GATE AG 2024 • Q65 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Evaporation and Drying

Subtopic: Psychrometry – properties of air-water vapour mixture

Question Statement:

Fish fillets at −1 °C are being frozen in Individual Quick Freezing (IQF) system using air at −40 °C. The product has a characteristic dimension of 10 cm with a density of 1200 kg·m⁻³. Thermal conductivity of the product is 2.5 W·m⁻²·K⁻¹, the convective heat transfer coefficient is 100 W·m⁻²·K⁻¹ and the latent heat of fusion is 300 kJ·kg⁻¹. If the fillet is considered as an infinite plate, the freezing time, in minutes, is __________. (Rounded off to 2 decimal places) -type split: MCQ — 31 questions; MSQ — 4 questions (Q.21–Q.24); NAT — 30 questions. Soil and Water Conservation Engineering was the single heaviest subject section at 16 marks, spread widely across Hydrology (3), Soil & Water Erosion (3), Fluid Mechanics, Soil Mechanics and Surveying. Farm Power and Engineering Mathematics tied at 13 marks each. Within Farm Power, Tractors and Power Tillers alone contributed 5 questions — with human engineering and safety appearing twice (Q.27 percentile design rule, Q.52 vibration decibels), an area candidates often neglect. Irrigation and Drainage Engineering was unusually light this year at 9 marks, in contrast to its heavier weight in other sessions. The paper contained a block of four MSQ questions (Q.21–Q.24), all 1 mark, all conceptual. MSQs carry no negative marking but require every correct option to be selected — partial selection earns nothing. Several questions rewarded recognising a convention or definition rather than heavy computation: Q.27 (95ᵗʰ percentile for clearance dimensions), Q.29 (bite length depends only on the speed ratio, so the answer is zero), Q.20 (k/h for a cylinder versus 2k/h for a sphere) and Q.31 (the USLE exponent m = 0.5 for slopes ≥ 5 %). Two questions warrant caution. Q.64 is convention-dependent — the official range is reproduced only by one of the two textbook pairings for representative particle size (see the note in that solution). Q.65 was cancelled with marks awarded to all, its thermal conductivity having been printed with heat-transfer-coefficient units.

Official Answer Key:

153.85

Step-by-Step Solution & Explanation

Plank’s equation for freezing time is: t = (ρ L_f)/(T_f − T_a) × [P a/h + R a²/k] For an infinite plate (slab): P = 1/2 and R = 1/8, with a = the full thickness. Step 1 — substitute the data: ρ = 1200 kg·m⁻³ ; L_f = 300 kJ·kg⁻¹ = 300,000 J·kg⁻¹ T_f − T_a = −1 − (−40) = 39 °C a = 0.10 m ; h = 100 W·m⁻²·K⁻¹ ; k = 2.5 W·m⁻¹·K⁻¹ Step 2 — the two shape terms: P a/h = (0.5 × 0.10)/100 = 5.0 × 10⁻⁴ R a²/k = (0.125 × 0.01)/2.5 = 5.0 × 10⁻⁴ Sum = 1.0 × 10⁻³ Step 3 — freezing time: t = (1200 × 300,000/39) × 1.0 × 10⁻³ = 9,230,769 × 1.0 × 10⁻³ = 9230.8 s Step 4 — convert to minutes: t = 9230.8/60 = 153.85 minutes Why the key is MTA. The question was cancelled and marks awarded to all candidates. The source of the ambiguity is visible in the question itself: the thermal conductivity is stated with the units W·m⁻²·K⁻¹, which are the units of a heat transfer coefficient, not of a thermal conductivity (W·m⁻¹·K⁻¹). There is also genuine ambiguity over whether the “characteristic dimension” of 10 cm is the full slab thickness a (as assumed above) or the half-thickness, which would change the answer substantially. The value above is the standard interpretation. APPENDIX A — CONSOLIDATED OFFICIAL FINAL ANSWER KEY APPENDIX B — SECTION-WISE WEIGHTAGE ANALYSIS

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