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!

Heat Flow Problem

  1. May 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a formal solution to the given initial boundary value problem.

    du/dt=5(d^2u/dx^2) 0<x<1 t>0
    u(0,t)=u(1,t)=0 t>0
    u(x,0)=(1-x)(x^2) 0<x<1

    2. Relevant equations

    1) u(x,t) = a0/2 + sum[an*e^(-b(n pi/L)^2*t) * cos(n pi x/L)

    2) Fourier series equation

    3. The attempt at a solution

    (1-x)(x^2) = a0/2 + sum(an * cos(n pi x) with cn = an

    I calculate a0=1/6

    an = 2* integral[(1-x)(x^2)(cos n pi x)dx] from 0 to 1


    I'm wondering if this is write so far? And if so, how do I proceed from here? Do I just plug everything back into the general u(x,t) equation?

    Thanks!
     
  2. jcsd
  3. May 9, 2009 #2
    You might not want to use the cosine series. Since one of your BC's is u(0,t) = 0. You will never satisfy that condition when cos(0) = 1. Try using the sine series instead.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Heat Flow Problem
  1. Flow problem (Replies: 0)

Loading...