# Reaction-Diffusion in a Two-Dimensional Catalyst Pellet

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Consider the reaction-diffusion in a two-dimensional catalyst pellet with governing equations and boundary condition:

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Contributed by: Housam Binousand Brian G. Higgins (May 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind, .

The Chebyshev derivative matrix at the quadrature points is an matrix given by

, , for , and for , , and ,

where for and .

The discrete Laplacian is given by where is the identity matrix, is the Kronecker product operator, , and is without the first row and first column.

References

[1] P. Moin, *Fundamentals of Engineering Numerical Analysis*, Cambridge, UK: Cambridge University Press, 2001.

[2] L. N. Trefethen, *Spectral Methods in MATLAB*, Philadelphia: SIAM, 2000.

[3] T. R. Marchant and M. I. Nelson,"Semi-analytical Solutions for One- and Two-Dimensional Pellet Problems," *Proceedings of the Royal Society A*, 460(2048), 2004 pp. 2381–2394. doi:10.1098/rspa.2004.1286.

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