In Problem $3.79$ the strip heater acts to guard against heat losses from the wall to the outside, and the required heat flux $q_{o}^{\prime \prime}$ depends on chamber operating conditions such as $\dot{q}$ and $T_{\infty, i}$. As a first step in designing a controller for the guard heater, compute and plot $q_{o}^{\prime \prime}$ and $T(0)$ as a function of $\dot{q}$ for $200 \leq \dot{q} \leq$ $2000 \mathrm{~W} / \mathrm{m}^{3}$ and $T_{\infty, i}=30,50$, and $70^{\circ} \mathrm{C}$.