A freezer with a $0\mathrm{.}7-$meter depth accumulated a buildup of ice on the inside, so it needed to be

thawed out. While the ice was melting, it seemed like a good time to model the system to

determine how often deicing should occur.

Here's what happened: When the freezer door was left open, the entrance to the freezer was

exposed to air with a $4$ v$/$v$\%$ humidity level. The water vapor in the air then diffused to the cold

walls of the freezer, where it instantly condensed and froze upon contact, as the freezer maintained

a constant temperature of $4\backslash$deg C$.$ At this temperature, the diffusivity of water vapor in air is $0\mathrm{.}23$

cm$^2/$s$.$

a$)$ Draw the system in a simplified diagram. Be sure to include the coordinate $($origin$),$

length scale$($s$),$ and direction of flux.

b$)$ What is the domain over which mass transfer is occurring?

Write out the GMB in the correct coordinate system, list assumptions and simplify the expression

to a solvable ODE.

c$)$ What is the initial condition? If it$$s not needed, state why.

d$)$ What are the boundary conditions?

e$)$ Solve for the concentration of water within the domain.

f$)$ What is the flux of water that is freezing?

g$)$ The freezer is no longer efficient after $2$ cm of ice accumulate. How long will it take to

for this to happen?