Discussion
A single effect vacuum evaporator has 100 tubes of 25 mm diameter. One thousand kg feed of milk per hour with 15% TS is concentrated to 20% TS in the evaporator. Film heat transfer coefficients on either sides of the tube are 5000 and 800 W m−2 K−1. Thermal conductivity of 1.5 mm thick SS tubes is 15 W m−1 K−1. Latent heat of vapourization under vacuum is 2309 kJ kg−1. For 10 °C temperature difference across the tube wall, the height of each tube, in m is
Answer: D
Each tube must be about 3.17 m high.
Solids balance: the feed carries 150 kg/h of solids, so the 20% concentrate is 750 kg/h and 250 kg/h of water is evaporated. The heat load and the overall coefficient through the two films and the tube wall are:
\[ \begin{aligned} q &= \frac{250 \times 2309}{3600} = 160.3\ \text{kW} \\ \frac{1}{U} &= \frac{1}{5000} + \frac{0.0015}{15} + \frac{1}{800} \\ U &= 645.2\ \text{W m}^{-2}\text{K}^{-1} \end{aligned} \]
\[ \begin{aligned} A &= \frac{q}{U\,\Delta T} = \frac{160347}{645.2 \times 10} = 24.85\ \text{m}^{2} \\ H &= \frac{24.85}{100\,\pi(0.025)} = 3.16\ \text{m} \end{aligned} \]
The key takes the 10 °C as the overall temperature difference driving heat through the films and wall. The shorter tubes would supply too little area for 250 kg/h of evaporation.
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