If a rectangular block of rubber (see Problem 18.12 for properties) is set out in air at 297 K to cool after being heated to a uniform temperature of 420 K, how long will it take for the rubber...

If a rectangular block of rubber (see Problem 18.12 for properties) is set out in air at 297 K to cool after being heated to a uniform temperature of 420 K, how long will it take for the rubber surface to reach 320 K? The dimensions of the block are 0.6 m high by 0.3 m long by 0.45 m wide. The block sits on one of the 0.3-m by 0.45-m bases; the adjacent surface may be considered an insulator. The effective heat-transfer coefficient at all exposed surface is 6.0 W/m²
K. What will the maximum temperature within the rubber block be at this time?

Problem 18.12

In the curing of rubber tires, the ‘‘vulcanization’’ process requires that a tire carcass, originally at 295 K, be heated so that its central layer reaches a minimum temperature of 410 K. This heating is accomplished by introducing steam at 435 K to both sides. Determine the time required, after introducing steam, for a 3-cm-thick tire carcass to reach the specified central temperature condition. Properties of rubber that may be used are the following: k
 0:151 W/mK, c_p
 200 J/kgK,
 1201 kg/m³,
 m²/s.

327:

Cast-iron cannonballs used in the War of 1812 were occasionally heated for some extended time so that, when fired at houses or ships, they would set them afire. If one of these the socalled ‘‘hot shot’’ were at a uniform temperature of 2000F, how long after being exposed to air at 0F with an outside convective heat-transfer coefficient of 16 But/h ft²
F, would be required for the surface temperature to drop to 600F? What would be the center temperature at this time? The ball diameter is 6 in. The following properties of cast iron may be used: