1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook