Diffusion Phenomena: Cases and Studies by Richard Ghez

Author:Richard Ghez
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2018-12-20T16:00:00+00:00

Inserting these into the Stefan condition (4.18b) and the diffusion equation (1.14), we obtain

Clearly, we have bought a simpler Stefan condition† at the expense of a convective term θx in the diffusion equation (5.11b). This term is nonlinear in C because, eliminating with Eq. (5.11a), it is proportional to Cx(0, t)Cx(x, t).

Following Boltzmann, let us assume that the concentration distribution depends only on the similarity variable

We must then compute the partial derivatives

Inserting these into Eqs. (5.11) and clearing fractions, we get

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