Math Help - Couette Flow differential equation

1. 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

2. Originally Posted by invincible110
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.