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Math Help - Couette Flow differential equation

  1. #1
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    Couette Flow differential equation

    Establishing Couette Flow

    I am taking a graduate level Fluids course and I have forgotten most of my differential equation skills. I need help on the how to solve this equation using fourier series:

    I need to solve for the velocity flow field u: and u if a function of y and t

    du/dt = a* d2u/dy2

    where a is some constant.

    Any help is greatly appreciated
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  2. #2
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    Quote Originally Posted by invincible110 View Post
    Establishing Couette Flow

    I am taking a graduate level Fluids course and I have forgotten most of my differential equation skills. I need help on the how to solve this equation using fourier series:

    I need to solve for the velocity flow field u: and u if a function of y and t

    du/dt = a* d2u/dy2

    where a is some constant.

    Any help is greatly appreciated
    Are there any given boundary conditions?

    You can start by trying a solution of the form U(y, t) = Y(y) T(t).

    I strongly advise you to thoroughly review solving partial differential equations because, as you were no doubt made aware before enrolling, it's an essential prerequisite for a subject like Fluid Dynamics.
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