BEAR $1.)(20$pts$)$ A disk of $20$ mm diameter is covered with a water film that is $4mm$ thick. Under steady$-$state conditions, a heater power of $300mW$ is required to maintain the disk$-$water film at $305$ K in air at $295$ K $.$ The surface of the water has an emissivity of $=0\mathrm{.}95$ and the surrounding temperature of $280$ K $.$ The rate of evaporation is measured at $2\mathrm{.}55{10}^{-4}k\frac{g}{h}.$ WATCH YOUR UNITS!

a$.)$ Determine the average heat transfer coefficient $($h$)$ at the surface of the water.

b$.)$ Determine how long it will take to fully evaporate the water.