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Heat Transfer
Heat Exchangers
GATE 2012
Hard

In a counter-flow double pipe heat exchanger, oil (ṁ=2 kg/s, Cp=2.1 kJ/kg.°C) is cooled from 90°C to 40°C by water (ṁ=1 kg/s, Cp=4.2 kJ/kg.°C) which enters the inner tube at 10°C. The radius of the inner tube is 3 cm and its length is 5 m. Neglecting the wall resistance, the overall heat transfer coefficient based on the inner radius, in kW/m².K, is

  • A0.743
  • 7.43
  • C74.3
  • D2475

Explanation

Q=ṁoilCp,oil(90−40)=2×2.1×50=210 kW. Water outlet: 210=1×4.2×ΔTwater ⟹ ΔTwater=50°C, Twater,out=60°C. ΔT1(90−60)=30, ΔT2(40−10)=30 — equal, so LMTD=30°C. Area=2πrL=2π×0.03×5=0.9425 m². U=Q/(A·LMTD)=210/(0.9425×30)≈7.43 kW/m².K.

Source: GATE CH 2012 (2012)

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