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Homework Help: Temperature distrubution in a cooling fin (result interpretation)

  1. Jul 3, 2011 #1
    I am analyzing the lengthwise temperature distribution in a cooling fin (length: 30mm, width: 10mm, the tip is assumed to be adiabatic, Biot number is smaller than 0.1).

    When I try to calculate the dimensionless temperature distribution (see calculation below), I obtain a curve which has a minimum at about 2/3 of the fin length and increases again after that (see attachment).

    I don't understand why the temperature should increase again towards the tip of the fin. Using Ansys to model the fin I obtained the other curve in the graph, which shows decreasing temperatures towards the tip of the fin (and makes more sense to me).
    I don't know whether I am making a mistake in my calculations, or whether there is a simple explanation.
    Any advice would be appreciated!

    calculation:

    distribution "theta" (x) = cosh(m*(1-x/L)) / cosh(m) ,

    where m= sqrt [ ( P*L*h) / (A*k) ]

    L=length
    P=perimeter
    A=area
    h=heat transfer coefficient
    k=thermal conductivity
     

    Attached Files:

  2. jcsd
  3. Jul 3, 2011 #2

    uart

    User Avatar
    Science Advisor

    Pretty sure you've made a mistake in evaluating the above. For "m" a constant that expression definitely achieves its minimum when x = L.
     
  4. Jul 5, 2011 #3
    Thanks for the suggestion uart, I'm not sure why it wasn't working, but it does now:)
     
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