A 2.5-cm-thick sheet of plastic initially at 21°C is placed between two heated steel plates that are maintained at 138°C. The plastic is to be heated just long enough for its mid-plane temperature to reach 132°C. If the thermal conductivity of the plastic is 1.1 ?? 10???3 W/(m K), the thermal diffusivity is 2.7 ?? 10???6m2/s, and the thermal resistance at the interface between the plates and the plastic is negligible, calculate: (a) the required heating time, (b the temperature at a plane 0.6 cm from the steel plate at the moment the heating is discontinued, and (c) the time required for the plastic to reach a temperature of 132°C 0.6 cm from the steel plate.

GIVEN

A sheet of plastic is placed between two heated steel plates

Sheet thickness (2L) = 2.5 cm = 0.025 m

Initial temperature (To) = 21°C

Temperature of steel plates (Ts) = 138°C

Heat until mid-plane temperature of sheet (Tc) = 132°C

The thermal conductivity of the plastic (k) = 1.1????? 10???3 W/(m K)

The thermal diffusivity (α) = 2.7 ?? 10???6m2/s

The thermal resistance at the interface between the plates and the plastic is negligible

ASSUMPTIONS

The initial temperature of the sheet is uniform

The temperature of the steel plates is constant

The thermal conductivity of the sheet isconstant

Plastic, T, = 21C 2L Steel T,- 138C Steel T- 138C