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Homework Help: Thermal conductivity of airplane

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    The passenger section of an airplane can be thought to have a shape of a cylindrical tube. For a small airplane, the tube is 35 m long and has an inner radius of 2.5 m. The exterior of the tubular wall is lined up with a 6- cm thick layer of insulating material of thermal conductivity 4 X 10-5 cal/s- cm-K. If the inside temperature is to be maintained at 25 °C, and the outside temperature is -35 °C, determine the rate that heat must be delivered to maintain this temperature difference.


    2. Relevant equations



    3. The attempt at a solution

    dQ/dt = kA(T(inside) - T(outside))/l

    I a having trouble identifying y variables

    k = 4E^-5, A = this is my confusion, is it the cross-sectional area of the inside or outside of the plane, l = .006 m
     
  2. jcsd
  3. Mar 9, 2010 #2

    ideasrule

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    You'll have to use calculus. Consider an infinitely very thin layer of material. It will have only one area, 2*pi*r*dr. Consider the heat flow through this thin layer, then use integration to get the rate of heat flow through the whole thing.
     
  4. Mar 9, 2010 #3
    kinda confused but r u saying that i have to find the area of the entire outside cylinder

    am i suppose to integrate 2pi r dr fro the inside radius to the outside radius
     
  5. Mar 9, 2010 #4

    ideasrule

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    No.

    Oops, I meant 2pi*r*L, which would be the surface area of a thin slice of the cylinder at radius r. H=kA*delta-T/delta-x, which you can rewrite as H=k*2pi*r*L*dT/dx. Do you know how to get the answer from here?
     
  6. Mar 9, 2010 #5
    what do i use for my radius, the inside or inside plus the insulation.

    also why did you put the delta-t on the other side, the answer is ging to be in jewls/seconds right.
     
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