tance wll be 1B(=1%1.2)&

:ample* a bod# 1, completel# enclo"ed b# a bod# 2, $!re below "+ow" t+e electrcal analo#&

42

22

2

21111

141 111 "

+F++"

19

( ) ( )

( )

+

=

+

==

+=

++=

=

++

=

111

&&

t+entoet+erclo"ever#arebode"A+en

)&(&&&&&&&&&&&&&&&&&&&&

111

11

111

111

11

1

111,tan

21

4

2

4

11

21

21

22

1

1

42

411

R

42

41

21

122

1

122

1

11

21

22

2

21111

1

""+,ei

++

c

+

+

""+

R

"",

++

+

+

+

+R

thereforeFhereand

+F++Rceresis"otal

"

"

"


20/26

+" latter e:pre""on $or t+e +eat tran"$er al"o apple" to t+e ca"e o$ two lare $lat parallel "!r$ace"

w+ere t+e "e o$ t+e "!r$ace" " lare compared wt+ t+er d"tance apart, &e& t+e radant ener#

e"capn to t+e "!rro!ndn" " nelble&

A+en more t+an two "!r$ace" e:c+ane +eat t+en an e!valent electrc crc!t can be drawn !"n

t+e e:pre""on" $or re""tance (e!aton (m) (n))&%or t+e ca"e "+own +ere a bod# 1 e:c+ane" +eat

wt+ bod# 2, t+e "!rro!ndn" 3 ben at a d$$erent temperat!re&

+e e!valent crc!t " "+own below wt+ t+e re""tance", potental" and c!rrent"&

=ppl#n O+m" law to eac+ part o$ t+e network we obtan ": e!aton"

=l"o $rom Crc+o$$" law o$ electrc crc!t"

M1


21/26

Note* %or convectve +eat tran"$er $rom a "!r$ace t" total area = "+o!ld be !"ed n t+e calc!laton&

Mn radaton +eat tran"$er $rom t+e "ame bod# t+e area o$ t+e "!r$ace envelope m!"t be !"ed&

;a" radaton

+e e$$ect o$ tran"m""on t+ro!+ t+e a"eo!" atmo"p+ere +a" been nelected> "ome "mall amo!nto$ radaton wll be ab"orbed, b!t t+" can be nelected, beca!"e t " "mall& ertan a"e" are

tran"parent to radaton> t+e"e ncl!de nert a"e" (e&& aron) and a"e" wt+ "#mmetrc datomc

molec!le" (e&& o:#en and ntroen)& ;a"e" wt+ certan t#pe" o$ a"#mmetrc molec!lar "tr!ct!re"

(e&& carbon mono:de and do:de, "!lp+!r do:de, and water vapo!r) radaton " ab"orbed $romand emtted to "!rro!ndn "!r$ace"& =b"orpton and em""on o$ radaton n a"e" " "electve,

occ!rrn onl# n certan band" o$ wavelent+"& adaton wt+n a $!rnace, $or e:ample, m+t need

to acco!nt $or t+e"e properte"&

(3) conden"er"> (4)

boler"> (5) evaporator", etc& +e proce""e" nvolve a l!d or a a" w+c+ re!re" to be +eated or

cooled&

+ree man t#pe" o$ +eat e:c+aner*

ec!perator* n w+c+ t+e $lown $l!d" e:c+ann +eat are on et+er "de o$ a dvdn

wall&

eenerator* n w+c+ t+e +ot and cold $l!d" pa"" alternatel# t+ro!+ a "pace contann a

matr: o$ materal t+at alternatel# provde" a "nk and a "o!rce $or +eat $low&

vaporatve t#pe* n w+c+ a l!d " cooled evaporatvel# and contn!o!"l# n t+e "ame

"pace a" t+e coolant&

21

( )( )( )

( )( )( )

( )

( )( )

( ) )&&&&&(&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&F

)&&&&&&&&&(&&&&&&&&&&&&&&&&&&&&

&&F

+ave&&&we$er,+eat tran"convecton%or&&

%rom

t&coe$$cen$er+eat tran"convectont+e# toanaloo!"l

de$ned"ometme"",radaton,$ortcoe$$cen$er+eat tran"=

21

R

21

2

2

2

121

R

2121

2

2

2

112121

2

2

2

1

2

2

2

1121

4

2

4

112121

r

ett+h

therefore

d""""Fh

writecanwethesecomparing+nd

tt+h

""""""+F,ei

""""+F

""+F,

h

r

r

w

Y

-

Y

-

=

++=

=

++=

+=

=


22/26

Double pipe heat exchanger

Garallel.$low (co.c!rrent) and o!nter.$low (co!nt.c!rrent) $low

(a) parallel $low (b) co!nt.c!rrent $lowNote* < temperat!re o$ +ot "tream, t


23/26

>m*or%an% !o%es:

( +e temperat!re o$ a wet vapo!r or boln $l!d reman" con"tant>

2 = reater temperat!re rane " po""ble $or co!nter.$low& 0oe'er, in parallel $low,t+e $nal temperat!re" m!"t be "omew+ere between t+e ntal val!e" o$ eac+ $l!d&

?+en m&c=< m&ct+en temperat!re d$$erence n co!nter.$low " t+e "ame all alon t+e t!belent+ beca!"e +eat ven !p b# $l!d = e!al" +eat receved b# $l!d

4&

$ross 9o recu*era%or

23

=

1

2

21R

ln

)(&&&

t

t

tt'lD,

tuetheof

areasurfacemeanthelD+andt+',"hen

differenceetemperaturmeanarithmicthe

tt

ttt

ygivenisdifferenceetemperaturmeanthe

&&&&&&&&&&&&&&&&&&&&&&&&&

lo&&&&&&&&&&&&

ln

ln

R

2

1

21ln

==

=

$low&.co!nter$orle"""re!redarea"!r$acet+e

c+ane",erat!reven temp$orand$l!d"twot+eo$$lowma""o$rate"ven$ort+at$ollow"Mt

le""&alwa#""o$val!eb!t t+e$low,.parallel$or

reater"tntal+e$low&.parallel$ort+an$low.co!nter$orreater"eneralMn

po""ble&a"larea"madebem!"tt+enE,o$mean val!evenaand=,area,vena$or

&&

ln

1ln

ln

ln

R

=

t

t

t

showst+',


24/26

+e cro"" $low rec!perator n t+" $!re +a" t!be $low (=) $rom le$t to r+t on t+e daram and cro""

$low () n t+e "+ell $rom top to bottom& +e tr!e mean temperat!re d$$erence depend" on t+e rato

o$ t+e prod!ct o$ t+e ma"" $low and "pec$c +eat capacte" o$ $l!d" = and , a" well a" on t+e rato

o$ t+e temperat!re d$$erence between t+e re"pectve nlet" and o!tlet"& able" o$ correcton $actor"are avalable $or varo!" val!e" o$ t+e rato"&

A+en t+e temperat!re d$$erence" at nlet and o!tlet are not "!b"tantall# d$$erent, t " a ood

appro:maton to !"e t+e art+metc mean temperat!re d$$erence, &e&

%or cro"".$low t+e re!red "!r$ace area " between t+at o$ co!nter.$low and parallel.$low&

ouing resis%ance

+e $lown $l!d " "eldom completel# $ree $rom drt, ol, rea"e, and c+emcal depo"t", and a

coatn tend" to collect on all metal "!r$ace"& +" ve" r"e to an ncrea"e n re""tance to +eat

tran"$er& =fouling resistance" added to t+e total t+ermal re""tance&

#pcal val!e" per "!are metre o$ "!r$ace area are' 1&8 CBkA $or $!el ol

' @&6 CBkA $or rver water

' @&2 CBkA $or boler $eed water


25/26

+e more e$$ectve +eat e:c+aner +a" a reater n!mber o$ tran"$er !nt"& +e rato o$ ma:m!m tomnm!m t+ermal capact# "R.Cmin/Cma); Rcan var# between 1 and @, namel# bot+ $l!d" +avn

t+e "ame t+ermal capact# and one $l!d +avn an n$nte t+ermal capact#& +" latter ca"e apple"

to a boln l!d or a conden"n vapo!r&

%or a co!nter $low +eat e:c+aner

25

mn

ln

&

C

+'&

t

sdifferenceetemperaturfluidtwotheofgreaterthe&

termsgeneralmorein

tu

tu

=

=

( )

( )R&

R&

tu

tu

eR

e

=1

1

&1

1

( )

( )11

21

ln

,

&tan,

"n,

&e:p

&1,

CH

CCtu

CHCH

CH

tt

tt&

e)changerthethroughouttconsiswhichfluidscoldandhot

the-etweendifferenceetemperaturtheeJualstand

CCcettcasethisFor

used-ecannotforressiona-ovethe

RCCwhen

e)changerheatflowcounteraFor

=

==

==


26/26

( )

( )

esseffectiventhee

condenserageRandtypefloweitherfor

e)changerheatflowparallelaforR

e

thatshownealsomayXt

&

&

givesderivationresultingtheand

tu

tu

&

R&

tu

tu

==

=

+

=

+=

+

1

Z&&Y@,

1

1

1

1

Lecture Notes for Students(1)

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Transcript of Lecture Notes for Students(1)