Solve the below:
Q: A re-cooperator is a heat exchanger that heats the air used in a combustion process by extracting energy from the products of combustion (the flue gas). Consider using a single-pass, cross-flow heat exchanger as a re-cooperator. Eighty (80) silicon carbide ceramic tubes (k = 20 W/m · K) of inner and outer diameters equal to 55 and 80 mm, respectively, and of length L = 1.4 mare arranged as an aligned tube bank of longitudinal and transverse pitches SL = 100 mm and ST = 120 mm, respectively. Cold air is in cross flow over the tube bank with upstream conditions of V = 1 m/s and Tc,i = 300 K, while hot flue gases of inlet temperature Th,i = ] 400 K pass through the tubes.
The tube outer surface is clean, while the inner surface is characterized by a fouling factor of R''f = 2 X 10-4 m2 · K/W. The air and flue gas flow rates are mc = 1.0 kg/s and mh = 1.05 kg/s, respectively. As first approximations, (1) evaluate all required air properties at 1 atm and 300 K, (2) assume the flue gas to have the properties of air at 1 atm and 1400 K, and (3) assume the tube wall temperature to be at 800 K for the purpose of treating the effect of variable properties on convection heat transfer.
(a) If there is a 1% fuel savings associated with each 10°C increase in the temperature of the combustion air (Tc,o) above 300 K, what is the percentage fuel savings for the prescribed conditions?
(b) The performance of the re-cooperator is strongly influenced by the product of the overall heat transfer coefficient and the total surface area, UA. Compute and plot Tc,o and the percentage fuel savings as a function of UA for 300 < ua="">< 600="" w/k.="" without="" changing="" the="" flow="" rates,="" what="" measures="" may="" be="" taken="" to="" increase="" ua?="">
