Heat Transfer

1. In a concentric tube heat exchanger, 1.76 m long, chilled water at 100 C entering the annulus at a velocity of 0.2 m/s is to cool a stream of air at 300 C, flowing through the pipe 10 m/s velocity. In both the annulus and the inner tube, ignore entrance effects. The heat exchanger is constructed from 2 mm thick stainless steel (AISI 304) tubes of inside diameters of 36 mm and 49 mm respectively.

(a) Calculate the overall heat transfer coefficient for the heat exchanger. (b) If the desired exit temperature of air is 200 C, can it be achieved in this heat exchanger?

40

36

49

SOLUTION Energy balance: mass flow x specific heat x temperature change for air = mass flow x specific heat x temperature change for water. Energy given up by air in cooling : 1.1614 x (π x 0.0362 /4) x 10 x 1007 x 10 Energy taken up by water : 1000 x (π x 0.0092 /4) x 0.2 x 4189 x ΔT ΔT of water = 2.230 C; Outlet temperature of water = 12.230 C.

17.77 10

Counterflow

7.77

20

Coflow

LMTD in counterflow = 13.5; LMTD in coflow = 12.94; Reynolds number of water flow in the annulus = V DH /ν; DH = (D0 – Di) = 1469.4 (Laminar) Reynolds number of air flow in the tube = 22649.2 (Turbulent) Heat transfer coefficient of air from: NuD = 0.027 (Re)0.8 Pr1/3 (The viscosity correction term is neglected as the temperature variation is small.) hair is calculated as = 53.56 W/m2 K Heat Transfer coefficient of water from NuD = 3.66 (Taken as constant wall temperature since variation of temperature of water is only 2.230 C. hwater is calculated as = 239.9 W/m2 K k for AISI 304 is 14.9 W/m K 1

Calculating overall coefficient U0 = A ΣR ; ΣR = (Rair + Rwall + Rwater) 0 Overall heat transfer coefficient U is = 39.95 W/m2 K The heat transfer required = [mass flow x sp. Heat x temp. drop]air = 119.044 W In counterflow, heat transfer = 119.37 (achieved) In coflow, heat transfer = 114.33 (not achieved)