$(4\mathrm{.}3-14)$ Critical Radius for Insulation. A metal steam pipe having an outside diameter of $30$ mm has a surface temperature of $400$ K and is to be insulated with an insulation having a thickness of $20$ mm and a k of $0\mathrm{.}08\frac{W}{m}.$ K $.$ The pipe is exposed to air at $300$ K and a convection coefficient of $30\frac{W}{m^2}.$K$.($a$)$ Calculate the critical radius and the heat loss per m of length for the bare pipe. $($b$)$ Calculate the heat loss for the insulated pipe assuming that the surface temperature of the pipe remains constant $($Answer: a$)0\mathrm{.}0027$ m and $282$ W ; b$)54$ W $)$