Long aluminum wires of diameter 3 mm ( = 2702 kg/m 3 , c p = 0.896

Long aluminum wires of diameter 3 mm (ρ = 2702 kg/m³, c_p = 0.896 kJ/kg · K, k = 236 W/m · K, and α = 9.75 × 10^-5 m²/s) are extruded at a temperature of 350°C and exposed to atmospheric air at 30°C with a heat transfer coefficient of 35 W/m² · K.

(a) Determine how long it will take for the wire temperature to drop to 50°C.

(b) If the wire is extruded at a velocity of 10 m/min, determine how far the wire travels after extrusion by the time its temperature drops to 50°C. What change in the cooling process would you propose to shorten this distance?

(c) Assuming the aluminum wire leaves the extrusion room at 50°C, determine the rate of heat transfer from the wire to the extrusion room.

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350°C Aluminum wire Tair = 30°C 10 m/min