Question Statement:
Fruit juice flowing at the rate of 600 kg h⁻¹ is to be heated using same flow rate of hot fruit juice in a countercurrent regenerator. The specific heat capacity of the fruit juice is 3.9 kJ kg⁻¹ K⁻¹. The overall heat transfer coefficient of the regenerator is 512 W m⁻² K⁻¹ and the area of the regenerator is 3.5 m². The effectiveness of the regenerator is
Options:
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(A) 0.547
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(B) 0.734
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(C) 0.837
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(D) 0.943
Step-by-Step Solution & Explanation
Mass flow ṁ = 600/3600 = 0.1667 kg/s; C_min = C_max = ṁ·cp = 0.1667 × 3900 = 650 W/K (equal flow rates/heat capacities on both streams — capacity ratio Cr = 1). NTU = UA/C_min = (512×3.5)/650 = 1792/650 = 2.757. For a counterflow exchanger with Cr = 1: effectiveness ε = NTU/(1+NTU) = 2.757/3.757 = 0.734, matching option (B).
Appendix A — Consolidated Answer Table
All answers below are Claude-solved and unofficial (no official answer key was available for this task).
* Claude-solved, unofficial answer — not cross-checked against an official GATE key.
Appendix B — Section-wise Weightage
Preparation Observations
• Agricultural Process Engineering (Section 6) carries the single largest share of this paper (23%, 13 questions) — covering engineering properties of produce, drying/psychrometry, size reduction and material handling, and storage systems. This is a high-yield area for GATE AG preparation.
• Irrigation & Drainage (17%) and Farm Machinery (19%) together account for over a third of the paper — both are calculation-heavy sections built on a small set of repeatable formulas (Hooghoudt/Darcy well equations, drainage-channel hydraulics, machine-design stress/torque relations, performance-parameter formulas for tillage/harvesting equipment).
• Farm Power (14%) and Soil & Water Conservation Engineering (14%) are evenly weighted and both draw heavily on applied numerical problems (I.C. engine cycles, tractor traction/transmission, earthwork/erosion-control hydraulics, surveying).
• Engineering Mathematics (7%) is the smallest section by marks in this particular paper, but every sub-topic tested (matrices, Poisson distribution, definite integrals, arc length, Laplace transforms, binomial probability) is a standard, short, high-speed-solve item — good for building early exam momentum.
• Dairy and Food Engineering (6%) is the smallest section overall in this paper; questions here were heat-and-mass-transfer and refrigeration-load calculations, reinforcing the importance of NTU-effectiveness and COP-based problems even when the section's overall weightage is low.
• Across the paper, roughly two-thirds of the two-mark questions reduce to a single well-known formula applied carefully with unit conversions (N to kg, mm to m, rpm to rad/s, wet-basis to dry-basis moisture content) — errors are far more often unit-conversion slips than conceptual gaps.