Lecture 5_May 2014 heat trasfer

5/24/2018 Lecture 5_May 2014 heat trasfer

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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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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


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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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


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!

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Lecture 5_May 2014 heat trasfer