Uploaded August 2016 | Updated September 2026, 2 weeks ago
In this video, I solve the diffusion PDE but now it has nonhomogenous but constant boundary conditions. I show that in this situation, it's possible to split the PDE problem up into two sub-problems: one which gives a steady-state solution, and another which gives a transient solution.
I show that the transient solution obeys homogenous boundary conditions, and that using the steady state solution helps to remove the non-homogeneity. Solving the transient solution is just a simple matter of separating variables, in which case these two videos should help:
youtube.com/watch?v=aq2DAkJIA2w
youtube.com/watch?v=5AkjTUD6TDw
Questions? Ask in the comments!
Prereqs: My PDE videos so far (see my playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD)
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMUFZiM2kwZ3pJYjQ/view?usp=sharing&resourcekey=0-GsMhHxOfzV274IDUHcR4Lg
Patreon Link: patreon.com/user?u=4354534
In this video, I solve the diffusion PDE but now it has nonhomogenous but constant boundary conditions. I show that in this situation, it's possible to split the PDE problem up into two sub-problems: one which gives a steady-state solution, and another which gives a transient solution.
I show that the transient solution obeys homogenous boundary conditions, and that using the steady state solution helps to remove the non-homogeneity. Solving the transient solution is just a simple matter of separating variables, in which case these two videos should help:
youtube.com/watch?v=aq2DAkJIA2w
youtube.com/watch?v=5AkjTUD6TDw
Questions? Ask in the comments!
Prereqs: My PDE videos so far (see my playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD)
Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMUFZiM2kwZ3pJYjQ/view?usp=sharing&resourcekey=0-GsMhHxOfzV274IDUHcR4Lg
Patreon Link: patreon.com/user?u=4354534
