Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
A single effect long-tube evaporator has ten tubes each of 2.5 cm diameter and 6 m length. It concentrates pineapple juice from 18 °Brix to 23 °Brix. The feed rate into the evaporator is 557 kg h⁻¹ at the boiling point of 70 °C (latent heat of vapourization = 2333.82 kJ kg⁻¹). Neglecting boiling point rise, the overall heat transfer coefficient in W m⁻² K⁻¹ for 12 °C temperature gradient across the tube walls is _____.
Official Answer Key:
1375 to 1395
Step-by-Step Solution & Explanation
Solids balance to find vapour evaporated: Feed(18°Bx) = Product(23°Bx), so Product P = 557×0.18/0.23 = 435.9 kg/h; Vapour evaporated V = 557 − 435.9 = 121.1 kg/h.
Heat duty Q = V×λ = 121.1×2333.82 = 282,666 kJ/h = 78,518 W.
Heat transfer area, A = n×π×d×L = 10×π×0.025×6 = 4.712 m².
U = Q/(A×ΔT) = 78518/(4.712×12) = 78518/56.55 = 1388 W/m²K. This lies within the accepted range 1375–1395.
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