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heat transfer gate notes 2016

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Hand written notes on heat transfer
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l'- :::-1:i;ai -.: _:r--. Ln1 (re* ,\ (> €c<- i_-_l /i.:1r \r!/ .6b i rj't !.::l ..::':.:, f::-'i ixl (,1 ,- i:j r! .: -.,) :+:;! ;i-.i -. ,:}: r:.; ts;
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Page 1: heat transfer gate notes 2016

l'- :::-1:i;ai -.: _:r--.

Ln1(re*

,\

(> €c<-i_-_l

/i.:1r\r!/

.6b

i rj't!.::l

..::':.:,f::-'i

ixl

(,1

,- i:j r!

.: -.,)

:+:;!

;i-.i

-. ,:}:

r:.;

ts;

ram
Text Box
HT- HEAT TRANSFER
Page 2: heat transfer gate notes 2016

To get all subject Notes: Just mail me [email protected] mailing within 2 minute you will get all subject note’sI have a polite request to you if you will forward these note’s to allyour friend I will very thankful of yoursIf you want to all subject notes regarding GATE ChemicalEngineering Please you can Join this group on Face book :https://www.facebook.com/groups/GateChemicals/Very soon we will update you with well organized printed material& practice papers :

Thanks to all of You :

Page 3: heat transfer gate notes 2016

Oct ol, I \

-14

HpmTrrn*trrx

-l-l-tl Csnluchon:-a)@-3) tadr'c.tiq

&".1^.tc.hur? :-

-t--

-...''.-.

I tlvtD

2o l.tl

t h4"

"F6tiet's )*ru : --qA "t{dx

herl llrr* ,^f JrodrcJ

E- =-k d1A 6,L

k=con lq"[ 6l- p^-pcrrho,"Li tU ( ]T,{",,1r1 Con&&,a!r3[*l .

+-krnuK-a) rfi

k='fo z Y*r.

Tzt4

"L-1",,o

lr -.!tLi

l.i

I

i

It.-

[,,tiE

he;oJ/-t^d4rynr- J e \a

tb',&*tn*{^ 1

l*t "r J eu-^J

*- gn* n^6w,.ql lo lr..- dft€lrb^ +he# d**|t^',

O{ssr^ptro'1 -t ) Csottror.r'ul

{) Cur*lq", T}ur}1"^l G",.t*hra}g .'rn ttr* N^*y + k*p.u rm1;ffff, d*U 'r,D #*.i*;,f enrr" arnr ef h,,J

PLqro r,o.llr,)Tz

i f4nt-F.f>Co.d.r"l' i.r.1,* it 1t oh.f-e, ltdrrh i

I l'u.}.' ls'

q) Slqdq *{,^L.

s) (lyw-drlrr,,*r;oa. hral d*^J.n- tx -aw.,tt>.,-r

Page 4: heat transfer gate notes 2016

Q,-ls Q oLVAr

olu- ^ -h-4ilT61^

.nol,( ? l1H! dr-l '{r

qf,,' ?- -'t Tl;:

t+rt{t = -# Ltr-T')

-z- RA Lr'-T)0q2-w

= ' k'A tn-r")

\Ws la,'o

?=u/kQ z Tr-Tz -

Y/PA )lT,.e,-r,4l \a"IJanca T. = onfug

bn*.hon -: -Neuhrn -Rik h-ants l..r,rt

tteal #r^* u Tury A'I{

$ x [rn'T- ) -

0.-{+

e z hA t-r*-7*)

h - %m"1. z

!

-fldrk-'

z L-- 2'

v/^{*l$o

rr+ rtlvI

&mtotc"-rard

lrr<L

V*"*I

-l

{ro {a

Page 5: heat transfer gate notes 2016

t'l-u:R

Tear"n" '. -.l- t a.+^ 'iUfsrwrr b'o ) '..:

$ * Fsuvth tm.,el,r$ fuoh'lo"O.,

0--hAr"1

I

H. f ,ir {akryuq ohe_o- bcr-

of *-n- r'+' h**1,.s^{a.r on r,..1,&'u1n-

0. z 6A

Ocb o3,rq

-

&t-rP"''ft, tn)&:'-

0 = T6-Ttx-T/tr"eo

effuvrvq"litvn

,,wb*,*,

<L--<"t**&i' 1. 1"1

&= -t-T' JAlcrm

O = Tr-Tl\ ?-

L'%,n

Y lr{Ful

ij

,{ *? H,tin atgrran} Y* * a;'Lb @ [fl-**'Jhp

t:b xvn'[fk

;

zY*+

t iLdrcl,l,f , h+, ';n;b;*,..,tff+o*nt, #r. t*ftr.i

, -g- .'T\Lt sr.f"n Boll3'r,an'" 6'*to,J'

I

+ tAe r,UrrcliU,*f rytor^er-r,,t-.

4 h*F o,dowt- otk)*r \(r\-t \ ;

hr-'n0

I

I

I

I

'Il

6rrr,<1 *-- bl-r --) t*,,1

LlaJ"*!'l*o

q

\aar$)e"

e{5-S,J*

lsi

.%K1 K2_ F6

Page 6: heat transfer gate notes 2016

Q = 'ls4v o=fl

Ka

Ao = A =At

h,u,Q''

ffioA Xz-

B'a#*foo

%R=(fo * fi*" o#" ffi-#,)e

Q= To-Ti,[ku.f;F* ffi+ ffi,"fotr

Q = un Lt-Ti)

- &l.o

T6-aiz{

il ,

J-tvy-ffi*

+-.k+J*htw

#*h

Ua Owtnll. t.ta$ fi**}eru coelF.r.^$

Q =- (Io-Tl) ,

%o

44L.-k"* |

6)t -+- b:Xz I

M -+- At,t<t<zy tr r

s.

t.) .

Page 7: heat transfer gate notes 2016

.:\'t;'._i

l ,.rr)

;G:-},,

,. :)

r: ::l' :,)

\. :.J

i')

' i:j,

.)

:

:::4:v

r-$

i,-)

L)

rl

f,jt)

(l

; -,t

:'1",

a'_l

,-:.1'l

t:::ll.r-);,

l.i)

!,]

\1/

'..,:

i,:J

ir tl

HoIlor^r M"dorr 6n q [t r"k pipe".-

(,)1'

k-L-0= -lrA dVat

z- -l<(zrr Y*1dT/ea-

l\at '-h

.*, @ z-"%q J;,-^'

-t eE! Crr-T,))n"/n, -

Q z Tr-az'l'.rftr

J- )n\4,kzrrt 'Rt-

GooA t xarrlp^h'5 r""lc-'Jihrn^bt bL uard ixo^'& ao kr

t^i[t o* * ,rt d lr"ada]ar

S<, i F sharfd vw t^otA

'sL oo ke

:l

.v

>t

V\a, I

Page 8: heat transfer gate notes 2016

tr'olr - kk rt-

{, V -0-

Q z- -ls F erAJL

z -l< ttr rn?) dTra:,

lT'drJf,

-ry Lrta)

L I kr'tr.r k'-T)trJ L4 a

Q z kqrr [T,-'T')

fk -L"-)

Q,z

&7- tT* -TLrD-7r)KQ ttlrY;

,aL-;.:/

,o3

eL: r)

f:a

Q13

sst?

O

sa

-r.3

a$f)

LJ

(}

$13

€.qJ

t.3

t-)

:_.,1

tr,

,J.i

iJ,1

wrT

-L l'tuh,

t+

J"ka),, Arep':

Q= -lrA"t:P

z- k,-Tr) .

t;4llritfdzna

tir,

.y'&-qn 'lrc.elirrn rf notro. sgry_-gf-KA.^ dr/aa

x*t+uL"-')tu-kr4fl-o1v2-

,r/ 2-oho

*v,lfl+z

lyn&'w^aaw

Page 9: heat transfer gate notes 2016

atz4l r

z. Lr, -lrr . -I .Tr{r

(kznr*i-11Tf__+_

:l

AnTrh, -- \7-A 1

tvn

?1qnl tJal!

L.oq v'{qrrR[odi- U-t"tR \ ,-Jrr^.ith; f

l( = t*. Lr to<r )

& = -lsA dr/a*

otnr.

)42

J ,,.

7lt

z -M-o

z,k6 tt+ur) h &Ao

z -|rLt +xr)e dlr.s-k Lr-'f-<T)A olT=J;

=-S Ir*"*l;

o

*(r+ocr)d'r

\1,*\t

l4z-\t = -e ltrr+n+)- Lr,*"{qI-kt ftt,-r,)+S Lrta3]

\t [tr,--r;Jtr +"ry))nl:

Yz-Jr

-

)rr^trh

Page 10: heat transfer gate notes 2016

&- koA Ir+a]r)tl'-Y)b-Nr

z Lc",B [r, -Tz]:VtrTLt'

Q=

aEr

f\

fll

*I€Ad-.,,

a

:

I

II

kp, =ko[tr"<'raJ6tt z )t>-Xt

;

I

&r.a

s"&

e0a

.@

s{3

€€,+3

@

€r,€3

@

f.a\d,

{3

q;)

.1

€f".:d

iS

I@

( q")*d z -l(A dran

( o,"* n) wa. !

i: ,

lit:l

ll

["i:':

1:

I:

l

cll

,:

I

uH

L'E

(er*ar)*, .--Q-tfuto;a*

z - ltA fi/ao * fi[-kA *^)l* ,

t6,,)cra z [od,,)^-+' t @*+d")emreAs40'"&tb"'

( O ar.)conv z ( oJ cn dn - (or*a*;.-,di

L -va1$1 : E k)ry*-t t- t" #" d")3

hqdrc Lr- -r* > :" tra9t'L d,*

lsAfl - h1/t--f*.)zodnL

Page 11: heat transfer gate notes 2016

Orc=

-\'dl=*

"i

Qr= -l(rddX\rAzQz*dz- =, 4udx,dgbrzo, -+ \, Ft =& ^J'%r)d'

cAo^y rn BE = (d*d.ga. C q*

Qr.+ Oy* QztX,er.rtu*-rry;

[-k*dr d 4)*[-q aoarl J + [:k d5d=g) + [e'or, dy d,)

z C*g*r*t*'\yM\l k t1 d,'izoBu )dr] +(xraya*45O+ |, [-k, dy a,l,a) r/rr)d.] +

L t il,. dg dz ) c tr,$,

*- C xv%n)dvg*r+ filyb,yw+}, Lx-dr4#:t**

$"'fuAgdo ^: (f c-AIA- 1 P,**

: Qru*d- -r0g*du + Qr*dr-

r +," t-rtpdydz*)d{+

d"-q d'.d*Woy

Page 12: heat transfer gate notes 2016

I

.bT_=r}JAt- o{ (EQ' 3C+l\. lv I

l*{ "ru

*=ft

l-,)

rn)

;

fl:,

f)

s.'::

l:t, :-

:.:

G:tjJ

-{.3

(iit i

-.n i: .]

:

r1?\ .

, .-l.,. ]

r.'.'.1

:,-\ 1

,:\Lfl T;i'.Pg .

:

::1

ffi,::I,qI

frI

T

E"*T E. iD

0c*o6iu

-L z tf^rr',^t /rf{.- rb ["()

tr"* c"+^^ly

--------+-------i+L&rn"j crno["''

Nr/-+*t^, Sh^dt.)a4r

..5tcaJ* A\ofi , 'kLNu t*+

frr,"r,tfr ,g z-O

s!''( cl.ir.'^l*riorr^,t [ =Tt<_ )

#vo

t\--h\,^td*'= Q,o!#y #n , T= Crr *Lz-

@dg&, Cod+r*" alr:_i ) . rr-=O ., T'Tt ; Ta - L2-

Li? )t-Lt T=T. i Tz. z C,t-+ c,Tz-- CrLt -tl

: ort lr* rl:-r" )

6L .:

/rrrht". l4Q*"W.I\

r3C}

6a

r.\\:t/

n€13

€L3

a0

"{$

e0$0

=toE1Z

4*rr.rr, can &ho,ro

?soFn?i- h^"&r^-[ ) ltr1, li'<Xzk7-K 'ca^rl^*-

l.[**+,- *+7*o' :lcbTk

W*H,.

L-t\-

r+*

#zo

\(

Page 13: heat transfer gate notes 2016

@d.w--

;.i) \ t'r eqL

; lr= -ryt+r1h*dbtiL,Jlonqqttt"khi",

ta / 5;r.z-f-L t-(rnot"qriY

L,i rnz.ftop= - ff,-fr)a I il*,alep= o;*O i -'--ff'=*,ndL

r.: I --&-r.)ai{,,9 1 ,:i\ \/ \

,

; . mrr' \ riri .= - tI -rL) tL,L ,

Y $1,\t/ " ;

't'.,'J J \Tt-T z trr-Z> tt/t I ii:-al I

Iffi i6)u l6-p[ - 'tl

-

r -) ' iw'b't\ tt6*&qa 'o ./rrr.-i*t-" 4"t* "l-

I.^*. d&LibulioniuDi.:'l --t' 7 i

, Tr^<-A^^.-'"1 elrr *'b #".t-- o .V_![)^ ;..,.J u ' . dtu hl 1i tr- _-L-1 *":j.) .-!nqdX , * z-=, & -+ rc+(_, Tk;-::1i:i:/tlf..,ii) ,,r',, i t"l*r.L1 a1arn , T = -.{, $.,c,x+cy i}z#iJ I tvt'1, !'ti

L@ c,'"J.'iLiolu a,n.s -- :

,.r, i i.) MzL 7 T-Ta; Tf , -V;E n*tror/ i

;i iilrt 2-Lr rz-'f*t ,+"= -{ifr-/" r

i - -r -'+ -' ,.-;i :.: t LCIL'O :

#z-\dd\"a ',il')

,L*O;

C* ,nqlc Je*p,

Page 14: heat transfer gate notes 2016

= _gk

"tr- -

o,t ernhre t zLzo - ;-lio*:

=To -toVl [-'F =

Tz-*,5+ro

?LztL, T-Txt, To-T...l=+q

atiw*;r-l(an'* '

\

\

I

#t,."P) -32Hr*.'*] ,f"rc*D

da[ tk*) =o

# f"rra,rr) *.)-oLk""L"r, kotr+xr) * =r,

tk-3*h"U o6u.ih, k6[ ,+ nt)= crrcrce

0l

C1

Bo,rn\ co.rpfihnra, a/w,t ) Tr-20 , 1-T, ,

ii .> ooL t 1 z-T7

lro [fr *x i) = e'L

IrocTzf i4yr7= cr1- + n (r, *ot )

k" ([Tr*r, )+ 4Cr**T,z) z c, L

Y (."(r,:r,r *{ Lr:-r'"J]

Ip,frr-T') fi +{ tryla

Page 15: heat transfer gate notes 2016

utt' o2

';v2

T

*

tMLr,+dr2r)

- [r,*,, n?r}= O

ttfi\f r/id\

oe 'P"us

,fl,rrntW

?

2-

,.<1, * L&TL -,W"*rf+?"6t+ffi

*l

I

!

fu Lr+ o€) = -ry Cr,-r') (t.d ry)f

+fu Lrr--rr> [ t+*h,*])E

-'l 2-t

T7--z-

J r- zx t-r ) [ n +vr'2)

=-ljal.

- 1 -+ Ct +oti, ) z Tr

74z L1--

z-l

.lLz O4?'

T= I

1 = - l t ^1, - 4 + L+ Lr'-rL) (rrot rqL)- [r' a*$

,

to(

ft, -t, + "( (tg) - F'* *'',,\

-rL^l

@ ,rz

Page 16: heat transfer gate notes 2016

O"hnr)dql Co -andirratr aU-- ', Yror Q

' Tz fr,*,\,e, a):f zT (ng?r -2,)

?4- z'Yc26 O I

: Y z YS.tnO

I =tr

,***'

, I tt el

*.#*ffi'-- )T )Y' 5E.'Eg

= .,^-s* igp-oE_aJ

bTbG=

_I Sirr g r tL,>B al

"SrL,ttradV,Cosoo&'Yg:zlr

bt{L

/J"Li''$rns$*ryt z fl_

Dtrd

OTE.DT&

r3: ,

a\L-; /

B=ia'3

r.1l

f)r1-*.',

:

€:

C3.

13

().

eri€,tQiIJ

:

S ;,.

r:) :

tJ,-,

f} :|:J I

i

iJl,t,

{Ji-':

@ui,::.(d :;:.:,:,

6s -ati./ ,:l

7"'J

i-J:

&:i-- :.ji;9,,

:

.:.4 .1--) '

U.,l,ti .'

i

sXe, 1;

.,.t,

ra i-=

6H

L11o( bT.

>r1b7

pa = )T >?LDB -az 'ffi

Dr:57 ,^sl*lfim

w^*rui)LY

Page 17: heat transfer gate notes 2016

t. :a.. : -. a ]1 t..::..:ir1' ; -...

S,rn0 )LI.l)r bY)0 -1

he*

_?:_b*

eCa0

-&nO,w

.A

.t':,

ltls,

r.t/-"\L::9

r.l:\

\a)

f,.4

1. l

,.\'i)

,^-\, .:;)

6:1jl

1r-6\

ll

t,r -'f

i,)(D

{)i .,1 ,)

(iJ

r"ii\\i9

&

#"i)

ii

t.' ,

0J

l-'r,r :- _J

t.,

,:ll

.1.:._.:),

i,j.-r

€3

0clogry

G*s aO - $rns b@- I @D? Y )S )zc

z b>eL- - 9rrg ? :bh- Y 'og

b[*)=bo?-t*il, ryUcno BI-

btT b, tbT\bOVtL /

bzr)L"

be f,r +W ,[.-

Fu"r*+c^s*il ry i[bo-ry#,]

vw > C65Le da +sn"o9+4' f -p--V-

'igg4)-W luet{-se}d')- aO I .rL- l- :;ffi--Hd,

Srne Cae #? ' ?o-)t..

+ Srng br9.aT .E- ,Sr*9 *T:-'"6* ) 91

jctJ = $ne bo -r f,r!$ nfr

t? '-7 E-

# =&t3{tsrr.e l"{s"'o* + 4-* )

t ry(sine**of T"l

# = $rns (s,,o + +- Qs-o. * -, ry** )-+ Orb O'.- Y (weg + Srvr s#?- ry+* q9 #) I

:

:

[,

li

Page 18: heat transfer gate notes 2016

Awra

&ra

13

ef}

e

fJ*blz +**r, *"*#* Wot^00' tET

l\ A-V

-r a'r ^-'elr6-'frfuo#r

z.$

ssm

I 't

.13

6o{'"t

iJ

flr. --l

."d{r'L'

*-%

1TzT1 )

1 ,IL;

€iu,

a--

.l

rai9rJ

w:ii...,.) .

i:3 'j

:

i.l

,,1t.. )

::i:

@iiii

(F.,.-,

i:i,.a [twta

-Ei|:!t't i:ws

\5, - C,{1,,r1-I"'4)

z C1 ln \k-z*- Lt )nrri

,

4* qr!e9

_W*Wd,

^2-ol,*?aTb?LL '552 =_ f,T

bY2--LltT'Tffi r +qa"

&\*.h,'r"g,

?^g'"n* T, T ,c.)-nr,-+t,

6*^.&\ o-olr*'- o-r,Vzh t

1gL,Lnr,n frluz- (,!n\r+/-o'

Tt-

cL

Page 19: heat transfer gate notes 2016

I-r-E )nv,16T4t

1-q- T, -Tz1' ^t?>t rtffi""""ttte'

bw"q'o,.dn\oD '16

'

1^%t

T -T",l^2,

')"\,=r,-T

)nt/" T' -TT, -f.

ryE=orL

)

S1*kr^d%,1";,'ts{l

? _Lt2rryr)1Vffi,),+

2- T, -Tz)-- t"k,kzrrL

IIh lwr'

6a\ =YZ

SotrJ .pip&_!irJU-

[g- rI r'"i

J}T?}T

\r***otEII d,1r8.)".-l.S

( Nt ''r' Rii t* --9 * or,ldYr\[ {-..-ilL*

.*{ r.

)"dQ7,

= e',rii

t.t-'hiE:'

Ii

iiI'tFli'

ct

T

Page 20: heat transfer gate notes 2016

LEi"-'

b'T_ * I ar\*' 5"E r.'

4+%,* r * Q.Lt E

fL * -.LIDtL n Iy'(#=*{-*^ro---5

d^r7 olv tr

*to*i, -*, '

-dA, = -t +*cr

*d. =ol<

dh,z-*ry"\-a'

la

aB6s€sse@

@

oe@

ssee€€

@

@

E6e€&{B.{.4+i,

@,

sr#

@

@

inkf'*lt? ff" %'T,4 W -rQ lnY tcz-

%^r&^r*1-l <

Cr.,.litior- E

C"

-?

^{z-o, *%, *z--W?*rrrf* b*- z*:vg

Yz' k , Tz-T*

1o=-fr qr cz_

E, Tza I TzTs ; 162_ ( ,_

r= H g^#x5#m'#h**jffi#^'^

Page 21: heat transfer gate notes 2016

t''

{-'\ii:J

t- --1

ai}

r,l l

liti a!)

,'.'1

r.:- l

'':.)

/a -,

fri.;r_:.:,

i. ]

,, 1

(:-J

/.1,J,

i.')

,:: \I ,J

f,,,':l

i..,

-.

r:,i

L.:.n

'::'11:l

..:_: r\(. -1

.t

.-t. ..

;.

::__'":s

,.-., I

'1.; -5

'(-.'jl

a)

yzo t Tn-'[o ) To z-(y

4 o -Q'te14t<

Ts-

Tz, tQ,

-a_. w.lc {1

t nroLt

*"2q- T,^: L a:

,=

a-o

-Ttt

Hnntv.aiOr{qa' tna ,

Q z -lrA dkr lr=R

!*trrr,.J l€H,-*7 6L' IT *L l'-o-

=- Q'rrRLL

d =-r< o^U,f-ei

2-ga[zrrzt)

J.

I

I

\

(

JJ-Ch^ .

I .2-Sc-j.

q -z- TL-T,

#+k;2-6D -La

,

ffi"" Lk-f_ =!vn ------4:|-e

Srxrrtn0tlfn , ,u., o

lt rr 'tvrar,.loH 0-D'

Qz-Ti

-Tolf

hi Ai **bY"k)12''l'{

Tu- 3'i =

d.

hiz tato 1 r.L(

2-t >'C- Sk'A'!'

'ly*rZ4AL\<

t+-'1t N/n

Page 22: heat transfer gate notes 2016

LC vnat,

@.@iG

ee&@

6s€@

@

sss63

{3

@

f)1.,J

@

@

(-

$2.' O k w.

&r Ry +o t-

>, ? 2-Cc,w,,Yrrk{cr'.,,

S z' l0i

fl,rrcJsr,.rr- d ir^o,,l^fi'or1 -

(

'{ = --lL -To

LeL#,'"*,*#Arrmrlttr , Vle- e+ tre D{r"61^ir^4l13, stcr^-lrl b-r "^inv-r 3

rr,iyrr"t, 'dQu . fl-o effi=o +1"!I = +\^a 6@

dflr azl)d:rr-

'l

-

l{1zr u

vt -. J- + .!+ * [-t^\t B'

-(L6; -, ' I, hgxznL ' tVJ 2s $

' z:x+,=ffi) ,gW,rySh^:

Yi ha&nL

z t (-+)o#*A=#LW#;f:AZz; |t!IL- \ 1 '; LTL Ll\ _,r)

dh**N,

Page 23: heat transfer gate notes 2016

= (tvl odfd<

!&.@srldJed'-

_hA,d.z 4(v t,

lo tr- r-)

qrhot. A=ct

/n t-rr -r* ) '' L t

)nLr-T', ) = -&a+)ntT-T*)

N/_rk u.

h.{-r,"1

.oclto,lY

Unsrcat -stqlt.th,trh40F;h^dDfcql

"zqPo")"t,o t -

#*X,.#-{=.

Unslca& st&, oilr )"hl- ff^#*,B -&'rr",*,ro-j e,ar,d,*c-tUr, nn

tc= +

, l,Uf h{.rn"al cry,&ctUt

-yfu'r-J \erirlancc t# W90'n&.chlr*, b *ghbl^., Il".,"all,bo L,yu *- W "t*'rrr, r.tL' '

Scrr*"hon a Mcuoaa in

l)TJfrrfr^olq nl

I

:

er*'rdr*tdt:d'

t,

T* alr... i

b1 aon"echx.,

fi,u- e" [c,lh"l e,*yl + t1^'- ',-ru1'4b!

( n Lr- r*)

dr-r4Cnq*I"6 ,

t = d^qldc lt'ristt- )-ii"6'th 'L

--l-CI-= + c,jvc

T {ti

co t:x*,E

Page 24: heat transfer gate notes 2016

ft .--1.TE'@ai:L\.P

ra

\:9

'a

&*ss0ss"8

@

&TJ

€$&{"}

€)

s

9

trdv-k-^!tLc'lc =

7- * z e-lu6-Ii-L

! .\L'/w

. knJlG< o-L

lrt^N|bu-^r Bt'

I

I

K *kTi -f.a

YL= hLhC

=, E^g CAr")

LA.Ar-hA

1 -7.<@

@

€ss@

I6€}

{}@

ara{\,,J

@

@

I,,V

VT'\

[R"t)con'trec,h'on

th .l-- .

t) s\taf

D) Cd"-

-eti(+il l- btzle+16r-

= t5/^ 2- 4,? /eLo

=fu,%z,*fir$ Tri" C,il,ein/.,,- t

Page 25: heat transfer gate notes 2016

iv

r.l

rlJ

R

r-:-)

r!/

i:-l

i:li

':?

::;')

'--t:,,ia+)

()

.\.J

'l-r)

':--l

,.)

,: ''l

tl.r

(;:;,

,€i\

.,.-:-:

,:.\

,,i.,)

i: r,

- :' ,t)

"1,-.1a

W =u*t4#\v -o^bx L

'245trc-|?/b +b,/ *L-/t<,A keA

o

??3 -

-l-.-|-::

'vfr.ld-b

a * H??-{ -7^j?'t',0 -' , q' z,

?K.fio-nH.

L\) $k*

D fh,'ct( plfu-

A) f.t + osih *Jl sho;n b'lu*

-G-Tt

V,<,A

Ca,r- -T - -tle- "L^*

.sLfu lde,{ace- k"t b lYo'c . i| }t,.- i

t1n^'clsnr^a$ W P ', d"ubtd eua@ il.>l-tv'. h"L i

n h + ,u F . issu\ t-s H€J= ea^Ar^..fir, ; acl&e(

i\2a i

\\ to y - il ) \o /- \il; ( ol ' 'lv) l[o'l'

w-gI

? r6X.-+;

.,tl

CAr>.--T

Page 26: heat transfer gate notes 2016

' , H:

d!fi.,-l"A*' \ 3i::

O-Qr-1tcnr 0CI-CI

/-' 13:,,+- eq_ + =-lc=d- . ai

f,?

s,6,, ffift €:t:si

7 eg oi'i.

v,d ' ?l-oi * ' ?,d/ z o.6Q

s Il,{\:

'i'''I

f-\\, ,'

8o R"-{^^"hu^ t -40'/' J i

:

?> & rg'a- %l,D €]

i

0i-ct

i:€i:rD O,Y Xltnr

€ i. ei

e) f*., puJ* *'{.,oI":T-1 ;rmil.,uUll ,f*., puJ* * "1"1 ';; ^^ &: . ?-t.Fu- 1*",n^!. co',&Jule;

$tW:'ffi:;i:h;Y*n,*"", :^ \7\{- {- ,.LJ,-U Uil*Mfi"**'"-tkl.' 13erA":

:

a_r Qz ffi *ry Lrrl

'{= T, t *W

Page 27: heat transfer gate notes 2016

,: \

,;E:-?

t -1i!]-1'

( rt.)

.,.')

i --)

.:.:.:t

''1o.).,\

. 'lr':/

i:'l-l

-.i"'r::.:l

i.J

.)2-,)

., )

,t \,:)

! r)

i..,.j

iig

t1:-:Jr:--l

.-:t:r:: "

|'. .i.':

;-.:;

' i: -l't)

l:--::

;'"...\

t) Tr,* * vtzo,

':'!

2? h& l1^ro aF

o= af

'.

\"

|<* zL

+ s6b + t1^t.,l1vva,D L ^rt

A 6hr- 1l+ 'vLzo *' \wlJo}t.a C"'t l'trr''

c*tv,v si& *;;' *'*o** a[ o' to'-U"f +ernp b T' GD a']$\rn'A

ff*yffi.ffirsffi,fem'tk&tl-bi* *..3 ii'n lno^Ah'

*v

V,', L

,Q tSuo,\' ;sL

fr- +{ z'odxu r\

eb- - -2du' - k

Page 28: heat transfer gate notes 2016

{- ,-o tdrc

oI [[il#,-w

{"tt,"t?

g-liu h"F cond,^ph\" i, qd€rtnd" q' o'.,_*W&tt e1* 0

3 vr +^Pk,*

z- vT rV!.

=, dr + vlq-

z- v4 't g7tt

Y, vd.,*rlr.- *fi * +f"J-'>'i

Tvrr-.o.^uc-.- ̂ b "saJJ d- anen b q"''t- "f ^

g ^'bd^I @ i

,A,a,*e\ vff"*srcu^rr sl,h fTtJ T?ii* 61"'b' e

prnfio,,rn Tt,ut' g a rr''J^ g-h* d*,;i & Tst =6(N'c 0n A ILL el :

ownorYteh^p t\w tr=#iF[i}-'qT *'". 3 [1<+, t-o*A* , lr* sol^x , \zb'3rr'trh-Lo'ts-,,tzo-rsr'r-, ; f

:fhLittltta, ,^r^ll h04+- i**{* Lae+l'b 4;frr{*'x ''+ t'dn}'d o i-

Td^#tb ol- t<g 4q t^mrpt O e"tt ^h&",( c" g $

-= 8L"4

l_{7 A"c

ffi,:a

8's,s{3l

a:

F.1 i:wr:t:

f),.e:

el!raLrgi

6@

e€it

s&,-@

e@

el

l@ :,:.i

@

€s@

tbT#nlla

dbL

,/ x*

r(o fnax l-c,*f oTr)^Yt *Y @

9>

CI)

drA la"-"

z ttdh*tk lr{zL

2 -k t#.)

d?

Page 29: heat transfer gate notes 2016

'" { ..::,: r.:::lil: i !-r ;::,;::.' ::: :'1:.r: j --;-t :11: : ;.r

re).\

gS; t's3;0'e(;o'a3 ?

a: .LUD*-t'Ci'o

Q 2 g---u's

lI

LtE

,: ::..!:.::

a:f\:./

':l

\

. ,j

II

--)

.t

\

.r<ob soxb

a= g{D- z o

n a9 r O''tLb Ko

.6rD-C @

'ojso

g2)bs

.Z6DX Lf = /4so

_L .t b.) n p,l)I5 ?a t<(}

;,S3,

*s*l(s ?

O) S rnt*c,-l.lic- l,r^[l dr* LTboF3/^s,anA sp*{. L*-Fo'1k$/drl'

4 &o ?,SCrn cb ail,,.rcrr ;.,o coo! in a^r- ol qr'a l;* n hil t*ryk,t1.,- b.11 ^,^ iz-s'c ;yf n h""d fio cool af 'tr*- 'vtJa at'4"c/n;o'l+li* i

tfur*"^I" Ita&t"l- i|..aeL th!- LEEJL A^t) Ut&l,.y/'f'l'*l' ' lh4- ,-:tT :

hBtT-To) = -tve %,

1.f

+' I e

korzo*J fu'1.

zo4n.*<{^;a{"

Page 30: heat transfer gate notes 2016

@i

4i> dr"['d.,creeq- hv,., 1nctca2l f .i

.'r.'- I vtv'L

0ilil 'tni,n^* 6iY'> {n"l- intwa'>z h"t" J,cx.zlc , ' e

4 o hrg ,?Andzr^ ",

rmh of' ,*+ Lass. fior" la. .r^#"* ,r}ild J*r*E''

$l) th!- h^| d,l,.^r^ fr"- .^^kbtq, l-o r-uelJ.. ac>osr orr, i *& ;u"ta[ lLu]rr^p.!^ |a"A^r}v,n^ O'ott N/1a1.. 0^dlll)r)r.*r- O'l$w '6$au/r@

Txo, kn"g +t,;{**Jl d -b'C tk4',hilrrcJl kw.pb *€e. @

2S'c ,30'c , 36'L t rto'c "(@

9-*

g- *l(D l:T"'XArt

1-t'- T-)tu ? qY t

r{

,uflrtYN'' , I

\fal

,q

l6nn -t

@

@

@

s6s€oe€

e€seegep

$e

( ^ ,r-j

r^-)-) $ o;\./t ii

f:-<l fr

l rb-as-

S) & ,'.,16.{ brtL 6'b rcoli'* .to.- * '^-|'* k4^tcl'1o'cin

, tul+in ax r*a so'6 a*^ 4Tb i* * 4ri*"*t *'"

56uD $/ns A o'Ll ,( 14$k n"4 'r fi z $o Y*"X'T!'<'

}e*.p q..^,k+. ;\pI../. r,,,-- uJilt ,,4^-.* T?, fur"" tzlfu;t h [u

fu #- 5".0t t" 0uut at $6'c tD

srs , si,.f t 0'l!7 &ElL-lR -1,o)= -{vt' a7'

{ \ s:ox-4rott'xoutno-'r (3o-(o)

-

> - =r'-r-L 3 u7p X 4/rrptl4r,ixo)#

o'1ad u v - :'i

Page 31: heat transfer gate notes 2016

..,..,,.1,,.)

r.}5-^*

1-Tn

-

n-u

)n T:-fn-Tl-k

0ss&n*- q h.T c.x# 6T hub"r b/nrt" M h'[- $a-" sr./ap" l"

tndmoJaled.

qni^or^lqlJ\

unirw^.tp[J

& 1or- 4r'a.$6oa Pip e tmnq r$l:6* + l-WZ .ca coxr.A,.d qn

ir^arrlalfaa , lU , O,6o/nolt'. { taru^ lLr} lo t1*' S,rruz&hd"d +5c

<-

:

:,!

$erl

a:

^,i

s^^oroll"otry. W!.Ytl )eobhrcz- qn^fl & \in*r;tlanot 4€t"*"+ ltt- *yff*ry " ecro'rl.r** "{n* &:.s

f-,t n*,

-gl.ah., nikh Scr^ i'^aJo^[att,

til L"1/ * ,{f4?TL. *"#vo'?\rY

Page 32: heat transfer gate notes 2016

0cHq,l{ -:'/ , ;i# A t*rn,rt lt' /l4l lltrt

? @ i

l-, t ur,r,..)r* h'L t*Pf' -l I| *'- - " o'L> F t'"' coe[f .

CI

&p7e! Qrnner-Licrn otr N.lu\*l Conwctt,eq ( I tlrltl € :

;; ai6,ru.dGrnech1-:- ', ;i'

" lwd p*"1*!*' ;

. , firr*nI aa,*r lo4prt t Axa,Hi €r !IIJ**'=uu r ,*frf*xFt* iw* 3 i

-2-' ' ',/ ' $lroj tffi" -. 2,

@ i,

yfio r.. i*s

#ebeaa s,r ,r;i1 gto,t,e# *

i

\zv* ,=yW a*+ 3i

5#- si

, clq. ?- c]anryp in rrebiQ " t1-otivtJ''n e i

l'

7b 4 -- o = el

2 PtIrrJ i.s ta*",r* il*t E i:

Iq-i ,.r-lb s i

-

,/'*'i'Yin$w'r^gs' ' *''La*ir,.n, - fl^, ''rtJ lot^fs/rno$Y r, J'"-l ,, ; i

bn*''oa T'''bAJ g i:

@ ^^o,H,r l"*r. f+,.,.o :

. i.-

loo *rno' eFra i:,L';

l.

\;t ,

;r.

= ^*. iiqp' H

-6 rtt€p E!

*x./,x

xx?{

Page 33: heat transfer gate notes 2016

z v:rlat)ry>)( n"eLr^rhn .

2 3 [s--ll-fz 3L . t3.tta: E uL*.

/.'t,\_

gsrrservJiq 44* - crt''hl^itY

"1n'r,. ilorurh* l4d)1ro.h^,n, €1,

- jur. dl .t-d5

4 /,/.l-L.-L

: /.;tVL

L-T

?&/4

i*3 w

fig?-#

: :::

.- ri..j._:..-1

fItoL

,, n*,q Err*g 4^

GD=::*':j*::5i3&Iff ii&SjlIi:ii*E.

lr-r, s' 3r 5c

Page 34: heat transfer gate notes 2016

ecrn4 z- -t gdll.,1, t t\'o

0rr, = l. e Lr,. -T*)

-kp4J z htr Lr--To)ar5 rfz D

.l-1 z (- n ff)*,@,

4 * ttl )

d'f, L

aTl*'

b!X&s_t /3"f- . ------:--;J-

vil'

^r^^,.= 5,laxdt

J&*'*tl

*h**ff,r">d't*

z dudgag+ O

fttst ava{)& s@

€@

\.r }"'bab.--4.tt-

i!:t:5:

l--i.:

r!t!-'

e:€i

&W4QSf k l oe t-Jlf 111-u+ @

n.qL-:'

e.f.t,.;.'

*,€

T16'l &

,-ft'L^ CI

---E-c 4@\ @

' nilU^ utP

g16l*n-ll

\'dxe*

sy4r' r*-_m^s )c,l - fn*t*& (w alt"ul

3 F= ;yffa3 +'**[rudgdtr r<xt'l") l:"--u

.au 3 I'/ I';u

'dY)do3 el'

-t S s2,r6g* $- tsru dtr r auD o i

J d,d3d?# * *; n&Yll H -r ( etrudv1t H=o

B II dn-dldi (P-* H "W)z'o :

*

t3 i,

e]fu'r?l o- si w*4 EH

Page 35: heat transfer gate notes 2016

tB gct tlrll.-i/

:r\ J'lr^rnlu,'--- %^- t-Gss

' .,)

i.)

.r}

f,)

a):/a-.::'.;:)

'..:'. /

,fJ

(., )

I\

')

iriI -,'

i').r ..)

I: -r,7

t:l,:.-;

.: ,.

I'- \

k-.:)

]1 \

ii

'i )

,.-:j

;:l

,: il.-':.:

.,.]

i,"1

';5d

"u- " ?9, oV'L ,J

flryI-rnfrnin?nv shrrr,{o,cc

T)s

t(vd'1'tYW

"Htih,*"lJ""'^".fu*,' !41e o? P0!*

r../il-r I sw+v++dl**Hrr)a - sd-&q ]

.

z- f ^ LW. $a r la* *-

tyg{4 * W- W*^"){l'

Sd"* f"Pk$)"r-['oStv

U1\P+?=

uc-Airc,.lrc'n *

{sudP}s- ?al9"Y^I'1o

'-(), (''cnhT 'ibq"

,*-rrb' , r* fu"D-^"-l.u>r rf,hon^t Ln^ <1^ '

'., Vdh '4 "'*.:")n+r)t 1-n- t

-

.tq$As) i

r------1 :-

3 (u+$ax){l :

(u+)U 3,.1W--E-tt

I ycL<rr"1 ,

lSvdrt't) q ' i

p+$r"Fs'' ll

'

\ hr,;']

,**,.$o

-> -/+',/.

8q laf4"-qfit

Page 36: heat transfer gate notes 2016

.{t

"w)t$=Lil{,*lq

&ru^&n'r tqerL

\ril\

Henu, I U It.l {qtr4^-q)dil= r,k lr=rlt-

Lh's L[t.t J-L" u.o r14t,-tyr]= A*]l_o

iui "h[tl At'-f,)rrl

k t J:r [qq-u,,-)*J= -/^t l5=o

I fl8qtu-q*)*l , ,^^ t-lr-o

@,{;?.

{.,?

€lj:

$$'e}l8i€;0€.i.€rqai

eiSi€i€-i{J "l

{}.:0:

63.6iSir€i

ei:

e:s,

:

€:i,

s,'€r ,.

:'

s.'.t.J

.l

@:r

sit) ,

liBL:@d

Ufs"ar'ir" Bt':gE

\( 'r"

-7 6-).L-dd- 1)t -

ttAx.t#l*

pJru%I * k pJs**rld! - [,:*rr*u#i,,.]r{v'r-ur,nr*kn h^*-]. rn-UhrunLr^ -e*Ity ' ;

z -Ad*klr,o :

;

k [l:,uuild 'l< -kpr'ruq,atr]d'c z - Pd*'ftI*o-.t

LbrL

ttorn^rfun i"k*r"'le4"'

1j, "r r.)-lh[#'as',1 aQ, ti t

-,ll

Page 37: heat transfer gate notes 2016

-l\'.r:)

''.-:)

,;-:n-

'.t 1:i

/5i :'r I

r-:\l.l

a:\E-...)

ti-?:\

[]'r:)

,,r,e fl\ . ,r: d&a*s;j, e'\

t:..)

i, -,.)

i.lts!

r')',t/i,)

'-: _,!

,it)

'J'::id

: t:1

r:.rJ

,,r,i

l.tl

[-),:i:l

:r':,

.!t il',: .::;

.*y'\l^". .P -^\

iii) g= E, " H=oiv)!z-o rb=o

DU,

L = +[t)= 6+b(+)" u[+f* d$)c

En ^dar.^,J

Con&Hau

I/ V=e. ,,

t \zUn )

hiit

x=oY=E

9z!-=

it-=

aqtb+ c+d

u.( of *c'z&-)! t.rc;ttf+)

f Iutz'{-{)."kflb+2.{'?) r Bd t+f = o

b+LL+}dz-o

a0

it ^ifu,-

)

I

,

I

t:

c,'> ?+o

fr*ti t 0' (

f!- z.L

D5 ? t t.* +sa"C)tl

z ts Lr.+(dHlLc+ d=afz;o]I

b+c d= 1

b+ct z- t-

b+Sd--o3d= -b

-1zd,= I

d__l/L

b=\/y

\-

t-lrt. ""

1..

r-V

f

Page 38: heat transfer gate notes 2016

Wry t("e' ) tffi,**if6,# - E'S,'lDEo"*' 6 t

b-fl J,, ::

*?:!) fz,f H -u,lkfl fr- z,t$*l(+fl4 e

'

u',lj t "/,1+)-+tp1'-?( SlLrri|1'* ?t+)L)"t+)'l/a E:-

a r (@i

,1 Z,\,9-'t't,'t' ?'bt='*- 'r\"+*+h

g-t iff: '

;,'flL- T'.Zs -!; * {t-hb B i

lL-r. uil

fes =*?o-h)t =W\ H,I

i qf i

a,-s let[:tzt#*i,';li

tr{"*rW.IH2+ I +lr*,+,1ts ut A,-t\ofi= T*_6b$ - reo Air- -ff -=*"

xk*T t

',

",c-o(e z z8r*_€

*=W#**L

$i,pisi.@il

iir:':a :t.

:ir:l

S:,'::6':t

::,

a'-a

'l

-:-:

i:tt}..

:,,. :

, {'_} ,

:..

: :,'::

,.i\ :t,,:., ,,

):.- - . ':i:l

l.:;!a i::.:w a.:::

t:;fP :'t

, -.- I .

,]:

e" iii\i, i.:.j

sH

/'/.?L '.

3 u..

-L7L2'-

z-Yr3

)A 't'L

3U.o L'

.,5 tf"qA'

n *2. Lto- S 4i-

=?-'13

*= JE*-a

Page 39: heat transfer gate notes 2016

:i::i:-: -i.-*-Ji-

_-/\a9

:g*:,i=ro4i:;at',i."'...n ": ,=li

:

l:

t = q-6q,L {-6

$ =. ,.'6qr"

{6a"yh+x*ale-1^* E*^'J"'d

, -2

)

D W&M27^c

SOou

l: i q^ tzt$ -v,L*fllt

i--rrr* lz*-t -'L*"ql:? $ tt* f 52. $-'4Sl

s7, 5Q* E

6rL(Er-t,) = ( ln,-- h, )

,

', Pv= R-r i, pzg(f :

'' k"3 i'

r s!l-, 'L t5-4.*a r., -.",\P:t{ni

' --.-'I ?. ldoF(1A - /t -'

r l-{k{7b

I

ARqtt 2- o4"l ,r*^^

;:

,> r.5:ri zUztli:-fr1atT--'s?

t"ff" linicl.ruao .

?r"r*\ z5sL.h"tr

1

A) Ar tf^ o\^rrL " flal- pt^h urrel.r v<l"cr\ * "- | v<. aI .. k*

,

* I].c . brfu)^^t""u th,e- ryurD fl*, inhro&r-.,A bho<rn' Ao cm 4 3och*

t*o *** ('^'lt"i * 4l't^d Yld'

l

X = 1t.69 tt .

J6*

Q"r, Bphr = ll'oud'g' 1

nt-ojj's udy.l

(rl"--,) '1

Page 40: heat transfer gate notes 2016

1 .rJ\4

, ,i; 3 ut:\?

w

'\:

/V'd,ch9j-*r5vitt'

--}r t b4'.go" -7

- ' fi'r 7,/.///./

S(q4q d*)&-1. B

1ft,<) 6)(p Lr+#A"S ;@

ss€ee@

€@

.@&B@

@

@

@

e

rr$caz, h"4 ^. E

I

s ug/*1 + s Yyldr- + Uia:*zQ*

= t l1y{*uS ol. +t$ J*)cPd3l

+pta*1ft"#e)lLy/.\rH*"'ffi"J-;ilI ;

l3rbk*"o$ 1 codae$

+tfrW1 caar{l It*#. *q$r) i*,4 *

An

{tr

A

+

t&Fu

"Hf dn{+*rc $ dr'45=

A[Pr)'* KHt a 4q

LA/-%

I;d"uur-El,. U-";r"tE'llPtrnlna e1n t

u "qylh*rh *"

"ri'ir^rt* bi\ $

\,qrY ,l.t*lt r"tu"t b' @ lir*6^ka @ I

t:

#@;

;@dtorfl+

ffi^svort't'f)ongtf..l{t

1 Yo.paaln urd h r:L- lr^ u *.J.tt "

Page 41: heat transfer gate notes 2016

- -+" .--

*-L\, ECf

Ero,r.dl\

Oclzr,tq

,.,(G)=t,/y

u..f+?t'owxlag each olt^{rL.

_L

-1o

' tlSL

'4/Zi(

lu, cgrlvecbvL L*l h,qn"1e} coeltae"* :-

h ,rtx ,MrL1;u., (p,01

\t-.C( ko, uD Le ,rd fu" SF )

K". = . ( kJ. [,'zel"{ - )' (-K%*)* c %;uc'eA"f

Jn)

safn

">

l<- a

Q .1^

I z-q+e, -l = -q-b-d

L 6 vqr1'od'D

t=Q+eL - q+b+d2- =q-b-c+d +a*

o z. ot-e*[q: t-e

-li;d -.-l+ I -{'i,b z + -oii/C =. -l+-l -lirr

:--q+b+c-ct-i}+

= -Q- e.

z d-e+$

Page 42: heat transfer gate notes 2016

?r z- c Lkr-e Luf Cr)-'*i (r^)t-L ccp)e c $t

h= .ttf t*)L (#f* e Hf tip).

Nu ,-> cRelPre

Nu '| [Re,?*) '

h't'Ca deerhdD' s[onql^, on Cp===- \, n

in tt.- lerm 4 v:"ui"l'tl.

ltrrr,**,t ,r.- 1Irt"[.ru-

pp"na in| ->7

L U 6o rSYr}c elhl'L vatiaL{ro

t^>ru' .dr o/l{- tt . pOroot {' Cp I U.

o

+*L \x lu{t''Jd*

ry'*fur'*

.taT?^a^rXm , Ea , -K'd*'t

a$v\' o

fz -- coa * tll sudu'r I d'c

' E'= Jlrudg'r'cp'T +$tJJsudY'trrlJr

ftt*?""? eryX}"lancn-:-

!" uiSS + cpr" h tll 3udg1& + [-+,.dt r']7$]o

z J: 5eAg6'g t htlf tua, hrlJx-

3- t-JI lu av urrJ a1*dil tII rqdx cP]lJ'?rl- L-' v- - '1I

,' =k%l-r r-

Page 43: heat transfer gate notes 2016

k briu lr= o ,

= ,.0& )r=o

I- f rhbL L Jo u (L-T)di ] z ot$

lr=o

bbx.

uroI rj'

tk-)

t T'-1""

z-b ) fa.,-r,^s) [a-L*.tr]H * #{

,4.-q ?A b21JDtZ

o z-) e fo*b+zc taA =

E : o1*r', z> ,Ao €= z-bot-

[b.'#l7-o .b'r_ =ot,To-T,oE--8z

'ltl )

('.l-Eb--Isl!..i1:

:.i.t:.E:'r:EEE;h;

obo^e T.B.L ; -l =T* *o Inl-,cqrrc.l b<Drrvazt)6o olk TG.L

Lr^-T,oJ

Llb-fr-T,,u

B.t1) 3-0, Sv=o ,

til 1- Er

iti) y, U *,

Tz- I..r -ii .>

= 1, i a,*U-rc +dz S+c+d _tiilbTE=

UL$fI'rJ z.o(,*ly=6

z q+b(+)".[*h a%arf

s+slO

-tiii,

rr:-k,u e*

Iv.)

Page 44: heat transfer gate notes 2016

b+d= L

bt3d =-o*zA=l

6, - -V2- t

= srr{*)

a-nl^t-,-" _Ta _1.^:

FI

$(1

13 i,

6lisl'

-7- Ta

a --TL

L-Ta,{*

e6J

*t z+!b5 lU,o

No^., t*^ t1'

%Ly-t)t [f U^ Lt-E*) rrl'o

kIJlkrr- #\r,l z fr_,-N;11""

Z_f]r,tll'[Ln, ) *rrl'Y,f) [t- "'tv;*t"|"

,sr - q - Ly:.*frS *rr+"\,'J, %*- q$i ?k+b'* \*e * "? f'r +- jt

Lt:eI

s*e$-

t3{3

ta

@

€ss&r.J

s{J

b6ffigS

3rbb

trtd

m

gS

.rEl.

gq

16T{r

3L

,)

trY

tra+i

tlATb.

L@)z6Y i

* l/Y

rbl1s aJ

"61

L.?.

*, u, -\ L *)'u* -+ fu l*I"T,,-, B*L-l-E)zt? l":+-18 tT7 r a/

-,J

B

:6

,L+Y-iW +|

Page 45: heat transfer gate notes 2016

__._(9*_

t

:

\2b

,-g--I\"3CEr)1 ,'?o Zsl Jr ttr) +

l3 *- Lr','\ 6Lzo zbo )

{"" :cr Izd

-

2 t+o t+-L [g:tl]lwLzn J Zt r..v'E

k Li,,"6lo(z-ffi

(.*6) a *}Yt!-alL

zsl swE0t

)e-

Nac En tc) |rl,rrl,wo:*

^r3 Lll & -rt.5 5r,r"

'os ["'U -+6- *] 2> #

$ = q^ [t{tt--',., Re x-

tL = l.fo K,13 tLt".Y

;L\

----1L) "

lhoa 4

to

?lo- a*l3 JQ.l

AELI*

zro &A 5U^

- \da1'@L*4 Au U-ls JtJ< )tt-

{t+ fr+"\Y*}'x

Page 46: heat transfer gate notes 2016

r-

*tqlTrc$ 13 'xt\ tyl

+ Qtzr -!-r-0tc

Grtt'c".-[

k-[- tJ l:(,

i

DY---dtt-:

LAJ6E

-v)

-#w zo

&?i.*"h'J

z= - tz-lYw

}lrzbrDx-

r.L )vv

--

Vx-"

+ \rn+Y z_oo D'Ll

3g)x- -rYrclY =- o

+Y+%'=.at"q*h1 , 2 )w>t*

Y

ln,J't +Ing -o

)'"\# ='ln L :

\.r,?, z- L

j!- o

lnc

t,.rarr,'^tL Sgar*fr,5^

i -- bg \rt5

C.Cru*hn*

i l" flr^J cI

\-= c).b/\

Y3.* 13| 1?r

z- c'tt)q

Page 47: heat transfer gate notes 2016

-,Ub

LS-)

v{ox-.Yo---)

l. b?69 Pv

#ft I Y=i3, od

i

q uuatirn ,e)i. b"dd,t- \ooo ( ,blq'+ f"" - 'th An "

,,1

Vc*\ , EL'o

-5/uYl" I

-y n:/\!9 Pz

-rs *''- v-3/\lY1,r

ce- o-=- C'

'2,lY Fr

t-zhtncrz

r) Y5-

7{oz- b )

l3@rz

'f= r-3 fit\k

h tg)"']

,t ^r5, 13 z,qh

)z / r \t"--\l.D?6q I prv"

)z I

l.ozs

Y=:. b.i

?..-'/z

Page 48: heat transfer gate notes 2016

t> i-+ >L ,

dr) P*=r tir)i) l'(j-r

ir< J- ,rz- L__ _,

}>t ,

rrurrnA Et < I8r=E

EulE'

q>E

HBL

@ri(.,3 t

Q',@i{}.:g

,i

*,s.

,.

6l:s.&.si

ii@ir

l.ei.*@iei&i'f5 ':'tt

.si'ls:

Al6;€i'

l:€iI

,@i

ti) I

€),

8-Et<t

/z ..//-----

.7 ,/ ,/

------) --=--_) Qe,,v1Qr',J -

-l<n*r z-hALrh,-T*)bg 15 =o

+,= -k *lo=oT^-T^,

z\(+) -r(+)'br=

.b3Ir.. -T^)

?- -k+

f g r--r #"f l}Lnu

a tL-To)zE*

t*lJf -T^ @E

ziL -"',

.i:

o,J ,,.1":.:

fA !,::\., i::

n:

Ga l,:E t-;

tr {bL

L* +fd* ib Yt*$

Page 49: heat transfer gate notes 2016

Wy

h"t. o\^ul lu gnhYr. hyn"t ptdt

h,.d*.

'A^fl

K-L ?rlb g. &,r^rcl,Dls \,f).

fr = o.ga t tg*, Br)'' P&

rltL_

K

%.t:

l oc"l carrrn l* *.+all,

-\(YT./***iffia,

3l( _z._J_ k

/-ozs

l"=

I.Ju, z o,l$a P"")'- -P)'*

.LL

,

I h+=

;I

tq"f

aL a. Z*, J*bn* L k fi;; *'t t"'-t ll L*'/ &'*aVW'?

al*lon- x'

i,loJ :

i '{r-I)-.rlLRJrf7"" i

iItl;

.i.i'i.

IEE

T = iJ;

lowJ At r^"oll AJ6 ,

0.6( q fre

i-t

wIrL d f\J,^rar-I,+ Np'

Nr, o*+

k1''L ,jtl'

Page 50: heat transfer gate notes 2016

gcbol, I t{

nr" *tq"g I"t'Et

?olr^.^.. {o**:lTYldP =

-T

2 4**

duzLdo,Ll+ /du_

#*;*,v"III

t

t/tscoul shqoq, t-^.zmrA.,cuz oho

,txdtl* .L

dY

3"1*'.1 , t+=**"r.-

Qz

u" = * [r-*.lat%tOhm YzO , V- Urr,^x rUo

U-o , rrfi ) o. t_L +c-' Ult drc-

c--t- d9tqlq" -dW

tJ'nqrko = 4 d?rt{ff '/d)L

G h%^h',eall' 4^ol u, -__j'l

-

Ro frr'ltqa- l2u'h> dfa '

1 ./tb\ qn,l- t.l -* 6l, l'\r1( dYl^n D -\t

"frffi,&

Page 51: heat transfer gate notes 2016

-

Sr&u rf Rz= Ji ,rtehL

, ;-3r;f*a,z f:.n llu"tr_r;),0"

=Senr,Jtf #,1:]

Ku,.o/illT+]4

,-tZzt

Llqv = U"/,

Te= UdJ

Rc

?, ( 2too

te ) Lsso

. ULjAL

= YYlct

II Lto.= Urntnx.

fJ

;t.

!,

F:

II

lI[.'[1-;EJb::

E

^L*!L8uL

4

^-r

l=-.s"r"x ttt^-jc'r a*rqofr^3w.

Larr,.tlort

-fifrbrrkJ

x &YtiltlYL

It"-'+^

,t+v}'*WV

J'*(."t &{^"

.rrDYJfXrr-r-?-41k- zrN---',

E-g-g

fi*- 9'-"fi"{Lviaa*

{"r*

Page 52: heat transfer gate notes 2016

7

//-11 QnaXAU-' ,r/ v)?

./-'

;?---, W-= ku zrniJ*p * r:

,b

k---da

os

,LY

c{g

#s{9

€ep

*63

r3rflt:J

.., 1

)_. J

r-a\wri*

@

}TT-la

+$ffi+$[xrz*dr*

z J u-atdrt*$A*

*(r*) = k u,*#*[,+,) =k* -r-rtvl W, I

l'*? ['*"iln'l '

kt *) z_qy&y*

*r L"T*) = u"( r-#:?*

r', = uot+- *t *+rc,.?uz 7,.- ?f t *

t1 -,r*k*)&

€\t*,-i;W ,!r'aYv

:::r:

@E13 :..::/

:

r3

k.r..

e

{),:

d:5

,d\ ,,

ei

€,I

al:

€i'

I-*J*hy t

,

t z u"L}-#ltt +14

' d v i-u"t+- #.,1 I 11+ ca.g,nr+ cL

Y-R,'T,r-fs..

Page 53: heat transfer gate notes 2016

i'11

.ail:-J

-;r\r-:\1---t

t.)

, .1_\|-./

T;q"(+_r1 \r_ur 'i =

iiF )* -t -r'o1+t{"o'=}*

uo/ t'_y1t 14 l[Rz

lia

krg lrdnh,*ft-

"J*tad)a-I[' -t^r qf t+"-#-?)]#

-w\o+bY'

B"U. eLtt+h a tulk h,.alo x 8p. l*J X {zan bt rkTeS.

z tsul'L Fnn",tf.lBullcrtqra X Sp l"c*t

^R, . - FI = $t,rur*raz)$J JoR ut a"Il U*rrtdv)q Jf urAr

A J.R wa,z Jo( ,r" (, -t*-) yolr

z. uo t4 #ll&z u"/ry-fl = o"q- ?

=.loouotr *flr-+$( #-#

T-T6+ _+R") *#

[*.,-"stJ' zo k"*f '

E"Ur tn{fulo"

o lou uTvdr

""1: r-*,),r"Jn[,-*lr

f r*+ Iq-

Y

T

I&

:(hLo-crUo

M\

.lt'---( n2-

-:+

-+)*t]*L# *-i)+*l dr

.6-t, s-,*.#u

Page 54: heat transfer gate notes 2016

zuo I t+-*)

= (lo

r**$tt--*.-gtLI

L-32qTzu.tg_S)o*+$

to,( +_

r,. + uiilh,E---[r..f SLr. - tl4t

)l>e<

t.:

[-+rLsQo R'

Ll

Qo RtT

;)

R'

t--lLqL

Ito I

!1_.b}(

>-Tffi-

[-br<.,

']

l1

l,{,

ory

It t&&" ,,.

Y k LY*=\hrfWYR ",

A lrr : T" - 'ke\R'oa t I' i I , . ,. r

he+ -{-t^^ >tnnoiv- t,^"loh*

cfi"k"* -

=+-E#&l,.o

au-/$:Q*''= Vtru-Tu)

kqlffi _ qu3 \lrUt,r4.{/lo( )%tzR

ln, - 2\-il

4\=-H+

--s l/K

ITll

.z t" &"-ro)

= !.96 9

la?

Page 55: heat transfer gate notes 2016

7

da, a

f* t*^t-t*?.r croli

^6

; g t' lr,'nr*'. ft""av,.r,ro., ft"" in q 1-,.^h" t- co,-lq^F ht tqq c"o,"&htn q*+i, appoxi*L\ A".t l. LybL t X'6 6 ,, s'+8 , L

sD &t**. fi^",+- La",r{,J zortl k*P .,4,'b6, 3J*, s')<z

O) A tu.l * tt,rl*^-l Cr"J^,Ar\ {t = | '6 r^:/nnf }for" i..-.. cr. t-tt,&r^rlspr/ tl^d r,..,rLl R{"zlf,rD th15wd'" ^ Fp,- "l- Jq re,o,' h h4

cdt tht m,&r1oo, t*t fl,* s unl6 t,dr k*r) barn\ ,^a;h,^*"i,{re.tMl{ go.s} 7 tl 3.{1 : \f eq , 36,s}' . rlr.(k J*'r^* ia. ^ ,I d ,, ,* {* uor."

"il"v'36's} ;9t'etr 1* u"t^ u'ta }

i

O) fro- hrr l1A i, xlok l loR. ho. 'tn brh,rho,L avul [^tJ# fl*\ra0. Iu"r

f,r, Roos ; * , R;.r,, p,f,u,".r; * rtu

2_

L'qmfir^r. 1^ , Tubu r^c"tl +.T, o"rlq"*.

Tt*Lo,)jqt* *to^

u = 3'66

in & hhr

N,r = O.OZaP"o'tPrh

fi7- 0'\I zo.3

Page 56: heat transfer gate notes 2016

P"tql/.t1 tY u

Cp-Cr^^rrer{ Ab ,

ItW *lr,t- lcoh. uq bn-,r"'41

Ict

wer

.3

@

aaf)

ssa€"-}

*s@

O

0si'1

t-j

o$s€

s€er

s@

ss

NovoltI

-H'f

Gtd

H€ab g,.h)vqnqx

C,aross Ph",

@fi,,

1c*

0/er"tl t4'T coc*l N/*t '

4" it.J

'.w+

!:

irY,.

-:J .

6.r:riy 9_:

tfraHWH

-I\l

.l?d(L

{^

0 t mnQLTr.,- Th, ) -lmc ca LI;L-T;

q z- U ACat)rnuonn

4c,

'tct I *tL

Page 57: heat transfer gate notes 2016

v

.8.

rillr

;::)

#rB1;1

fr)t'.al

f.

.j)

r': J

r,l\.: J

.,:\f,-;:/

,;.:.)

in- -

:-. )-J

,:l

:.1

..,)

:\

i,\

J

.J

-i-)a/

--:1

e.\rd

-l

a

i::i

\

._r

A Lr^tr)(J^-r")

frc*-t"ldr u"^)

l, Thr-\e,

,SQ = udA LTa[)

$0."-rn1t1{r8 0 ; rry--cdTc

d rl = -_0q-t ich

d[g. = 6Q'rn Ca

")T;.dL=sam '

d.frn-r.-) = u; #[rh:t"i(# u #) !

: -udAt# -#)i- [L uao

"t rfr. *r)-r[d*^ * tr)^

JV*\-/^

uA f a-\-nnz 4- -T.r-1

1L-- a- J

= uA [q,-r.,)- Lrnr*Te)

jt' = LrA Car,- aL)

uA I ar' -aTr)frr or/*^

6t, - 67._

T4Jc1

.0n I,-Tqlnt1ct

ATiLTz,

Q=

q

h xr,71tt,

5W;;kry&

i,i..t.Ii1tt:

Eit:,-.fj.

l,'l.t,LI[,.,Ii.'rn.Ei,]sI:.:;B

, UOCAT

Page 58: heat transfer gate notes 2016

@

e$€,

o

Tao

rv@Tc2

-50

@

^teot<ctrya)q,^<-o?^o .

)

{-& h"l'r4 o-*- Lh,)

l4l .

0 Tnr

Tc,

q = hhCn Ln -rr)*

ee@

6@

ea

@

6e

h-(c C'rn- Tr-) Ts,,firt Jr,,T,rrm

I [LA?D )cnrrl,^iar,-r- l@

I lr.lwrr) rodtt e

)h,*L,tl*,@2I b bcl*__ t -^\4"^t ldt+ :tuLrv5, ;

{

\q6q = --vn,c.dT. , dTc'- ,E0_

h.Cc

Se=-%%drr,, dTr=

dTr.,- dT" =

dCt -1") z

ct tT,- T")

r,r,ti$.u{r . (Tn- T"l

-sorJ-_ -t \ "

L tur.or. ^.r. ) I

-UdA tr^-t"l 1+ -{-\ hr,cr, hck-

=-f-uao (#r- -ft")

1l

!:I

r' I

;:

i

t:

ft

@

@

GP

er9

e€)

s)

€e;.tr-:.J

@

@5

L

k

L ['-udo ( -L - LJl L n1,r^ hact.

Page 59: heat transfer gate notes 2016

a

)n Tnr-T%Trui:lcn

Jn rr.,,-T.,

\r- Tr,

: -un [du - #)-t oA f 9,-T, {L -u---

: uA G,-r;, ) * tTn;Trr)

T, -T.r1--l OJ

q=UA

a

AI - AT-)n Ar,/or,

z UA ATI^- af,)^ Otr/Art \ anrt^ u,^ro't^

tzv,-*V^cwaffiffi' 4t-'

)

&)

I:i

::: #^

..:li

l

. { :z uA (tfw-rl )

Ut , L&-r bt

Y:Xj;r".--b{tr l-o\vr4-"

6o'c I *o,r',ta'L J/

*nt, ) ts)1/sc-c, n'. t i/o l{lvk

so:t\,to Il,{

LoL {Lt , 3a'c

&a z to'

(o-ro + y4,10S5'(',) ^ {2()

Iil[.,i--^

hl?:t.' Ik':l

N.It.i,r.FiEIriEE

:_-

Page 60: heat transfer gate notes 2016

Ut Ir" !&*F '

qo'?

uro \soc\ ad c

\__* ro,auo

Qr- UftCAC) trcov^

ii@i;er;

Q..:!

&:j€..CI,:

:

Q,'.

*Jl

6i:-.:

13 ;'

{}'{,.} ,.'

:-:

eli€I

i:,

m':

$jLJ ;.,

{t

)

r):tlr€l

$i'@it}i,

.:

s::t)

i,

.rt) ,

k'j;1

u,

i3.i'1

?L

46

{ o'Lqb

LtO -3o

@,

o)

ytrtl b z '1,

uA

e D ^c ',^ T^e-a ^ h,^T Nilt '

? Ac[*l ]"'] l"qfu. i; t

Ftg,.n'nu* \\'"V fuaY'ol4/L '

-z hn*, ch ( Tr,i -Tr,J w nrt+(E :Q \'fl

\$Tn r)

Tc,

.: .l

€'iai

I

'')i

+.-B :E

raI\ir. I

ht-Tc)

Page 61: heat transfer gate notes 2016

-UAi

-

fLlhla

t--

tJ ) we'PJl y'tooott

Gh = nr\, (i",-tL)

V*y ttn,-rq)

\n TrtTr,Tt,4r,

? *NTu tt"")

f; -LLT,,rr)l*,*5,

(,r,4)* c(T',

=-# (ffi., *ffJ:w"

[*.')

-h<^E- n(trwY,W

:, Hr{aYi[ =I e=^.?*n_#',,-;

:

|L: Nb 4 d'7a""h'"Ir'i

tC r"hn NfU . I

,,0{ kr|)

II

C*,n- = Ct mlut

NTU -N ,

LI$

)/3

z- Lrplrv (rtcl]

T6,Ac1

Th,-T.,

G,-t,)-Tt,-I.l

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4"* +tl,u- ?ld .. , , - A (/h-/ . ff\^at lhJ-'w+t* ?le*r.. ]l.s h'Fwft 4 rw Y" il_-ep"lvrt4

k^. ?fu a,Uarxa A -t'^* i^f * so'c' h^a[ n

^lYl\L ?lt^t'

, h z rswl"J.Y

R.Jt rh"ib +rv.t @' t

'1

"4t3.'{,*

3,r5^ 9o L

-#h1 O

::::

:

:.

A{rvrra t^t :

q

t te| l4e^I ed,a,.y

b-,.;") u

b"ra^ t * *hs^b Nu- "y tl^t

( -d L,6'o

E dEaEr--"4o(

=l%

w k^p'

l-*

EtL--' zE5bTJdr dr-

Lt-7-{l

L,, Ld,L.

EB_o(c,

b-aEs

Jc(3

9-Lkb

?* Ar,*

l<tvylaft,t

65

.fi

Page 82: heat transfer gate notes 2016

'ji1

.:@

e

,e# + e,,',W

Qrz = A,F,z c Lr,q )

Qrr " frr1re(f{1i

Nol^ -f *y z A,Er, eTn - A,frt rTz '|

'^y'l t'f, lu^ [w" bo;x^ a.,p- ^*tu Aawn]-f

ArEr' 'T\

'SI:

e:,e,'€f ::

:.eiB,'eisi

i:gi,€;

::

@;.

@r:

@rri

Sls,'

:

€:t.;

€ig:

i

6l.,':

@i:

€x€,sj

:

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€,&J,

7

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€TT

b5

:

rJl;1

Eh iitgi,

RliYri(

Arfr, 'T'\

Net- h",& fuV - o, T,-Tz" ., *t -

eT't {A,frL - Drqr)= o

&Er-Hru=o rv

Ar E, ziAzErY'&"'\ 1k*"'"4

Page 83: heat transfer gate notes 2016

-; .l)rr.,. t*O* * *e,hl^ t/at h* t&" N"'ltz'tn"ls1'n:',,' ilt'lf b -

" )-.)- t ji.) n 7ri,G,E€;t A tF,r' ArFrL

IE t -q(:) tLL- :

r,.') F rr- {f.+F,.rriir 'zl " LL

5, -- t- fr/arAt

- 1- tatrto* 9-I') /' I ?-,u rRrf I

1)

,1-}.|t

t.I'ti^,b-

E-.

Page 84: heat transfer gate notes 2016

t-___r__

Ftnhr .a clr^,l6- &^ri\ &H _

f-,* CqlgtNl-[

{"

3,Lr,h,fr ,L,h, bTrt

p.z i Hl'lp

Burl;ad y*

#='[*l|il'Is)'Eilf ""ie-

-J-T

= LI,-L') fr

lr-.!L? Y,( r'rP1T ) . :

J,- !r = {, -J, ( rtPor )

: 2_ A,gttjr&o'

rr" { U,+|t^rkr, t0otJ]

l*cfflq',r. J3, *tpkl7

p+*[1/ L-b+d31 -l z -c-d - rIMr :- Z; -Yt-t-4+e"!

t<- r -t --b- 4

tI* r-o z q-6t e::)

Page 85: heat transfer gate notes 2016

A!{!i/

€.-.1

@-eBg3

eE3

,eelt, ,f tr.qo /.Yo ,r-:#" tpa,g:+J ;0

iL.flpyLvff +) 3&

+-Lf Cryn)L(#),1 X:g,

"q,f prt ] ?- L 0", ?r" ) 3@

Nqz-c L i

t!:L)^^,ue-x I €

l*),^-?"H, g

Nhz I-(qo-,U) ss

Vt- 271 esillh' C Cc,".fy)b€3

W,k , aaXuiil\ ^,0-

( R" ) L3

N u, C nJ $r).) -u,z\ B

I cil)^q^- f{* ayq- <#? <wr,r = 0'51 R:,"- lVq'o's:6r1" @

T4WA hrrtry, ) l'$- NrAn, o'','nf-'-"- N't'' al3Ro*'l I@

L*b-qzb-t{

Page 86: heat transfer gate notes 2016

II

I

:illiG

w:'tl

' 4?r

I]YJ

tr..)

Cr^/rrr*hb1

E c'trr"* et,:7l,w-+at'

i-t 6ap@[gtl r , .y1 i,; -5t ,r' o^ "p*h^ uarrt l,, crr',&'^ari. a, /\oll. +"rrvr-vohliltf.) Srlt^L !, u vot li6 solw*f L,,rh,* ,,*^\ )'AP-h* or'xa[wr] o i

s voprrisr4l +o ptod^trr te carcrv,hdkd aolh i.:o Cap".cih r .1,.,,.r,.,,,-l-\ r

:l , ,11-.F h, A4.\"1. as ttu ,*.elk cfr ,*f^?vlr,c*) vaparr)r,l'

-:: oY e^,aPoraJtel PI'L ttn^'L'

!i

.,1, fr^ttst'u1. a - r ,

i , ,&teavn t";1. l" tar- evporolel. l'e- IJAD kr^oorr aa 6teou.r uay$w1d.

(.) ir


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