Steam at $300C$ flows in a stainless steel pipe $(k=15\frac{W}{m}*K)$ whose inner and outer diameters are $5$ cm and $5\mathrm{.}5$ cm $,$ respectively. The pipe is covered with $3-$cm$-$thick glass wool insulation $(k=0\mathrm{.}038\frac{W}{m}*K).$ Heat is lost to the surroundings at $5C$ by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of $22\frac{W}{m^2}*K.$ Taking the heat transfer coefficient inside the pipe to be $80\frac{W}{m^2}*K,$ determine the rate of heat loss from the steam per unit length of the pipe. Also, determine the temperature drops across the pipe shell and the insulation.

The rate of heat loss from the steam per unit length of the pipe is W$.$

The temperature drops across the pipe shell and the insulation are $C$ and $C,$ respectively.