Steam moves through a horizontal pipe $2in.$ O$.$D$.$ The pipe with surface

temperature at $120C$ is in contact with air at $5C.$ The external heat transfer

coefficient is $10\frac{W}{m}2K.$

a$)$ Determine the rate of heat loss per unit length of the pipe from the steam to

the air.

b$)$ The pipe is going to be insulated with a layer of glass wool $(k=0\mathrm{.}4\frac{W}{m}K).$

Calculate the critical radius of the insulation for the heat loss to decrease when

the thickness is increased.

c$)$ Assuming the external heat transfer coefficient remains constant determine

the rate of heat loss per unit length of the pipe if the insulation thickness is $\frac{1}{2}$ in$.$

d$)$ Calculate the temperature on the outside surface of the insulation.