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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.

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.

Refrigeration and Air Conditioning Technology (MindTap Course List)
Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter1: Heat, Temperature, And Pressure
Section: Chapter Questions
Problem 17RQ: Convert 22C to Fahrenheit.
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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
Transcribed Image Text: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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