QUESTION $3$

Superheated steam at an average temperature $200C$ is transported through a steel pipe $(k=50\frac{W}{m}*C).$ The inner and outer diameter of the pipe are $6$ cm and $8$ cm $,$ respectively and the total length of the pipe is $20$ m $.$ The pipe is insulated with a $4$ cm thick layer of gypsum plaster $(k=0\mathrm{.}5\frac{W}{m}*K.$ The insulated pipe is placed horizontally inside a warehouse where the average air temperature is $10C.$ The steam and air heat transfer coefficient are $800$ and $200\frac{W}{m^2}*K,$ respectively. Determine:

a$)$ Draw the thermal resistance network for the above system.

b$)$ The daily rate of heat transfers from the superheated steam.

c$)$ The temperature on the outside surface of the gypsum plaster insulation.