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Temperature problem in fluids mechanics

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Assume the temperature of the exhaust in an exhaust pipe can be approximated by
    T=T0(1+ae-bx)[1+c cos([itex]\omega[/itex]t)]
    T0=100oC,
    a=3,
    b=0.03m-1,
    c=0.05,
    [itex]\omega[/itex]=100 rad/s.

    If the exhaust speed is a constant 3 m/s, determine the time rate of change of temperature of the fluid particle at x=0 and x=4 m when t=0.

    2. Relevant equations
    We know the equation of the temperature in function of the time and the position
    T=T0(1+ae-bx)[1+c cos([itex]\omega[/itex]t)]




    3. The attempt at a solution
    We know that the time rate of change of temperature of the fluid particle is dT/dt

    [itex]\frac{dT}{dt}[/itex]=T0(1+ae-bx)[-c [itex]\omega[/itex] sin([itex]\omega[/itex]t)]

    When t=0, dT/dt=0... unfortunately that isn't the answer, since I don't use the exhaust speed (and have no idea how I could use it).

    Thank you
    PytLove
     
  2. jcsd
  3. Feb 9, 2012 #2
    What if you treated x and t as a variables....
     
  4. Feb 9, 2012 #3
    Seems like a wonderful idea and totally worked, that problem was so different from the others I've done in fluid mechanics... I have no idea that I needed to use x(t) in my dT/dt.

    Thank you Lawrence

    PytLove
     
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