  A new solution to the mono-dimensional diffusion equation for time-variable
first kind boundary condition is presented where the time-variable function at
the surface is derived proposing a surface saturation model. This solution may
be helpful in the treatment of diffusion processes where the overall time of
diffusion is comparable with the time taken by the surface of the solid body to
saturate achieving a dynamical equilibrium between the diffusing elements
supplied by the external source and the ones transferred internally through the
diffusion kinetic mechanisms. Worked examples for constant diffusion
coefficient are presented and discussed.
