Consider a cross-flow engine oil heater that uses ethylene glycol flowing at a temperature of 110°C to heat the oil initially at 10°C. The ethylene glycol enters a tube bank consisting of copper tubes (k = 250 W/m·K) with staggered arrangement in a 0.5 m × 0.5 m plenum. The outside diameter of the 0.5-m-long copper tubes is 25 mm and has a wall thickness of 2 mm. The longitudinal and transverse pitch of the rod bundles is 0.035 m each. The engine oil to be heated flows inside the tubes with a mass flow rate of 4.05 kg/s. Take the heat transfer coefficient of the oil to be 2500 W/m²·K. If the minimum desired exit temperature of oil is 70°C and the measured exit temperature of ethylene glycol is 90°C, determine

(a) Mass flow rate of ethylene glycol

(b) Number of tube rows. In your calculation use the following properties for the ethylene glycol.

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p = 1062 kg/m3 k = 0.262 W/m-K Pr = 26.12 u = 2.499 x 10-3 kg/m-s c, = 2742 J/kg-K Pre40c - 96.97 %3D s@40°C 0.5 m 0.5 m Ethylene glycol 110°C Ol 10°C 00