Solve the below:
Q: Hot water for an industrial washing operation is produced by recovering heat from the flue gases of a furnace. A cross-flow heat exchanger is used, with the gases passing over the tubes and the water making a single pass through the tubes. The steel tubes (k = 60 W/m · K) have inner and outer diameters of Di = 15 mm and Do = 20 mm, while the staggered tube array has longitudinal and transverse pitches of ST = SL = 40 mm. The plenum in which the array is installed has a width (corresponding to the tube length) of W = 2 m and a height (normal to the tube axis) of H = 1.2 m. The number of tubes in the transverse plane is there-fore NT = H/ST = 30. The gas properties may be approximated as those of atmospheric air, and the convection coefficient associated with water flow in the tubes may be approximated as 3000 W/m2 · K.
(a) If 50 kg/s of water are to be heated from 290 to 350 K by 40 kg/s of flue gases entering the exchanger at 700 K, what is the gas outlet temperature and how many tube rows NL are required?
(b) The water outlet temperature may be controlled by varying the gas flow rate and/or inlet temperature. For the value of N L determined in part (a) and the prescribed values of H, W, ST, mc, and Tc,i compute and plot Tc,o as a function of mh over the range 20 < mh="">< 40="" kg/s="" for="" values="" of="" th,i="500," 600,="" and="" 700="" k.="" also="" plot="" the="" corresponding="" variations="" of="" th,p="" if="" th,o="" must="" not="" drop="" below="" 400="" k="" to="" prevent="" condensation="" of="" corrosive="" vapors="" on="" the="" heat="" exchanger="" surfaces,="" are="" there="" any="" constraints="" on="" mh="" and="" th,i?="">