GATE 2022 CH – Question 55
A single-effect evaporator with a heat transfer area of 70 m$^2$ concentrates a salt solution using steam. The salt solution feed rate and temperature are 10000 kg h$^{-1}$ and 40 °C, respectively. The saturated steam feed rate and temperature are 7500 kg h$^{-1}$ and 150 °C, respectively. The boiling temperature of the solution in the evaporator is 80 °C. The average specific heat of the solution is 0.8 kcal kg$^{-1}$ K$^{-1}$. The latent heat of vaporization is 500 kcal kg$^{-1}$. If the steam-economy is 0.8, the overall heat transfer coefficient is ________ kcal h$^{-1}$ m$^{-2}$ K$^{-1}$ (rounded off to the nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 765
Explanation
The steam economy is the vapour produced per kg of steam used, so $\frac{V}{7500} = 0.8$ and $V = 6000$ kg/h. The heat given up by the condensing steam is $7500 \times 500 = 3.75 \times 10^6$ kcal/h. This heat passes through the area with the temperature difference $150 - 80 = 70$ K: $U = \frac{3.75 \times 10^6}{70 \times 70} = 765$ kcal h⁻¹ m⁻² K⁻¹.