GATE 2024 AG – Question 62
Countercurrent juice pasteurization uses juice flow .3 kg/s, cp3.8 kJ/(kg·K),inlet30°C. Water flow is .4 kg/s, cp4.2 kJ/(kg·K),inlet97°C, outlet65°C. Overall U=1 kW/(m²·K). Find exchanger area in m²,to three decimals.
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Correct answer: 1.900 to 2.200
Explanation
Water heat loss is $q=.4(4.2)(97-65)=53.76$ kW. Juice outlet is $30+53.76/[.3(3.8)]=77.157895$°C. Counterflow terminal differences are $97-77.157895=19.842105$ K and 65−30=35 K. Their log mean is $(35-19.842105)/\ln(35/19.842105)=26.707977$ K. Hence $A=q/(U\Delta T_{lm})=53.76/26.707977=\mathbf{2.013}$ m².