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Homework Help: What would be my boundary conditions? Heat Equation

  1. Apr 27, 2010 #1
    1. I have a rod of length 4,cross section 1 and thermal conductivity 1.Nothing is mentioned about the end at the origin x=0, but at the opposite end x=4, the rod is radiating heat energy at twice the difference between the temperature of that end and the air temperature of 23 celcius. Find the boundary conditions at this x=4 end of the rod to be used in the one dimensional heat equation.



    2. Heat flows out of rod at -[tex]\lambda A u_{x}(a,t)[/tex]




    3. with my substitutions i get -[tex]u_{x}(4,t)=2(u(4,t)-23)[/tex]
    So that my first boundary condition is the above. But i think " they " want another boundary condition here at x=4,but what ? I was thinking something like [tex] u(4,t)=u(4,0)-tu_{t}(4,t)[/tex] in other words temperature now = initial temperature - time*rate of temperature loss. i am not very experienced with these problems,can someone please point me in the right direction ?
     
  2. jcsd
  3. Apr 28, 2010 #2

    lanedance

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    Homework Helper

    so based on the boundary condition the you can calculate the heat moving out teh end of the rod
    [tex] Q = 2(u(4,t) - 23)) [/tex]

    Assuming the heat flow is reasonably continuous which is a good assumption you should be able to relate the heat flow to the thermal gradient at the end of the rod [tex] u_x(4,t), using the thermal conductivity
     
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