The top surface of an \(L=5\)-mm-thick anodized aluminum plate is irradiated with \(G=1000 \mathrm{~W} / \mathrm{m}^{2}\) while being simultaneously exposed to convection conditions characterized by \(h=50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(T_{\infty}=25^{\circ} \mathrm{C}\). The bottom surface of the plate is insulated. For a plate temperature of \(400 \mathrm{~K}\) as well as \(\alpha=0.14\) and \(\varepsilon=0.76\), determine the radiosity at the top plate surface, the net radiation heat flux at the top surface, and the rate at which the temperature of the plate is changing with time.