A $10-cm$ outside diameter by $6-cm$ inside diameter steel pipe $-$steel $=43\frac{W}{m.K}$ carries steam. The steel pipe is wrapped in $10-cm$ layer of asbestos insulation $($ k asbestos $=0\mathrm{.}156\frac{W}{m.K}),$ which is further covered by $1-cm$ thick layer of plaster $($ k plaster $=0\mathrm{.}107\frac{W}{m.K},$ as shown in the figure below. If the temperature of the inside wall of the steel pipe is $980C,$ and the temperature on the outside surface of the plaster is $41\mathrm{.}6C,$ determine the rate of heat conduction per unit length though the pipe$-$insulation$-$plaster system. $(25$ Points$).$