Question

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 5 m², and the design value of the overall convection coefficient (without any fouling) is 38 W/m²K. During a test run, engine oil flowing at 0.1 kg/s is cooled from 110^oC to 66^oC by water supplied at a temperature of 25^oC and a flow rate of 0.18 kg/s. Determine whether fouling has occurred during the service period. If so, calculate the fouling factor, R^”_f (m²K/W). Specific heat of engine oil is 2166 J/kgK, and water is 4178 J/kgK.

What is R^”_f = x 10^-3 m²K/W?

Answer 1

during a test following data were collected

m_h = 0.1 kg/sec

m_c = 0.18 kg/sec

C_poil = 2166 J/kgK

C_pwater = 4178 J/kgK

A = 5 m²

t_h1 = 110⁰C

t_h2 = 66⁰C

t_c1 = 25⁰C

heat transfer from oil

Q = mc_p(t_h2 - t_h1)

Q = 0.1 * 2166 * (110 - 66)

Q = 9530.4 J/sec

now,

heat rejected from oil = heat absorbed by water

   m_oil c_poil (t_h2 - t_h1)   = m_water c_pwater (t_c2 - t_c1)

0.1 * 2166 * (110 - 66) = 0.18 * 4178 * ( t_c2 - 25 )

t_c2 = 37.6 ⁰C

we know that, Logarithmic mean temperature difference (LMTD) is given by

where,

= t_h1 - t_c2

= t_h2 - t_c1

= 50.91⁰C

Total heat transfer rate is given by

Q = U_d A

9530.4 = U_d * 5 * 50.91

U_d = 37.43 W/m²K

we can estimate fouling factor by the given relation

where

U_d = tested overall heat transfer coefficient (with fouling)

U₀ = designed overall heat transfer coefficient (without any fouling)

put the values

R_f = 0.000397 m²K/W

R_f = 0.397 x 10^-3 m²K/W