$(1)$
求めるべき熱流束を$q$で表すと
\[
\begin{align}
q&=\frac{80-5}{\frac{0.05}{40}+\frac{1}{400}}\\
&=75\times\frac{800}{3}\\
&=\underline{20000\, \rm{W/m^2}}
\end{align}
\]
$(2)$
求めるべき表面温度を$T$で表すと
\[
\begin{align}
q&=20000=400\times[80-(T-273.15)]\\
\therefore T&=80-50+273.15\\
&=\underline{303.15\, \rm{K}}
\end{align}
\]
或いは
\[
\begin{align}
20000&=\frac{40}{0.05}\times[(T-273.15)-5]\\
\therefore T&=\frac{20000}{800}+5+273.15\\
&=\underline{303.15\, \rm{K}}
\end{align}
\]
