A single-pass, shell-and-tube heat exchanger will be used to generate saturated steam by cooling a hot CO₂ gas stream. In the present process, boiler feed water at 100°C (373 K) and 1 atm (saturation condition, enthalpy of vaporization of 2257 kJ/kg water) is fed to the shell side of the heat exchanger and exits as saturated steam vapor at 100°C and 1 atm total system pressure. The CO₂ enters the tube side at 1 atm and 450 K (177°C) and exits at 400 K (127°C). The tube side gas is in turbulent flow. 

The process must produce 0.50 kg/s of saturated steam. The shell-side heat-transfer coefficient (h₀) for the vaporizing water is 10,000 W/m² · K. The desired tube side heat- transfer coefficient in each tube (h_i) is 50 W/m² · K. It is also desired to use schedule 40 steel pipe of ¾-inch nominal diameter (inner diameter = 0.824 inch, outer diameter = 1.050 inch, thickness 0.113 inch, thermal conductivity 42.9 W/m · K; Appendix M). Properties of CO₂ at 375 K, 1 atm (Appendix I): ρ = 1.268 kg/m³, C_p = 960.9 J/kg. K, µ = 2.0325 × 10^-5 kg/m-sec, k = 0.02678 W/m · K.

a. What is the heat exchanger area, based on the desired h_i of 50 W/m² ·  K?

b. What is the CO₂ gas flow rate needed for the process to operate?

c. What is the velocity of CO₂ in a single tube for the desired h of 50 W/m² · K?