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One dimensional Diffusion Equation with time-dependent BC

Hi everyone! I have been struggling with this problem. Im trying to find an analytical solution to the problem below:

Attachment 20519

All coefficients are known constants.

I know that it has been solved using Laplace transforms, but the source I have doesn't explain how, and the publications my source are reffering to are impossible to find.

I am having trouble when applying the boundary condition at z=0. When I Laplace transform the boundary condition i get:

z=0:

dF/dz = (VMK/ZRTDA)*Fs

where F(x,s)=L{C(x,t)}

Can anybody give me a little help as to how I should solve this?