(Solved): Q2. Consider a steam pipe of length L=15m, inner radius r1=2m, outer radius r2=2.4m, an ...

Q2. Consider a steam pipe of length $L=15\mathrm{m}$, inner radius $r_1=2\mathrm{m}$, outer radius $r_2=2.4\mathrm{m}$, and thermal conductivity $k=7.5\mathrm{W}/{\mathrm{m}}^{\circ }\mathrm{C}$. Steam is flowing through the pipe at an average temperature of $250^{\circ }\mathrm{C}$, and the average convection heat transfer coefficient on the inner surface is given to be $h=1.25\mathrm{W}/{\mathrm{m}}^{2{}^{\circ }}\mathrm{C}$. If the average temperature on the outer surface of the pipe is $T_2$ $=160^{\circ }\mathrm{C}$, (a) express the differential equation and the boundary conditions for steady onedimensional heat conduction through the pipe, (b) obtain a relation for the variation of temperature in the pipe by solving the differential equation, (c) find the temperature at the inner surface of the pipe using the relation of temperature variation as a function of radial distance obtained in part (b), and (d) evaluate the rate of heat loss from the steam through the pipe. (Note: work in SI units and the final result should be in SI units)