Linear Diffusion from a Wall

In this section, a simple example of the solution of a mass transfer problem is presented. When one solves differential equations, it is very important to state the boundary conditions clearly. In the present example, diffusion takes place in the 

It is also assumed that the diffusion coefficient D is independent of location in the solution (x 0). 

The second condition implies that diffusion does not occur for a very long time, so that the concentration far from the wall is zero. The boundary condition with 

The variable 5 now contains the information about the time dependence of the problem. Applying Laplace transformation to the derivative on the right-hand side of equation (6.5.1), one obtains 

Laplace transformation of the left-hand side is more difficult and requires use of the product rule. In the present case, this gives 

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