A long electnical resastance wire of radius -02 cm has a thermal conductivity Kwire 15 W/m-K. Heat is generated uniformly in the wire as a result of resistance heating at a constant rate of 1.2 W/cm. The wire is covered with polyethylene insulation with a thickness of 05 cm and thermal conductivity of kins = 0.4 W/m K. The outer surface of the insulation is subjected to convection and radiation with the surroundings at 20C. The combined convection and radiation heat transfer coetficients is 7 Wim2 K. Formulate the temperature profiles for the wire and the polyethylene insulation. Use the temperature profiles to determine the temperature at the interface of the wire and the insulation and the temperature at the center of the wire. The ASTM D1351 standard specifies that thermoplastic polyethylene insulation is suitable for use on electrical wire with operation at temperatures up to 75°C. Under these conditions, does the polyethylene insulation for the wire meet the ASTM D1351 standard? is the temperature protie for the wire Ta (r)- T + (-P)? the temperature profie for the wire - Teue (r)- Ty+ -) Yes Is the temperature profie for the insulation layer Tu (r)- + In) + Tur ? the temperature profie for the insulation layer is v Tu () - ) + T 'C The temperature at the interface of the wire and the insulation is The temperature at the center of the wire is INo the polyethylene insulation for the wire does not meet the ASTM DI351 standard

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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Transcribed Image Text:A long electrical resistance wire of radius = 0.2 cm has a thermal conductivity kwire = 15 W/m-K. Heat is generated uniformly in the wire as a result of resistance heating at a constant rate of 12 W/cm. The wire is covered with polyethylene insulation with a thickness of 05 cm and thermal conductivity of kins = 0.4 W/m-K. The outer surface of the insulation is subjected to convection and radiation with the surroundings at 20C. The combined convection and radiation heat transfer coefficients is 7 W/m2 K. Formulate the temperature profiles for the wire and the polyethylene insulation. Use the temperature profiles to determine the temperature at the interface of the wire and the insulation and the temperature at the center of the wire. The ASTM D1351 standard specifies that thermoplastic polyethylene insulation is sultable for use on electrical wire with operation at temperatures up to 75°C. Under these conditions, does the polyethylene insulation for the wire meet the ASTM D1351 standard? is the temperature protie for the wire T (F)-Tr+ (ri-P)? the temperature profile for the wire is - Teue (P)-T+ (H-P) Yes is the temperature profie for the insulation layer Tu (r)- + In) + Tur ? the temperature profie for the insulation layer is - T ()- in) + Tur Yes The temperature at the interface of the wire and the insulation is The temperature at the center of the wire is No the polyethylene insulation for the wire does not Vmeet the ASTM DI351 standard

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