11.20 A concentric tube heat exchanger for cooling lubricating oil consists of a thin-walled inner tube of 25-mm diameter carrying water and an outer tube of 45-mm diameter carrying the oil. The exchanger operates in counterflow with an overall heat transfer coefficient of 55 W/m2 K and the tabulated average properties. To,out To,in = 100°C Water m 0.1 kg/s L w,in = 30°C Tw.out Properties p (kg/m³) Water Oil 1000 800 Cp (J/kg - K) 4200 1900 v (m²/s) 7 × 10-7 1 x 10-5 k (W/m K) 0.64 0.134 Pr 4.7 140 Oil m = 0.1 kg/s (a) If the outlet temperature of the oil is 50°C, determine the total rate of heat transfer and the outlet temperature of the water. (b) Determine the length required for the heat exchanger.