a$.1-$m diameter cylindrical shape fire occurred in a compartment due to the burning of a sofa as shown in FIGURE Q$2.$ The fire heat release rate is $2$ MW $.$ The compartment ceiling is made of $5$ mm thick steel and furniture made of wood $($bed$,$ desk and chair$)$ is placed on the upper floor. Assume the ambient temperature is $\backslash (22^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ flame temperature is $\backslash (900^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and furniture is placed on a ceiling area of $\backslash (2\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$

FIGURE Q$2$ Fire in a Compartment

i$.$ Assess whether the desk will ignite due to fire and support your answer with a calculation. Assume furniture ignition temperature is $\backslash (325^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and steel deck thermal conductivity, $\backslash ($ K $\backslash )$ is $\backslash (45\mathrm{.}3\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$[8$ marks$]$

ii$.$ If the fire heat release rate is reduced by $\backslash (30\backslash \%\backslash ),$ predict if the chair on the upper floor will ignite. Justify your answer with calculations.

$[7$ marks$]$