Copper Wire Heat Transfer Copper Wire Heat Transfer During manufacturing, a very

Question

Copper Wire Heat Transfer

Copper Wire Heat Transfer During manufacturing, a very long strand of pure Copper wire that is 1 cm in diameter is extruded. The wire exits the die at 600 K, and is the passed under a blower of cold air to decrease the temperature. Specifications state that following the cooling process, the temperature of the wire must be no greater than 50% of the initial temperature. If the convective coefficient from the blower is = 500 W/(m^2K), and T infinite = 275 K, how long must the strand of copper be exposed to the blowers? At the finalization of the minimal cooling process, what is the temperature of the surface of the wire? (exam question)

Explanation / Answer

Since it is a case of transient heat transfer, first we will check the biot number.

Bi = h*Lc / kb = 500 * radius (in case of cylinder) / 385(kb of pure copper) = 0.006493

which is << than 0.1. so we will use lumped capacitance model

so. (T- Tamb) /(To - Tamb) = exp (-t/ tau)

here rho *V*Cp/ h*A = tau

tau = 8.02 * 0.5* 385/ 2*500 = 1.543s

25/325 = exp (-t/ 1.54)

t = 3.95 seconds

for t = 3.95 final temp of wire will be

T = (exp (-3.95/1.54)* 325 )+ 275 = 300k

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