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Conical Fins - Heat Transfer

  1. Oct 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Derive a differential equation (do not solve) for the temperature distribution in a straight conical fin. Assume one dimensional heat flow. This equation is assumed to be 1-D steady state conduction.

    2. Relevant equations

    For this problem, we can use the generalized fin equation. Please see the attached image of the equation because I do not know how to use the equation editor on here.


    3. The attempt at a solution

    For the conical fin problem I understand that the cross sectional area is non-uniform and it changes with position. I need to simplify the generalized fin equations using the assumptions of a conical shape fin and then acquire an ordinary differential equation for temperature distribution. I am unsure of any other assumptions I can use for conical fins to further simplify the generalized equation into an ordinary differential equation.
     

    Attached Files:

    Last edited: Oct 21, 2013
  2. jcsd
  3. Oct 22, 2013 #2
    If R0 is the radius at the base of the cone, and L is the height of the cone, what is the local radius at x as a function of x, R0, and L? What is the local cross sectional area? What is the local surface area between x and x+dx?
     
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