Q$2.(35$ points$)$ A pipe carying steam at $220C$ has an intemal diameter of $15$ cm $.$ The

convection coefficient on the inside is $60\frac{W}{m^2}K.$ The pipe wall thickness is $15$ mm $,$ and

the thermal conductivity is $35\frac{W}{m}K.$ The pipe wall is covered with an insulation loyer of

$3$ cm thickness with thermal conductivity of $0\mathrm{.}12\frac{W}{m}K$ and a contact resistance of $6$

${10}^{-1}{m}^2\frac{C}{W}.$ The outside is exposed to a chemical at $130C$ with a convection

coefficient of $15\frac{W}{m^{-K}}.$ Determine the heat flow and pipe surface temperatures. Also

colculate the overal heat transfer coefficient based on outside area.