Water flows through a pipe at an average temperature of T = 90C. The inner and

Question:

Water flows through a pipe at an average temperature of T_∞ = 90°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 400 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that the entire 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. Assuming constant thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of the heat conduction in the pipe during steady operation. Do not solve.