For one$-$dimensional chambered flame, $($i$)$ provide detailed derivation to show

$\frac{\text{t}\text{i}\text{l}\text{d}\text{e}(T{)}_f-\text{t}\text{i}\text{l}\text{d}\text{e}(T{)}_o}{\text{t}\text{i}\text{l}\text{d}\text{e}(Y{)}_{F,o}}+\frac{\text{t}\text{i}\text{l}\text{d}\text{e}(T{)}_f-\text{t}\text{i}\text{l}\text{d}\text{e}(T{)}_l}{\text{t}\text{i}\text{l}\text{d}\text{e}(Y{)}_{O,l}}=1$

$($ii$)$ compute the mass fluxes of fuel, oxidizer, and product at $x=0$ and $x=l$; $($ii$)$ based on the mass fluxes of fuel and oxidizer at the boundaries, determine the equivalence ratio of the combustion system in terms of tilde$(Y{)}_{F,O}$ and tilde$(Y{)}_{O,l}$; $($iii$)$ determine the net thrust $($per unit area$)$ generated by the combustion chamber, assuming $Y_{P,o}$ and $Y_{P,l}$ are nonzero.