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"