The top surface of an $L=5-$mm$-$thick anodized aluminum plate is irradiated with $G=900\frac{W}{m^2}$ while being simultaneously exposed to convection conditions characterized by $h=40\frac{W}{m^2}*K$ and $T_{}=25C.$ The bottom surface of the plate is insulated. For a plate temperature of $400K$ as well as $=0\mathrm{.}14$ and $=0\mathrm{.}76,$ determine the radiosity at the top plate surface, in W$/$m$^2,$ the net radiation heat flux at the top surface, in $\frac{W}{m^2},$ and the rate at which the temperature of the plate is changing with time, in K$/$s$.$

$J=,\frac{W}{m^2}$

$q_{\text{r}\text{a}\text{d}}^{\text{'}\text{'}}=,\frac{W}{m^2}$

$\frac{dT}{dt}=,\frac{K}{s}$