A $10$ m long pipe with an inner radius r$1=25$ mm and outer radius r$2=40$ mm is used to transfer steam at a temperature of T$1=200$C$.$ The heat transfer coefficient on the inner surface is h $=1400$ W$/$m$2.$C and the thermal conductivity of the pipe is k $=18$ W$/$m$.$C$.$ If the temperature on the outer surfaces of the pipe is T$2=20$C$,$ a$.$ Derive the differential equation and express the boundary conditions for steady one dimensional heat conduction through the pipe b$.$ Obtain a relation for variation of temperature in the pipe c$.$ Calculate the rate of heat loss from the pipe $($please solve it step by step on the paper $)$