A long cylindrical wood log (k = 0.17 W/mK and = 1.28 10 -7 m

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 15°C. It is exposed to hot gases at 550°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 420°C, determine how long it will be before the log ignites. Solve this problem using analytical one-term approximation method (not the Heisler charts).