A thick wood slab $($k $=0\mathrm{.}17$ W$/$m$$K and $=1\mathrm{.}28$ X $107$ m$2/$s$)$ that is initially at a uniform temperature of $25$C is exposed to hot gases at $550$C for a period of $5$ min. The heat transfer coefficient between the gases and the wood slab is $35$ W$/$m$2$K$.$ If the ignition temperature of the wood is $450$C$,$ determine if the wood will ignite.