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).
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