Fluid Dynamics: Flame front in a channel

  • #1
A flame front accelerates exponentially in a channel of width 2R with non-slip boundary conditions at the walls. Flame acceleration creates pressure gradient -deltaP/density=exp(sigma*t) (x-direction) directed parallel to the channel walls.

Assuming a plane-parallel flow, find velocity distribution in the channel.

I started with the Navier-Stokes equation and because of the plane-parallel flow and pressure gradient I came to this equation:

du/dt=exp(sigma*t)+my*du2/dy2

But now I don't know how I will continue, someone has an idea? Maybe I'm on the wrong track?

Mythbuster - "There's your problem"
 

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