A shell-and-tube heat exchanger with single shell and tube passes (Figure) is used to cool the oil of a large marine engine. Lake water (the shell-side fluid) enters the heat exchanger at 2 kg/s and 15°C, while the oil enters at ] kg/s and 140°e. The oil flows through 100 copper tubes, each 500 mm long and having inner and outer diameters of 6 and 8 mm. The shell-side convection coefficient is approximately 500 W/m² ∙ K.

(a) What is the oil outlet temperature?

(b) Over time there is some degradation in the performance of the engine's water pump, as well as an accumulation of deposits on the outer surface of the tubes. To assess the effect of these changes on heat exchanger performance, obtain two plots of the oil outlet temperature as a function of water flow rate in the range from 1 to 2 kg/s. One should correspond to a clean outer surface (R''_f,c = 0) and the other to surface conditions for which R''_f,c = 0.0003 m² ∙ K/W.