$($Quintiere $7\mathrm{.}6-$ modified$)$ A thin layer of Masonite $($wood veneer$)$ is attached to an insulating

layer of glass wool. The Masonite is $zmm0\mathrm{.}5mm$ thick. It has the following properties:

$k=0\mathrm{.}1\frac{W}{m}K$

$=0\mathrm{.}640\frac{g}{m^3}$

$c_p=2\mathrm{.}85\frac{J}{g}K$

$T_{ig}=300C$

The total radiative$-$convective heat transfer coefficient in still air at $25C$ is $30\frac{W}{m^2}K.$

a$.$ Calculate the time to ignition for Masonite when subjected to a radiant heat flux of

$50k\frac{W}{m^2}$

b$.$ Calculate the time to ignition for Masonite is instead subjected to a transient radiant heat

flux of $0\mathrm{.}05t^{2}k\frac{W}{m^2}$ where $t[s]$

c$.$ What is the critical or minimum heat flux for ignition?

d$.$ After ignition, what is the initial upward spread rate if the flame heat flux is uniform at

$30k\frac{W}{m^2}$ and the flame extends $0\mathrm{.}2$ m beyond the ignited region of $0\mathrm{.}1$ m $?$