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Homework Help: Boundary condition for PDE heat eqaution

  1. Dec 9, 2017 #1
    1. The problem statement, all variables and given/known data
    I am having an issue, not with the maths but with the boundary conditions for this question.

    A bar 10 cm long with insulated sides, is initially at ##100 ^\circ##. Starting at ##t=0##
    Find the temperature distribution in the bar at time t.

    The heat flow equation is

    $$\frac{\partial ^2u}{\partial x^2}=\frac{1}{k}\frac{\partial u}{\partial t}$$

    where ##u(x,t)## is the tempreture, Because the sides of the bar are insulated, the heat flows only in the, the same happens for a slab of finite thickness but infinitely large.

    The initial condition is ##u(x,0)=100## and the boundary condition for ##t>0## is ##
    u
    (0
    ,t
    ) =
    u
    (10
    ,t
    ) = 0.
    ##

    Have read this incorectly but if the sides are insulated then surely the boundary condtions are,

    ##U_{x}(0,t)=U_{x}(L,t)=0##

    as the heat is moving along the x direction?
     
  2. jcsd
  3. Dec 9, 2017 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. The sides that are insulated are the curved sides, not the ends. That is what makes it a one dimensional flow equation with the heat flowing through the ends. So those partials with respect to ##x## are not zero.
     
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