One of the standard experimental tests used in the study of fluid motion through porous materials consists of determining the displacement u when the material is given a constant load. The governing differential equation in this case is:
H[1+(du/dx)^3]*d^2u/dx^2=du/dt
Boundary Conditions: du/dx = -1 at x=0 and u=0 as x --> infinite
Initial Condition: u=0 at t=0
a) What are the dimensions of the constant H?
b) Find the dimensionally reduced form for the solution and then use this to transform the above diffusion problem into one involving a nonlinear ordinary differential equation. Make sure to state what happens to the boundary and initial conditions. You do not need to solve this problem.
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