Water flows through a pipe at an average temperature of T[infinity] = 70°C. The inner and outer radii of the pipe are r1 = 6 cm and r2 = 6.5 cm, respectively. The outer surface of the pipe is wrapped with a thin electric heater that consumes 300 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that all heat generated in the heater is transferred to the pipe. Heat is transferred from the inner surface of the pipe to the water by convection with a heat transfer coefficient of h = 85 W/m2⋅K. Assume that the thermal conductivity is constant and the heat transfer is one-dimensional. Required:
Express the mathematical formulation (the differential equation and the boundary conditions) of the heat conduction in the pipe during steady operation.