Consider the rayleigh problem, where the plate is moved with the velocity vx(y = 0; t) = t n, where the exponent n is a parameter. by looking for similarity solutions show that the velocity may be written as vx(y; t) = t ϵg(y t β). what are the values of β and ϵ? write the ordinary differential equation that g must satisfy with the corresponding boundary conditions. solve this equation for n=1/2. comment on how the diffusion length scales with time?