$($a$)$ A steam$-$carrying pipe with an outer diameter of $25$ cm and a length of $225$ meters is insulated with two layers of thermal insulation: The first layer $($high$-$temperature insulation$)$ is $5$ cm thick and has a thermal conductivity of $k_1=0\mathrm{.}095\frac{W}{m}K,$ the second layer $($low$-$temperature insulation$)$ is $4$ cm thick and has a thermal conductivity of $k_2=0\mathrm{.}065\frac{W}{m}K.$ The inner surface of the high temperature insulation is at $400C$ and the outer surface of the low temperature insulation is at $50C$ Aasume steady$-$state conditions and heat transfer only in radial directions. $($a$)$ Calculate the total heat loss per hour through the pipe. $($b$)$ Determine the temperature at the interface between the two insulation layers.