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  • 17 votes cast
Jan
18
comment Problem solving a second-order PDE
I would say it's pretty bad. In general, r represents the reaction rate and is a complicated function of concentrations and temperatures involving multiple exponentials. A typical expression will look like that :image.slidesharecdn.com/…
Jan
17
comment Problem solving a second-order PDE
So in this case your strategy is to look for an exact solution with w as a parameter, then replace w with its value ? Do you think it will work with more complicated functions for r, with definite dependence on w ?
Jan
17
awarded  Commentator
Jan
17
revised Problem solving a second-order PDE
edited body
Jan
17
comment Problem solving a second-order PDE
@KellenMyers I have been wondering about that, but I have tested similar conditions on simpler differential equations and had no issues.
Jan
17
comment Problem solving a second-order PDE
@MichaelE2 re: bc1 etc, you are correct, sorry that was another typo which I fixed. When I say I removed w, I meant I removed it from NDSolve, as in the edit.
Jan
17
revised Problem solving a second-order PDE
edited body
Jan
17
awarded  Editor
Jan
17
comment Problem solving a second-order PDE
@MichaelE2 The new error message is now included in my edit.
Jan
17
comment Problem solving a second-order PDE
@Fabian I took your advice and removed the w dependence in NDSolve (ans fixed a typo). I am now getting a different error message, as described in my edit.
Jan
17
revised Problem solving a second-order PDE
added 220 characters in body
Jan
16
awarded  Promoter
Jan
15
comment Problem solving a second-order PDE
Thanks for the correction. At the moment, I'm still unable to get results. The error mesage reads : NDSolve::femcnmd: The PDE coefficient {{2/x,0}} does not evaluate to a numeric matrix of dimensions {1,2}. >>
Jan
14
comment Problem solving a second-order PDE
This is basically a version of equation 12-11 p. 6 of this document : umich.edu/~essen/html/byconcept/chapter12.pdf
Jan
14
comment Problem solving a second-order PDE
Well, the equation is designed to model diffusion/reaction of chemicals inside a catalyst pellet of spherical shape. The boundary conditions describe the absence of particle flow at the center of the pellet (x=0) and at the surface (x=1) the flow is governed by the concentration gradient in the boundary layer. In this, w is a parameter that describe the axial location in a reactor, but the mass transfer I am looking at is only diffusion through the pellet.
Jan
14
asked Problem solving a second-order PDE
Nov
7
comment Best fit equation from a scanned image
Thanks, that's a lot of information for me to go through. With regard to the actual curve, it's in fact not Planck's law which I merely used as a convenient example here, since I'm not at a liberty to disclose my original data.
Nov
7
accepted Best fit equation from a scanned image
Nov
6
asked Best fit equation from a scanned image
Sep
24
awarded  Autobiographer