Chapter 13, Problem 13.126P

A steam generator consists of an in-line array of tubes, each of outer diameter $D=10\text{mm}$ and length $L=1\text{m}$ . The longitudinal and transverse pitches are each $S_L=S_T=20\text{mm}$ , while the numbers of longitudinal and transverse rows are $N_L=20$ and $N_T=5$ . Saturated water (liquid) enters the tubes at a pressure of 2.5 bars, and its flow rate is adjusted to ensure that it leaves the tubes as saturated vapor. Boiling that occurs in the tubes maintains a uniform tube wall temperature of 400 K.

(a) Consider case (a) for which products of combustion enter the tube bank with velocity and temperature of $V=10\text{m/s}$ and $T_{m,i}=1200\text{K}$ , respectively. Determine the average gas-side convection coefficient, the gas outlet temperature, and the rate of steam production in kg/s. Properties of the gas may be approximated to be those of atmospheric air at an average temperature of 900 K.
(b) An alternative steam generator design, case (b), consists of the same tube arrangement, but the gas flow is replaced by an evacuated space with electrically heated plates inserted between each line of tubes. If the plates are maintained at a uniform temperature of $T_p=1200\text{K}$ , what is the rate of steam production? The plate and tube surfaces may be approximated as blackbodies.
(c) Consider conditions for which the plates are installed, as in case (b), and the high-temperature products of combustion flow over the tubes, as in case (a). The plates are no longer electrically heated, but their thermal conductivity is sufficiently large to ensure a uniform plate temperature. Comment on factors that influence the plate temperature and the gas temperature distribution. Contrast (qualitatively) the gas outlet temperature and the steam generation rate with the results of case (a).