An ordinary egg can be approximated as a sphere with a diameter of a few centimeters and whose properties are roughly k $=0\mathrm{.}55$ W$/($m$*$K$)$ and thermal diffusivity of $1\mathrm{.}5$E$-7$ m$2/$s$.$ The egg is initially at a uniform temperature of $9$C and is dropped into boiling water, which is maintained at $99$C$.$ Taking the convection heat transfer coefficient to be $1600$ W$/($m$2$K$),$ estimate the maximum diameter that the egg can have if raising the temperature in the middle of the egg to $90$C can take no more than one hour.