Chapter 4, Problem 4.57P

Steady-state temperatures at selected nodal points ofthe symmetrical section of a flow channel are knownto be $T_2=95.47°\text{C,}{T}_3=117.3°\text{C,}{T}_5=79.79°\text{C,}{T}_6=77.29°\text{C,}{T}_8=87.28°\text{C,}$ and $T_{10}=77.65°\text{C}\text{.}$ Thewall experiences uniform volumetric heat generation of $\stackrel{.}{q}={10}^6{\text{W/m}}^3$ and has a thermal conductivity of $k=10\text{W/m}\cdot \text{K}\text{.}$ The inner and outer surfaces of the channelexperience convection with fluid temperatures of $T_{\infty ,i}=50°\text{C}$ and $T_{\infty ,o}=25°\text{C}$ and convection coefficientsof $h_i=500{\text{W/m}}^2\cdot \text{K}$ and $h_o=250{\text{W/m}}^2\cdot \text{K}\text{.}$

1. Determine the temperatures at nodes 1, 4, 7, and 9.
2. Calculate the heat rate per unit length (W/m) fromthe outer surface A to the adjacent fluid.
3. Calculate the heat rate per unit length from theinner fluid to surface B.
4. Verify that your results are consistent with an overallenergy balance on the channel section.