Convection Group Cooler Bag Report

HEC 3521 Process Heat Transfer

HEC 3521 PROCESS HEAT HEAT TRANSFER ASSIGNMENT INSULATED COOLER AG

!" Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5( Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

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Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

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Executive Summary T+$s reort #$sc)sse# a4o)t t+ree #$fferent t!es of cooer cooer 4a/s t+at 4)$t fro t+ree #$fferent t!es of cons$#ere# $ns)ate# ater$as6 T+ese cooer 4a/s are 4)$t to act as an $ns)ator to 7ee t+e canne# #r$n7 as co# as oss$4e6 Goo# $ns)ator $s nee#e# to re8ent an# re#)ce t+e rate of +eat transfer fro s)rro)n#$n/ to t+e canne# #r$n76

T+ese cooer 4a/s +a8e 4een a#e of f$4er/ass9 e// carton ater$a an# r)44er foa at6 T+ese ater$as are encose# 4! a a!er of +ar# $nter$n$n/ :+$c+ otent$a! to +o# t+e cooer 4a/s $n sta4e os$t$on6 T+e #es$/n of t+ese cooer 4a/s $s ta7en acco)nt $nto t+e reasona4e reasona4e r$c$n/9 aearance9 aearance9 an# re$a4$$t! re$a4$$t! to t+e e;er$ent6 e;er$ent6 It $s essent$a to ro8$#e ro8$#e a /oo# $ns)ate# cooer 4a/ as ost of t+e +eat :$ not 4e #$ss$ate# o)t fro t+e canne# #r$n76 Genera!9 t+e cooer 4a/s are #es$/ne# $n c!$n#r$ca s+ae as one #$ens$ona +eat transfer $s on! nee#e# $n t+$s ro
ase# on t+e e;er$ent9 e;er$ent9 t+e res)t +as s+o:n t+at f$4er/ass f$4er/ass cooer 4a/ +as t+e 4est $ns)ator a4$$t! as t+e /ra#$ent of t+e f$4er/ass $s t+e st$ffest as s+o:n on t+e /ra+ :+$c+ coare# to t+e st$ffness of /ra#$ent of foa an# e// carton ater$a6 F$4er/ass cooer 4a/ $s a4e to 7ee t+e canne# #r$n7 as co# as 4efore coare# to foa an# e// carton ater$a6 Aon/ t+e t+ree #$fferent t!es of ater$as9 f$4er/ass 4a/ +as t+e east rate of +eat transfer 4et:een s)rro)n#$n/ an# t+e canne# #r$n76 Ho:e8er9 $ro8eents can 4e #one on t+e cooer cooer 4a/s 4a/s to ens)re ens)re 4etter 4etter coo$n/ coo$n/ effect effect cooer cooer 4a/s 4a/s :$t+o) :$t+o)tt t+e $$tat $$tat$on $onss on t$e t$e constra$nts6


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Acknowledgements F$rst!9 :e :o)# $7e to e;ress o)r s$ncere /rat$t)#e to o)r ect)rer9 Ms6 Ea$ne >e) for t+e cont$n)o)s s)ort9 $ense 7no:e#/e9 at$ence an# ot$8at$on t+ro)/+o)t t+e :+oe ass$/nent6 Her /)$#ance +a# +ee# )s $n a t+e t$e of researc+ an# t+e rocess of a7$n/ t+e $ns)ate# cooer 4a/s6 .e co)# not +a8e $a/$ne# +a8$n/ a 4etter ect)rer an# entor6

O)r s$ncere t+an7s aso /o to a4 off$cers of S:$n4)rne Un$8ers$t! of Tec+noo/! Sara:a79 :+o :as :$$n/ to en# )s t+e a4 e=)$ent s)c+ as t+eroco)es9 t+eroeters an# s)c+6 .$t+o)t t+e$r +e an# /)$#ance #)r$n/ t+e er$o# of t+$s ro
.e :o)# aso $7e to t+an7 o)r feo: /ro) ates for t+e st$)at$n/ #$sc)ss$ons :+$e )tt$n/ $n a 8ast ao)nt of effort an# for a t+e f)n :e +a# :+$e ro#)c$n/ t+e cooer 4a/s6 Last 4)t not east9 :e :o)# $7e to t+an7 o)r arents t+e$r cont$n)o)s s)ort an# t+e$r s)! of f)n#s t+at $s re=)$re# for t+$s ro

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Table of Contents Section T$te Pa/e A#8ert$seent Poster E;ec)t$8e S)ar! Ac7no:e#/ents Ta4e of Contents 16, T+eor! 26, Toos?E=)$ent?Mater$as 36, Deta$e# Des$/n Doc)entat$on 361 Ass)t$ons 362 Mater$a Proert$es 263 Des$/n Cons$#erat$ons 26& Aroac+ 265 Des$/n Conc)s$ons

&6, 56,

-6, '6, 06, 6, 1,6, 116,

Page 1 2 3 & 5 0

 1, 12 1& 15

E;er$ent Proce#)re Res)ts 561 Cac)at$ons 562 Gra+s

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En/$neer$n/ Dra:$n/s Ans:ers to Pro4es D$sc)ss$on Conc)s$ons References Aen#$ces 1161 Aen#$; 1" P+otos 1162 Aen#$; 2" Ta4)ate# Data of t+e Res)ts 1163 Aen#$; 3" MatLa4 Co#es for @)est$on 1-%4(

5, 53 -2 -& -5


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-0 '' 0,

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1.0

Teory Cooer 4a/ $s #es$/ne# 4ase# on t+e a$cat$on of t+eor! of t+era $ns)at$on6

Cooer 4a/ $s #es$/ne# to a$nta$n t+e teerat)re of t+e canne# #r$n7 as co# as oss$4e for a certa$n er$o# of t$e6 Cooer 4a/ :$t+ /oo# $ns)ator ater$a $s a4e to re#)ce an# re8ent t+e rate of +eat transfer 8$a t+e :a6 T+e resence of t+e fo: of +eat $s #)e to t+e #$fference of teerat)re :+ere +eat fo:s fro +$/+ teerat)re to o: teerat)re re/$on6

In t+$s e;er$ent9 one#$ens$ona9 stea#!state +eat con#)ct$on $s a$n! #$sc)sse# for t+e +eat transfer of cooer 4a/6 T+e e=)at$on of one#$ens$ona9 stea#! state +eat con#)ct$on $s roose# as

q =-k ∇ T

q =−kA

dT dx

:+ere t+e ne/at$8e s$/n s+o:s t+at os$t$8e fo: of +eat occ)rs $n t+e oos$te teerat)re /ra#$ent6 In t+e e=)at$on9

q $s t+e +eat f);9

q $s t+e rate of +eat fo:9

∇ T an#

dT $s t+e #$fference $n teerat)re9 A $s t+e tota s)rface area :+ere con#)ct$on e;$sts9 dx $s t+e en/t+ 4et:een t+e t:o #$fferent teerat)res6 T+e t+era con#)ct$8$t!9 7 $s t+e eas)re of certa$n ater$a t+at con#)cts +eat :$t+ t+e resence of teerat)re /ra#$ent as

k =

−q dx A dT

T+e t+era res$stance of con#)ct$on affect t+e +eat fo: t+ro)/+ t+e $ns)ate# ane :a as

R t,cond =

L ∆ T = kA q x

:+ere L $s t+e en/t+ of ane :a9

q x $s t+e rate of +eat fo:6 T+e t+era res$stance $s

essent$a as t+e 4$//er t+e 8a)e of R9 t+e +ar#er t+e +eat to fo: 8$a t+e :a6 A /oo# cooer 4a/ nee#s ater$as :$t+ +$/+ t+era res$stance to re8ent t+e +eat to fo: o)t $nstant!6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

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HEC 3521 Process Heat Transfer es$#es9 t+e t+era contact res$stance +as aso $act on t+e +eat fo: as t+ere $s a teerat)re /ra#$ent or #ro 4et:een t+e a!ers of ater$a coos$te :as6 } = {∆T} over {{q} rsub {x} rsup {

R t , c

¿

ase# on t+e Ne:tonBs La: of Coo$n/9

q x =U A ∆ T

as q x =

∆T Rtotal

∴ R total

:+ere

=

1

UA

U $s t+e tota +eat transfer coeff$c$ent6 It $s t+e tota of +eat res$stance t+at tra8es

aon/ t+e contact so$# fro one to anot+er6


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Tools"E#ui$ment"%aterials

Cooer a/ A

Cooer a/ 

16 as$c cross st$tc+ fa4r$c

16 as$c cross st$tc+ fa4r$c

26 Foa

26 E// carton ater$a

36 A)$n$) c)4oar# s+eet

36 A)$n$) c)4oar# s+eet

&6 Inter$n$n/

&6 Inter$n$n/

56 ecro atc+

56 ecro atc+

-6 N!on stra %+an#e(

-6 N!on stra %+an#e(

'6 @)$c7 reease 4)c7es

'6 @)$c7 reease 4)c7es

Cooer a/ C 16 as$c cross st$tc+ fa4r$c 26 F$4er/ass 36 A)$n$) c)4oar# s+eet &6 Inter$n$n/ 56 ecro atc+ -6 N!on stra %+an#e( '6 @)$c7 reease 4)c7es


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'etailed 'esign 'ocumentation

&.1

Assum$tions

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T+e +eat con8ect$on an# +eat con#)ct$on coeff$c$ent $s constant t+ro)/+o)t t+e

e;er$ent6 26

T+e #ens$t! of t+e ater$as )se# $n eac+ of t+e cooer 4a/s rea$n t+e sae

re/ar#ess of an! teerat)re c+an/e6 36

T+e e//s tra!s :ere soa7e# an# $s ater cr)s+e# to f$ t+e saces of t+e cooer 4a/6

T+e soa7e# an# cr)s+e# e// tra!s are ass)e# to 4e coete! ac7e#6 T+ere $s no a$r sace or /a $n 4et:een t+e cr)s+e# an# soa7e# e// tra!s6 1,, t+era con#)ct$on occ)rre# t+ro)/+o)t t+e e// tra!s6 &6

T+e t+eroeter an# t+eroco)e +a8e t+e sae eff$c$enc! for teerat)re

#etect$on :$t+ , of ercenta/e error6 56

T+e teerat)re of t+e en8$ronent an# a4$ent $s t+e sae re/ar#ess of t+e :eat+er

c+an/es s)c+ as ra$n!9 co)#! or s)nn! #a!6 -6

H)$#$t! $s constant t+ro)/+o)t t+e test r)n for t+e t+ree cooer 4a/s6

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T+e #$ens$ons of t+e cooer 4a/s are #one :$t+o)t an! errors6

06

D)r$n/ t+e rea#$n/ t$e of t+e t+eroeter9 an ao)nt of t$e :$ 4e nee#e# to rea#

t+e rea#$n/s9 t+)s $t $s ass)e# t+at t+e teerat)re :$ not c+an/e :+$e t+e recor#$n/ $s )n#er ro/ress6 6

T+e $nner s)rface an# o)ter s)rface of t+e cooer 4a/ $s ass)e to +a8e t+e sae

teerat)re for a t+e cooer 4a/s6


1,

HEC 3521 Process Heat Transfer &.!

%aterial Pro$erties

T+e )t$ate /oa of t+e cooer 4a/ :as to re#)ce t+e +eat transfer fro t+e s)rro)n#$n/s $nto t+e canne# #r$n7 to 7ee t+e #r$n7 coo as on/ as oss$4e6 T+)s9 after a on/ rocess of #$sc)ss$ons an# researc+9 a fe: t!es of $ns)ators :ere seecte# to carr! o)t t+e #)t! of 7ee$n/ as )c+ +eat o)t as oss$4e6 A tota of 3 cooer 4a/s cons$st$n/ of 3 #$fferent t!es of $ns)ator ater$as :ere a#e for t+$s ass$/nent6

.e )se# a 4as$c cross st$tc+ fa4r$c to 4e a#e as t+e 4a/ for a 3 cooer 4a/s6 T+e cross st$tc+ fa4r$c :as c+osen 4eca)se $t eas$! so)rce#9 $/+t an# #)ra4e eno)/+ for )se6 T+e cross st$tc+ fa4r$c aso oo7e# neat an# resenta4e6

.e +a# aso )se# a a!er of $nter$n$n/ %$nner $n$n/ fa4r$c( :+$c+ :as t+e ater$a t!$ca! )se# as an e;tra $n$n/ 4et:een t+e or#$nar! $n$n/ of t+e fa4r$c of ta$ore# /arents9 c)rta$n an# ot+ers6 A /oo# e;ae of $ts )se :o)# 4e $ts a$ca t$on $n t+e coars of enBs fora s+$rts6 It $s rat+er a rat+er t+$n ater$a 4)t $s stron/ an# +ar#6 T+e )rose of a##$n/ t+$s ater$a to t+e $ns)ate# cooer 4a/s :as to stren/t+en t+e cooer 4a/s an# re8ent $t fro coas$n/6

T+e 3 a$n $ns)ators )se# $n t+$s ro

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HEC 3521 Process Heat Transfer For cooer 4a/ 9 :e +a# seecte# t+e rec!ce# e// carton ater$a :+$c+ $s an)fact)re# fro t+e co4$nat$on of 8ar$o)s ater$as s)c+ as rec!ce# aer an# o)#e# )6 In or#er to )se t+e e// tra!s as $ns)ator ater$as9 t+e! are cr)e# ) an# o)#e# $nto t+e re=)$re# s+ae6 T+$s rocess creates ots of a$r oc7ets $n t+e o)#e# e// )6 A$r $tsef $s area#! a /oo# $ns)ator so :e #ec$#e# t+at an! ro#)ct t+at $s caa4e of tra$n/ a$r :o)# a7e a /oo# $ns)ator6

For cooer 4a/ C9 :e +a# #ec$#e# to /o :$t+ f$4er/ass as t+e $ns)at$n/ ater$a6 T+e f$4er/ass $s a t!e of f$4re re$nforce# ast$c create# fro $$ons of rea! t$n! f$4res t+at are :o8en $nto a fa4r$c %H$//$ns Ins)at$on 2,15(6 As an $ns)ator9 t+e f$4er/ass so:s t+e srea# of +eat an# co# 4! tra$n/ t+o)san#s of $tte oc7ets of a$r 4et:een t+ese f$4res %Gro$c7o & S+ear# n6#6(6 T+e f$4re/ass $s aso not a4sor4ent6 T+$s eans $t :$ not a4sor4 an# reta$n :arer :ater 8ao)r %o$st)re( fro t+e s)rro)n#$n/ a$r :+en e;ose# to +)$#$t! $n t+e a$r6 In a##$t$on9 t+e f$4er/ass $s aso nonco4)st$4e an# e;tree! #)ra4e %O:ens Corn$n/ n6#6(6


12

HEC 3521 Process Heat Transfer !.&

'esign Considerations

.+en #es$/n$n/ an $ns)ate# cooer 4a/ to ao: )sers to en
! +a8$n/ a t+$c7er $ns)ator of t+e cooer 4a/ eans t+at ore +eat $s 4e$n/ trae# $n t+e 4a/6 T+$s $s 4eca)se t+e a!ers of $ns)ator :$ act as a 4arr$er or a res$stance for +eat to escae6 T+e t+$c7er $t $s9 t+e +ar#er $t :$ 4e for +eat to 4e escae# to t+e cooer s)rro)n#$n/s6 T+)s9 t+e so:er $t $s for +eat to ass t+ro)/+6 A c!$n#r$ca s+ae cooer 4a/ co)# aso re8ent +eat ost as +eat co)# on! 4e #$ss$ate# $n one#$ens$on on!6

In or#er to effect$8e! re#)ce +eat fo:s 4e$n/ #$ss$ate# 4! con#)ct$on9 an $ns)ator a#e of a 8er! sa ao)nt of so$# ater$a or of #$scont$n)o)s f$4res $s re=)$re# so t+at +eat co)# 4e trae# %na)f Ins)at$on 2,1-(6 ase# on .oo#for# %2,15(9 4! ao:$n/ an a$r /a 4et:een t+e can an# t+e $nner a!er of t+e cooer 4a/ co)# +e $n$$s$n/ +eat ost as con8ect$on +eat fo: osses ess +eat coare# to con#)ct$on6

Accor#$n/ to )rt)s %2,1&(9 4etter $ns)ators are nora! t+ose ater$as t+at are ess #ense as ess #ense ater$as are oose! ac7e#6 T+ese oose! ac7e# atos +es $n $n$$s$n/ t+e rate of transfer of ener/! as t+e ato #oes not transfer ener/! as effect$8e as a #enser ater$a6 A #ense ater$a $ncreases t+e rate of +eat ener/! 4e$n/ transfer #)e to t+e atos t+at are cose! ac7e# to/et+er $n t+e ater$a co)# en+ance t+e t+e +eat transfer fro a ater$a to t+e ot+ers6 T+e coon $ns)ators t+at are )se# are ater$as s)c+ as f$4er /ass9 :oo9 cotton9 stra:9 aer9 o!st!rene foa9 o!ester as :e as ce)ose are t+e e;aes of /oo# $ns)ator %T+era;; *ac7ets 2,11(6


13


.+en cons$#er$n/ t+e t!e of ater$as )se#9 one s+o)# aso ta7e $nto acco)nt of t+e r$ce an# t+e so)rce of t+ese ater$as6 Genera!9 c+eaer ater$as :+$c+ +a8e /reater erforance :$ 4e s)$ta4e as t+$s co)# re#)ce t+e coerc$a r$ce of t+e cooer 4a/ $tsef6 It $s aso an a#8anta/e $f t+e ater$as are eas$! so)rce# so t+at t+e! cae $n a4)n#ance an# :$ not 4e cost!6

In a##$t$on9 $t $s aso cr)c$a to #es$/n t+e cooer 4a/ $n s)c+ a :a! t+at $t $s $/+t :e$/+te# an# orta4e to ena4e )sers to carr! aro)n# t+e cooer 4a/ eas$!6 Hence9 ater$as t+at are $/+t are refera4e6 T+e s$e of t+e cooer 4a/ s+o)# 4e cons$#ere# as to ena4e )sers to carr! $t :+ere8er t+e! :ant6 For e;ae9 t+e s$e of t+e T)er:are :ater 4otte +o#er :$ 4e a s)$ta4e s$e as $t :$ not 4e too 4)7! to 4r$n/ aro)n# an# +as stras t+at co)# 4e eas$! +an#e for 7$#s too6

In or#er to en+ance t+e ar7eta4$$t! of t+e cooer 4a/9 an attract$8e aearance s+o)# 4e resente# too6 At+o)/+ t+e f)nct$on an# =)a$t! of t+e cooer 4a/ $s t+e f$rst t+$n/ c)stoers cons$#ere#9 t+e aearance :$ aso affect t+e$r #ec$s$ons as eoe no:a#a!s refer soet+$n/ t+at are st!$s+ an# rett!6


1&

HEC 3521 Process Heat Transfer !.(

A$$roac

T+ese cooer 4a/s are a$e# at re8ent$n/ an# re#)c$n/ t+e transfer of +eat ener/! fro t+e s)rro)n#$n/ to t+e :a of canne# #r$n7s :+ere t+e #r$n7s are a4e to 4e 7et co# as on/ as oss$4e6 Goo# $ns)at$on of ater$as :as c+osen to 4e a$e# to t+$s ro
T+e cooer 4a/s :ere a$n! a#e fro f$4er/ass9 e// carton ater$a an# r)44er foa at6 as$ca!9 cross st$tc+$n/ +as 4een )se# to f$r t+e a!ers of cooers 4a/s6 La!ers an# a!ers of st$tc+$n/ are )se# to sec)re t+e a!ers to re8ent t+e ater$as fro searat$n/ $nto $eces6 R)44er foa at an# e// carton ater$a +a8e a$r sace str)ct)re :+$c+ ao: a$r to store +eat ener/!6 T+$s ena4es t+e ater$a to act as a /oo# $ns)ator to re#)ce +eat transfer 4et:een t+e canne# #r$n7 an# t+e s)rro)n#$n/6 Moreo8er9 f$4er/ass +as aso $$ons of t$n! a$r oc7ets as f$4er/ass $s ract$ca! fore# fro $$ons of t$n! f$4res :+$c+ are a4e to re#)ce srea#$n/ of +eat ener/! fro t+e canne# #r$n7 to t+e s)rro)n#$n/6

T+ese cooer 4a/s :ere a$n! #es$/ne# :$t+ resect to t+ree asects :+$c+ are t+$c7 a!ers of $ns)ators9 $/+t :e$/+t of $ns)ators9 an# ess )sa/e of so$# ater$as6 T+$c7 a!ers of $ns)ators are )se# to re8ent t+e esca$n/ of +eat ener/! to t+e s)rro)n#$n/6 L$/+t :e$/+t of $ns)ators $s a4e to $ncrease t+e a4$$t! to store t+e +eat ener/! as $t +as oose ac7e# atos t+at re#)ce# t+e rate of +eat transfer6 As coare# to cose! ac7e# atos9 +eat ener/! :$ 4e transferre# aon/ t+e atos $n a fast see# as #$stance 4et:een t+e atos $s s+orter6


15

HEC 3521 Process Heat Transfer !.)

'esign Conclusions

T+e t+$c7ness of t+e cooer 4a/s are 2 c6 T+e cooer 4a/s :ere a a#e :$t+ t+$c7 $ns)ate# :as to ens)re t+at t+e s)rro)n#$n/ +eat $s )na4e not enter t+e $ns$#e of t+e cooer 4a/s eas$!6 T+e t+$c7er t+e :as of t+e 4a/s9 t+e on/er t+e t$e for t+e cans $ns$#e t+e 4a/ to reac+ t+era e=)$$4r$) :$t+ t+e en8$ronent6 Hence9 t+e ore eff$c$ent t+e f)nct$on of t+e cooer 4a/s are6

T+e t!es of ater$a )se# to asse4e t+e t+ree cooer 4a/s :ere r)44er foa at9 a)$n$) c)4oar# s+eet an# e// tra!s6 T+ese ater$as :ere c+osen to 4e t+e ater$a )se# for ro#)ct$on :as #)e to t+e ater$asB a4$$t! to re8ent +eat fro #$ss$at$n/ $nto t+e6 Hence9 cooer 4a/s a#e fro r)44er foa at9 a)$n$) c)4oar# s+eet an# e// tra!s are /oo# ater$as )se# to $ns)ate t+e can #r$n7s6

T+e #es$/n of t+e cooer 4a/s :ere #es$/ne# to 4e $n t+e s+ae of ar/e :ater 4ottes6 T+e $ns$#e of t+e cooer 4a/s :ere s+ae# to 4e c!$n#er fors so t+at t+e can #r$n7s can 4e ace# $ns$#e t+e 4a/s eas$! :$t+o)t 4e$n/ )nsta4e6 T+e c!$n#r$ca s+ae of t+e $ns$#e of t+e 4a/s aso ao:s t+e )ser to reo8e t+e can #r$n7s eas$!6 Hence9 t+e #es$/nate# cooer 4a/s :as rea! con8en$ent to )se6

T+e )rose of a##$n/ t+e +an#es to t+e cooer 4a/s :as for orta4$$t!6 .$t+o)t t+e +an#es9 $s #$ff$c)t to carr! t+e t+ree cooer 4a/s at once9 :$t+ t+e a##$t$on of t+e +an#es9 t+e )ser can carr! t+ree 4a/s at once an# $s a con8en$ence for transortat$on )roses6

T+e ater$as %r)44er foa at9 a)$n$) c)4oar# s+eet an# e// tra!s( :as not on! c+osen for t+e )rose of $ts a4$$t! $n ters of $ns)at$on 4)t aso 4eca)se of t+e fact t+at t+e ater$as are eas$! store#6 T+ese ater$as can 4e store# $n conta$ners or t+e or$/$na ast$c 4a/s $f t+e )ser +a8e not coete! f$n$s+ t+e cooer 4a/s $n one #a!6 T+)s9 t+e ater$as can 4e store# eas$! an# can 4e )se# a/a$n for t+e ne;t #a! to cont$n)e t+e ro#)ct$on of t+e 4a/s6 T+e ater$as are aso en8$ronenta! fr$en#!6 An! 4ro7en $eces of Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

1-

HEC 3521 Process Heat Transfer t+ese ater$as :+$c+ :ere acc$#enta! eft on t+e foor %$n#oor or o)t#oor( :$ not +ar t+e en8$ronent6 T+e ater$as are aso eas$! so)rce#6 T+e! can 4e fo)n# an!:+ere $n t+e ar7et at affor#a4e r$ces6


1'


(.0

Ex$eriment Procedure .e teste# t+e 3 cooer 4a/s to #eter$ne :+$c+ cooer 4a/ co)# 7ee t+e :ater $n t+e

canne# #r$n7 co# for t+e on/est ao)nt of t$e6 T+e ater$as re=)$re# an# t+e test$n/ roce#)res are as foo:s6

%aterials *e#uired

16 & et! so#a cans 26 Co# :ater 36 T+eroco)es &6 T+eroeters 56 Sto:atc+ -6 3 cooer 4a/s '6 Lato

Procedures

16 T+e Teerat)re Data Lo//er soft:are %Eas!Lo/ US( :as #o:noa#e# $nto t+e co)ter6 26 Eac+ t+eroco)e :as :$re# ) an# )//e# $nto t+e co)ter to set ) an# start t+e Data Lo//er6 T+e #ata o//er :as set to recor# t+e teerat)re $n $nter8as of 2 $n)tes6 36 T+e t+eroco)es :as t+en caref)! a4ee# 4ase# on t+e$r resect$8e aceent ocat$ons :+$c+ :as t+e $nner s)rface :+$c+ :as $n contact :$t+ t+e so#a can9 t+e o)ter s)rface :+$c+ :as e;ose# to t+e a4$ent of t+e cooer 4a/ an# $ns$#e t+e :ater $n t+e so#a can6 &6 Fo)r et! so#a cans t+at :as area#! :as+e# an# ceane# :as f$e# :$t+ aro;$ate! 33,  of co# :ater :$t+ teerat)re aro)n# 5  -C6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

10

HEC 3521 Process Heat Transfer 36 T+e o)ter :as of t+e 3 of t+e so#a cans :ere :$e# #r! an# $nserte# $nto t+e 3 cooer 4a/s6 &6 T+e fo)rt+ can :as eft o)ts$#e an# :o)# ser8e as a contro6 56 T+e t+eroco)es :ere ace# $nto t+e $nner s)rface an# o)ter s)rface as :e as $ns$#e t+e :ater $n t+e so#a can of t+e cooer 4a/s6 -6 T+e cooer 4a/s :ere cose# an# seae# t$/+t! an# strae# on )s$n/ t+e n!on stra6 '6 A t+eroeter :as $nserte# $nto Cooer a/ C :+$c+ +as f$4er/ass as t+e $ns)ator an# t+e contro so#a can #)e to t+e $ns)ff$c$ent ao)nt of t+eroco)es6 06 T+e teerat)re of t+e :ater $n Cooer a/ C an# contro can :as ta7en an)a! e8er! 1, $n)tes6 6 A t+e res)ts :ere #o:noa#e# fro t+e Data Lo//er an# sa8e# $nto t+e co)ter6 Res)ts o4ta$ne# an)a! fro t+e t+eroeter rea#$n/s :ere aso recor#e# on t+e #ata ta4e reare#6 1,6 T+e /ra+ of teerat)re 8ers)s t$e for a fo)r so#a cans :ere otte#6 Teerat)res of a fo)r so#a cans :ere /ra+e# on one set of a;es an# :ere s+o:n )s$n/ #$fferent $nes9 #as+es an# s!4os to #$st$nct! reresent eac+ so#a can6


1


).0

*esults

).1

Calculations

1-6 %a( E;ress t+e #$fferent$a e=)at$on an# t+e 4o)n#ar! con#$t$ons for stea#! one #$ens$ona +eat con#)ct$on t+ro)/+ t+e cooer 4a/" Assumptions:

16 Stea#!state 26 One #$ens$ona +eat con#)ct$on 36 Heat oss fro t+e to an# 4otto :a $s ne/$/$4e &6 L$=)$# an# roo teerat)res $s ass)e# to 4e t,s

Te eat e#uation for cylindrical coordinates 1 ∂

r ∂r

(

kr

)

(r , ϕ , z ) can be ex$ressed as+

( ) ( )

∂ T 1 ∂ ∂ T ∂ ∂ T ∂ T + 2 + + q´ = ρ c p k k ∂r ∂ϕ ∂z ∂z ∂t r ∂ϕ

According to te assum$tions taken above, te eat transfer tus terefore becomes+

(

∂ T 1 ∂ kr r ∂r ∂r

(

)=

0

)

∂ ∂ T =0 kr ∂r ∂r

-oundary conditions are+

T ( r 1 ) = T s , 1 T ( r 2 ) = T s , 2

%4( O4ta$n a reat$on for t+e 8ar$at$on of teerat)re $n t+e cooer 4a/ 4! so8$n/ t+e #$fferent$a e=)at$on" ntegrating te differential e#uation of te eat transfer e#uation+


2,


r

∂ T = C 1 ∂r

∂T C 1 = ∂r r ntegrating to second order+

T ( r )= C 1 ln r + C 2

Substitute te boundary conditions+

T s , 1=C 1 ln r 1+ C 2

%1(



T s , 2=C 1 ln r 2+ C 2

%2(



E#uation /1 minus /!+

T s , 1−T s , 2=C 1 ln

C 1 =

r1 r2

T s , 1 −T s ,2 ln

r 1 r2

Substitute

T s , 2=

C 1

T s , 1−T s , 2 r 1 ln r2

C 2 =T s , 2−

Substitute

into e#uation /!+ ln r 2 + C 2

T s , 1−T s , 2 r 1 ln r2

C 1

ln r 2

and

C 2 into te original e#uation to obtain te tem$erature

distribution e#uation+ Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

21


T ( r )=

T s , 1 −T s , 2

( r )=

∴ T

r 1 ln r2

ln r + T s , 2−

T s , 1−T s , 2 ln

r 1 r2

ln

T s , 1−T s , 2 r 1 ln r2

ln r 2

r + T s , 2 r2

C2E* -A3 A+ *4--E* 5A% %AT

Ts92

Ts91

Ts93

Aluminiu m cardboar d sheet

Foa m

r1

TJ

r2

r3

F$/)re 1" Coos$te :a 8$e: of Cooer a/ A

-ased on te general e#uation+

T ( r )= C 1 ln r + C 2 ∂T C 1 = ∂r r


22

HEC 3521 Process Heat Transfer 5or tis case+

T 1 ( r )=C 1 ln r + C 2 T 2 ( r )=C 3 ln r + C 4

5rom ex$eriment+

T s , 1=12.97 ℃ , T s , 3 = 14.24 ℃ ,T ∞ =28.16 ℃ l = 245 mm =0.245 m r 1=35 mm =0.035 m r 2=53 mm =0.053 m r 3=55 mm =0.055 m k 1=1.39

W W ∧ k 2=235 m K m K

At te boundary conditions+ At constant surface temperature:

At

r 3=0.055 m , T 2 ( r )=T s , 3 =14.24 ℃

T 2 ( r )=C 3 ln r + C 4 14.24 ℃ =C 3 ln ( 0.055 m ) + C 4 14.24 ℃ =−2.9 C 3+ C 4 −−¿( 1 )

Boundary at k 1

d T 1 dr

|

r =r 2

r2 

=k

2

d T 2 dr

|

r =r 2


23


k 1

C 1 r2

=k 2

C 3 r2

1.39 C 1=235 C 3−−¿(2 )

T 1 ( r )=T 2 ( r ) C 1 ln r + C 2=C 3 ln r + C 4 C 1 ln 0.053 + C 2=C 3 ln0.053 + C 4

−2.94 C + C =−2.94 C + C −−¿( 3) 1

2

3

4

Constant surface temperature:

At

r 1=0.035 m ,T 1 ( r )=T s ,1=12.97 ℃

T 1 ( r )=C 1 ln r + C 2 12.97 ℃=C 1 ln ( 0.035 m ) + C 2 12.97 ℃=−3.35 C 1 + C 2−−¿( 4 )

nsert e#uations /1 6 /( in a matrix and by using %atlab to obtain te results for te unknowns. Te codes are attaced in te a$$endix.

[

0 1.39

0 0

−2.94 −3.35

1 1

−2.9 −235 2.94 0

1 0

][ ] [ ] C 1 C 2

−1 C 3 0

C 4

=

14.24 0 0 12.97

Te values of te unknowns obtained were

C 1 =3.10 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

2&


C 2 =23.34 C 3 =0.02

C 4=14.29

Te tem$erature distribution is obtained as

T 1 ( r )=3.10 ln r + 23.34 where 0.035  r  0.053 m T 2 ( r )= 0.02ln r + 14.29 where 0.053  r  0.055 m

C2E* -A3 -+ E33 T*A7 CA*T8

Ts91 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

Ts92

Ts93

TJ

25



Egg tray k1

r1

r2

r3

F$/)re 2" Coos$te :a 8$e: of Cooer a/ 

-ased on te general e#uation+

T ( r )= C 1 ln r + C 2 ∂T C 1 = ∂r r

5or tis case+

T 1 ( r )=C 1 ln r + C 2 T 2 ( r )=C 3 ln r + C 4

5rom ex$eriment+

T s , 1=12.74 ℃ ,T s , 3 = 14.81 ℃ , T ∞=28.16 ℃ l =245 mm =0.245 m r 1=35 mm =0.035 m r 2=53 mm =0.053 m Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

2-


r 3=55 mm =0.055 m k 1= 0.21

W W ∧ k 2=235 m K m K


At

r 3=0.055 m , T 2 ( r )=T s ,3 = 14.81 ℃

T 2 ( r )=C 3 ln r + C 4 14.81 ℃ =C 3 ln ( 0.055 m ) + C 4

14.81 ℃ =−2.9 C 3 + C 4−−¿( 1 )

Boundary at

k 1

k 1

d T 1 dr C 1 r2

|

r =r 2

=k 2

r2 

=k 2

d T 2 dr

|

r =r2

C 3 r2

0.21 C 1= 235 C 3−−¿( 2 )


−2.94 C + C =−2.94 C + C −−¿( 3) 1

2

3

4


At

r 1=0.035 m ,T 1 ( r )=T s , 1=12.74 ℃


2'


T 1 ( r )=C 1 ln r + C 2 12.74 ℃ =C 1 ln ( 0.035 m ) + C 2 12.74 ℃ =−3.35 C 1+ C 2−−¿( 4 )


[

0

0

0.21

0

−2.94 −3.35

−2.9 −235

1 0

1

2.94

−1

1

0

0

][ ] [ ] C 1 C 2 C 3 C 4

14.81

=

0 0

12.74


C 1 =5.0483 C 2 =29.6519 C 3 =0.0045 C 4=14.8231


T 1 ( r )=5.0483 ln r + 29.6519 where 0.035 r  0.053 m T 2 ( r )= 0.0045ln r + 14.8231 where 0.053 r  0.055 m

C2E* -A3 C+ 5-E*32ASS


20


TJ Ts93

Ts92

Ts91


Fibr e Glas

r1

r2

r3

F$/)re 3" Coos$te :a 8$e: of Cooer a/ C -ased on te general e#uation+

T ( r )= C 1 ln r + C 2 ∂T C 1 = ∂r r

5or tis case+

T 1 ( r )=C 1 ln r + C 2 T 2 ( r )=C 3 ln r + C 4

5rom ex$eriment+

T s , 1=10.85 ℃ , T s , 3= 14.41 ℃ , T ∞ =28.16 ℃ l =245 mm =0.245 m r 1=35 mm =0.035 m r 2=53 mm =0.053 m Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

2


r 3=55 mm =0.055 m k 1= 0.04

W W ∧k 2 =235 m K m K


At

r 3=0.055 m , T 2 ( r )=T s ,3 = 14.41 ℃

T 2 ( r )=C 3 ln r + C 4 14.41 ℃ =C 3 ln ( 0.055 m ) + C 4

14.41 ℃ =−2.9 C 3 + C 4−−¿( 1 )

Boundary at

k 1

k 1

d T 1 dr C 1 r2

|

r =r 2

=k 2

r2 

=k 2

d T 2 dr

|

r =r2

C 3 r2

0.04 C 1= 235 C 3 −−¿ ( 2)


−2.94 C 1 + C 2=−2.94 C 3 + C 4−−¿( 3)


At

r 1=0.035 m ,T 1 ( r )=T s , 1=10.85 ℃


3,


T 1 ( r )=C 1 ln r + C 2 10.85 ℃ =C 1 ln ( 0.035 m ) + C 2 10.85 ℃ =−3.35 C 1 + C 2−−¿( 4 )


[

−2.9 1 0 0 0.04 0 −235 0 −2.94 1 2.94 −1 −3.35 1 0 0

][ ] [ ] C 1 C 2 C 3 C 4

=

14.41 0 0 10.85


C 1 =8.6828 C 2 =39.9373 C 3 =0.0015 C 4=14.4143


T 1 ( r )= 8.6828ln r + 39.9373 where 0.035  r  0.053 m T 2 ( r )= 0.0015 ln r + 14.4143 where 0.053  r  0.055 m

%c(

Pot t+e teerat)re #$str$4)t$on aon/ t+e cooer 4a/ t+$c7ness"

Cooler -ag A Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

31


1 "#$%  30.'($ ) 1.(( *+  0.'(

14 12 10 !

,inear #%  4 2 0 0

0.01

0.02

0.03

0.04

0.05

0.0

Gra+ 1" Teerat)re #$str$4)t$on aon/ t+$c7ness Cooer a/ A6

Cooler -ag 1 "#$% & 30.'($ ) 1.(( *+ & 0.'(

14 12 10 !

,inear #%  4 2 0 0

0.01

0.02

0.03

0.04

0.05

0.0

Gra+ 2" Teerat)re #$str$4)t$on aon/ t+$c7ness Cooer a/ 6

Cooler -ag C Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

32


1 "#$%  30.'($ ) 1.(( *+  0.'(

14 12 10 !

,inear #%  4 2 0 0

0.01

0.02

0.03

0.04

0.05

0.0

Gra+ 3" Teerat)re #$str$4)t$on aon/ t+$c7ness Cooer a/ C6

%#( E8a)ate t+e rate of +eat transfer fro t+e so#a #r$n7s t+ro)/+ t+e t+ree %3( $ns)ate# cooer 4a/s t+at !o) #es$/n" C2E* -A3 A+ *4--E* 5A% %AT

r 3 ,T s , 3

-oundary at

−k

2

−k 2

d T 2 dr

C 3 r3

−235

|

=h ( T s , −T ❑) 3

r =r 3

= h (T s , 3−T ❑)

0.02 =h ( 14.24−28.16 ) 0.055

h =6.14

W 2

m K

5ormulae for eat transfer rate+


33


q=

∆ T R tot ln

r2

R cond =

r1 2 !lk

R con" =

1 h ( 2 !rl )

5rom

r 1 to r 2 +

0.053 ln 0.035 K R 1= =0.19 W 2 ! ( 0.245 )( 1.39 )

5rom

r 2 to r 3 +

0.055 ln K 0.053 =0.0001 R 2= W 2 ! ( 0.245 )( 235 )

5rom

R 3=

r3

by convection+

1 K =1.92 W 6.14 ( 2 ! ) ( 0.055 )( 0.245)

Terefore, rate of eat transfer+

q=

T s , 1−T s , 3 R tot

− = 12.97 ℃ 14.24 ℃ =−0.60 W ( 0.19 + 0.0001 +1.92 )

C2E* -A3 -+ E33 CA*T8 %ATE*A2 -oundary at

r 3 ,T s , 3


3&


−k

2

−k 2

d T 2 dr

C 3 r3

−235

|

=h ( T s , −T ❑) 3

r =r 3

= h (T s , 3−T ❑)

0.0045 =h (14.81 −28.16 ) 0.055

h =1.44

W 2

m K


q=

∆ T R tot ln

R cond =

R con" =

5rom

r2 r1

2 !lk

1 h ( 2 !rl )

r 1 to r 2 +

0.053 ln 0.035 =0.19 K R 1= W 2 ! ( 0.245 )( 1.39 )

5rom

r 2 to r 3 +

0.055 ln 0.053 K =0.0001 R 2= W 2 ! ( 0.245 )( 235 )

5rom

r3

by convection+


35


R 3=

K 1 =8.20 W 1.44 ( 2 ! ) ( 0.055 )( 0.245)


q=

T s , 1−T s , 3 R tot

℃− 14.81 ℃ = 12.74 =−0.25 W ( 0.19 + 0.0001 + 8.20)

C2E* -A3 C+ 5-E*32ASS

r 3 ,T s , 3

-oundary at

−k 2

−k 2

d T 2 dr C 3 r3

−235

|

r=r3

=h ( T s , 3 −T ❑)

= h (T s , 3−T ❑)

0.0015 =h (14.41 −28.16 ) 0.055

h =0.47

W 2

m K


q=

∆ T R tot ln

r2

R cond =

r1 2 !lk

R con" =

1 h ( 2 !rl )

5rom

r 1 to r 2 +


3-

HEC 3521 Process Heat Transfer 0.053 ln 0.035 K R 1= =0.19 W 2 ! ( 0.245 )( 1.39 )

5rom

r 2 to r 3 +

0.055 ln 0.053 K =0.0001 R 2= W 2 ! ( 0.245 )( 235 )

5rom

R 3=

r3

by convection+

K 1 =25.13 W 0.47 ( 2 ! ) ( 0.055 )( 0.245)


q=

1'6

T s , 1−T s , 3 R tot

=

10.85 ℃ −14.41 ℃ =−0.14 W (0.19 + 0.0001+ 25.13)

ase# on t+e e;er$enta res)ts ac=)$re# an# a7e !o)r ass)t$ons9 #eter$ne t+e

con8ect$on +eat transfer coeff$c$ent fro e;ter$or :a of so#a canne# #r$n7s to t+e a4$ent6 Rear7" T+e cac)at$ons of t+e + 8a)e are s+o:n $n =1- %#(6

Cooler -ag A+ *ubber 5oam %at

h =6.14

W 2

m K

Cooler -ag -+ Egg Carton %aterial

h =1.44

W 2

m K


3'


Cooler -ag C+ 5iberglass

h =0.47

106

W 2

m K

T+e so#a canne# #r$n7s $s ass)e $n$t$a! at a )n$for teerat)re of TC %t+e

teerat)re t+at !o) eas)re at t,s(6 T+e so#a can $s ace# $n a roo at TJC %t+e roo teerat)re t+at !o) eas)re#(6 If t+e +eat transfer coeff$c$ent fro t+e so#a can to a4$ent $s + .?2KC %f$n# fro =)est$on 1'(9 #eter$ne +o: on/ $t :$ ta7e for t+e a8era/e teerat)re of t+e #r$n7 to r$se to 12C6 Ans"

dT dt

s#nce −q o$t = ρ c p

t

∫ dt = 0

t =

− ρ% c p 12 ℃ q o$t

− ρ% c p q o$t

∫ dT T #

( 12 ℃ −T # )

3 .ater at a8era/e teerat)re of 10 ℃ an# 0.000325 m 6

ρ= 999.8

k& m

, c p= 4192 3

' k& K

For cooler bag A, Foam:

−999.8 k&3 (0.000325 m 3 ) t =

m

−0.60 W


(

4192

' k& K

)(

12 ℃ −7 ℃ )=11351 s =189 m#n

30


For cooler bag B, Egg Carton Material:

−999.8 t =

k& m

(0.000325 m3 )

3

(

4192

' k& K

)(

12 ℃ −5 ℃ )=38139 s =635 m#n

' k& K

)(

12 ℃ −6.5 ℃ ) =53512 s =891 m#n

−0.25 W

For cooler bag C, Fiberglass:

−999.8 t =

16

k& m

(0.000325 m3 )

3

−0.14 W

(

4192

Deter$ne t+e difference e#uations at t+e s)rface of a so#a canne# #r$n7s %ass)e

a;$s!etr$c c!$n#r$ca /eoetr!(9 aon/ t+e $ns)at$on t+$c7ness an# at t+e $ns)ate# s)rface :$t+ con8ect$8e 4o)n#ar! con#$t$on6 Ass)e )n$for so#a %$=)$#( teerat)re an# stea#!state con#$t$ons6 S$nce Cooer 4a/ A9  an# C are of sae #$ens$ons9 t+e t+$c7ness of t+e :a of a t+ree of t+e cooer 4a/s $s t+e sae6 T+e on! #$fference $s t+e 8a)e of t+era con#)ct$8$t!9 7 of eac+ ater$a %foa9 f$4re/ass an# e// tra!s(6 T+e tota t+$c7ness of t+e :a of t+e cooer 4a/  2,  ,6,2 Ass)e t+at t+e #$stance 4et:een eac+ no#es $s ,6,,59 r  ,6,,5 T+erefore t+ere are a tota of 5 no#es9 $ Tota  56

r #= 1=r 1=35.0 mm =0.035 m

-y alying energy balance e/uation E

r #= 2= 44.0 mm=0.044 m

in

) Eout  Egen  E

st

Ein 0

r #= 3=r 2 = 53.0 mm=0.053 m


3


r #=4 =54.0 mm=0.054 m r #= 5=r 3 = 55.0 mm=0.055 m

i1 i  21

i  2)1!

i  1'

Ts92

Ts91

r 1

r Mater$a )se#

i  20

TJ

Ts93

r 2

r 3 A)$n$) car#4oar# s+eet9 7D

F$/)re " Coos$te :a 8$e: of Cooer a/ :$t+ aternat$8e ater$as Cooler bag A95oam

7 A  163.? 7 D  7 A)$n$)  235 .? T∞ Tcontro for o)ter :a  2061&oC +  -61& .? 2

´ ¿ =0 At # = 2 ¿ 18 , ( q1 + q 2!1= 0 ∆ r T #− 1−T # ∆ r T # +1 − T # ( )+ k A 2 !L r #+ ( )= 0 ∆r ∆r 2 2

( )

k A 2 !L r #−


( )

&,


∆ r T #−1−T # ∆ r T #+1− T # ( )+ r #+ ( )= 0 ∆r ∆r 2 2

( ) r #−

( (

r# ∆r

( )

) (

− 1 T #−1− 2

T #−1 +

2∆r

( ) [( T =−

∆r

T # =

[(

∆r

) (

2 r # −∆ r

−2 r #

r#

2 r #−∆ r 2∆r

2

r# ∆r

) (

∆r 2

) (

2∆r

+ 1 T #+1− 2

−2 r # + ∆ r −2 r #−∆ r 2∆r

2 r #− ∆ r 2∆r

#

) (

− 1 T # +

) ( ( ) T #−1+

) ( T #− 1+

2 r# + ∆ r 2∆r

T #+

2 r# + ∆ r 2∆r

r#

)

+ 1 T #=0

2 r #+ ∆ r

)

T # +1=0

) ] T # +1

) ] T #+ 1

2 r#

∆r

r#− T # =

∆r 2

2r#

r #+ T # −1 +

∆ r 2

2 r#

T #+ 1

´ ¿ =0 At # = 19! ( q 2!1 + q2!2= 0

( )(

k A 2 !L r #−

∆r 2

T #− 1−T # ∆r

)

( )(

+ k ) 2 !L r # +

T #+1− T # ∆r

)=

0

( )(

T #−1−T # ) + k ) r # +

( )

( )

( )

( )

[ ( ) ( )]

( )

( )

k A r #−

k A r #−

∆r 2

( )(

∆r 2

∆r 2

T #+1−T # ) =0

∆r ∆r ∆r ∆r T #−1− k A r #− T # + k ) r #+ T #+1− k ) r # + T # =0 2 2 2 2

−k A r # −

∆r ∆r ∆r ∆r − k ) r # + T #=−k A r # − T #−1 −k ) r # + T #+1 2 2 2 2


&1


[ ( ) ( ) ] [ ( ) ( )]

− k A r # − T # =

∆r ∆r T #−1 + k ) r #+ T #+ 1 2 2

− k A r #−

∆r ∆r +k ) r # + 2 2

[ ] [ − ]+ [ + ] k A r #−

T # =

∆r

k A r #

2

∆r

k ) r #

2

[ ] [ − ]+ [ + ]

∆r

k ) r # +

T #−1 +

∆r

k A r #

2

2

∆r 2

k ) r #

∆r

T # +1

2

´ ¿ =0 At # = 20! ( q 2!2+ q3!1= 0

( )

k ) 2 !L r # −

∆r 2

(

T #−1−T # ∆r

( (

r# ∆r

2

T # +1− T #

(

∆r

)= 0

( )

) (

− 1 T #−1− 2

2 r # −∆ r 2∆r

∆r

[(

r# ∆r

) ( T #−1 +

( ) [( −2 r #

T # =

∆r

∆ r T #−1−T # ∆ r T #+1− T # ( )+ r #+ ( )= 0 ∆r ∆r 2 2

( ) r #−

( )

)+ k ) 2 !L r #+

T =− #

2 r #−∆ r 2∆r

) (

− 1 T # + 2

r# ∆r

) (

∆r 2

) (

2∆r

+ 1 T #+1− 2

−2 r # + ∆ r −2 r #−∆ r 2∆r

T #+

r#

)

+ 1 T #=0

2 r #+ ∆ r

)

T # +1=0

) ]

) (

2 r #− ∆ r 2 r# + ∆ r T #− 1+ T # +1 2∆r 2∆r

) ( ( ) T #−1+

2 r# + ∆ r 2∆r

) ] T #+ 1

2 r#

∆r


&2

HEC 3521 Process Heat Transfer ∆r

r#− T # =

r #+

2

T # −1 +

2r#

∆ r 2

2 r#

T #+ 1

´ ¿ =0 At # = 21! ( q3! 1+ qcon" =0

( )(

k ) 2 !L r # −

∆r 2

( )(

k ) r #−

k ) ∆r k ) ∆r

T #− 1−T # ∆r

∆r

T # −1 −T #

2

∆r

)

( )

+ h 2 !L r #+

) ( ) ( +h r# +

)

∆r 2

(

∆ r ( T ∞ −T # ) =0 2

T ∞−T # )=0

(

r #−

∆r ∆r T #− 1−T # ) + h r # + ( ( T ∞−T # )= 0 2 2

(

r #−

k ) ∆r ∆r ∆r ∆r T #− 1− r #− T # + h r # + T ∞−h r # + T # = 0 ∆r 2 2 2 2

)

( ) ( )

[ ( ) ( )] −k ) ∆r

− T # =

r #−

∆r ∆r −h r #+ 2 2

T # =

−k ) ∆r

( )

( ) r #−

( )

∆r ∆ r T #− 1−h r #+ T ∞ 2 2

[ ( − ) + ( + ) ] −[ ( − )+ ( + )] k )

∆r

r#

∆r ∆r T #− 1 h r # T ∞ 2 2

k ) r ∆r #

∆r 2

h r#

[ ] [ − ]+ ( + ) k )

T # =

)

∆r

k ) r ∆r #

r#−

∆r 2

∆r 2

h r#


∆r 2

∆r 2

( ) [ − ]+ ( + ) h r #+

T # −1+

k ) r ∆r #

∆r 2

∆r 2

∆ r h r# 2

T ∞

&3

HEC 3521 Process Heat Transfer Cooler bag -9Egg tray

7   ,621.? 7 D  7 A)$n$)  235 .? T∞ Tcontro for o)ter :a  2061&oC +  16&& .? 2

´ ¿ =0 At # = 2 ¿ 18! ( ∆ r T #− 1−T # ∆ r T # +1−T # ( )+ k * 2 !L r # + ( )=0 2 2 ∆r ∆r

( )

k * 2 !L r #−

T # =

( )

∆r ∆r r #+ 2 2 T # −1 + T #+ 1 2r# 2 r#

r#−

´ ¿ =0 At # = 19! (

( )(

k * 2 !L r #−

∆r 2

T #− 1−T # ∆r

[ ] [ − ]+ [ + ] k * r #−

T # =

)

k * r #

∆r

∆r 2

k ) r #

2

( )(

+ k ) 2 !L r # +

∆r 2

∆r 2

T # +1−T # ∆r

0

[ ] [ − ]+ [ + ] k ) r # +

T #−1 +

)=

∆r

k * r #

2

∆r 2

k ) r #

∆r

T # +1

2

´ ¿ =0 At # = 20! (

( )

k ) 2 !L r # −

r#− T # =

∆r 2

(

T #−1−T #

∆r 2

2r#

∆r r #+

T # −1 +

( )

)+ k ) 2 !L r #+

∆r 2

(

T # +1− T # ∆r

)= 0

∆ r 2

2 r#


T #+ 1

&&


´ ¿ =0 At # = 21! (

( )(

k ) 2 !L r # −

∆r 2

∆r

)

∆r

k ) r ∆r #

r#−

∆r 2

∆r 2

h r#

( )

+ h 2 !L r #+

[ ] [ − ]+ ( + ) k )

T # =

T #− 1−T #

∆r 2

∆ r ( T ∞ −T # ) =0 2

( ) [ − ]+ ( + ) h r #+

T # −1+

k ) r ∆r #

∆r 2

∆r 2

∆ r h r# 2

T ∞

Cooler bag C95iberglass

7 C  ,6,&.? 7 D  7 A)$n$)  235 .? T∞ Tcontro for o)ter :a  2061&oC +  ,6&' .? 2

At # = 2 ¿ 18! ´ (¿ =0

( )

k C 2 !L r #−

r#− T # =

∆r 2

(

T #−1−T # ∆r

∆r 2

2r#

r #+ T # −1 +

( )

)+ k C 2 !L r #+

∆r 2

(

T # +1−T # ∆r

)=0

∆ r 2

2 r#

T #+ 1

´ ¿ =0 At # = 19! (

( )(

k C 2 !L r #−

∆r 2

T #−1 −T # ∆r


)

( )(

+ k ) 2 !L r # + ∆ r 2

T # +1− T # ∆r

)=

0

&5


[ ] [ − ]+ [ + ] k C r # −

T # =

∆r

k C r #

∆r 2

k ) r #

2

∆r

[ ] [ − ]+ [ + ] k ) r #+

T # −1+

∆r

k C r #

2

∆r 2

∆r

k ) r #

2

T #+1

2

´ ¿ =0 At # = 20! (

( )

k ) 2 !L r # −

T # =

∆r 2

(

T #−1−T # ∆r

( )

)+ k ) 2 !L r #+

∆r 2

(

T # +1− T # ∆r

)= 0

∆r ∆r r #+ 2 2 T # −1 + T #+ 1 2r# 2 r#

r#−

´ ¿ =0 At # = 21! (

( )(

k ) 2 !L r # −

∆r 2

2,6

∆r

)

∆r

k ) r ∆r #

r#

∆r 2

∆r 2

h r#

( )

+ h 2 !L r #+

[ − ] [ − ]+ ( + ) k )

T # =

T #− 1−T #

∆r 2

∆ r ( T ∞ −T # ) =0 2

( ) [ − ]+ ( + ) h r #+

T # −1+

k ) r ∆r #

∆r 2

∆r 2

∆ r h r# 2

T ∞

So8e t+e e=)at$ons $n =)est$on 1 an# #eter$ne t+e teerat)res aon/ t+e cooer

4a/ t+$c7ness 4! )s$n/ MATLA9 Mat+eat$ca or MS E;ce6 Cooer a/ A MatLa4 Co#e


&-


Gra+


&'


Teerat)re #$str$4)t$on fro f$rst to ast no#e

Cooer a/  MatLa4 Co#e


&0



&

HEC 3521 Process Heat Transfer Gra+

Teerat)re #$str$4)t$on fro f$rst no#e to ast no#e"

Cooer a/ C


5,

HEC 3521 Process Heat Transfer MatLa4 Co#e

Gra+ Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

51


Teerat)re D$str$4)t$on fro f$rst no#e to ast no#e"


52

HEC 3521 Process Heat Transfer ).!

3ra$s

Inner Wall Temperature 25.00

20.00

15.00 Fiberglass emerature#o%

Egg rays

Foam

10.00

5.00

) 4211 !24 4211 '3 4211 104! 4211 1200 4211 1312

ime

Gra+ &" Gra+ of t+e $nner :a teerat)res of t+e 3 cooer 4a/s6


53


Outer Wall Temperature 35.00

30.00

25.00

20.00 Foam emerature #o%

Fiberglass

Egg rays

15.00

10.00

5.00

) 4211 !24

4211 '3 4211 104! 4211 1200 4211 1312

ime

Gra+ 5" Gra+ of t+e o)ter :a teerat)res of t+e 3 cooer 4a/s6


5&


Water Temperature 20.00 1!.00 1.00 14.00 12.00 10.00 !.00

Foam Egg rays emerature #o% .00

Fiberglass

4.00 2.00 )

ime

Gra+ -" Gra+ of t+e :ater teerat)res of t+e 3 cooer 4a/s6


55


:.0

Engineering 'rawings


5-



5'



50


;.0

Answers to Problems

16

.+at t+ree t+$n/s #o !o) t+$n7 +eat #een#s on

T+era ener/! Heat $s #escr$4e# as t+era ener/! $n trans$t6 T+erefore9 t+ere co)# on! 4e +eat :+en t+e o4
Teerat)re Teerat)re refers to t+e ao)nt of t+era ener/! store# $n a atter6 Heat on! transfers fro t+e o4
Mater$a Mater$as t+at are cass$f$e# as /oo# con#)ctors s)c+ as etas $7e a)$n$) or $ron ao:s +eat to fo: t+ro)/+ t+e faster6 On t+e ot+er +an#9 $ns)ator ater$as s)c+ as :oo or St!rofoa con#)ct +eat 8er! so:!6 Rate of +eat con#)ct$on $n ater$as aso #een# on t+e ater$aBs t+$c7ness9 area an# t+era con#)ct$8$t!9 79 of t+e ater$a $tsef %T+e P+!s$cs Cassroo 2,13(6

26 Ho: #o !o) t+$n7 +eat an# teerat)re are reate# Do !o) t+$n7 teerat)re $s t+e sae t+$n/ as +eat Heat an# teerat)re are reate# as < = cm >T :+ere c $s t+e sec$f$c +eat an# m $s t+e ass6 Teerat)re an# +eat are #$fferent concets6 Heat $s t+e ener/! fore# fro t+e art$c)ar ot$on of t+e s)4stances6 Heat #een#s on t+ree factors :+$c+ are 8eoc$t! of t+e art$ces9 t+e n)4ers of s)4stances9 an# t+e t!e of s)4stances $n an o4
5

HEC 3521 Process Heat Transfer s)4stances6 Teerat)re #oes not #een# on an! factors :+$c+ $ste# as a4o8e6 %Ha4! *6 n6#6( %Na8e R6 n6#6(

36

Does atter st$ +a8e +eat ener/!9 e8en $n t+e co#est en8$ronent !o) can $a/$ne Accor#$n/ to %T+e TEA Pro
sa ao)nt of +eat ener/! :+$c+ $s ere! eas)ra4e t+at e;$sts as +eat ener/! $s sa$# to 4e resent $n a atter6

&6

Does an! of t+e ener/! of t+e s)n reac+ t+e eart+ 4! con#)ct$on or con8ect$on >es6 ot+ con#)ct$on an# con8ect$on rocess #oes transfer ener/! to t+e eart+6 In

or#er for a con#)ct$on rocess to occ)r9 a e#$) $s re=)$re#6 Ho:e8er9 not a e#$) :$ /$8es a /oo# con#)ct$on of +eat6 .oo# $s a 4a# e;ae of e#$) for con#)ct$on :+$e etas $7e a)$n$) are a /oo# e#$) for con#)ct$on rocess6 T+e e#$) for t+e s)n to trans$t t+e ener/! to eart+ $s t+e ne$/+4o)r$n/ oec)es $n t+e a$r6 A$r $s aso a oor con#)ctor of +eat6 Most of t+e con#)ct$on rocess occ)rs at t+e eart+Bs s)rface %Intro#)ct$on to t+e atos+ere 2,1-(6 On t+e ot+er +an#9 +eat ener/! $s transferre# t+ro)/+ con8ect$on 4! trans$tt$n/ stac7s of a$r oec)es $n f)$#s s)c+ as t+e atos+ere6 On t+e eart+Bs e=)ator $s :arer t+an t+e oes9 t+)s t+e a$r :$ 4e ess #ense an# e8ent)a! r$ses9 ca)s$n/ t+e #enser a$r at t+e oes to s$n76 Hence9 a con8ect$on rocess occ)rre# %Intro#)ct$on to t+e atos+ere 2,1-(6

56

Def$ne e$ss$8$t! an# a4sort$8$t!6 .+at $s $rc++offBs a: of ra#$at$on

E$ss$8$t! E$ss$8$t! refers to t+e ao)nt of t+era ra#$at$on e$tte# 4! t+e s)rface of a ater$a6 E$ss$8$t! $s #ef$ne# as t+e ener/! ra#$ate# fro t+e ater$aBs s)rface o8er t+e ra#$ant e;$tance fro a 4ac74o#! %a erfect e$tter( at s$$ar teerat)re9 :a8een/t+ an# 8$e:$n/ con#$t$ons %Nat$ona P+!s$ca La4orator! 2,1&(6 T+e e$ss$8$t! of a s)rface t!$ca! Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

-,

HEC 3521 Process Heat Transfer #een#s on t+e ater$a an# t+e nat)re of $ts s)rface6 T+erefore9 a eta :$t+ soot+ o$s+e# s)rface :o)# +a8e a o:er e$ss$8$t! as coare# to a ro)/+ene# an# o;$#$e# eta s)rface6 Not on! t+at9 t+e s)rface teerat)re an# :a8een/t+ as :e as an/e aso a! affect t+e e$ss$8$t! 8a)e of a s)rface %en/e9 C$4aa  T)rner 2,12  ',(6

A4sort$8$t! A4sort$8$t! refers to t+e fract$on of t+era $rra#$at$on a4sor4e# 4! t+e s)rface of a ater$a6 Un$7e e$ss$8$t!9 t+e a4sort$8$t! of a ater$a $s $n#een#ent of s)rface teerat)re6 Instea#9 t+e a4sort$8$t! #een#s on t+e teerat)re of t+e so)rce :+ere t+e $nc$#ent ra#$at$on $s or$/$nat$n/ fro6 A4sort$8$t! :o)# 4e +$/+er $n #) or ro)/+ s)rface as coare# to s+$n! s)rfaces %en/e9 C$4aa  T)rner 2,12  ',(6

$rc++offBs La: of Ra#$at$on $rc++offBs La: states t+at t+e a4sort$8$t! of an! ater$a +as to 4e e=)as to $ts e$ss$8$t! at e8er! :a8een/t+9 #$rect$on an# teerat)re $n t+ero#!na$c e=)$$4r$) #αλ  ελ%. It $$es t+at /oo# a4sor4ers are /oo# ra#$ators6 $rc++offBs a: aso #e#)ce# t+at t+e e$ss$8$t! cannot e;cee# one as rea 4o#$es ra#$ate ess effect$8e! t+an a 4ac7 4o#! :+$e at e=)$$4r$) %en/e9 C$4aa  T)rner 2,12  '2(6

-6 Can a t+ree o#es of +eat transfer occ)r s$)taneo)s! %$n arae( $n a e#$) Pract$ca!9 t+ree o#es of +eat transfers can 4e con#)cte# s$)taneo)s!6 Con#)ct$on an# con8ect$on can occ)r s$)taneo)s! as +ot f)$# $s transorte# to co# f)$# 8$a an $n8ert$n/ 4arr$er6 T+$s can 4e #$sc)sse# as t+e +eat $s rece$8e# fro t+e :a 8$a con8ect$on an# ra#$at$on9 an# t+en con#)ct$on $s carr$e# o)t to t+e ne;t :a s)rface9 t+en con8ect$on an# ra#$at$on $s con#)cte# a/a$n to reease t+e +eat fro t+e :a s)rface6 %ot+an#araan C6P6 2,,-(


-1

HEC 3521 Process Heat Transfer '6

Can a e#$) $n8o8e %a( con#)ct$on an# con8ect$on9 %4( con#)ct$on an# ra#$at$on9

or %c( con8ect$on an# ra#$at$on s$)taneo)s! G$8e e;aes for t+e !esQ ans:ers6 %a( No6 A e#$) cannot $n8o8e con#)ct$on an# con8ect$on s$)taneo)s!6

%4( >es6 Con#)ct$on an# ra#$at$on co)# occ)r s$)taneo)s! $n a se$transarent so$# e#$) 4)t not aon/ :$t+ con8ect$on or across an oa=)e so$# %en/e9 >9 C$4aa9 *  T)rner9 R 2,12(6 For e;ae9 t+e +ot s)rface on t+e ce$$n/6

%c( >es6 Con8ect$on an# ra#$at$on can occ)r s$)taneo)s! too6 T+$s $s 4eca)se +eat transfer ta7es ace :+en a so$# s)rface oses +eat or /a$ns +eat fro t+e s)rro)n#$n/ a4$ent %SOM9 S 2,,0(6 For e;ae9 t+e +)an 4o#! ra#$ates +eat to t+e s)rro)n#$n/6

06

.+at are t+e 4est a4sor4ers of t+era ra#$at$on .+at are t+e :orst e$tters of

t+era ra#$at$on est a4sor4ers of t+era ra#$at$on are s)c+ $7e att 4ac7 ater$as :+ereas s$8er 4ase# ater$as are terr$4e a4sor4ers of t+era ra#$at$on6 Mater$as :$t+ att 4ac7 s)rfaces ten#s to 4e t+e :orst e$tters :+$e ater$as :$t+ s+$n! an# s$8er! s)rfaces are 8er! /oo# e$tters of t+era ra#$at$on %Doe 2,,19 /6 1,-(6

6

L$st at east t+ree #$fferent ro#)cts9 #e8$ces or str)ct)res for :+$c+ en/$neers a$e#

t+e$r )n#erstan#$n/ of +eat transfer r$nc$es $n #es$/n$n/ s!stes or c+oos$n/ ater$as for t+e )rose of teerat)re re/)at$on6 Hoes can /et rat+er c+$! #)r$n/ :$nters $n an# +ot #)r$n/ s)ers6 T+erefore9 en/$neers +a# #e8eoe# f$4er/ass $ns)ators to act as a 4arr$er to +eat fo: an# $s essent$a to 7ee +oes :ar $n :$nters an# coo #)r$n/ s)ers6 F$4er/ass $s a4e to so: o8eent of +eat 4! tra$n/ t+o)san#s of $tte a$r oc7ets 4et:een $$ons of t$n! f$4res Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

-2

HEC 3521 Process Heat Transfer t+at $s :o8en $nto a fa4r$c es+ %Mos+er 2,13(6 F$4re/ass $ns)ators +a8e +$/+er R8a)es :+$c+ $s caa4e to for an a$r 4arr$er9 :+$c+ can e$$nate soe of t+e costs ar$s$n/ fro eectr$c$t! 4$s an# ot+er +oe o#$f$cat$ons %U6S6 Deartent of Ener/! n6#6(6 A$r con#$t$oners are one of t+e ost re8o)t$onar! teerat)re re/)at$on #e8$ces $n t+$s cent)r!6 A$r con#$t$oners can on! re/)ate a rooBs teerat)re :$t+ t+e +e of t+e e8aorator an# con#enser co$s $n t+e6 En/$neers +a# seecte# coer9 stee or a)$n$) to an)fact)re t+ese co$s 4eca)se t+ese etas con#)ct +eat eas$!6 As t+e cooant $n t+e a$r con#$t$oner fo:s9 t+e 4o:er fan #ra:s +ot roo a$r $n an# $s a4sor4e# 4! t+e cooant :+$c+ asses o8er t+e e8aorator co$6 T+e co$ carr$es t+at +eat o)t#oors9 an# reeases $t $nto t+e a$r o)t#oors $nstant! coo$n/ t+e roo %>o)ra$re;erts6co 2,15(6 T+e con#enser co$ #oes $ts art :+en t+e :ar refr$/erant /as reenters $nto t+e con#enser co$s6 T+e con#enser +as ent! of co$s t+at $ncrease t+e ao)nt of t$e t+e cooant $s $n t+e at+ of 4o:$n/ a$r9 /$8$n/ $t ent! of t$e to reease t+e +eat $t a4sor4e# fro t+e +oe 4efore cont$n)$n/ $ts c!ce 4ac7 to t+e e8aorator co$s %>o)ra$re;erts6co 2,15(6

Heat s$n7s are /enera! #es$/ne# to coo #o:n t+e +eat /enerate# 4! eectron$c or ec+an$ca #e8$ces6 Fan cooe# +eat s$n7s are coon! )se# $n co)ters to #$ss$ate +eat /enerate# 4! /ra+$c rocessors an# centra rocess$n/ )n$ts %Co)terHoe6co9 n6#(6 Heat ea8es t+e +eat s$n7 t+ro)/+ t+e f)$# $n ot$on to a$nta$n t+e teerat)res o: to rotect t+e coonents fro 4)rn$n/ or et$n/ %Aa8$# T+erao!9 n#(6 T+e fans aso ens)re a stea#! a$r fo: o8$n/ t+ro)/+ t+e f$ns6 T+ese +eat s$n7s are often a#e o)t of coer or a)$n$) #)e to $ts +$/+ t+era con#)ct$8$t! an# e;ceent +eat a4sort$on roert$es6

1,6

.+at ater$as a7e /oo# $ns)ators D$sc)ss t+e roert$es of t+e ater$a6 F$4er/ass fa4r$cs are /oo# $ns)ators6 F$4er/ass fa4r$cs +a8e /oo# c+e$ca

res$stance6 F$4re/ass fa4r$cs :$ not #eca! or rot :+en $n contact :$t+ t+e c+e$ca s)c+ as ac$#s6 es$#es9 f$4re/ass fa4r$cs +a8e aso /oo# t+era roert$es6 Goo# t+era roert$es ena4e t+e ater$a to s)sta$n s$/n$f$cant ao)nt of +eat :+ere f$4er/ass +as +$/+ t+era con#)ct$8$t!6 Moreo8er9 f$4er/ass +as +$/+ t+era en#)rance :+ere $t cannot 4e 4)rne# an# $s not affecte# 4! t+e s)rro)n#$n/ teerat)re6 %Proert$es of F$4er/ass Fa4r$cs n6#6( Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

-3


116

If !o) :ere /o$n/ to a7e an $ns)ate# cooer 4a/ to 7ee !o)r so#a canne# #r$n7s at

coo teerat)re as on/ as oss$4e9 :+$c+ ater$as :o)# :or7 4est .+! #o !o) t+$n7 t+ese ater$as :or7e# 4est D$# !o) e;ect t+ese ater$as to :or7 4est .+! or :+! not Foa  It conta$ns 4$$ons of trae# 4)44es6 T+$s roert! +$n#ers +eat con#)ct$on as t+e$r oec)es are far aart a7$n/ $t #$ff$c)t for ot+er oec)es to co$#e :$t+ t+e %T+era;; *ac7ets 2,11(6 F$4er /ass  It $s a#e of f$ne :o8en s$$con stran#s of /ass o:#er an# aso t$n! s+ar#s of /asses :+$c+ can effect$8e! re#)ce t+e rate of +eat transfer %T+era;; *ac7ets 2,11(6 E// tra!s  T+e! are a#e ) of 8ar$o)s ater$as s)c+ as o#e# )s or ce)oses6 T+ese ce)oses are a /oo# for of $ns)at$on as $t $s a coact of ater$as :+$c+ $s e;ceent $n $n$$$n/ f$re #aa/e %T+era;; *ac7ets 2,11(6 T+ese ater$as :or7 4est as $ns)ator as t+e! +a8e t+e roert$es t+at can tra +eat to ens)re t+e canne# #r$n7s are 7ee coo6 After con#)ct$n/ t+e test$n/ of cooer 4a/s a#e of t+e a4o8e ater$as9 $t ro8es t+at t+e cooer 4a/ :$t+ f$4er /ass as t+e $ns)ator $s t+e 4est at 7ee$n/ t+e #r$n7s coo after 3 +o)rs6 .e +a8e not e;ect f$4er /ass to 4e t+e 4est $ns)ator as :e t+o)/+t o#e# e// tra!s a! erfor 4etter #)e to $ts t+$c7ness of o# :e a#e6

126

Ho: are $ns)ators )sef) .+en $/+t !o) )se one .+en $/+t !o) not Ins)at$on $s $ortant $n rocess +eat transfer st)#$es 4eca)se $t $s )se# to re#)ce t+e

ao)nt of +eat oss to t+e en8$ronent %T+era $ns)at$on ater$as9 tec+n$ca c+aracter$st$cs an# seect$on cr$ter$a 2,1-(6 For e;ae9 I :$ )se $ce 4o;es :$t+ /oo# $ns)at$ons :+en I /o for f$s+$n/ to store t+e f$s+es t+at I ca)/+t6 Hence9 t+e f$s+ store# $n t+e $ce 4o;es can 4e store# for a on/er er$o# of t$e :$t+o)t /ett$n/ so$t6 In ot+er cases s)c+ as :+en I a coo7$n/9 $ns)at$on ater$as s)c+ as :oo#en ots are not a#8$sa4e to )se Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

-&

HEC 3521 Process Heat Transfer 4eca)se I :ant t+e foo# to 4e coo7e# as soon as oss$4e6 T+)s9 a8o$#$n/ $ns)at$n/ ater$a as t+e coo7$n/ )tens$ $s a /oo# ract$ce to ens)re a;$) +eat transfer fro t+e f$re to t+e con#)ct$n/ ot6 136

D$sc)ss t+e araeters t+at affect t+e rate of +eat con#)ct$on t+ro)/+ t+e $ns)ate#

cooer 4a/6 T+e araeters t+at $/+t affect t+e rate of +eat con#)ct$on t+ro)/+ t+e $ns)ate# cooer 4a/ $nc)#es t+e t!e of $ns)ator ater$a )se#6 Eac+ ater$a +as t+e$r o:n t+era con#)ct$8$t! 8a)es6 T+e ater$a :$t+ a +$/+er t+era con#)ct$8$t! 8a)e transfers +eat ore ra$#! %T+e P+!s$cs Cassroo 2,13(6 For t+e )rose of a7$n/ $ns)ate# cooer 4a/s9 :e a#e s)re t+e ater$a c+osen are ater$as :$t+ reat$8e! o: t+era con#)ct$8$t!6 Mater$as :$t+ trae# a$r oc7ets $nterserse# 4et:een so$# f$4res s)c+ as foa an# f$4er/ass are /oo# $ns)ators coare# to so$# )re etas s)c+ as a)$n$) an# 4rass6

T+e t+$c7ness of t+e cooer 4a/ aso affects t+e rate of +eat con#)ct$on6 It co)# 4e #e#)ce# t+at t+e t+$c7er t+e $ns)at$on $s9 t+e o:er t+e rate of +eat transfer6 T+$s $s 4eca)se9 t+e t+$c7er t+e $ns)at$on ater$a9 t+e f)rt+er t+e #$stance +eat )st tra8e %Honer 2,11(6 T+erefore9 $t $s $7e! t+at not a t+e +eat can a7e $t a t+e :a! t+ro)/+ t+e $ns)at$on ater$a6 Not on! t+at9 +eat :o)# aso escae or enetrate ore ra$#! t+ro)/+ a t+$n ater$a t+an a t+$c7 ater$a %Honer 2,11(6

F)rt+erore9 rate of +eat con#)ct$on $n t+e cooer 4a/ $s aso #een#ent on t+e s)rface area of t+e 4a/6 More +eat :o)# 4e a4sor4e# 4! a ar/er s)rface t+an t+ro)/+ a saer area ater$a of t+e sae coos$t$on an# t+$c7ness %Honer 2,11(6 T+$s $s 4eca)se eac+ $n#$8$#)a art$ce t+at $s on t+e s)rface of t+e o4

-5


1&6

Def$ne t+era con#)ct$8$t! an# e;a$n $ts s$/n$f$cance $n +eat transfer6 Is t+e

t+era con#)ct$8$t! of t+e ater$a !o) c+oose for !o)r cooer 4a/ #es$/n9 $n /enera9 constant or #oes $t 8ar$es :$t+ teerat)re T+era con#)ct$8$t! $s t+e eas)re of transferr$n/ of +eat ener/! 8$a a so$# t+ro)/+ con#)ct$on6 Mater$as :$t+ +$/+ t+era con#)ct$8$t! :$ con#)ct +eat faster t+an a ater$a t+at +as o:er t+era con#)ct$8$t!6 Con#)ct$8$t! of so$#s an# $=)$#s are /enera! #een#$n/ on t+e 8ar$at$on of teerat)re6 F$rst!9 t+era con#)ct$8$t! of f$4re/ass #oes not 8ar! :$t+ teerat)re as roo teerat)re +as on! $tte effect on t+e t+era con#)ct$8$t!6 Secon#!9 t+e t+era con#)ct$8$t! of aer %e// carton ater$a( #oes not /et affecte# 4! t+e teerat)re #$fference fro t+e s)rro)n#$n/ :+$c+ s+o:n fro t+e ta4e6 Last!9 t+e t+era con#)ct$8$t! of r)44er foa at $s constant t+ro)/+o)t an! teerat)re6 %T+era roert$es of eta9 con#)ct$8$t! con8ers$on 2,1-( %Et+!ene 8$n! acetate n6#6(

Mater$as

T+era Con#)ct$8$t! at 25C %.? ( ,6,& ,63& ,6,5

T+era Con#)ct$8$t! at 125C %.? (

T+era Con#)ct$8$t! at 225C %.? (   

F$4er/ass  R)44er foa at  Paer %E//  Carton( Ta4e 1" T+era Con#)ct$8$t! for #$fferent ater$as at #$fferent teerat)res %En/$neer$n/ Tooo; %n6#6(6

156

.+at /eoetr! :o)# !o) recoen# for cooer 4a/ so t+at t+e +eat transfer fro

t+e so#a canne# #r$n7s to a4$ent can ass)e to 4e one #$ens$ona C!$n#r$ca /eoetr!6

@)est$ons 1- to 2, are $nc)#e# $n t+e Cac)at$ons sect$on of t+e reort fro a/es 1 to &-6


--

HEC 3521 Process Heat Transfer 216

.+at $s t+e #$fference 4et:een t+e ana!t$ca an# e;er$enta aroac+ to +eat

transfer D$sc)ss t+e a#8anta/es an# #$sa#8anta/es of eac+ aroac+6 Accor#$n/ to en/e9 C$4aa9  T)rner %2,12(9 Ana!t$ca aroac+ $s to st)#! +eat transfer rocess 4! ana!s$s or cac)at$ons :+$e e;er$enta aroac+ $s to st)#! t+e rocess t+ro)/+ test$n/ an# ta7$n/ eas)reents6 T+e a#8anta/es of ana!t$ca aroac+ are $t $s fast an# $ne;ens$8e coare to e;er$enta aroac+ :+$e $ts #$sa#8anta/e $s t+e res)ts o4ta$ne# a! 4e #een#ent on t+e acc)rac! of t+e ass)t$ons an# $#ea$at$ons a#e $n t+e ana!s$s rat+er t+an t+e rea$t! %en/e9 C$4aa  T)rner 2,12(6 For e;er$enta aroac+9 $t ena4es )s to #ea :$t+ act)a +!s$ca s!ste :$t+ t+e #es$re# =)ant$t! 4e$n/ eas)re# :$t+$n t+e $$ts of e;er$enta errors6 Ho:e8er9 t+e s!ste t+at $s 4e$n/ ana!e# )s$n/ t+$s aroac+ a! not e;$st an# $t $s e;ens$8e9 t$e cons)$n/ an# ost! )nfeas$4e too %en/e9 C$4aa  T)rner 2,12(6


-'


?.0

'iscussion T+e constant of t+e 4o)n#ar$es %C19 C29 C3 an# C&( are cac)ate# )s$n/ MatLa4 $n

atr$; for6 .$t+ t+e constants o4ta$ne#9 t+e teerat)re #$str$4)t$on aon/ t+e a!ers of t+e cooer 4a/ $s ac+$e8e#6 E;ce :as )se# to ot t+e /ra+ of teerat)re #$str$4)t$on a/a$nst ra#$)s of t+e cooer 4a/6 T+e f$rst ra#$)s 8a)e :as set to a 8a)e :+$c+ a7es t+e teerat)re to aost ero9 so $t can 4e coare# to t+e $n$t$a teerat)re of t+e contro :+$c+ :as a4o)t 2 oC6 T+e o)ter teerat)re of cans :+$c+ :as Ts93 :as aro)n# 1&62& oC to 1&601oC an# t+e a4$ent teerat)re $s 20 oC6

! coar$n/ t+e Ts93 of t+e 4a/s an# t+e contro %:+$c+ :as 2565& oC(9 $t can 4e ro8e# t+at t+e contro %:$t+o)t an! cooer 4a/( $s t+e fastest to reac+ a4$ent teerat)re6 T+e ot+er 3 cans :$t+ t+e s)ort of t+e $ns)ators $n t+e cooer 4a/s st$ +a8e a on/ #)rat$on of t$e to /o 4efore t+e! reac+ a4$ent teerat)re6 T+)s9 $t $s effect$8e to sa! t+at t+e cooer 4a/s are f)nct$on$n/ =)$te :e6 Cooer 4a/ A a#e of foa +as a +eat transfer rate of ,6- .9 cooer 4a/  a#e of e// tra!s +as a +eat transfer rate of ,625 . an# cooer 4a/ C a#e of f$4er/ass +as a +eat transfer rate of ,61& .6

It :as o4ser8e# t+at cooer 4a/ C +as t+e east ao)nt of +eat enter$n/ t+e cooer 4a/6 T+)s9 t+e canne# #r$n7 $ns$#e cooer 4a/ $s $ns)ate# $n a 4etter e8e as coare# to t+e ones $n cooer 4a/s A an# 6 T+e effect$8eness of t+e cooer 4a/s $ncreases fro cooer 4a/ A9  to C6 Cooer 4a/ C aso +as t+e o:est con8ect$on +eat transfer coeff$c$ent :+$c+ +as t+e 8a)e of +  ,6&' .?% 26(6 T+e res)ts of t+e cooer 4a/s $/+t not 4e as effect$8e as t+e cooer 4a/s so# $n t+e ar7et #)e to soe oss$4e errors6 Iro8eents an# s)//est$ons to f$; t+e errors are state# 4eo:6

Poss$4e Errors 16

T+e t+eroeter )se# $/+t not 4e as sens$t$8e as t+e t+eroco)e6 D)r$n/ t+e test

r)n9 o)r /ro) $s ac7 of t:o t+eroco)es9 so t+e teerat)re of t+e contro e;er$ent $s eas)re# )s$n/ a t+eroeter an)a!6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

-0

HEC 3521 Process Heat Transfer 26

T+e teerat)re of t+e $nner an# o)ter s)rface of t+e cooer 4a/s $/+t 4e s$/+t!

#$fferent fro eac+ ot+er6 36

C+an/es $n t+e teerat)re of t+e s)rro)n#$n/s :$ aso affect t+e res)ts of t+e test

r)n an# #ata6 D)r$n/ t+e 4e/$nn$n/ of t+e test r)n9 t+e :eat+er $s a 4$t co)#! an# $t s)##en! c+an/es to s)nn! $n t+e $##e of t+e test r)n of t+e cooer 4a/s6 Hence9 t+ere $s s$/+t c+an/es $n t+e a4$ent teerat)re :+$c+ +a# occ)rre#6 &6

T+e cooer 4a/s are se: 4! +)an +an#9 t+e 4a/s are +an#a#e an# t+e effect$8eness

of t+e 4a/s $/+t not f)nct$on as effect$8e as t+e ones $n t+e ar7et6 T+e 4a/s so# $n ar7et $s se: an# crafte# 4! ac+$nes :$t+ 8er! o: errors :+$c+ a7es t+e ore effect$8e t+an t+e cooer 4a/s t+at :ere crafte# 4! t+$s /ro)6

Iro8eents 16

T+e t+eroco)e $/+t 4e ore sens$t$8e as coare# to t+e t+eroeter as a

t+eroco)e can recor# t+e teerat)re rea#$n/ #$/$ta! :$t+o)t a7$n/ an! +)an errors or araa; errors :+$c+ a t+eroeter $/+t enco)nter6 T+)s9 $t $s a#8$sa4e to )se t+eroco)es to eas)re an# recor# t+e teerat)re rea#$n/s rat+er t+an )s$n/ t+eroeter6 26

It $s 4etter to )se t:o t+eroco)es to eas)re t+e teerat)re of t+e s)rface of t+e

cooer 4a/s9 one t+eroco)e for t+e $nner s)rface :+$e t+e ot+er t+eroco)e for t+e o)ter s)rface of t+e cooer 4a/s6 36

It $s enco)ra/e# to /o on$ne an# c+ec7 t+e :eat+er reort for t+e c+an/es $n c$ate

4efore carr!$n/ o)t t+e test r)n for t+e cooer 4a/s as t+e c +an/es $n a4$ent teerat)re :$ affect t+e res)ts $n cac)at$on6 If t+e c+an/es $n a4$ent teerat)re $s sa9 t+en :e can ne/ect t+e teerat)re c+an/e# $n a4$ent6 If t+e c+an/es $n a4$ent teerat)re $s too /reat9 $t $s a#8$sa4e to carr! o)t t+e test r)n a/a$n on ot+er #a!s to re#)ce errors $n t+e foo:$n/ res)ts an# cac)at$ons6


-


@.0

Conclusions In conc)s$on9 t+e o4
ass$/nent6 T+e cooer 4a/ t+at $s a#e fro t+e 4est $ns)ator :as a4e to 4e 4)$t an# #es$/ne#6 T+e cooer 4a/ $s a$e# at 7ee$n/ t+e canne# #r$n7 as co# as oss$4e $n a sec$f$e# er$o# of t$e )n#er t+e con#$t$on of +ot :eat+er 8$a a!$n/ t+e 7no:e#/e of +eat transfer t+at :as ta)/+t 4! Ms Ea$ne6 After carr!$n/ o)t a et$c)o)s test$n/ rocess9 t+e f$4er/ass cooer 4a/ :as fo)n# to 4e t+e 4est $ns)ator cooer 4a/ aon/st t+e t+ree cooer 4a/s as t+$s cooer 4a/ :as a4e to transfer t+e east +eat 8$a t+e :a of $ns)ator $n t+e t+ree +o)rs e;er$ent t$e6 F$4er/ass cooer 4a/ +as t+e east teerat)re #$fference of 1,C :+ereas r)44er foa at an# e// carton ater$a cooer 4a/s +a8e 12C an# 1,65C teerat)re #$fference resect$8e!6 Aso9 t+e f$4er/ass cooer 4a/ +a# t+e o:est +eat transfer rate at on! ,61& .6


',


10.0 *eferences Aa8$# T+erao! n6#69 Fan Heat Sinks9 Aa8$# T+erao!9 8$e:e# 1- Ar$ 2,1-9 +tt"??:::6aa8$#6co?so)t$ons?fan+eats$n76 Aer$can Foor Mats n6#69 Rubber Gym Flooring Flooring: Specifications9 Aer$can Foor Mats9 8$e:e# 1- Ma! 2,1-9 +tts"??:::6aer$canfoorats6co?content?ro#)ct?f$e?#oc)ent?R)44er2,G! 2,Mats2,2,Sec2,S+eet6#f6 en/e9 >9 C$4aa9 *  T)rner9 R 2,129 Fundamentals of Thermal-Fluid Sciences9 McGra: H$9 oston6 Comparing Fiber Glass and Cellulose Insulation n6#69 O:ens Corn$n/9 8$e:e# 1 Ar$ 2,1-9 +tts"??:::6rfc$nc6co?#f?$ns)at$onco6#f6 thylene !inyl acetate n6#69 Ma7e It Fro9 8$e:e# 1 Ma! 2,1-9 +tt"??:::6a7e$tfro6co?ater$aroert$es?Et+!ene$n!AcetateEA6 Glass"ool Insulation # Fibreglass Insulation n6#69 H$//$ns$ns)at$on6co6a)9 8$e:e# 1 Ar$9 2,1-9 +tt"??+$//$ns$ns)at$on6co6a)?/ass:oof$4re/ass$ns)at$on?6 Gro$c7o9 N  S+ear#9  n6#69 Fiberglass Insulation: History$ Ha%ards and <ernati!es9 Nac+$6or/9 8$e:e# 2, Ar$9 2,1-9 +tts"??:::6nac+$6or/?f$4er/ass$ns)at$on+$stor! +aar#saternat$8es6+t6 Ha4! *6 n6#69 The difference bet"een temperature and heat 9 T+e .eat+er Pre#$ct$on9 8$e:e# 22 Ma! 2,1-9 +tt"??:::6t+e:eat+erre#$ct$on6co?+a4!+$nts?3?6 Honer9 S 2,119 'nderstanding Heat Conduction and the Factors that &ffect It 9 D)$es6co9 8$e:e# 1 Ar$ 2,1-9 +tt"??:::6#)$es6co?+o: to?content?)n#erstan#$n/+eatcon#)ct$onan#t+efactorst+at6+t6 na)f Ins)at$on 2,1-9 The Science of Insulation (plained 9 na)f$ns)at$on6co6a)9 8$e:e# 1' Ar$ 2,1-9 +tt"??:::67na)f$ns)at$on6co6a)?ena)?ore?$ns)at$one;a$ne#6as;6 ot+an#araan C6P6 2,,-9 Fundamental of heat and mass transfer 9 P6S6G Coe/e of Tec+noo/! Co4atore9 8$e:e# 2, Ma! 2,1-9 +tts"??4oo7s6/oo/e6co6!?4oo7s $#+I8$T25..IEC/PA0#=canVt+reeVo#esVofV+eatVtransferVocc)rsVs$)taneo) s!+ensaW8e#,a+UE:0HaHF >@):UIACX8onea/e=can2,t+ree2,o#es2,of2,+eat2,transfer 2,occ)rs2,s$)taneo)s!ffase6 )rt)s9 R 2,1&9 Thermal Insulation9 Sc+ooforc+a$ons6co9 8$e:e# 10 Ar$ 2,1-9 +tt"??:::6sc+ooforc+a$ons6co?sc$ence?t+eraY$ns)at$on6+tX6;ZM3s5URAZ6 Mos+er9 M 2,139 Insulation9 >o)r+oe6/o86a)9 8$e:e# 13 Ar$9 2,1-9 +tt"??:::6!o)r+oe6/o86a)?ass$8e#es$/n?$ns)at$on6


'1

HEC 3521 Process Heat Transfer Na8e R6 n6#69 Specific Heat 9 H!er+!s$cs9 8$e:e# 2, Ma! 2,1-9 +tt"??+!er+!s$cs6+! astr6/s)6e#)?+4ase?t+ero?s+t6+t6 P+!s$cs Reso)rces Data4ase n6#69 P+!s$cs6)s!#6e#)6a)9 8$e:e# 1- Ma! 2,1-9 +tt"??:::6+!s$cs6)s!#6e#)6a)?teac+Yres?#4?#,,,5e6+t6 )roperties of Fiberglass Fabrics n6#69 L:eco Sec$at! Pro#)cts9 8$e:e# 1 Ma! 2,1-9 +tt"??:::6e:cosec$at!ro#)cts6co?re$nforceentfa4r$cs?Proert$esofF$4er/ass Fa4r$cs6 Radiation surface absorpti!ity n6#69 En/$neer$n/too4o;6co9 8$e:e# ' Ar$ 2,1-9 +tt"??:::6en/$neer$n/too4o;6co?ra#$at$ons)rfacea4sort$8$t!#Y10,56+t6 Rates of Heat Transfer 2,139 P+!s$cscassroo6co9 8$e:e#  Ar$ 2,1-9 +tt"??:::6+!s$cscassroo6co?cass?t+eraP?Lesson1?RatesofHeatTransfer6 SOM9 S 2,,09 I*TR+,'CTI+* T+ H&T TR&*SFR9 PHI Learn$n/ P8t6 Lt#69 8$e:e# 13 Ar$ 2,1-9 +tts"??4oo7s6/oo/e6co6!?4oo7s $#c<=E8>n==IC/PA2-/PA2-#=canVaVe#$)V$n8o8eVcon#)ct$onVan#Vc on8ect$onVs$)taneo)s!so)rce4ots$C Yo#5s$/5FDf2HYGDoG:PGL2:c4F.SM1c+ensaWre#$rYesc!X8onea /e=can2,a2,e#$)2,$n8o8e2,con#)ct$on2,an#2,con8ect$on 2,s$)taneo)s!ffase6 Teacher ackground Information Thermal nergy n6#69 Sc$ence$#eas6or/9 8$e:e# 0 Ar$ 2,1-9 +tt"??:::6sc$ence$#eas6or/?Teac+erReso)rces?$n#erEner/!?Ta43?Teac+er ac7/ro)n#InfoT+eraEner/!6#f6 T+e Concor# Consort$) 2,139 Heat Transfer Conduction9 T+e Concor# Consort$)9 8$e:e# 5 Ar$ 2,1-9 +tts"??concor#6or/?s$tes?#efa)t?f$es?ro
'2


T+era;; *ac7ets 2,119 0 /ost Common Thermal Insulation /aterials 9 Therma(( 1ackets9 8$e:e# 1& Ar$ 2,1-9 +tt"??:::6t+era;;o)ra$re;erts6co9 8$e:e# 1' Ar$ 2,1-9 +tt"??!o)ra$re;erts6co?art$ce?:+atare e8aoratoran#con#enserco$san#+o:#ot+e!+ecoo!o)r+oe6 3hat is emissi!ity and "hy is it important6 2,1&9 Nat$ona P+!s$ca La4orator!9 8$e:e# 5 Ar$ 2,1-9 +tt"??:::6n6co6)7?reference?fa=s?:+at$se$ss$8$t!an#:+!$s$t $ortant%fa=t+era(6 3hat is heat sink6 2,1-9 Co)ter+oe6co9 8$e:e# 1& Ar$ 2,1-9 +tt"??:::6co)ter+oe6co?e)9 E 2,1-9 Chapter 7: Introduction to Conduction 9 HEC3521 Process Heat Transfer9 Lect)re Notes on ac74oar#9 S:$n4)rne Un$8ers$t! of Tec+noo/!9 5 Ar$ 2,1-9 8$e:e# 13 Ar$ 2,1-6


'3


11.0 A$$endices 11.1

A$$endix 1+ Potos

T+ese +otos :ere ta7en t+ro)/+o)t t+e an)fact)r$n/ rocess of t+e cooer 4a/s6

F$/)re &" T+e ater$as re=)$re# to start o)t t+e fa4r$cat$on rocess of t+e cooer 4a/6

F$/)re 5" Ma$n $ns)ators of Cooer a/ A $nc)#es a)$n$) s+eet an# r)44er foa at6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

'&


F$/)re -" Cassan#ra ar7$n/ t+e en/t+ of t+e r)44er foa at to 4e c)t6

F$/)re '" Roc+ester c)tt$n/ t+e r)44er foa at 4ase# on t+e ar7$n/s an# #$ens$ons6

F$/)re 0" San#ra eas)r$n/ an# ar7$n/ t+e en/t+ of t+e 4as$c cross st$c+ fa4r$c to 4e c)t6

F$/)re " *$a Po+ c)tt$n/ t+e cross st$tc+ fa4r$c accor#$n/ to t+e eas)re en/t+6


'5


F$/)re 1," T+e r)44er foa at $s a roe# ) $nto an! a!ers

F$/)re 11" T+e a)$n$) c)4oar# s+eet :as roe# $nto a s$n/e a!er :+$c+ :as ater se:n onto t+e 4a/6

F$/)re 12" T+e a)$n$) c)4oar# s+eet an# r)44er foa at roe# $nto an! a!ers $s f$tte# $nto t+e 4a/6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

'-


F$/)re 13" Cassan#ra eas)r$n/ t+e aror$ate en/t+ t+at s+o)# 4e c)t off t+e $nter$n$n/6

F$/)re 1&" Cassan#ra #o$n/ soe 4as$c se:$n/ to en# t+e torn a)$n$) c)4oar# s+eet6

F$/)re 15" T+e a$n $ns)at$on ater$a for Cooer a/  :as f$4er/ass6


''


F$/)re 1-" T+e f$4er/ass :as caref)! c)t $nto t+e aror$ate +e$/+t an# en/t+ 4ase# on t+e +e$/+t an# #$aeter of t+e canne# #r$n76

F$/)re 1'" T+e f$4er/ass :as roer! :rae# aro)n# t+e canne# #r$n76

F$/)re 10" C$rc)ar cas :ere a#e fro t+e efto8er r)44er foa at to co8er t+e canne# #r$n7 $n t+e $ns)ate# cooer 4a/s6 Cassan#ra S$a %&315'15( La) *$a Po+ %1,,,-55-2( Roc+ester .on/ %&32011-( San#ra S$ %&31'5(

'0


F$/)re 1" T+ese cas can no: 4e f$tte# $n t+e $ns)ate# cooer 4a/s to so: t+e +eat transfer6

F$/)re 2," T+e a$n $ns)at$on ater$a for Cooer a/ C :as e// tra!6

F$/)re 21" efore t+e e// tra! :as coet! #r$e#9 $t :as o)#e# $nto t+e re=)$re# s+ae


'


F$/)re 22" T+e o#e# e// tra! :as eft to #r! coete! $n t+$s os$t$on an# s+ae6

F$/)re 23" T+e 4a/ :as se:n neat! an# ecro stras :ere a##e# to t+e oen$n/ of t+e 4a/ to ens)re t+e 4a/ can 4e cose# t$/+t!6

F$/)re 2&" T+e ecro stras aon/ :$t+ a)$n$) c)4oar# s+eet $s no: se:n neat!6


0,


F$/)re 25" T+e f$na ro#)ct of t+e $ns)ate# cooer 4a/s coete :$t+ n!on stra +an#es6

F$/)re 2-" T+e t+eroco)es t+at :ere :$re# ) an# to 4e )//e# $n to t+e co)ter to set ) t+e #ata o//er an# start t+e teerat)re recor#$n/ rocess6

F$/)re 2'" Gro) e4ers f$$n/ t+e a & so#a cans :$t+ as )c+ co# :ater as oss$4e6


01


F$/)re 20" T+eroco)es $nserte# $nto t+e :ater an# $nner s)rface of t+e cooer 4a/6

F$/)re 2" T+e cooer 4a/s seae# t$/+t! e;cet for Cooer a/ C :+$c+ teerat)re :as eas)re# an)a! )s$n/ a t+eroeter6

11.! A$$endix !+ Tabulated data of te results


02


e 1 $ T

&?21?2,1- ", &?21?2,1- "11 &?21?2,1- "13 &?21?2,1- "15 &?21?2,1- "1' &?21?2,1- "1 &?21?2,1- "21 &?21?2,1- "23 &?21?2,1- "25 &?21?2,1- "2' &?21?2,1- "2 &?21?2,1- "31 &?21?2,1- "33 &?21?2,1- "35 &?21?2,1- "3' &?21?2,1- "3 &?21?2,1- "&1 &?21?2,1- "&3 &?21?2,1- "&5 &?21?2,1- "&' &?21?2,1- "& &?21?2,1- "51 &?21?2,1- "53 &?21?2,1- "55 &?21?2,1- "5'

n e $ 4 1 (A C o % J T 9 e r ) t

256, , 256, , 256, , 2-6, , 2-6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, ,

.ater Teerat)re9 Ts91 %oC( s ! a r T / / E

s s a 5 / r e 4 $ F

'6,,

-65,

'6,,

Inner .a Teerat)re9 Ts92 % oC( 1 a o F

s ! a r T / / E

s s a 5 / r e 4 $ F

56,,

1165,

65,

-65,

56,,

1,65,

'65,

-65,

56,,

06,,

-6,,

06,,

O)ter .a Teerat)re9 Ts93 % oC( 1 a o F

s ! a r T / / E

s s a 5 / r e 4 $ F

1,625

2'65,

2365,

2,6,,

65,

6'5

2'6,,

2365,

2265,

1,6,,

65,

625

2'6,,

2365,

2&6,,

565,

1,65,

65,

6,,

2-65,

2365,

2&65,

-65,

-6,,

1,6,,

65,

6,,

2-6,,

2365,

2&65,

06,,

-65,

-6,,

1,65,

65,

625

2565,

236,,

2&65,

065,

'6,,

-6,,

1,65,

1,6,,

65,

2565,

2365,

2&65,

065,

-65,

-6,,

1,65,

1,6,,

625

256,,

236,,

2&65,

065,

'6,,

-65,

1,65,

1,6,,

65,

256,,

236,,

2&65,

065,

'6,,

-65,

1,65,

1,6,,

65,

256,,

236,,

2&65,

6,,

'65,

'6,,

116,,

1,65,

1,6,,

256,,

2365,

2&65,

6,,

'65,

'6,,

116,,

1,65,

1,6,,

256,,

236,,

2&65,

6,,

'65,

06,,

116,,

1,65,

1,6,,

256,,

236,,

2&65,

65,

06,,

06,,

116,,

116,,

1,625

256,,

236,,

2&65,

65,

06,,

06,,

116,,

116,,

1,625

256,,

236,,

2&65,

1,6,,

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1165,

116,,

1,625

256,,

2365,

2&65,

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065,

6,,

1165,

1165,

1,6'5

256,,

2365,

2&65,

1,6,,

065,

6,,

1165,

1165,

1,6'5

256,,

236,,

2&65,

1,6,,

6,,

6,,

1165,

1165,

116,,

256,,

2365,

2&65,

1,6,,

6,,

6,,

126,,

1165,

11625

256,,

236,,

256,,

1,65,

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6,,

126,,

126,,

11625

256,,

2365,

2&65,

1,65,

65,

6,,

126,,

126,,

1165,

256,,

2365,

256,,

1,65,

65,

6,,

126,,

126,,

1165,

256,,

2365,

2&65,

1,65,

1,6,,

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1265,

1265,

12625

256,,

2365,

256,,

116,,

1,6,,

6,,

1265,

1265,

126,,

256,,

2365,

2&65,

1 a o F


03


&?21?2,1- "5 &?21?2,11,",1 &?21?2,11,",3 &?21?2,11,",5 &?21?2,11,",' &?21?2,11,", &?21?2,11,"11 &?21?2,11,"13 &?21?2,11,"15 &?21?2,11,"1' &?21?2,11,"1 &?21?2,11,"21 &?21?2,11,"23 &?21?2,11,"25 &?21?2,11,"2' &?21?2,11,"2 &?21?2,11,"31 &?21?2,11,"33 &?21?2,11,"35 &?21?2,11,"3' &?21?2,11,"3 &?21?2,11,"&1 &?21?2,11,"&3 &?21?2,11,"&5 &?21?2,11,"&' &?21?2,11,"& &?21?2,11,"51 &?21?2,11,"53 &?21?2,11,"55

2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'6, , 2'65 , 2'65 , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 206, , 2065 , 2065 , 2065 , 2065 , 2065 , 2065 , 206, ,

116,,

1,6,,

6,,

1265,

1265,

126,,

2565,

2365,

256,,

116,,

1,6,,

6,,

1265,

1265,

126,,

2565,

2365,

256,,

116,,

1,65,

6,,

1265,

136,,

1265,

256,,

2&6,,

256,,

1165,

1,65,

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1265,

136,,

12625

2565,

2365,

256,,

1165,

1,65,

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136,,

136,,

1265,

2565,

2&6,,

2565,

126,,

116,,

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136,,

1365,

126'5

2565,

2&6,,

2565,

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116,,

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136,,

1365,

126'5

2-6,,

2&6,,

2565,

126,,

1165,

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1365,

136,,

2565,

2&6,,

2565,

126,,

1165,

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136,,

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2&6,,

256,,

126,,

1165,

1,6,,

1365,

1365,

13625

2-6,,

2&6,,

2565,

1265,

1165,

1,6,,

1365,

1&6,,

13625

2565,

2&6,,

2565,

1265,

126,,

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1365,

1&6,,

1365,

2565,

2&6,,

2565,

1265,

126,,

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1365,

1&6,,

1365,

2565,

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2565,

1265,

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2565,

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1,6,,

1&6,,

1&65,

1&6,,

2-6,,

2&6,,

2565,

136,,

1265,

1,6,,

1&6,,

1&65,

1&6,,

2-6,,

2&6,,

2565,

136,,

1265,

1,6,,

1&6,,

1&65,

1&6,,

2-6,,

2&6,,

2565,

136,,

1265,

1,6,,

1&6,,

156,,

1&625

2-6,,

2&6,,

2-6,,

136,,

136,,

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1&65,

156,,

1&6'5

2-65,

2&65,

2-6,,

136,,

136,,

116,,

1&6,,

156,,

1&65,

2-6,,

2&65,

2-6,,

1365,

136,,

116,,

1&65,

156,,

1&65,

2-65,

2&65,

2-6,,

1365,

1365,

116,,

1&65,

156,,

1&6'5

2-65,

2&65,

2-6,,

1365,

1365,

116,,

1&65,

1565,

156,,

2-65,

2&65,

2-6,,

1365,

1365,

116,,

1&65,

1565,

156,,

2-65,

2&65,

2-6,,

1365,

1&6,,

116,,

1&65,

1565,

15625

2-65,

2&65,

2-6,,

1&6,,

1&6,,

126,,

156,,

1565,

15625

2-65,

2&65,

2-6,,

1&6,,

1&6,,

126,,

156,,

1565,

15625

2-65,

2&65,

2-6,,

1&6,,

1&6,,

126,,

156,,

1-6,,

1565,

2-65,

2&65,

2-65,

1&6,,

1&6,,

126,,

156,,

1-6,,

1565,

2-65,

2&65,

2-65,


0&

HEC 3521 Process Heat Transfer &?21?2,11,"5' &?21?2,11,"5 &?21?2,111",1 &?21?2,111",3 &?21?2,111",5 &?21?2,111",' &?21?2,111", &?21?2,111"11 &?21?2,111"13 &?21?2,111"15 &?21?2,111"1' &?21?2,111"1 &?21?2,111"21 &?21?2,111"23 &?21?2,111"25 &?21?2,111"2' &?21?2,111"2 &?21?2,111"31 &?21?2,111"33 &?21?2,111"35 &?21?2,111"3' &?21?2,111"3 &?21?2,111"&1 &?21?2,111"&3 &?21?2,111"&5 &?21?2,111"&' &?21?2,111"& &?21?2,111"51 &?21?2,111"53

26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 26, , 265 , 265 , 265 , 265 , 265 , 265 , 265 , 3,6, , 3,6, , 3,6, , 3,6, , 3,6, ,

1&6,,

1&65,

126,,

156,,

1-6,,

156'5

2-65,

2&65,

2-65,

1&65,

1&65,

126,,

1565,

1-65,

1-6,,

2'6,,

2&65,

2-65,

1&65,

1&65,

126,,

1565,

1-65,

1-6,,

2'6,,

2&65,

2-65,

1&65,

156,,

126,,

1565,

1-65,

1-625

2'6,,

256,,

2-65,

1&65,

156,,

126,,

1565,

1-65,

1-625

2'6,,

2&65,

2-65,

1&65,

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136,,

1565,

1-65,

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2&65,

2-65,

1&65,

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1-65,

2'6,,

256,,

2-65,

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1'6,,

1-6'5

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2-65,

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1'6,,

1-6'5

2'6,,

256,,

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2-65,

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1-65,

1'65,

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2'65,

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1-65,

1'65,

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2'65,

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1565,

1-65,

1365,

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1'65,

1'65,

2'65,

2565,

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1565,

1-65,

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1-65,

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1'6'5

2'65,

2565,

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1-65,

1365,

1-65,

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1'65,

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1-65,

1365,

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106,,

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2565,

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1065,

10625

2065,

2565,

2'65,

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1065,

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1-65,

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1065,

106,,

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1-65,

1'65,

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1'65,

1065,

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2065,

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1-65,

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106'5

2065,

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1'65,

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1065,

2065,

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05

HEC 3521 Process Heat Transfer &?21?2,111"55 &?21?2,111"5' &?21?2,111"5 &?21?2,112",1 &?21?2,112",3 &?21?2,112",5 &?21?2,112",' &?21?2,112",

3,6, , 3,6, , 3,6, , 3,6, , 3,6, , 3,6, , 3,6, , 3,6, ,

A8era/e

2061 -

1-65,

1'65,

156,,

1'65,

16,,

106'5

2065,

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1065,

2065,

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2065,

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2-65-

2&6&&

256-

Ta4e 2" Res)ts o4ta$ne# #)r$n/ t+e test$n/ of t+e cooer 4a/6


0-

Convection Group Cooler Bag Report

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