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Heat Current in Cylinder

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    A hollow cylinder of length L has inner radius, r1, outer radius, r2 , and
    thermal conductivity, k. It is in dynamic thermal equilibrium, with its interior
    held at temperature T1 and its exterior at a different temperature, T2. What is the
    radial temperature dependence, T(r), within the cylinder, r1 ≤ r ≤ r2 ?


    2. Relevant equations
    Heat Current = KA(T-T)/L


    3. The attempt at a solution
    I know heat current out equals heat current in and than you solve for T. However, I cannot figure out how to calculate the heat currents since the area is changing.
     
  2. jcsd
  3. Jan 26, 2010 #2

    ideasrule

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    Homework Helper

    You need to use calculus. Consider a very thin shell surrounding the center of the cylinder, of thickness dr. The area of one side isn't very different from the area of the other, so you can use that heat conduction equation.
     
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