Chapter 13, Problem 13.105P

The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin wall, is shown.

Sides 1 and 2 are maintained at temperatures of $T_1=600\text{K}$ and $T_2=400\text{K}$ , respectively, while the mean temperatures of gas flows through ducts 1 and 2 are $T_{g,1}=571\text{K}$ and $T_{g,2}=449\text{K}$ , respectively. The foregoing temperatures are invariant in the axial direction. The gases provide surface convection coefficients of $h_1=h_2=5{\text{W/m}}^{\text{2}}\cdot \text{K}$ while all duct surfaces may be approximated as blackbodies $\left({\epsilon }_1={\epsilon }_2={\epsilon }_w=1\right)$ . What is the duct wall temperature, T_w? By performing an energy balance on the gas in side 1, verify that T_g,1 is, in fact equal to 571 K.