lecture notes for students(1)
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8/14/2019 Lecture Notes for Students(1)
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Thermodynamics 2: EG40JK
Dr Yakun Guo
y.guo@abdn.ac.uk, ! 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
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8/14/2019 Lecture Notes for Students(1)
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) !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
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8/14/2019 Lecture Notes for Students(1)
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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$an.oltmann -aw *where . the emissivity of the surface and < 5&669:1@.8ABm2C4(te$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$$cent (+) . relatn to $l!d $low pattern
adaton* Ce# parameter* em""vt# . a propert# o$ t+e "!r$ace, radaton " proportonal to
4&
$onduc%ion
ond!cton* +eat tran"$er t+ro!+ a "nle.la#er wall%rom %o!rer" law*
Ae +ave
+en
R.)/#+0)
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8/14/2019 Lecture Notes for Students(1)
4/26
$ombina%ion o9 conduc%ion and con'ec%ion overall +eat tran"$er coe$$cent U$or $l!d $lm and
"old wall* !"n electrcal analo#*
'
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8/14/2019 Lecture Notes for Students(1)
5/26
Thermal resistance in a different form: !"n lo mean area or lo mean rad!" o$ 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*
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8/14/2019 Lecture Notes for Students(1)
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$$ectn a p+#"cal p+enomenon, t+en t+e"e n mant!de" ma#
be ro!ped nto (n.r) ndependent dmen"onle"" parameter" (o$ten re$erred a" ")
:ample* o $nd a "et o$ dmen"onle"" ro!p" $or t+e problem o$ t+e $low o$ an ncompre""ble
$l!d t+ro!+ a ppe&
()-"t relevant varable"*
' p < pre""!re drop
' D < ppe dameter
' Em < mean veloct#
' - < lent+ o$ ppe
' < v"co"t#
' < den"t#
() =""!me t+e $ollown relaton"+p*
() Arte t+e dmen"on o$ t+e varable"
Harable" Dmen"on Ent
Gre""!re (G) IB-2 Ga (NBm2)
Den"t# () IB-3 kBm3
H"co"t# () IB- k B" m
Heloct# (E) -B mB"
-ent+ (D, -) - m
(v) !b"tt!te t+e"e nto above e!aton #eld"*
(v)!atn ndce" #eld"*
%or I* 1 < a J b (1)%or -* .1 < .3a . b J c J d J e (2)
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8/14/2019 Lecture Notes for Students(1)
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%or * .2 < .b . c (3)
(v) olvn above e!aton" and !"n e:perment" #eld"
mm Dutcons
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+e"e de$ne $rcton coe$$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$$erence between "!r$ace and $l!d7tand $l!d veloct# !, t+en we +ave
h.f(53 63 *3 cp,7t3 u3 l$.+ 5a6*ccp
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8/14/2019 Lecture Notes for Students(1)
8/26
d$$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 $lm temperat!re (" J a)B2
8
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8/14/2019 Lecture Notes for Students(1)
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Mn man# ca"e" o$ 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
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8/14/2019 Lecture Notes for Students(1)
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2& Gre""!re drop n a non.crc!lar c+annel
Iet+od a)* $rcton coe$$cent can be obtaned $rom e:perment"
Iet+od b)* orrelaton" $or crc!lar t!be" are !"ed and D " replaced wt+ t+e 0#dra!lc (e!valent)Dameter (D+)
D+
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8/14/2019 Lecture Notes for Students(1)
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!aton" (1) and (2) are e!valent $or c
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8/14/2019 Lecture Notes for Students(1)
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En"tead# or tran"ent +eat tran"$er problem", ar"n w+en "#"tem bo!ndar# condton" c+ane, are
ver# d$$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
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8/14/2019 Lecture Notes for Students(1)
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8/14/2019 Lecture Notes for Students(1)
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$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$$erence&
Pith Lc.!/+s, we +ave
T is thermal diffusivity; Fo" dmen"onle"" tme, w+c+, wt+ ot n!mber, c+aractere" t+e
tran"ent cond!cton problem&
+e l!mped capactance met+od can be !"ed to (1) anal#e t+e tme re!red $or t+e +eat tran"$erproce"" to reac+ "ome $nal temperat!re > (2) anal#e t+e $nal temperat!re re"!ltn $rom a tme
perod o$ t "econd" o$ a +eat tran"$er proce""&
Note:1oth the &usselt numer and the 1iot numer have the same form (hL/*)& 0owever, $or t+e
ot n!mber, t+e t+ermal cond!ctvt# k !"ed " t+at $or t+e "old> $or calc!latn N!""elt n!mber t+ek val!e a" t+at o$ t+e $l!d& +e ot n!mber " a mea"!re o$ t+e rato o$ t+e temperat!re drop n t+e
"old materal and t+e temperat!re drop between t+e "old and t+e $l!d& +e N!""elt n!mber " a
dmen"onle"" ver"on o$ t+e temperat!re radent at t+e "!r$ace between t+e $l!d and t+e "old, andt t+!" provde" a mea"!re o$ t+e convecton occ!rrn $rom t+e "!r$ace&
; No
totall# black bod# e:"t" n practce, b!t man# "!r$ace" appro:mate to t+e de$nton&
ner# radated $rom a bod# per !nt area per !nt tme " called t+e emmissive power
= black bod# " t+e be"t po""ble emtter a" well a" t+e be"t po""ble ab"orber&
+e em""vt# o$ a bod# " de$ned b#
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8/14/2019 Lecture Notes for Students(1)
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=b"orptvt# e!al" em""vt# w+en t+e two bode" are at t+e "ame temperat!re& +" " called
Crc+o$$" 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
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8/14/2019 Lecture Notes for Students(1)
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%!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, =
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8/14/2019 Lecture Notes for Students(1)
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%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
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8/14/2019 Lecture Notes for Students(1)
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+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
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-
8/14/2019 Lecture Notes for Students(1)
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#&
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8/14/2019 Lecture Notes for Students(1)
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
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8/14/2019 Lecture Notes for Students(1)
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$$ect o$ tran"m""on t+ro!+ t+e a"eo!" atmo"p+ere +a" been nelected> "ome "mall amo!nto$ radaton wll be ab"orbed, b!t t+" can be nelected, beca!"e t " "mall& ertan a"e" are
tran"parent to radaton> t+e"e ncl!de nert a"e" (e&& aron) and a"e" wt+ "#mmetrc datomc
molec!le" (e&& o:#en and ntroen)& ;a"e" wt+ certan t#pe" o$ a"#mmetrc molec!lar "tr!ct!re"
(e&& carbon mono:de and do:de, "!lp+!r do:de, and water vapo!r) radaton " ab"orbed $romand emtted to "!rro!ndn "!r$ace"& =b"orpton and em""on o$ radaton n a"e" " "electve,
occ!rrn onl# n certan band" o$ wavelent+"& adaton wt+n a $!rnace, $or e:ample, m+t need
to acco!nt $or t+e"e properte"&
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boler"> (5) evaporator", etc& +e proce""e" nvolve a l!d or a a" w+c+ re!re" to be +eated or
cooled&
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ec!perator* n w+c+ t+e $lown $l!d" e:c+ann +eat are on et+er "de o$ a dvdn
wall&
eenerator* n w+c+ t+e +ot and cold $l!d" pa"" alternatel# t+ro!+ a "pace contann a
matr: o$ materal t+at alternatel# provde" a "nk and a "o!rce $or +eat $low&
vaporatve t#pe* n w+c+ a l!d " cooled evaporatvel# and contn!o!"l# n t+e "ame
"pace a" t+e coolant&
21
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-
8/14/2019 Lecture Notes for Students(1)
22/26
Double pipe heat exchanger
Garallel.$low (co.c!rrent) and o!nter.$low (co!nt.c!rrent) $low
(a) parallel $low (b) co!nt.c!rrent $lowNote* < temperat!re o$ +ot "tream, t
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8/14/2019 Lecture Notes for Students(1)
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>m*or%an% !o%es:
( +e temperat!re o$ a wet vapo!r or boln $l!d reman" con"tant>
2 = reater temperat!re rane " po""ble $or co!nter.$low& 0oe'er, in parallel $low,t+e $nal temperat!re" m!"t be "omew+ere between t+e ntal val!e" o$ eac+ $l!d&
?+en m&c=< m&ct+en temperat!re d$$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&
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23
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showst+',
-
8/14/2019 Lecture Notes for Students(1)
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$$erence, &e&
%or cro"".$low t+e re!red "!r$ace area " between t+at o$ co!nter.$low and parallel.$low&
ouing resis%ance
+e $lown $l!d " "eldom completel# $ree $rom drt, ol, rea"e, and c+emcal depo"t", and a
coatn tend" to collect on all metal "!r$ace"& +" ve" r"e to an ncrea"e n re""tance to +eat
tran"$er& =fouling resistance" added to t+e total t+ermal re""tance&
#pcal val!e" per "!are metre o$ "!r$ace area are' 1&8 CBkA $or $!el ol
' @&6 CBkA $or rver water
' @&2 CBkA $or boler $eed water
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8/14/2019 Lecture Notes for Students(1)
25/26
+e more e$$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
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8/14/2019 Lecture Notes for Students(1)
26/26
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