A long electrical resistance wire of radius = 0.25 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 0.5 W/cm³. The wire is covered with polyethylene insulation with a thickness of 0.25 cm and thermal conductivity of kins = 0.4 W/m-K. The outer surface of the insulation is subjected to free convection in air at 20°C and a convection heat transfer coefficient of 2 W/m²K. 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 that operates at temperatures up to 75°C. Under these conditions, does the polyethylene insulation for the wire meet the ASTM D1351 standard? Interface Air, 20°C Wire h = 2 W/m²K Insulation Is the temperature profile for the wire Twire (r) = T1 + égen 4k-wire (r² = r²)? Yes , the temperature profile for the wire is égen Twine (1) = T1 + ( − 1²). 4k-wire Is the temperature profile for the Insulation layer Tis (r) = (1+4)+T∞? ëgenr1 h gen No , the temperature profile for the insulation layer is not ✓ Tins (r) = = 2kins kins h (+)+ +Too The temperature at the interface of the wire and the insulation is The temperature at the center of the wire is 178.9576 °C. 179.0096 °C. No the polyethylene insulation for the wire does not meet the ASTM D1351 standard.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.54P

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Transcribed Image Text:A long electrical resistance wire of radius = 0.25 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 0.5 W/cm³. The wire is covered with polyethylene insulation with a thickness of 0.25 cm and thermal conductivity of kins = 0.4 W/m-K. The outer surface of the insulation is subjected to free convection in air at 20°C and a convection heat transfer coefficient of 2 W/m²K. 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 that operates at temperatures up to 75°C. Under these conditions, does the polyethylene insulation for the wire meet the ASTM D1351 standard? Interface Air, 20°C Wire h = 2 W/m²K Insulation Is the temperature profile for the wire Twire (r) = T1 + égen 4k-wire (r² = r²)? Yes , the temperature profile for the wire is égen Twine (1) = T1 + ( − 1²). 4k-wire Is the temperature profile for the Insulation layer Tis (r) = (1+4)+T∞? ëgenr1 h gen No , the temperature profile for the insulation layer is not ✓ Tins (r) = = 2kins kins h (+)+ +Too The temperature at the interface of the wire and the insulation is The temperature at the center of the wire is 178.9576 °C. 179.0096 °C. No the polyethylene insulation for the wire does not meet the ASTM D1351 standard.

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