A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 oC in a furnace. One surface of the plate is heated while the other surface of the plate can be approximated to be adiabatic. The initial temperature of the steel plate is 20 oC. The thermal conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10-5 m2/s respectively. The convective heat-transfer coefficient is 174 W/m2 K. (The pictures are the conduction charts given) a) Find the time necessary to raise the surface temperature of the steel plate to 500 oC. b) Find the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a). c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a).
A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 oC in a furnace. One surface of the plate is heated while the other surface of the plate can be approximated to be adiabatic. The initial temperature of the steel plate is 20 oC. The thermal conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10-5 m2/s respectively. The convective heat-transfer coefficient is 174 W/m2 K. (The pictures are the conduction charts given) a) Find the time necessary to raise the surface temperature of the steel plate to 500 oC. b) Find the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a). c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a).
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 oC in
a furnace. One surface of the plate is heated while the other surface of the plate can be
approximated to be adiabatic. The initial temperature of the steel plate is 20 oC. The thermal
conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10-5 m2/s
respectively. The convective heat-transfer coefficient is 174 W/m2 K.
(The pictures are the conduction charts given)
a) Find the time necessary to raise the surface temperature of the steel plate to 500 oC.
b) Find the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a).
c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a).
Transcribed Image Text:1.0
0.7
T(0,1)-T, 0.5
04
0.3
T-T,
0.2
0.1
0.07
0.05
0.04
0.03
0.02
1.0
0.9
0.8
(0) 0.7
0.6
0.5
0.4
0.3
0.2
0.01
0.007
0005
0.004
0.000
0.000
0.001
T(xt)-T, 1.0
T(0,1)-7 0.9
0.8
0.7
0.6
0
0.1
0
10-5
0.1
1
Bi=
0.4
0.5
0.6
0.5 0.7
0.4 0.8
0.3
0.2
2
x/L=0.2
0
0.01
SE
Tit
HIND
0.9
1.0
al
k
0.1
3
Bi
4 8 12 16 20 24 28 40 60 80
Bi=
al
k
1.0 101 100
7 Bi
10-4 10-3 10-2 10-1
J
1
10
Bi=
G
aL
100 120 140 200 300 400 500 600
Foutk/pcl²
102
103
Bi Fo=1² kpc
Figure 1 - Dimensionless Transient Temperatures and Heat Transfer for an Infinite Slab
104
1.0
0.7
0.5
0.4
T(0,1)-T, 03
T-T, 02
0.1
0.07
0.05
0.04
0.03
0.02
0.01
0.007
0.005
0.004
0.003
0.002
0.001
0.5
0.4
0
1.0
T(r.)-T 0.9
T(0,1)-T, 0.8 0.4
0.7 0.5
0.6 0.6.
r/R=0.2
0.3
0.2 0.9-
0.1
1.0
a) 0.9
(1)
(0) 0.8
0.7
0.6
0.5
0.4
0.7
0.8
0
0.01
4
1.0
12
0.1
aR
Bi==
k
f
65
1206557
3 4 8 12 16 20
1.0
Bi=
aR
10
0.3
0.2
0.1
0
10-5 10-4 10-3 10-2
Bi
100
Bi
24 28 40
1
Bi=
10
60 80 100 120 140 200 300
Fo=tk
tk/pcR²
10-1
Bi³ Fo=to/kpc
Figure 2 - Dimensionless Transient Temperatures and Heat Transfer for a Long Cylinder
aR
all
k
102 103
104
Transcribed Image Text:1.0
0.7
0.5
0.4
T(0,1)-T, 03
0.2
T-T,
0.01
0.007
0.005
0.004
0.003
0.002
0.8
0.7
0.6
0.1
0.07
0.05
0.04
0.03
0.02
0.001
1.0
20.9
O(0)
1.0
T(r.1)-T, 0.9
T(0,1)-T, 0.8 0.4
0.7 0.5
0.6
0.5
0.4
0
0.5 1.0 1.5
r/R=0.2
0.6
0.7
0.3 0.8
0.2 0.9
0.1
0.5
0.4
0.3
0.2
0.1
0
10-5
1.0
0
0.01
Bi =
aR
k
0.1
10-4
2.0
2.5
Bi = 0.001
0.002
0.005
0.01-
10-3
1.0
0.02-
3 4 5 6 7 8 9 10
Bi
Bi
0.05-
0.1
10-2
10 Bi 100
10-1
ולי
30
40
10
70
110
Bi=
Fo-tk
102
aR
k
130 170
***
PCR²
210 250
103
104
Bi² Fo=to²/kpc
Figure 3 - Dimensionless Transient Temperatures and Heat Transfer for a Sphere
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