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Derive differential equation that describes temperature

  1. Feb 17, 2016 #1
    I'm taking an engineering heat transfer course as an elective.

    1. The problem statement, all variables and given/known data


    Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q”rad to the top surface of the plate, while the bottom surface is well insulated. The top surface is also exposed to a fluid at T that provides for a uniform convection coefficient h.

    (a) Derive the differential equation that governs the temperature distribution T(x) in the plate.
    (b) Obtain a solution to the differential equation for appropriate boundary conditions.

    2. Relevant equations

    Conduction, convection, and radiation

    3. The attempt at a solution

    I want to first analyze a differential control volume.

    Ac = yt
    As = ydx

    qcond + qrad = qconv + qcond, x + dr

    -kAcdT/dx + εσ[T4(x) - T4] ydx = h[T(x) - T] ydx + -kAcdT/dx -kd/dx(AcdT/dx)

    Of course, t is constant and we're assuming that temperature does not vary with the y-coordinate. However, I wanted to start with an actual volume and see where y factors out. Am I on the right track?
     
    Last edited: Feb 17, 2016
  2. jcsd
  3. Feb 22, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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