1. Hot lubricating oil is cooled by exchanging heat with water in a L = 8 m length double pipe heat exchanger. The heat exchanger consists of an inner pipe (with an inner diameter Di) and an outer pipe (with an outer diameter Do) (see Figure 3). The oil (heat capacity 𝐶𝑝,𝑜 = 2090 J kg-1 K-1) flows through the inner pipe at a rate of 𝑚̇ 𝐻 = 0.75 kg s-1 , enters and leaves the heat exchanger at 𝑇𝐻1 = 450 K and 𝑇𝐻2 = 350 K, respectively. Water (heat capacity 𝐶𝑝,𝑤 = 4177 J kg-1 K-1) flows through the annulus, enters the heat exchanger at 𝑇𝐶1 = 298 K at a flow rate of 𝑚̇ 𝐶 = 0.8 kg s-1 . The overall heat transfer coefficient from the oil to the water based on the inner surface of the inner pipe is U = 280 W m-2 K-1 . Figure 3: lubricating oil and water double pipe heat exchanger. (a) By neglecting the heat loss and by considering steady state, calculate the heat transfer rate from the oil to water, 𝑄 ̇ . [2 marks] (b) Determine the outlet water temperature 𝑇𝐶2 . [3 marks] PLEASE TURN OVER CP204/208 Fluid Flow and Heat Transfer Page 8 of 8 (c) For a countercurrent arrangement of the heat exchanger, compute the inner diameter of the inner pipe, Di . [5 marks] (d) For a co-current arrangement of the heat exchanger, compute the inner diameter of the inner pipe, Di . [5 marks] (e) After the heat exchanger was used for long time, it was turned off to allow the external surface of the heat exchanger to cool down. The heat transfer coefficient at the external surface is h = 12 W m-2 K-1 , the external diameter of the outer pipe is DO = 1 m, the mass of the outer pipe is mO = 10 kg, the heat capacity of the material of the outer pipe is Cp,pipe = 850 J kg-1 K-1 . Considering the ambient temperature T0 = 298 K and assuming that the outer pipe has the same temperature with the water outlet temperature TC2, calculate how long time does it need to cool the external surface from TC2 to Tfinal = 300 K.

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