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Heat conduction

  1. Mar 6, 2005 #1

    Wiz

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    Hi,
    I have to find the rate of heat flow through a cross-section of the rod in steady state as shown in the figure.Thermal conductivity of the rod is K.
    I have used a $(dollar) sign for theta.
    The formula i know is ΔQ/Δt = [KA($2 - $1)] /x
    where ΔQ/Δt is the heat current,where A is area of cross section and x is the thickness.
    since the area of cross section varies.i think integration will be used.....
    can ANYBODY GUIDE ME THROUGH..??
    [NOTE - THE FIGURE READ THAT $2 > $2 , which is a mistake and the correction is $2 > $1.]
    Thanks,
     

    Attached Files:

  2. jcsd
  3. Mar 6, 2005 #2
    1. assume that the steady state
    2. get a thin slice of tube
    3. since steady state: heat enter=heat exit
    4. this means H is constant over all x
    5. our equation:
    H=-kA(dT/dx)​
    H=-k*pi*r^2*(dT/dx)​
    7. well, pi is constant over all x
    8. well, r is not constant over all x
    9. good luck integrating...
     
  4. Mar 7, 2005 #3

    Wiz

    User Avatar

    ??

    how do i relate x and r......
    there are 3 variables and we need only 2 for integration.
    hope u understand,
    wiz

    (btw - all the steps u wrote were know to me already0
     
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