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

(a) With no partition and a gas flow rate of m_g = 0.05 kg/s. what is the rate of heat transfer per unit length, q', to the tube?

(b) For a gas flow rate of mg = 0.05 kg/s and emissivities of Es = E" = 0.5, determine the partition temperature T_p and the total rate of heat transfer q' to the tube.

(c) For mg = 0.02, 0.05, and 0.08 kg/s and equivalent emissivities ε_p = ε_s == ε, compute and plot T= and q' as a function of E for 0.1 < E < 1.0. For in_g = 0.05 kg/s and equivalent emissivities, plot the convective and radiative contributions to q' as a function of E.

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Gas Tg : Tube. T,, &, Partition, T. e,