In a metal wire manufacturing facility, continuously drawn copper wire with a 2.5 mm diameter is annealed by heating it from its initial temperature of 450C to 400oC in a soaking oven. The oven inside air temperature is 7000C with an average heat transfer coefficient of ch =45 W/(m2 K). Estimate the soaking annealing time required. Also if the oven is 3.5 m long and the drawn wire is continuously fed through the oven (entering at one end and pulled out at the other longitudinal end), what should be the drawing speed or velocity?

Question

GIVEN

• Copper wire with diameter (D)= 2.5 mm=0.0025 m

• Initial temperature of the wire(To) = 45°C

• Oven air temperature(T?) = 700°C

• Heat transfer coefficient ( ch ) = 45 W/(m2 K)

• Length of the oven(L)=3.5 m

FIND

• The soaking annealing time required for the wire to 400°C

• Drawing speed through the oven(v)

ASSUMPTIONS

• Constant thermal conductivity

• End effects are negligible

• The wire is very long compared to its diameter

• There is radial conduction only in the wire

SKETCH

Answer 1

(a) The Biot number is calculated first to check if the internal resistance is negligible



Therefore, the internal resistance of the rod is negligible.

The temperature-time history of the rod,



Solving for the time



The time required to reach 88°C is



(b) Drawing speed through oven

Length of the oven(L)=3.5 m

Time required for soaking annealing to 4000C(t)=37 seconds

Thus drawing speed(v)=L/t= 3.5 m/37 s=0.095 m/s =9.5 cm/s