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Temperature drop in an insulated pipe over 12 hours

  1. May 17, 2018 #1
    Hello all,

    I have been having some problems and would appreciate any help:

    I have a length of insulated pipe filled with engine oil at rest, the variables are as follows:

    Toil: 40 oC
    Tair: 5 oC
    h1 (LO): 3600.63 W/m2/K
    r1 (pipe inner): 0.1 m
    r2 (pipe outer): 0.1095 m
    r3 (insulation): 0.1695 m
    L (length): 21.5 m
    A1 (pipe inner area): 13.50884841 m2
    k1 (carbon steel): 50 W/m.K
    k2 (mineral wool): 0.0421 W/m.K
    h2 (air): 11.6 W/m2/K
    A3 (insulation outer area): 22.89749806 m2
    Cp (LO): 1928 J/kg.K
    Time: 43200 s
    Density: 877.8 kg/m3
    Volume: 0.68 m3
    Mass: 596.904 kg

    I am trying to calculate the temperature of the oil in the pipe after a period of 12 hours, assuming that the ambient air temperature remains constant at 5 oC. I have been able to calculate the heat transfer through the pipe and insulation but am having issues calculating the temperature drop over time.

    I have derived down to the following equation that gives me the temperature as a function of time: $$T(t)=5+35e^{-\frac{UAt}{mCp}}$$

    U: Overall heat transfer coefficient
    A: Surface Area
    t: time
    m: Mass of oil in pipe
    Cp: Specific heat capacity of the oil

    I calculated U as 0.3848 using U = 1 / Rt, where Rt is the total thermal resistance of the pipe and insulation.

    After plugging in the numbers I get a value of 17.83oC.

    If anyone could let me know if I am on the right track and that the formula I have used to calculate the temperature is appropriate that would be great.

    Many thanks,

  2. jcsd
  3. May 17, 2018 #2
    I didn't check the calculation, but the final formula seems correct.
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