Consider the Rayleigh problem, but allow the plate velocity to be a function of time, V(t). By differentiation show that the shear stress, tau = du/dy*absolute viscosity, obeys the same diffusion equation that the velocity does. Suppose that the plate is moved in such a way as to produce a constant surface shear stress. What are the velocity profile and the surface velocity for this motion.
I'm not sure that these are actually relavant but here is what I assume:
Shear Stress = - Absolute Viscosity*V0 / SQRT(PI *kinematic viscosity*t)
density*dv/dt = absolute viscosity*d^2v/dy^2 => simplified momentum eqn.
The Attempt at a Solution
I'm not sure how to even get started on this problem. Any suggestions or help would be appreciated. Thanks