The Mathematical Theory Of Diffusion In Solids: Time Dependent First Kind Boundary Conditions

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.