It is desired to determine the rate of diffusion of unreacted monomer out of a newly synthesized sheet of

polymer. The sheet is thin in the $x$ direction compared to its lengths in the $y$ and $z$ directions, so we

assume the monomer concentration is $={}_{x_{,}t}.$ The model to be employed assumes that the monomer.

is initially at uniform concentration $(x,0)=1$ and that at $t=0$ the sheet is immersed in a well$-$stirred

container of solvent in which the concentration is always negligible, with Biot number large enough to

located at $x=0,$ we'll model only half the sheet between $0x1.$ Mirror symmetry yields the solution in

the $-1x0$ portion. We've assumed a nondimensionalization based on the sheet half$-$thickness L$,$ the

initial monomer concentration $C0,$ and the diffusion time $\frac{L^2}{D}.$

b$)$ Calculate the average monomer concentration remaining in the sheet, $(t).$ Based on the convergence

behavior of the FFT series in part $($b$),$ describe qualitatively whether or not you expect the FFT series for

$(t)$ to be reliable?

c$)$ Determine the outward flux of monomer at the surface, both in dimensionless and in dimensional form.

Based on the convergence behavior of the FFT series in part $($b$),$ describe qualitatively whether or not you

expect the FFT series for the surface flux to be reliable?