Question 2. Answer all parts of this question a) A shell and tube heat exchanger is to heat 10,000 kg h–1 of water from 16 to 84°C using hot oil entering at 160°C and leaving at 92°C. The oil will flow through the shell of the heat exchanger. The water will flow through 11 brass tubes of 22.9 mm inside diameter and 25.4 mm outside diameter, with thermal conductivity 137 W m–1 K–1, with each tube making two passes through the shell.
i) Using the Colburn Equation, given
Nu = 0.023Re0.8 Pr0.333 show that the convection heat transfer coefficient of the water flowing through the tubes is about 3300 W m–2 K–1. (Assume the density of water is 988 kg m–3 and find the other thermophysical properties of water from steam tables. Don’t forget to divide the total flowrate by the number of tubes to get the flowrate through each tube, in kg s–1.) [10 marks]
ii) The shell side heat transfer coefficient is 400 W m–2 K–1. Calculate the overall heat transfer coefficient based on the outside area of the tubes, assuming negligible fouling resistances. [4 marks] Answer: 351 W m–2 K–1
iii) Using the correction factor chart shown in Figure 2.1, determine the appropriate correction factor. [5 marks] Answer: 0.85
b) The oil in part (a) is pumped into the heat exchanger using a centrifugal pump. i) Power has dimensions of ML2T–3. Use dimensional analysis to derive a relationship between pumping power (P), fluid density ( ?), impeller diameter (D) and impeller rotational speed (N) of the form: P = K ? aNbDc [5 marks] Answer: P = K ? N 3 D
5 ii) A centrifugal pump is an example of a rotodynamic pump. Discuss the advantages and disadvantages of centrifugal pumps compared with positive displacement pumps. [6 marks]
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