Project ForgeAn oil with a flow rate of 1000 kg/h is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of 70°C to 40°C. Water enters the exchanger at 25°C and leaves at 40°C. The specific heats of oil and water are 2 kJ kg⁻¹ K⁻¹ and 4.2 kJ kg⁻¹ K⁻¹, respectively. The overall heat transfer coefficient is 0.2 kW m⁻² K⁻¹. The minimum heat exchanger area (in m²) required for this operation is _____
Explanation
Q=m·Cp·ΔT=1000×2×(70−40)=60,000 kJ/h=16.667 kW. Counter-current terminal ΔT's: ΔT1=70−40=30°C, ΔT2=40−25=15°C. LMTD=(30−15)/ln(30/15)=15/0.6931=21.64°C. Minimum area (achieved at the maximum possible LMTD, i.e. true counter-current flow with these terminal temperatures) = Q/(U·LMTD)=16.667/(0.2×21.64)≈3.85 m².
Source: GATE CH 2014 (2014)
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