A wooden sphere of diameter 5 cm is initially at a uniform temperature of 21 °C. Its surfacetemperature is suddenly raised to 83 °C. The thermal conductivity and thermal diffusivity ofthe wood are 0.15 W/m K and 0.82 x 10-7 m^2/s, respectively. a) Calculate the temperature 2 cm beneath the surface of the sphere 30 min after the sudden increase in temperature.b) Calculate the energy gained by the sphere during this time. T(0,1)-T,T-T,0.80.70.61.020.9Q(oc)1.00.010.0070.0050.0040.0030.0020.50.40.30.20.0010.50.40.10.070.050.040.030.021.0T(r.1)-T, 0.9T(0.1)-T,0.30.20.100.5 1.0010-50.8 0.40.7 0.50.60.60.50.4 0.70.3 0.80.2 0.90.11.000.01Bi=r/R=0.2THANaRT15 2.010-40.12.5 3 4 5 6 7 8 9 101.0Bi= 0.0010.002-0.005.0.01-10-3Bi=02-0.020.0510 Bi 1002010-2 10-130 4017010103104Bf Fo=to²/kpcFigure 3- Dimensionless Transient Temperatures and Heat Transfer for a SphereBi=DRnoi110 130 170 210Fo-tkpcR²102250

The diameter of the wooden sphere, The initial temperature of the sphere, The final surface…

Answered: A wooden sphere of diameter 5 cm is…

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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Question

A wooden sphere of diameter 5 cm is initially at a uniform temperature of 21 °C. Its surface
temperature is suddenly raised to 83 °C. The thermal conductivity and thermal diffusivity of
the wood are 0.15 W/m K and 0.82 x 10-7 m^2/s, respectively.

a) Calculate the temperature 2 cm beneath the surface of the sphere 30 min after the sudden increase in temperature.

b) Calculate the energy gained by the sphere during this time.

T(0,1)-T,
T-T,
0.8
0.7
0.6
1.0
20.9
Q(oc)
1.0
0.01
0.007
0.005
0.004
0.003
0.002
0.5
0.4
0.3
0.2
0.001
0.5
0.4
0.1
0.07
0.05
0.04
0.03
0.02
1.0
T(r.1)-T, 0.9
T(0.1)-T,
0.3
0.2
0.1
0
0.5 1.0
0
10-5
0.8 0.4
0.7 0.5
0.6
0.6
0.5
0.4 0.7
0.3 0.8
0.2 0.9
0.1
1.0
0
0.01
Bi=
r/R=0.2
THAN
aR
T
15 2.0
10-4
0.1
2.5 3 4 5 6 7 8 9 10
1.0
Bi= 0.001
0.002-
0.005.
0.01-
10-3
Bi=
02-
0.02
0.05
10 Bi 100
20
10-2 10-1
30 40
1
70
10
103
104
Bf Fo=to²/kpc
Figure 3- Dimensionless Transient Temperatures and Heat Transfer for a Sphere
Bi=
DR
noi
110 130 170 210
Fo-tk
pcR²
102
250

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