This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 10.6.1
We want to find the steady-state solution for the partial differential equation 2 uxx = ut , subject to the boundary conditions u(0, t) = 10, u(50, t) = 40. By definition, steady-state means that u is not changing as time changes; that is ut = 0. Plugging this into our PDE, we find that uxx = 0. Thus we find the general steady-state solution to our PDE has the form u = Ax + B. We now apply the boundary conditions. u(0, t) = 10, so u = Ax + 10. Since u(50, t) = 40, we conclude that the steady-state solution is 3 u = x + 10. 5 ...
View Full Document