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!

Unknown in PDE

  1. Sep 3, 2011 #1
    unknown in PDE!!

    Hi,

    I'm solving a problem which determines the flow between a porous material and an impermeable material, using the slip-flow boundary conditions as proposed by Beavers and Joseph in '67. I can solve the whole problem as stated below, which gives the velocity [itex]u[/itex] of the fluid in the x-direction over the gap height (y-direction). However, in this equation I still have one unknown namely [itex]u_{B}[/itex] which is the slip velocity. How can I write this [itex]u_{B}[/itex] in function of the other variables so that this unknown disappear in my equation of [itex]u[/itex] ? A hint can maybe be enough!

    Poiseuille motion:

    [itex]\frac{d^2u}{dy^2} = \frac{1}{\mu}\frac{dP}{dx}[/itex]

    boundary conditions:

    1. [itex]u = 0[/itex] at [itex]y = h[/itex]

    2. [itex]\frac{du}{dy} = \frac{\alpha}{\sqrt{k}}u_{B}[/itex] at [itex]y = 0[/itex]

    Solution of this PDE is:

    [itex]u = \frac{1}{2\mu}\frac{dP}{dx}(y^2-h^2) + \frac{\alpha}{\sqrt{k}} u_{B} (y-h)[/itex]
     
    Last edited: Sep 3, 2011
  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: Unknown in PDE
  1. Solving PDE (Replies: 3)

  2. Unknown X in rectangle (Replies: 4)

Loading...