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!

Homework Help: Nondimensionalization of diffusion equation

  1. Apr 23, 2017 #1
    1. The problem statement, all variables and given/known data
    We let a dye diffuses into an environment of dimension L. We inject that dye into a box by one face, at t = 0 on x = 0. The linear density c follows that equation :
    upload_2017-4-23_11-22-49.png

    with the conditions :
    upload_2017-4-23_11-22-40.png
    2. Relevant equations / questions
    a. nondimensionalize the equations and the conditions
    b. reveal a term homogeneous to time, and its signification
    c. compare the characteristic lenghts of these equation systems

    3. The attempt at a solution
    By nondimensionalize this equation, I found this :
    upload_2017-4-23_11-24-30.png
    But I think it's wrong... I use the "formal way" to nondimensionalize the equation as shown in the Khan academy video on youtube.
    May I ask for help ?
    Thanks a lot
     

    Attached Files:

  2. jcsd
  3. Apr 23, 2017 #2

    hilbert2

    User Avatar
    Science Advisor
    Gold Member

    I think you should start by finding out the numbers ##\alpha_1 , \alpha_2 , \alpha_3##, ##\beta_1 , \beta_2 , \beta_3##, ##\gamma_1 , \gamma_2 , \gamma_3## so that the variables

    ##\tilde{x}=L^{\alpha_1}m_0^{\alpha_2}D^{\alpha_3}x##
    ##\tilde{t}=L^{\beta_1}m_0^{\beta_2}D^{\beta_3}t##
    ##\tilde{c}=L^{\gamma_1}m_0^{\gamma_2}D^{\gamma_3}c##

    become dimensionless. ##L## is any characteristic length of the system you want to choose.
     
  4. Apr 23, 2017 #3
    Hi, I've tried what you've advised me, here are my results :
    upload_2017-4-23_16-42-1.png
    We therefore have:
    upload_2017-4-23_16-43-59.png

    For the conditions I found:

    upload_2017-4-23_16-42-42.png

    I'm not quite sure about the integral term though..
     

    Attached Files:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...