GATE AG 2017 • Q48 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Working principles of heat exchangers

Question Statement:

In a vertical tube single effect evaporator, the boiling film coefficient inside the tubes is 1350 W m⁻² K⁻¹. Steam condensation film coefficient outside is 7500 W m⁻² K⁻¹. Thermal conductivity of 20 tubes made of SS 304 is 16 W m⁻¹ K⁻¹. The vertical tubes are 4.3 m long and are of 25 mm ID and 27 mm OD, maintaining a steady 15 °C temperature difference across the tube walls. Assume no boiling point rise, no heat losses, the feed enters the evaporator at the boiling point and the latent heat of vaporization of water is 2346.3 kJ kg⁻¹. Total water evaporation rate from the evaporator bundle of tubes in kg h⁻¹ will be __________.

Official Answer Key:

168 to 169

Step-by-Step Solution & Explanation

• Resistances in series per unit tube length (radial, cylindrical geometry): inside film, tube wall (conduction), outside film. • R_i = 1/(hi·2πri) = 1/(1350×2π×0.0125) = 1/106.03 = 0.009431 m·K/W. • R_wall = ln(ro/ri)/(2πk) = ln(0.0135/0.0125)/(2π×16) = ln(1.08)/100.53 = 0.07696/100.53 = 0.000766 m·K/W. • R_o = 1/(ho·2πro) = 1/(7500×2π×0.0135) = 1/636.17 = 0.001572 m·K/W. • Total R (per unit length) = 0.011768 m·K/W. Heat flow per unit length = ΔT/R = 15/0.011768 = 1274.7 W/m. • Total heat duty = 1274.7 × 4.3 m × 20 tubes = 1274.7 × 86 ≈ 109,624 W. • Evaporation rate = Q/hfg = 109,624 W × 3600 / (2,346,300 J/kg) ≈ 394,646,400/2,346,300 ≈ 168.2 kg/h, inside the accepted range 168–169.

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