Under the conditions described in Example 10.6, what is the average rate of heat loss per unit area from the ground to the air during the 12-h period? The thermal conductivity of soil is 0.7 W/m-°C.

Example 10.6

A flat slab of plastic initially at 70°F (21.1°C) is placed between two platens at 250°F (121.1°C). The slab is 1.0 in. (2.54 cm) thick.

(a) How long will it take to heat the slab to an average temperature of 210°F (98.9°C)?

(b) How much heat, in Btu, will be transferred to the plastic during this time per square foot of surface? The density of the solid is 56.2 lb/ft³ (900 kg/m³), the thermal conductivity is 0.075 Btu/ft-h-°F (0.13 W/m-°C), and the specific heat is 0.40 Btu/lb-°F (1.67 J/g - °C).