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Need help for heat conduction problem with multiple BC

  1. Sep 21, 2010 #1
    Dear all, I have difficulty in solving this problem (see the figure in attached thumbnails)

    I have a rectangular shape with length/height of L and the thickness/width of [tex]\delta[/tex]
    Within the rectangular area, a heat conduction occurred. I would like to determine the temperature profile within the rectangular.

    Based on the right hand side figure, I take a small cell with size of dx times dy. Applying the energy balance within the cell.

    I have attached all the equation that I can think of, and also the boundary conditions. I have difficulty in solving the differential equation.

    Thanks in advance.

    note:

    [tex]\lambda[/tex] is thermal conductivity
    [tex]\alpha[/tex] is heat transfer coefficient, it is suppose to be dependent on x-location and time. I am going to simulate the heat transfer coefficient as a periodic function.
     

    Attached Files:

  2. jcsd
  3. Sep 22, 2010 #2
    Still no answer...
    Hmmm...

    :confused:
     
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