To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (thermal conductivity = 35 W/m-K) has an inside diameter of 150 mm and wall thickness of 10 mm, while the outer steel pipe has an inside diameter of 250 mm and a wall thickness of 10 mm. The ocean water is at T[infinity],0 = -5°C and provides an external convective heat transfer coefficient of 500 W/m^2-K. The convective coefficient associated with the flowing crude oil is 450 W/m^2-K. It is required that the polyurethane foam insulation (thermal conductivity = 0.075 W/m-K) between the two pipes does not exceed its maximum service temperature of 70°C Required:
a. Draw a thermal circuit for this cylindrical pipe-in-pipe configuration.
b. Determine the maximum allowable crude oil temperature such that the polyurethane foam insulation does not exceed its maximum service temperature.
c. For these conditions, also determine the heat transfer per unit length of the pipe.