Answer to Question #48068 in Differential Equations for Austin

Question

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.