Problem $4(5$ points$)$: Steam at an unknown temperature flows through a steel tube $(35\frac{W}{m}-K)$ of $150-$mm inner

radius and $30-mm$ wall thickness. Assume the inner surface temperature of the steel tube is the same as the

steam. A $20-mm$ layer of insulation $(0\mathrm{.}10\frac{W}{m}-K)$ is applied to the outside of the tubes, and then wrapped with

a very thin sheet of aluminum having an emissivity of $0\mathrm{.}2.$ Surrounding wall temperature is $27$ deg$-$C $($ignore

convection$).$

Calculate the three radii $(r_1,r_2,r_3)$ in meters, as defined in the figure.

What is steady$-$state steam temperature required to maintain the outer aluminum sheet at $50$ deg$-$C$?$