PROBLEM 08 A 1-inch diameter wire of 10-ft length (which has an internal resistance of 3 kQ, and thermal conductivity of 300 W/m-C) experiences a current of 10 amperes. Because of this, the heat generated from the caused the melting of the wire starting from the center (the melting temperature of the wire is 2300°C). It was found that the melted part of the wire has a radius of 0.1 in from which conduction of electricity no longer generates heat. Other given: Q = 2.02 x 108 W/m³ a. What would be the temperature profile of the wire (T = f(r)) if the constants from integration where found to be C1 = 271,088.04 W/m, and C2 = 929,466.79 W/m? b. What would be the temperature of the wire at r = 0.5 in? c. What would be the heat flowrate at r = 0.1 in?

PROBLEM 08 A 1-inch diameter wire of 10-ft length (which has an internal resistance of 3 kQ, and thermal conductivity of 300 W/m-C) experiences a current of 10 amperes. Because of this, the heat generated from the caused the melting of the wire starting from the center (the melting temperature of the wire is 2300°C). It was found that the melted part of the wire has a radius of 0.1 in from which conduction of electricity no longer generates heat. Other given: Q = 2.02 x 108 W/m³ a. What would be the temperature profile of the wire (T = f(r)) if the constants from integration where found to be C1 = 271,088.04 W/m, and C2 = 929,466.79 W/m? b. What would be the temperature of the wire at r = 0.5 in? c. What would be the heat flowrate at r = 0.1 in?

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