Chapter 8, Problem 43P

In the thermos shown in Fig. P8.43, the innermost compartment is separated from the middle container by a vacuum. There is a final shell around the thermos. This final shell is separated from the middle layer by a thin layer of air. The outside of the final shell comes in contact with room air. Heat transfer from the inner compartment to the next layer $q_1$ is by radiation only (since the space is evacuated). Heat transfer between the middle layer and outside shell $q_2$ is by convection in a small space. Heat transfer from the outside shell to the air $q_3$ is by natural convection. The heat flux from each region of the thermos must be equal that is, $q_1=q_2=q_3$. Find the temperatures $T_1\text{ and }{T}_2$ at steady state, $T_0\text{ is 500}°\text{C and }{T}_3=\text{25}°\text{C}$.

$\begin{array}{l}{q}_1={10}^{-9}\left[{\left(T_0+273\right)}^4-{\left(T_1+273\right)}^4\right]\\ q_2=4\left(T_1-T_2\right)\\ q_3=1.3{\left(T_2-T_3\right)}^{4/3}\end{array}$

FIGURE P8.43