Solve the following problem twice once using the LMTD method

Solve the following problem twice, once using the LMTD method and once using the NTU method: Exhaust gas from a furnace is used to preheat the combustion air supplied to the furnace burners. The gas, which has a flow rate of 15 kg/s and an inlet temperature of 1100 K, passes through a bundle of tubes, while the air, which has a flow rate of 10 kg/s and an inlet temperature of 300 K, is in cross flow over the tubes. The tubes are unfinned, and the overall heat transfer coefficient is 100 W/m2 · K. Determine the total tube surface area required to achieve an air outlet temperature of 850 K. The exhaust gas and the air may each be assumed to have a specific heat of 1075 J/kg · K. Assume both fluids are unmixed

Solution

using usual notations and E - NTU method and solve the problem :

Cc =McCp.C = 10x1.075 = 10.75 Cmin

Cn = MnCp.n= 15x1.075 = 16.13 Cmax

Cmin/Cmax = 10.75/16.13 = 0.666

E = (Tc,o-Tc,i)/(Tn,i-Tc,i) = (577-27)/(820-27) = 0.694

From E-NTU chart for one fluid mixed and other unmixed:

    NTU = 2.3 = UA/Cmin

the total tube surface area is,

        A = (2.3x10.75x1000)/100

           = 247.25 m²