It is common practice to treat wooden telephone poles with tar-like materials to prevent damage by water and insects. These tars are cured into the wood at elevated temperatures and pressures.
Consider the case of a 0.3-m-diameter pole, originally at 25°C, placed in a pressurized oven. It will be removed when the tar has penetrated to a depth of 10 cm. It is known that a 10-cm depth of penetration will occur when a temperature of 100°C is achieved. For an oven temperature of 380°C and h = 140 W/m² · K, determine the time required for the pole to remain in the oven. Properties of the wooden pole are

k = 0.20 W/m · K

α = 1.1 × 10^-7 m²/s