Problem 2. Convection heat transfer A fluid at a temperature of -40C (Tm,i) needs to be pumped at a mass flow rate of N = 2 kg/s through a thin-walled round pipe (diameter d=1 m) to a well-insulated receiving tank 300 m away from the pumping site. The air in the summer has a high temperature of Tair = 35C and is blowing at an average velocity of U air = 2.5 m/s. The thermophysical properties of the fluid and the air are listed in the following table. Fluid Air -40C 10C 5C 35C Cp (kJ/kg:K) 4.5 4.5 1.01 1.01 k (W/m-K) 0.6 0.6 0.024 0.026 u (Ns/m) 1.3 x 104 1.1 x 10-4 1.72 x 10 1.85 x 10 p (kg/m) 1.0 1.0 1.20 1.16 a) Estimate the convection heat transfer coefficients on the air side (h.) and in the tube (hi). [Ans: h;= 37.78 W/mK: h, =7.85 W/mK] b) Determine the fluid temperature in the receiving tank (Tm ) and the maximum fluid temperature (T30) during transportation. [Ans: Tmo = -2.97C, T5,0 = 3.56 C] c) It is necessary to keep the fluid temperature always below -4C. One way to do it is to cover the pipe with a layer of an insulation material. Determine the thickness of the insulation material required if it has a thermal conductivity of k=0.1 W/m-K. [Ans: 7.2 mm] 1 d) Determine the pressure drop AP required for pumping the fluid. e) If someone suggested to use a smaller pipe (d=0.5 m), discuss how that may change the insulation thickness and