Ch2 Problems
Ch2 Problems
Ch2 Problems
kA = 150 W/m C
kB = 30
T = 370C
kC = 50
kD = 70
2.5 cm
AB = AD
AC = 0.1 m2
B
C
A
D
7.5 cm
T = 66C
5.0 cm
(NEXT)
PANKAJ R. CHANDAR
2-4
Solution:
x
0.025
, RA
1.667 x10 - 4 /A
k A
150 A
2 0.075 0.01
RB
30 A
A
0.05
0.001
RC
50 A
A
2 0.075 0.0043
RD
70 A
A
1
R RA RC
2.667 x10 - 2
1
1
RB
RD
R
T
370 66
R
2.667 x10 - 2
11400 W
PANKAJ R. CHANDAR
mW
k FOAM 18
m C
4k (Ti TO )
2
q
h 4 rO (TO - T )
1
1
ri
rO
0.018 (120 40)
2
(25) rO ( 40 15)
1
1
0.5 rO
rO 0.5023 m
thickness rO ri 0.0023 m
q (w/insul.) 25 (4) (0.5023) 2 ( 40 15)
1982 W
PANKAJ R. CHANDAR
k
5 x10 - 4 2x10 - 4 7 x10 - 4
h
k 7x10 - 4 120 0.084 W
m C
q (bare wire) (0.001)120(400 - 40)
135.7 W
m
q (insulated) 135.7 (0.25) 33.93 W
rO
400 - 40
rO
ln
-4
1
5 x10
2 (0.084)
2 (120) rO
33.93
PANKAJ R. CHANDAR
(L = 1 m)
5
2-27 Solution:
q
h (T3 T ) 15 (55 - 40) 225 W
2
m
A
q
1000 400
kM
x M 0.24 m
A
x M
q
400 55
kF
x F 0.0644 m
A
x F
PANKAJ R. CHANDAR
d T
q
0
2
dx
k
T1
T2
L
L
X
dT
q
x C1
dx
k
q x2
T C1 x C 2
2k
(NEXT)
PANKAJ
R. CHANDAR
2) at X=L, T=T2
q x2
T C1 x C 2
2k
q
T T1
T T2
( L2 X 2 ) 2
X 1
2k
2L
2
For temp. distribution on the wall.
PANKAJ R. CHANDAR
q
T1 T2
2
T0
L
2k
2
5x10 5 (0.015) 2
200 50
127.8 C
2 (20)
2
PANKAJ R. CHANDAR
10
2-45
2
r r
r sin
1
T
q
1 T
r 2 sin 2 2
k
t
This reduces to :
2
1 d ( rT)
q
d ( rT)
qr
r d r2
k
d r2
k
Integrating yields :
q r2
C2
T
C1
6k
r
(NEXT)
PANKAJ R. CHANDAR
11
1)
d T
qr
d r
3k
dT
3)
d r
2) T TW @ r R
0 , then C1 TW
q R2
6k
C2 0
T - TW
R 2 r2
6k
PANKAJ R. CHANDAR
12
R 2 r2
6k
1x10 6 (0.02) 2
T0 - TW
4.17 C
6 (16)
4
q qV q
R 3 h 4 r 2 (TW - T )
3
1x10 6 (0.02)
TW - T
444.4 C
3 (15)
T - TW
PANKAJ R. CHANDAR
13
1
1
W
U
32.11
-2
R
3.114 x10
m 2 C
PANKAJ R. CHANDAR
14
W
d
2 .5
,
L
15
C
m C
4
4
16.25 cm
1
m LC
15 0.025 4 2
h P
3.43
2
k A
204
0
.
025
h Pk A
tanh m L C
(0.025)
15 0.025 ( 204)
42.41 W
2
260 16
PANKAJ R. CHANDAR
tanh 0.5573
15
W
k 210
m C
t
LC L
6.4 0.8 7.2 mm
2
r2C r1 L C 1.25 0.72 1.97
r2C
1.576
r1
PANKAJ R. CHANDAR
16
2-67
Solution contd.
k AM
0.0072
23
210 1.152 x10 -5
0.0596
From Fig. 2 - 11, f 97 %
q MAX 2 h r2C
r1
T 4.523 W
q (0.97)(4.523) 4.387 W
PANKAJ R. CHANDAR
17
h
k AM
0.249,
f 0.91
100 30
14.83 W
PANKAJ R. CHANDAR
18
k
A
M
f 0.88
160
0.0105 2
204
0
.
001
0
.
0105
0.294
(NEXT)
PANKAJ R. CHANDAR
19
419
A 0.025 3.2 *10 3 0.05
m2
386
0.16
0.038
PANKAJ R. CHANDAR
20
44000
260 38
0.05 0.025
A
386 0.038
2
A 130.4m
PANKAJ R. CHANDAR
21
69.78 2
0
.
10
0
.
025
A
m
0.69 0.05
PANKAJ R. CHANDAR
22
A R
300
175 80
0.04 0.015
A
386 0.038
A 1.247m 2
PANKAJ R. CHANDAR
23
313 2
A R
m
PANKAJ R. CHANDAR
24
Take A 1m 2
x 0.004
1
1
R SS
0.00025; R overall
0.00833
k
16
U 120
TSS
R SS
0.00025
25
999.8kg/m 3
V (0.25)(0.4)(1.0) 0.1m 3
m 100kg
g (100)(330 *103 ) 3.3 *107 J
PANKAJ R. CHANDAR
26
0.8146
kA (0.033)(1.86)
1
R0
0.04
hA0
Rs
R 0.8596
Q 3.3 *107
25 - 0
PANKAJ R. CHANDAR
27
4k(i T0 )
q
1 1
ri r0
W
(k 204
)
mC
(4)4)(20100 - 50)
5127W
1
1
0.02 0.04
PANKAJ R. CHANDAR
28
k A 0.166
k f 0.0485
W
mC
315 Ti
Ti 38
ln(31.4/25) ln(56.4/31.4)
0.166
0.0485
0.7283(315 Ti ) 0.0828(Ti 38)
Ti 286.7C
PANKAJ R. CHANDAR
29
30
PANKAJ R. CHANDAR
31
Asbestos
k 0.1547 x 8.0cm
W
brick
k 0.69
x 10cm h 15 2 * 2
m C
1
W
U
0.70 2
2 (2)(0.012) 0.08
0.1
m C
15
0.038
0.154 0.69
PANKAJ R. CHANDAR
32
25.7C
2k
(2)(21)
q LA hA(TW - T )
33
q AL hPL(Tw T )
(35.3 *10 6 )(0.025) 2 (4000)(4)(0.025)(Tw 20)
Tw 75.16C
PANKAJ R. CHANDAR
34
2k
2
(2)(20)
2
462.5C
PANKAJ R. CHANDAR
35
T w 100C
PANKAJ R. CHANDAR
36
W
mC
1
1.45
ln(
) (0.025)
1
0.025 1
1.25
( )
500
(2 )(43)
0.029 12
1
2
13
.
54
W
/
m
C
3
5
3
2 *10 4.31*10 71.84 *10
PANKAJ R. CHANDAR
37
38
PANKAJ R. CHANDAR
39
A 1m 2
R glass x/k 0.005 6.41*10 3
x
0.004 0.1538
k
R conv1 1/h 1/12 0.0833
R air
PANKAJ R. CHANDAR
40
d 2 hP
0
2
dx
kA
let m hP , T 38 L 30cm h 17
kA
PANKAJ R. CHANDAR
41
1
q hPdx hP ( )[0.91e mx 161.09e mx ]0L
m
0
hPkA[0.91e mx 161.09e mx ]00.3
1
2 2
PANKAJ R. CHANDAR
42
10.05W
PANKAJ R. CHANDAR
43
44
PANKAJ R. CHANDAR
45
h 1/2
) 0.723
kA m
f 0.75
q (0.75)(20)()(0.15)200 15) 833
W
depth
m
PANKAJ R. CHANDAR
46
k 16 h 40 T0 250C T 90C
P (4)(0.0125) 0.05m
A (0.0125) 2 1.565 *10 4 m 2
q hPkA 0
[(40)(0.05)(16)(1.565 *10 4)]1/2 (250 90)
11.31W
PANKAJ R. CHANDAR
47
L c 2.075cm
h 1/ 2
Lc (
)
kA m
3/2
f 42%
48
h 1/2
) 0.41
kA m
r2c
2.37 f 0.81
r1
q (80)80)(552 0.0152 )(2)(200 20)(0.81) 75.9W
PANKAJ R. CHANDAR
49
PANKAJ R. CHANDAR
50
h 1/2
) 1.96
kAm
f 0.33
g (0.33)(2)(0.02555)(500)(125 - 20) 885W/m
PANKAJ R. CHANDAR
51
PANKAJ R. CHANDAR
52
PANKAJ R. CHANDAR
53
PANKAJ R. CHANDAR
54
PANKAJ R. CHANDAR
55
h
LC
k
A
M
f 0.92
3
0.218
h
LC
k
A
M
f 0.95
3
0.186
56