Along 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/m^2∙k on the surface. if the ignition temperature of the wood is 420°c, determine how long it will be before the log ignites.