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A thin electric heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm, respectively. The steel rod (A) has a thermal conductivity of KA = 15 W/m.K and the plastic tube (B) has a thermal conductivity of kB = 0.8 W/m.K. The outer surface of the tube is subjected to convection with a fluid at a temperature of T = -5°C and heat transfer coefficient of 50 W/m²K. The thermal contact resistance between the cyl- inder surfaces and the heater is negligible. (40 points) (a) Determine the electrical power per unit length (W/m) that is required to maintain the outer surface of cylinder B at 5°C for steady state conditions. (b) Based on part (a), what is the steady state temperature at the center of cylinder A? (c) If the heater is turned off, estimate the time for the steel rod to drop 15°C. Assume steel has a density of p= 7900 kg/m³ and specific heat of c = 400 J/kg.K. Thin electric heater Too, h TA TB A tube B rod

A thin electric heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm, respectively. The steel rod (A) has a thermal conductivity of KA = 15 W/m.K and the plastic tube (B) has a thermal conductivity of kB = 0.8 W/m.K. The outer surface of the tube is subjected to convection with a fluid at a temperature of T = -5°C and heat transfer coefficient of 50 W/m²K. The thermal contact resistance between the cyl- inder surfaces and the heater is negligible. (40 points) (a) Determine the electrical power per unit length (W/m) that is required to maintain the outer surface of cylinder B at 5°C for steady state conditions. (b) Based on part (a), what is the steady state temperature at the center of cylinder A? (c) If the heater is turned off, estimate the time for the steel rod to drop 15°C. Assume steel has a density of p= 7900 kg/m³ and specific heat of c = 400 J/kg.K. Thin electric heater Too, h TA TB A tube B rod

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A thin electric heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm, respectively. The steel rod (A) has a thermal conductivity of KA = 15 W/m.K and the plastic tube (B) has a thermal conductivity of kB = 0.8 W/m.K. The outer surface of the tube is subjected to convection with a fluid at a temperature of T = -5°C and heat transfer coefficient of 50 W/m²K. The thermal contact resistance between the cyl- inder surfaces and the heater is negligible. (40 points) (a) Determine the electrical power per unit length (W/m) that is required to maintain the outer surface of cylinder B at 5°C for steady state conditions. (b) Based on part (a), what is the steady state temperature at the center of cylinder A? (c) If the heater is turned off, estimate the time for the steel rod to drop 15°C. Assume steel has a density of p= 7900 kg/m³ and specific heat of c = 400 J/kg.K. Thin electric heater Too, h TA TB A tube B rod
Transcribed Image Text:A thin electric heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm, respectively. The steel rod (A) has a thermal conductivity of KA = 15 W/m.K and the plastic tube (B) has a thermal conductivity of kB = 0.8 W/m.K. The outer surface of the tube is subjected to convection with a fluid at a temperature of T = -5°C and heat transfer coefficient of 50 W/m²K. The thermal contact resistance between the cyl- inder surfaces and the heater is negligible. (40 points) (a) Determine the electrical power per unit length (W/m) that is required to maintain the outer surface of cylinder B at 5°C for steady state conditions. (b) Based on part (a), what is the steady state temperature at the center of cylinder A? (c) If the heater is turned off, estimate the time for the steel rod to drop 15°C. Assume steel has a density of p= 7900 kg/m³ and specific heat of c = 400 J/kg.K. Thin electric heater Too, h TA TB A tube B rod
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