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Transport Processes and Separation Process Principles (Includes Unit Operations) Fourth Edition by Christie John Geankoplis

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7.7. NUMERICAL METHODS FOR UNSTEADY-STATE MOLECULAR DIFFUSION

7.7A. Introduction

Unsteady-state diffusion often occurs in inorganic, organic, and biological solid materials. If the boundary conditions are constant with time, if they are the same on all sides or surfaces of the solid, and if the initial concentration profile is uniform throughout the solid, the methods described in Section 7.1 can be used. However, these conditions are not always fulfilled, in which case numerical methods must be used.

7.7B. Unsteady-State Numerical Methods for Diffusion

1. Derivation for unsteady state for a slab

For unsteady-state diffusion in one direction, Eq. (7.1-9) becomes

Equation 7.7-1

Since this equation is identical mathematically to the unsteady-state ...

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