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GATE 2020 CH – Question 55

Heat Transfer · Heat exchangers and evaporators: types and design · 2 marks · Numerical answer

A suspension at 60°C enters the first effect of a double-effect forward-feed evaporator at 1.25 kg/s. Combined water evaporation from both effects is 1.0 kg/s. Exit temperatures are 100°C and 60°C, respectively. Take specific heat 4 kJ/(kg K) and latent heat 2200 kJ/kg constant. Find steam economy in kg evaporated/kg steam, to two decimal places.

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Correct answer: 1.70 to 1.90

Explanation

Let first-effect evaporation be v₁, so second-effect evaporation v₂ = 1 − v₁. The second receives latent heat 2200v₁ and sensible heat released by the first-effect liquid cooling 40 K: $2200v_2=2200v_1+4(1.25-v_1)(40)$. This gives $v_1=2000/4240=0.471698$ kg/s. First-effect steam demand is $s=[1.25(4)(40)+2200v_1]/2200=0.562607$ kg/s. Economy is $(v_1+v_2)/s=1/0.562607=1.78$.

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