Project ForgeIn a double pipe counter-current heat exchanger, the temperature profile shows hot fluid entering at 100°C and leaving at 60°C, while cold fluid enters at 40°C and leaves at 80°C. During operation, due to fouling inside the pipe, the heat transfer rate reduces to half of the original value. Assuming that the flow rates and the physical properties of the fluids do not change, the LMTD (in °C) in the new situation is
- A0
- B20
- 40
- Dindeterminate
Explanation
Originally ΔT1=100−80=20°C and ΔT2=60−40=20°C — a 'balanced' exchanger where the temperature difference is constant along the length (equal heat-capacity rates). If Q halves while flow rates and Cp are unchanged, the temperature RANGE of each stream also halves (from 40°C to 20°C for each), since Q=ṁCpΔT. With inlet temperatures fixed at 100°C and 40°C, new outlets are 100−20=80°C (hot) and 40+20=60°C (cold). New ΔT1=100−60=40°C and ΔT2=80−40=40°C — again equal, so LMTD=40°C (the well-defined limiting value when ΔT1=ΔT2).
Source: GATE CH 2013 (2013)
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