A hollow pure aluminum sphere with an electrical heater in the center is used in tests at steady-state conditions to determine the thermal conductivity of insulating materials. The inner diameter of the sphere is 0.350m; the outer diameter is 0.400m. For this test, the inner surface temperature of the pure aluminum sphere is held at a constant temperature of 250.0°C. The pure aluminum sphere is uniformly covered with an insulating material, 0.0900m thick. The outside surface of the insulating material is exposed to convection; T_inf = 22.0°C, h_inf = 25.0 W/(m2-K). The power required to keep the inner surface of the sphere at 250.0°C is 85.0W (this is assumed to be equal to the heat transfer rate, q). Ignoring contact resistance, determine the thermal conductivity of the insulating material, k.
A hollow pure aluminum sphere with an electrical heater in the center is used in tests at steady-state conditions to determine the thermal conductivity of insulating materials. The inner diameter of the sphere is 0.350m; the outer diameter is 0.400m. For this test, the inner surface temperature of the pure aluminum sphere is held at a constant temperature of 250.0°C. The pure aluminum sphere is uniformly covered with an insulating material, 0.0900m thick. The outside surface of the insulating material is exposed to convection; T_inf = 22.0°C, h_inf = 25.0 W/(m2-K). The power required to keep the inner surface of the sphere at 250.0°C is 85.0W (this is assumed to be equal to the heat transfer rate, q). Ignoring contact resistance, determine the thermal conductivity of the insulating material, k.
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter21: Heat And The First Law Of Thermodynamics
Section: Chapter Questions
Problem 21PQ
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A hollow pure aluminum sphere with an electrical heater in the center is used in tests at steady-state conditions to determine the thermal conductivity of insulating materials. The inner diameter of the sphere is 0.350m; the outer diameter is 0.400m. For this test, the inner surface temperature of the pure aluminum sphere is held at a
constant temperature of 250.0°C. The pure aluminum sphere is uniformly covered with an insulating material, 0.0900m
thick. The outside surface of the insulating material is exposed to convection ; T_inf = 22.0°C, h_inf = 25.0 W/(m2-K). The power required to keep the inner surface of the sphere at 250.0°C is 85.0W (this is assumed to be equal to the heat transfer rate, q). Ignoring contact resistance, determine the thermal conductivity of the insulating material, k.
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