A long cylindrical wood log (k = 0.17 W/m⋅K and α = 1.28×10−7 m2/s) is 10 cm in

A long cylindrical wood log (k = 0.17 W/m⋅K and α = 1.28×10−7 m2/s) is 10 cm in diameter and is initially at a uniform temperature of 27°C. It is exposed to hot gases at 455°C in a fireplace with a heat transfer coefficient of 13.6 W/m2⋅K on the surface. If the ignition temperature of the wood is 375°C, determine how long it will be before the log ignites. Solve this problem using the analytical one-term approximation method.