An analytical solution of the time dependent diffusion equation in a composite slab

The time-dependent, one-dimensional diffusion equation is solved for a finite slab of two layers. An external source is supplied to one of the layers. The differential equations are subject to the reflecting boundary conditions at the two outer boundary surfaces. The flux and the current density are continuous across the interface between two media. The exact analytical solution is expressed in terms of a Green's function. The solution is developed by the application of the Laplace transformation.