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UNIT OPERATIONS II:
HEAT TRANSFER
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Introduction Heat transfer is the study of thermal energy (heat)
flows Heat always flows from hot to cold
Examples are ui!uitous"
# heat flows in the ody# home heating$cooling systems
# refrigerators% o&ens% appliances
# automoiles% power plants% the sun% etc'
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ypical *esign +rolems
o determine"
# o&erall heat transfer coefficient
, e'g'% for a car radiator
# highest (or lowest) temperature
# e'g'% in a gas turine
# temperature distriution (related to thermal
stress) , e'g'% in the walls of a spacecraft
# temperature response in time dependentheating$cooling prolems , e'g'% how long does it
ta-e to cool down a case of soda.
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HEAT TRANSFER
HE/, Energy in transit
E0+E/E# heat measured as a
property
HEAT TRANSFER# science in&ol&ing the
study of principles that go&ern and the
methods that determine the rate of heat
transfer
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emperature 0easurement of
a&erage -inetic
energy ofmolecules in a
sustance
0easurement ofinternal thermal
energy
Heat hermal energy
that is transmitted
from one o5ect to
another
Energy in transit
emperature &s Heat
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APPLICATIONS
Chemical engineering# process e!uipment%chemical plants
Mechanical engineering# oilers% heat
exchangers% turines% internal
comustion engines Nuclear engineering# remo&al of heat
generated y nuclear fission%
design of nuclear rods Electrical engineering# cooling system for
generators% motors% chips%
transformers6
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APPLICATIONS
Metallurgical engineering# furnaces% heattreatment
Civil engineering# design of suspension
ridges% insulation of uildings%
air conditioning Cryogenic engineering# production% storage%
transportation of cryogenic
li!uids Aeronautical engineering# design of space
crafts% missiles% roc-ets
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9uclear +ower +lant
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:
;team
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1=
Ski Dubai: largest indoor ski resorts in the world
Hydropolis: world's first underwter lu!ury resort
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11insulators conductors
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/ metal all has a diameter that is slightly greaterthan the diameter of a hole that has een cut intoa metal plate' he coefficient of linear expansionfor the metal in the all is greater than that for theplate' >hich one (or more) of the following
procedures can e used to ma-e the all passthrough the hole. /" raise the temperatures of the all and plate y
the same amount
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Answer: $ nd %
;ince the coefficient of linear expansion of
the all is greater than the plate% it will
shrin- more per change in temperature as
the temperature of oth is lowered' /lso%
y cooling the all you will decrease its
si@e and y heating the plate you willincrease the si@e of the hole'
T"er#l E!pnsion
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hermal expansion is
a property of the
material
different materials
expand differently Engineers need to
ta-e this into account
in their designs"
expansion 5oints in
ridges
i,metal strip
T"er#l E!pnsion
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his is howthermostats wor-,
imetallic strips in
refrigerators% o&ens%
etc' open and close a
switch as the
imetallic strip ends
one way or the otherdue to temp changes
T"er#l E!pnsion
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&O%ES OF HEAT TRANSFER
&ode Trnsfer &e"nis# Rte of Trnsfer
Condution *iffusion of energy due torandom
molecular motion
Con(etion *iffusion of energy due torandom
molecular motion plusul- motion
RditionEnergy transfer yelectromagnetic
wa&es
dx
dTkAQ wallcond =
,
)(
= TThAQ SSconv
)( 44 surrSSrad TTAQ =
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Condution Het Trnsfer
?onduction is the transfer of heat ymolecular interaction
In a gas% molecular &elocity depends on
temperature# hot% energetic molecules collide with
neighors% increasing their speed
In solids% the molecules and the latticestructure &irate
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1:
STEA%) HEAT CON%UCTION IN
PLANE *ALLS
Heat transfer
, temperature gradient
, not in the direction where no
change in temperature
, normal to the wall surface
, no significant heat transfer in other
directions
, If in and outside remain constant
Stedy nd one+di#ensionl
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Ener,y -lne for t"e wll
rate of
heat transfer
into the wall
rate of
heat transfer
out of the wall
rate of change
of the energy
of the wall, A
dt
dEQQ walloutin =
0=dt
dEwall
consQwallcond =
,
steady operationB since there is no change in the
temperature of the wall with time at any point
he rate of heat transfer through the wall is constant
If there is no heat generation
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FOURIER.S LA* OF HEAT
CON%UCTION
wallcondQ ,
dx
dTkAQ wallcond =
,
(>)
and / constant% then
dx
dT constant also
emperature through the wall &aries linearly
with x' emperature distriution in the wall
under steady conditions is a straight line'
==
=
2
1,0
T
TTwallcond
L
x kAdTdxQ
L
TTkAQ wallcond
21
,
=
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Con(etion Het Trnsfer
?on&ection is mo&ement of heat with a fluid E'g'% when cold air sweeps past a warm
ody% it draws away warm air near the ody
and replaces it with cold air
ody
T
ThTThq body == )(
a&erage heat transfer coefficient (>$m2,C)=h
!
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NE*TON.S LA* OF COOLIN/ FOR
CON0ECTION HEAT TRANSFER RATE
)(
= TThAQ SSconv
conv
S
convR
TTQ
=
S
conv
hA
R 1=
convR
h
?on&ection resistance of surface
(>)
(=? $ >)
?on&ection heat transfer
coefficient
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adiation Heat ransfer
hermal radiation is emission of energy as
electromagnetic wa&es
Intensity depends on ody temperature and
surface characteristics
Important mode of heat transfer at hightemperatures and natural con&ection prolems
Examples"
# toaster% grill% roiler
# fireplace# sunshine
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RA%IATION
rad
surrSsurrSSradrad
RTTTTAhQ ==
)(
Srad
rad
AhR
1=
)( surrSS
rad
radTTA
Qh
=
radconvcombined hhh +=
)( 44 surrSSrad TTAQ =
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ONE DIMENSIONAL STEADY HEAT
FLOW
ate of
heat con&ection
from the wall
ate of
heat con&ection
into the wall
ate of
heat conduction
through the wall
A A
)()( 22221
111
=
== TTAhL
TTkATTAhQ
Ah
TT
kAL
TT
Ah
TTQ
2
2221
1
11
/1//1
=
=
=
2,
2221
1,
11
convwallconv R
TT
R
TT
R
TTQ
=
=
=
adding the numerators and denominators
totalR
TTQ 21 =
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he thermal resistance networ- for heat transfer through a plane wall
su5ected to con&ection on oth sides and the electrical analogy
THER&AL RESISTANCE NET*OR1
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HE0/D E;I;/9?E
wall
wallcondR
TTQ 21
,
=
kA
LRwall=
(>)
(=? $ >)
*epends on the geometry
and the thermal properties
of the medium
eR
VVI 21
= A
LR ee =
eR 21 VV eElectrical resistance oltage differenceacross the resistance
Electrical
conducti&ity
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2:
t"rou," two+lyer plne
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THER&AL RESISTANCE
NET*OR1S
)11
)((21
21
2
21
1
21
21RR
TTR
TT
R
TTQQQ +=
+
=+=
totalR
TT
Q
21
=
21
111
RRRtotal+=
21
21
RR
RRRtotal
+=
esistances are parallel
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totalR
TTQ = 1
convconvtotal RRRR
RRRRRR ++
+=++= 3
21
21312
33
3
3Ak
LR =
3
1
hARconv =
11
11
Ak
LR =
22
22
Ak
LR =
?F0
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Totl T"er#l Resistne
totalRTTQ 21
=
AhAk
L
Ak
L
AhR
RRRRR
total
convwallwallconvtotal
22
2
1
1
1
2,2,1,1,
11+++=
+++=
TUAQ =
totalRUA
1=
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?onduction Example
?ompute the heat transfer through the wall
of a home"
shingles
-A='14 >$m2,C
sheathing
-A='14 >$m2,C
fierglas
insulation
-A='==3 >$m2
,C
2x6 stud
-A='14 >$m2,C
sheetroc-
-A='3 >$m2,C
outA 2= outA 68
/lthough slight% youcan see the thermal
ridging effect
through the studs
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T"er#l Contt Resistne
a!contact QQQ +=
er"acec TAhQ int=
er"ace
cT
AQh
int
/
=
(>$m2=?)
(m2=?$ >)
AQ
T
hR
er"ace
c
c
/
1 int
==
h?" thermal contact conductance
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hermal contact resistance is in&erse of
thermal contact conduction%
*epends on
;urface roughness%
0aterial properties%
emperature and pressure at interface% ype of fluid trapped at interface
T"er#l Contt Resistne
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Effet of #etlli
otin,s on
t"er#l ontt
ondutne
or soft metals with
smoot surfaces athigh pressures
hermal contact
conductance
hermal contact
resistance
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HE/ ?F9*?IF9 I9 ?JDI9*E;
/9* ;+HEE;
;teady,state heat conduction
Heat is lost from a hot,
water pipe to the air outside
in the radial direction'
Heat transfer from a long
pipe is one dimensional
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A LON/ C)LIN%ERICAL PIPE
dr
dTkAQ cylcond =
,
ourierKs law of conduction
=
cylcondQ
,constant
==
= 21
2
1
, T
TT
r
rr
cylcondkdTdr
A
Q
rLA 2=
)/ln(2
12
21
,rr
TTLkQ
cylcond
=
cyl
cylcondR
TTQ 21
,
=
Lk
rrRcyl
2
)/ln( 12=
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F ;+HEE;
24 rA =
krr
rrRs!h
21
12
4
=
s!h
s!hcondR
TTQ 21,=
including con&ection
2
2
221
12
4
1
4 hrkrr
rrRtotal
+
=
totalR
TTQ = 1
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3=
CRITICAL RA%IUS OF INSULATION
)2(
1
2
)/ln(
2
12
11
LrhLk
rr
TT
RR
TTQ
convins
+
=
+
=
0/ 2 = drQd
h
kr cylindercr =,
hermal conducti&ity
External con&ection heat
transfer coefficient
show
?JDI9*E
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CHOSIN/ INSULATION THIC1NESS
cr
cr
cr
rr
rr
rr
>=