1. Limited time only! Sign up for a free 30min personal 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!

Heat Transfer PDE SOV with piecewise BC

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Heat transfer problem with 3 insulated sides and heat flux in and out on one boundary.
    given values: q & k

    2. Relevant equations
    Governing Equation:
    [tex]
    \frac{\partial^{2}{T}}{\partial{x}^{2}} + \frac{\partial^{2}{T}}{\partial{y}^{2}} = 0
    [/tex]

    Boundary Conditions:
    [tex]
    @ x = 0 ;
    \frac{\partial{T}}{\partial{x}} = 0
    [/tex]
    [tex]
    @ x = L ;
    \frac{\partial{T}}{\partial{x}} = 0
    [/tex]
    [tex]
    @ y = 0 ;
    \frac{\partial{T}}{\partial{y}} = 0
    [/tex]
    [tex]
    @ y = H ;
    \frac{\partial{T}}{\partial{y}} = \frac{q}{k} ; 0 < x < \frac{L}{2}
    [/tex]
    [tex]
    @ y = H ;
    \frac{\partial{T}}{\partial{y}} = \frac{-q}{k} ; \frac{L}{2} < x < L
    [/tex]

    3. The attempt at a solution
    I did the separation of variable method and applied the first 3 boundary conditions, @ x=0,L and @ y=0.

    I'm stuck at this.
    [tex]
    T(x,y) = \sum_{n=0}^\infty C_n \cos{\frac{n \pi x}{L}} \cosh{\frac{n \pi y}{L}}
    [/tex]
    n = 0,1,2,3.....
    How do i solve for Cn, and apply the piecewise boundary condition?
    I know i have to use the Orthogonality property of Cosine.

    Thanks.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Heat Transfer PDE SOV with piecewise BC
  1. PDE Heat Eq (Replies: 20)

Loading...