In the vulcanization of tires, the carcass is placed into a jig and steam at 149°C is admitted suddenly to both sides. If the tire thickness is 2.5 cm, the initial temperature is 21°C, the heat transfer coefficient between the tire and the steam is 150 W/(m2 K), and the specific heat of the rubber is 1650 J/(kg K), estimate the time required for the center of the rubber to reach 132°C.

Question

GIVEN

• Tire suddenly exposed to steam on both sides

• Steam temperature (T?) = 149°C

• Tire thickness (2L) = 2.5 cm = 0.025 m

• Initial tire temperature (To) = 21°C

• The heat transfer coefficient (hc) = 150 W/(m2 K)

• The specific heat of the rubber (c) = 165 J/(kg K)

FIND

• The time required for the central layer to reach 132°C

ASSUMPTIONS

• Shape effects are negligible, tire can be treated as an infinite plate

SKETCH

Answer 1

The significance of the internal resistance is determined from the Biot number



Therefore, the internal resistance is significant and the approximate solution will be used.

At center of rubber x=0, we have





for infinite slab