Project ForgeWater (Cp=4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air (Cp=1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is
- A40
- B20
- 10
- D5
Explanation
Water's capacity rate Cw=0.5×4.18=2.09 kW/K; air's Ca=2.09×1=2.09 kW/K — equal (Cr=1). Qmax=Cmin(80−30)=2.09×50=104.5 kW. Q=ε·Qmax=0.8×104.5=83.6 kW. Temperature change of each stream: ΔT=Q/C=83.6/2.09=40 K, so water exits at 40°C and air exits at 70°C. For a counterflow exchanger with Cr=1, the terminal temperature differences are equal (80−70=10°C and 40−30=10°C), so LMTD equals this constant difference directly: 10°C.
Source: GATE ME 2012 (Booklet Code A) (2012)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.