lecture 5_may 2014 heat trasfer
DESCRIPTION
heat transfer lecture from UTP university for chapter 3TRANSCRIPT
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HEATTRANSFER MCB 3033
4Jun2012
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1. Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall whose representative
cross section is as shown below. The thermal conductivities of various materialsused, in W/mC, are k
A
= kF
= 2, kB
= 8, kC
= 20, kD
= 15, andkE
= 35. Theleftand right surfaces of the wall are maintained at uniform temperatures of 300Cand 100C, respectively. Assuming heat transfer through the wall to be one-dimensional, determine:
(a) the rate of heat transfer through the wall,(b) the temperature at the point where the sections B, D, and E meet, and
(c) the temperature drop across the section F. Disregard any contactresistances at the interfaces.
Problem 3-59
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1. Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall whose representative cross section is as shown
below. The thermal conductivities of various materials used, in W/mC, are kA= kF= 2, kB= 8, kC= 20, kD= 15, andkE= 35. Theleft and right surfaces of the wall are maintained at uniform temperatures of 300Cand 100C, respectively. Assuming heat transfer through the wall to be one-dimensional, determine:
(a) the rate of heat transfer through the wall,(b) the temperature at the point where the sections B, D, and E meet, and(c) the temperature drop across the section F. Disregard any contact resistances at the interfaces.
Problem 3-59
2m12.0112.0 A
C/W16.0)m04.0(C)W/m8(
m05.0
C/W06.0)m04.0(C)W/m20(
m05.0
C/W04.0)m12.0(C)W/m2(
m01.0
23
242
21
B
B
C
C
A
A
kA
LRR
kA
LRRR
kA
LRR
C/W25.0)m12.0(C)W/m2(
m06.0
C/W05.0)m06.0(C)W/m35(
m1.0
C/W11.0)m06.0(C)W/m15(
m1.0
27
o
26
2o5
F
F
E
E
D
D
kA
LRR
kA
LRR
kALRR
section)m1m0.12a(forW572C/W349.0
C)100300(
C/W349.025.0034.0025.004.0
C/W034.0
05.0
1
11.0
1111
C/W025.006.0
1
16.0
1
06.0
11111
21
72,1,1
2,
652,
1,
4321,
total
midmidtotal
mid
mid
mid
mid
R
TTQ
RRRRR
R
RRR
RRRRR
W101.91 5
2m12.0
m)8(m)5(W)572(totalQ
R1
R2
R3
R4
R5
R6
R7
T2T1
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1. Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall whose representative cross section is as shown
below. The thermal conductivities of various materials used, in W/mC, are kA= kF= 2, kB= 8, kC= 20, kD= 15, andkE= 35. Theleft and right surfaces of the wall are maintained at uniform temperatures of 300Cand 100C, respectively. Assuming heat transfer through the wall to be one-dimensional, determine:
(a) the rate of heat transfer through the wall,(b) the temperature at the point where the sections B, D, and E meet, and(c) the temperature drop across the section F. Disregard any contact resistances at the interfaces.
Problem 3-59
2m12.0112.0 A
section)m1m0.12a(forWC/W
CC/W
572
349.0
)100300(349.025.0034.0025.004.0
21
72,1,1
total
midmidtotal
R
TTQ
RRRRR
W101.91 5
2m12.0
m)8(m)5(W)572(totalQ
R1
R2
R3
R4
R5
R6
R7
T2T1
C/W065.0025.004.01,1 midtotal RRR
C263
C/W)W)(0.065572(C30011
total
total
RQTTR
TTQ
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1. Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall whose representative cross section is as shown
below. The thermal conductivities of various materials used, in W/mC, are kA= kF= 2, kB= 8, kC= 20, kD= 15, andkE= 35. Theleft and right surfaces of the wall are maintained at uniform temperatures of 300Cand 100C, respectively. Assuming heat transfer through the wall to be one-dimensional, determine:
(a) the rate of heat transfer through the wall,(b) the temperature at the point where the sections B, D, and E meet, and(c) the temperature drop across the section F. Disregard any contact resistances at the interfaces.
Problem 3-59
2m12.0112.0 A
section)m1m0.12a(forWC/W
CC/W
572
349.0
)100300(349.025.0034.0025.004.0
21
72,1,1
total
midmidtotal
R
TTQ
RRRRR
W101.91 5
2m12.0
m)8(m)5(W)572(totalQ
R1
R2
R3
R4
R5
R6
R7
T2T1
C143
C/W)W)(0.25572(FF
RQTR
TQ
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Problem 3-54A 4-m-high and 6-m-wide wall consists of a long 15-cm X 25-cm crosssection of horizontal bricks (k= 0.72 W/mC) separated by 3-cm-thick plasterlayers (k= 0.22 W/mC). There are also 2-cm-thick plaster layers on each
side of the wall, a 2-cm-thick rigid foam (k= 0.026 W/mC) on the inner sideof the wall. The indoor and the outdoor temperatures are 22C and 4C,and the convection heat transfer coefficients on the inner and the outer sidesare h1= 10 W/m
2C and h2= 20 W/m2C, respectively. Assuming 1-D heat
transfer and disregarding radiation, determine the rate of heat transferthrough the wall.
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Learning Outcome
To solve heat transfer problemsusing thermal resistance
networkfor cylinders andspheres.
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HEAT CONDUCTION IN CYLINDERS AND SPHERES
Heat transfer through a pipecan be modeled as steady
and one-dimensional.
T =T(r).
This can be used for longcylindricalpipes and spherical
containers.
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is the conduction resistance of the cylinder layer.
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is the conduction resistance of the spherical layer.
A spherical shellwith specifiedinner and outersurfacetemperatures T1and T2.
24 rA
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for a cylindricallayer, and
for a sphericallayer
where
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Multilayered Cylinders and Spheres
The thermal resistancenetwork for heat transferthrough a three-layeredcomposite cylindersubjected to convectionon both sides.
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Steam at 250C is flowing through a steel pipe (k = 15.5 W/mC) whose innerand outer diameters are 10 cm and 12 cm, respectively, in an environment at15
C. The pipe is insulated with 7-cm-thick fiberglass insulation (k = 0.033
W/mC). If the heat transfer coefficients on the inside and the outside of thepipe are 180 and 40 W/m2C, respectively, determine the rate of heat loss fromthe steam per meter length of the pipe. What is the error involved in neglectingthe thermal resistance of the steel pipe in calculations?
250C
Problem 3-77
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Ri
T1
Rinsulation RoT2Rpipe
2
2
m8168.0m)1(m)26.0(
m314.0m)1(m)1.0(
LDA
LDA
oo
ii
C/W78.30306.073.300187.00177.0
C/W0306.0)m8168.0(C).W/m40(
11
C/W73.3)m1(C)W/m.033.0(2
)6/13ln(
2
)/ln(
C/W00187.0)m1(C)W/m.5.15(2
)5/6ln(2
)/ln(
C/W0177.0)m314.0(C).W/m180(
11
21
2o2
232
121
22
oitotal
oo
o
ins
insulation
pipe
pipe
ii
i
RRRRR
AhR
Lk
rrRR
LkrrRR
AhR
W62.2
C/W3.78
C)15250(21
totalR
TTQ
If the thermal resistance of the steel pipe is neglected, thenew value of total thermal resistance will be
C/W778.30306.073.30177.02 oitotal RRRR
0.053%
100
C/W78.3
C/W)778.378.3(%error
250C
Steam at 250C is flowing through a steel pipe (k = 15.5 W/mC) whose inner and outer diameters are 10cm and 12 cm, respectively, in an environment at 15C. The pipe is insulated with 7-cm-thick fiberglassinsulation (k = 0.033W/mC). If the heat transfer coefficients on the inside and the outside of the pipe are180 and 40 W/m2C, respectively, determine the rate of heat loss from the steam per meter length of the
pipe. What is the error involved in neglecting the thermal resistance of the steel pipe in calculations?
Problem 3-77
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Problem
Consider a 2-m-high electric hot water heater that has a
diameter of 40 cm and maintains the hot water at 55C. The
tank is located in a small room whose average temperatureis 27C, and the heat transfer coefficients on the inner andouter surfaces of the heater are 50 and 12 W/m2C,respectively. The tank is placed in another 46-cm-diametersheet metal tank of negligible thickness, and the spacebetween the two tanks is filled with foam insulation (k = 0.03
W/mC). The thermal resistances of the water tank and theouter thin sheet metal shell are very small and can beneglected. The price of electricity is $0.08/kWh, and thehome owner pays $280 a year for water heating. Determinethe fraction of the hot water energy cost of this householdthat is due to the heat loss from the tank.
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Exercise
Study Examples 3-1, 3-2, 3-6andsolve Prob lems 3-35 and 3-58.
Test 1
Date: Thursday, 3rdJuly 2014
Venue: Multi-Purpose HallTime: 4 5 PM
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Thank You!