(Solved): After the heat recovery steam generator (HRSG) of a combined cycle power plant, a proposed heat exc ...

After the heat recovery steam generator (HRSG) of a combined cycle power plant, a proposed heat exchanger is used to cool the exhaust to further enhance the sustainability of the plant. Large cylindrical tubes are suspended within the walls of the $HX$, such that exhaust gasses flow over the tubes in cross flow. Inside the tubes, water evaporates as heat is transferred from the exhaust gasses to the tube. Outside the tubes, exhaust gases are reduced in temperature from 425 to $400\mathrm{K}$. Use air properties to model exhaust gas for this project. Water inside the tubes evaporates at $350\mathrm{K}$. If the tubes are limited to $12\mathrm{m}$ tall and are $20\mathrm{cm}$ in diameter (19.5 $\mathrm{cm}$ inner diameter), how many tubes would we need to achieve enough surface area to remove the heat from $1000\mathrm{kg}/\mathrm{s}$ of exhaust gases? You can take the inner heat transfer coefficient to be $h_i=1000\mathrm{W}/{\mathrm{m}}^2\cdot \mathrm{K}$. The thermal conductivity of the wall is low, since metal cannot be used given the presence of acidic compounds in the condensed water: $k_w=4.0\mathrm{W}/\mathrm{m}\cdot \mathrm{K}$