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

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6.6. NUMERICAL METHODS FOR STEADY-STATE MOLECULAR DIFFUSION IN TWO DIMENSIONS

6.6A. Derivation of Equations for Numerical Methods

1. Derivation of methods for steady state

In Fig. 6.6-1 a two-dimensional solid shown with unit thickness is divided into squares. The numerical methods for steady-state molecular diffusion are very similar to those for steady-state heat conduction discussed in Section 4.15. Hence, only a brief summary will be given here. The solid inside of a square is imagined to be concentrated at the center of the square at cn,m and is called a “node”, which is connected to adjacent nodes by connecting rods through which the mass diffuses.

Figure 6.6-1. Concentrations and spacing of nodes for two-dimensional steady-state molecular ...

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