Chapter 13, Problem 13.120P

The fire tube of a hot water heater consists of a long circular duct of diameter $D=0.07\text{m}$ and temperature $T_s=385\text{K}$ , through which combustion gases flow at a temperature of $T_{m,g}=900\text{K}$ . To enhance heat transfer from the gas to the tube, a thin partition is inserted along the midplane of the tube. The gases may be assumed to have the thermophysical properties of air and to be radiatively nonparticipating.

(a) With no partition and a gas flow rate of ${\stackrel{\dot{}}{m}}_g\text{=0}\text{.50}\text{kg/s}$ , what is the rate of heat transfer per unit length, q’, to the tube?
(b) For a gas flow rate of ${\stackrel{\dot{}}{m}}_g\text{=0}\text{.05}\text{kg/s}$ and emissivities of ${\epsilon }_s={\epsilon }_p=0.5$ , determine the partition temperature T_pand the total rate of heat transfer q’ to the tube.
(c) For ${\stackrel{\dot{}}{m}}_g\text{=0}\text{.02, 0}\text{.05}$ , and $\text{0}\text{.08}\text{kg/s}$ and equivalent emissivities ${\epsilon }_p={\epsilon }_s\equiv \epsilon$ compute and plot T_pand q’ as a function of $\epsilon$ for $0.1\le \epsilon \le 1.0$ . For ${\stackrel{\dot{}}{m}}_g\text{=0}\text{.05}\text{kg/s}$ and equivalent emissivities, plot the convective and radiative contributions to q’ as a function of $\epsilon$ .