Chapter 11, Problem 11.18P

A counterflow, concentric tube heat exchanger is designed to heat water from 20 to 80°C using hot oil, which is supplied to the annulus at 160°C and discharged at 140°C. The thin-walled inner tube has a diameter of $D_i=20$ mm, and the overall heat transfer coefficient is $500{\text{ W/m}}^2\cdot \text{K}$ . The design condition calls for a total heat transfer rate of 3000 W.
(a) What is the length of the heat exchanger?
(b) After 3 years of operation, performance is degraded by fouling on the water side of the
exchanger, and the water outlet temperature is only 65°C for the same fluid flow rates and inlet
temperatures. What are the corresponding values of the heat transfer rate, the outlet temperature of the oil, the overall heat transfer coefficient, and the water-side fouling factor, $R_{f,c}^n$ ?