Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

First-Order Nonlinear ODE from transient heat transfer

  1. Jun 26, 2012 #1
    A problem from a heat transfer book with conduction and radiation led me to a differential equation like this:

    T'(t) = a - b*T(t) - c*T(t)^4

    Although my professor said that there wouldn't be an analytical solution for this one and to get the answer by an iterative method I got curious and tried Wolfram Alpha. For my surprise it gave a solution, but I just can't understand the answer and neither the steps for solving it

    Here it is:
    http://www.wolframalpha.com/input/?i=T'(t)+=+a+-+b*T(t)+-+c*T(t)^4

    Could anyone give me some light here?
     
  2. jcsd
  3. Jun 27, 2012 #2
    The solution is shown in attachment.
    WolframAlpha gives a closed form of the integral in terms of the four roots of the polynomial :
    a - b*T - c*T^4 = c*(T-w1)*(T-w2)*(T-w3)*(T-w4)
     

    Attached Files:

  4. Jun 27, 2012 #3
    Thanks mate! That's simpler than I thought. So problably he was referring to an analytical solution for T(t)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: First-Order Nonlinear ODE from transient heat transfer
Loading...