Project ForgeHeat Transfer
Heat Exchangers
GATE 2019
Hard
Stream A (CpA=2000 J/kg·K) is cooled from 90°C to 45°C in a counter-current double-pipe HX with area 8m². Cold stream B (CpB=1000 J/kg·K) enters at 1 kg/s, 40°C. U=250 W/m²K. Using the arithmetic mean temperature difference AMTD=[(TA,in+TA,out)/2]−[(TB,in+TB,out)/2], the mass flow rate of A (kg/s) is (rounded off to two decimal places)
0.31 kg/s(± 0.02 accepted)
Explanation
Energy balance: mA×2000×45=1×1000×(TB,out−40) ⟹ TB,out=40+90mA. AMTD=67.5−(40+TB,out)/2=27.5−45mA. Q=UA·AMTD=2000×(27.5−45mA)=90000mA (=mA×2000×45). Solving: 180000mA=55000 ⟹ mA=0.306 kg/s.
Source: GATE CH 2019 (2019)
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