1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Diff. Eq. with heat flow

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data

    The fluid inside the pipe shown has a temperature of
    350 K, but the temperature of the air in the room is only 306 K.
    Therefore, heat flows at a constant rate from the fluid, through
    the pipe walls, and into the room. The inner pipe radius is 4
    cm, and the outer radius is 8 cm. The heat equation is:

    dQ/dt = kA(dT/dx)

    where x is the direction of heat flow, A is the area through
    which the heat flows (i.e., perpendicular to x), and k is the
    conductivity of the material through which the heat is flowing.
    Determine the temperature of the pipe metal at r = 5.92 cm.

    2. Relevant equations

    T(r>8) = 306
    3. The attempt at a solution

    I've tried this a bunch of times, but can't see to get it. I have done:

    where Q' is a constant


    dT=Q'/(k*pi*r^2) *dr


    I let Q'/k = c2



    After imposing the initial conditions:

    350 = c1 - c2/4pi

    306 = c1 - c2/8pi

    from this
    c1 = 262
    c2= 1105.84

    and got the temperature at r=5.92 to be 321.46 K, but this wasn't right.

    Any ideas?

    I think I went wrong with the initial conditions somewhere
  2. jcsd
  3. Apr 11, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There's a mistake here, since the area through which the heat flows must depend on the length of the pipe.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted