A water$-$resistant sheet used for water$-$proofing applications is

formed from an impermeable polymeric material. The

microstructure of the sheet is engineered to provide open pores

of diameter $D=10m$ that extend through the entire thickness of

the $L=100m$ thick sheet. The pore diameter is large enough to

allow water vapor to be transferred through the pore, but is

sufficiently small to prohibit liquid water from penetrating

through the sheet.

a$)$ Determine the rate $(mo\frac{l}{s})$ at which water vapor is

transmitted through a single pore when saturated liquid exists on the top of the sheet and

moist air at a relative humidity of $50\%$ exists on the bottom side of the sheet at a temperature

of $T=298K$ and a pressure of $P=1$atm. At $298K,$ the diffusion coefficient for water vapor

through air is$,D_{AB}=0\mathrm{.}26{10}^{-4}\frac{m^2}{s}.$

b$)$ Determine the rate $(mo\frac{l}{s})$ at which water vapor is transmitted through a single pore in the

absence of advection. Comment on the results.

c$)$ Investigate the sensitivity of the transfer rate, both including and neglecting advection, to

temperature. Consider a temperature range from $300K$ to $360K.$ Comment on the results.