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

Physics & Space Science

You might also like to view...

Some globular clusters have three main sequence tracks. This indicates:

A) three different stellar compositions. B) three episodes of star formation, separated by billions of years. C) stars evolve through three different mechanisms. D) the stars were observed from three different telescopes.

Physics & Space Science

The most striking example of solar variability was the

A) Dust Bowl drought of the 1930s. B) Maunder Minimum from 1645-1715. C) Sporer Minimum that doomed the Anasazi. D) fall of Rome. E) Joseph's seven lean years in the Old Testament.

Physics & Space Science

What is the most accurate physical analog for a particle in a box?

a. A guitar string b. A rope driven with a sinusoidal oscillation on one end and fixed on the other end c. A pan-flute pipe (open on both ends) d. An organ pipe open on only one end e. A jump rope with a girl on each end driving the end to a rhythm

Physics & Space Science

The ________ theory offers a likely explanation for the formation of ________.

A. density wave; spiral arms B. high rotation speed; spiral arms C. density wave; Galactic bulge D. high rotation speed; dark matter

Physics & Space Science