Consider a chilled-water pipe of length L, inner radius r₁, outer radius r₂, and thermal conductivity k. Water flows in the pipe at a temperature T_f and the heat transfer coefficient at the inner surface is h. If the pipe is well-insulated on the outer surface,

(a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe

(b) Obtain a relation for the variation of temperature in the pipe by solving the differential equation.