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.
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
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
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