Consider a steam pipe containing steam at $250\backslash$deg C and thermal

conductivity k$=12$ W$/$m $\backslash$deg C$.$ The pipe of diameter $50$ mm and a thickness of $9$ mm is made from stainless steel alloy $($layer A$)$ having a thermal conductivity k$=65$ W$/$m $\backslash$deg C$.$ Two layers of insulation follow. The outer surface of the steel pipe is wrapped in a thin layer of insulation material $($layer B$)$ made from calcium silicate having a thickness of $8$ mm and having a thermal conductivity k$=0\mathrm{.}06$ W$/$m $\backslash$deg C$.$ The outer insulation layer $($layer C$)$ comprises mineral fibres,having a thickness of $40$ mm and a thermal conductivity k$=0\mathrm{.}035$ W$/$m $\backslash$deg C$.$ Assume that heat is lost to the surroundings at a temperature of T$\backslash$infty $=5\backslash$deg C by natural convection with a heat transfer coefficient of $\backslash$infty $=18$ W$/$m$2\backslash$deg C$.$ The steam thermal coefficient $$ of steam$=61$ W$/$m$2\backslash$deg C$.$

Determine:

i$.$ The rate of heat loss from the pipe per unit length of pipe,

And

ii$.$ The temperature on the outside wall of the pipe