21. A counterflow, concentric tube heat exchanger used for engine cooling has be

Question

21. A counterflow, concentric tube heat exchanger used for engine cooling has been in service for an extended period of time. The heat transfer surface area of the exchanger is 4.764 m2, and the design value of the overall convection coefficient is 50 W/m2.K. During a test run, engine oil flowing at 0.1 kg/s is cooled from 116°C to 66°C by water supplied at a temperature of 25°C and a flow rate of 0.2 kg/s. Determine whether fouling has occurred during the service period. If so, calculate the fouling factor, R, (m2 .KIW) (water at 300K, cp 4400 J/kg-K; engine oil at 360K, cp 2200 J/kg-K) (Problem 11.21)

Explanation / Answer

We know Q' = UATLMTD

Now, by heat balance if subscript w represents water and o befor oil,

m'oCp,oTo = m'wCp,wTw = Q'

For engine oil, we have complete information.

We get Q' = (0.1 kg/s) x 2200 J/kg-K x ( 116 - 66)K

Q' = 11,000 J/s = 11 kW -- actual heating occuring

For water, we get 11000 = (0.2 kg/s) x 4400 J/kg-K x Tw

Tw = 12.5 C

Thus, water outlet temperature = 25 + 12.5 = 37.5 C. Thus digarm is:

Oil: 116 C -------> -------- 66 C

Water: 37.5 C ------ < ----- 25 C

Thus, on the hotter side, temp difference T1 = 116 C - 37.5 C = 78.5 C

Cold side temp difference T2 = 66 C - 25 C = 41 C

Thus, TLMTD = (T1 - T2 ) / ln(T1/T2) = 57.7349 C

Thus, by overall heat transfer coefficient, we get theoritically heat transferred

Q' = UATLMTD = 50 W/m2-K x 4.764 m2 x 57.7349 K = 13,752 W = 13.752 kW

Since actually lesser heat transfer is occuring w.r.t the theoritical values, fouling has occured.

Effective overall heat transfer coefficient = Q'actual/ATLMTD = 11000 W/(4.764 m2 x 57.7349 K)

Ueff = 40 W/m2 - K

Also, we have since these are in series,

1/Ueff = 1/U + Rf

Thus, we get Rf = 0.005 m2-K/W

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