A steel pipe carrying steam at $250$C has an internal diameter of $100$ mm and an external diameter of $120$mm$.$ The pipe is insulated using an inner layer of specially treated plastic$-$based composite $40$ mm thick, with an outer layer of felt $50$ mm thick. The ambient temperature surrounding the pipe is at $20$C$.$ Calculate the overall thermal resistance of the assembly and so find the heat loss per unit length of the pipe. Also calculate the temperature on the outer surface of the pipe assembly. Assume that the heat transfer rates for the internal and external surfaces of the pipe assembly are $500$ and $15$ W$/$m$^2$ and the thermal conductivities of the steel, plastic composite and felt are $45,0\mathrm{.}2$ and $0\mathrm{.}05$ W$/$m K$,$ respectively.