Write your answer in the format given in the class slide. The answers be graded

Question

Write your answer in the format given in the class slide. The answers be graded if the template was not followed. Consider a cross-flow engine oil heater (shown in figure 1a) that uses ethylene glycol flowing at a temperature of 110 degree C to heat the oil initially at 10 degree C. The ethylene glycol enters a tube bank consisting of copper tubes (thermal conductivity, k = 250 W/m^* K) with staggered arrangement in a 0.5 times 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 foe 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/sec. Take the heat transfer coefficient of the oil to be 2500 W/m^2_*K. If the minimal desired exit temperature of oil is 70 degree C and the measured exit temperature of ethylene glycol is 90 degree C, determine Mass flow rate of ethylene glycol (for 10 tokens) and Number of lubes for ethylene glycol (for 30 tokens). In your calculations use the following properties for oil and ethylene glycol (EG): Oil: Specific heat at constant pressure for oil, C_p.oil = 1.964 KJ/kg^* K Ethylene glycol properties: Density, p = 1062 kg/m^3; Viscosity, mu = 2.499 times 10^-3 kg/m^* s; Thermal conductivity, k = 0.262 W/m^* K; Specific heat at constant temperature for EG, C_p.EG = 2.742 KJ/kg^* K; Pr = 26.12;Pr_s (at 40 degree C) = 96.97 Nu_D = 0.35Rc_D^0.6 Pr^0.36(Pr/Pr_s)^0.25, Where Re_D = pVD_0/mu and V is the average velocity of ethylene glycol passing through the tube bundle.

Explanation / Answer

a) mass flow rate of ethylene glycol = 4.05 * (250/0.262) * (273.15 + 10)/(273.15 + 110) * (1/10) * (0.5 * 0.5)

                                                           = 71.39 kg/sec

b)    Number of tubes for ethylene glycol =   [(3.14 * 250 * 250 *25)/(3.14 * 25 * 25 *35)] * 30

                                                                 =   2143 tubes

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