Subtopic: Simultaneous heat and mass transfer in agricultural processing operations
Question Statement:
Density, specific heat capacity and thermal conductivity of air are 0.99 kg m⁻³, 1 kJ kg⁻¹K⁻¹, 0.03 W m⁻¹K⁻¹. Convective heat transfer coefficient of air medium and equimolar counter-diffusion mass transfer coefficient of water vapour into air are 35 W m⁻²K⁻¹ and 0.32 m s⁻¹. The mass diffusivity of water vapour into air in m² s⁻¹ is
Options:
(A) 2.46×10⁻⁵
(B) 4.62×10⁻⁵
(C) 8.25×10⁻⁴
(D) 2.85×10⁻³
Official Answer Key:
A
Step-by-Step Solution & Explanation
Chilton–Colburn / Lewis-relation analogy links convective heat and mass transfer coefficients: h/(ρ·cp·k_c) = Le^(2/3), with Le = α/D_AB (α = thermal diffusivity = k/(ρ·cp)). α = 0.03/(0.99×1000) = 3.03×10⁻⁵ m²/s. h/(ρ·cp·k_c) = 35/(990×0.32) = 0.1105 = Le^(2/3) ⇒ Le = 0.1105^1.5 = 0.0367. D_AB = α/Le = 3.03×10⁻⁵/0.0367 = 2.46×10⁻⁵ m²/s (consistent with the known order of magnitude of water-vapour-in-air diffusivity).
Appendix A — Consolidated Answer Table
Appendix B — Section-wise Weightage
Preparation observations
Core subject dominance. Sections 2–7 (Farm Machinery through Dairy & Food Engineering) together account for the large majority of marks, consistent with GATE AG's usual ~70–75% core-subject weightage; Engineering Mathematics and General Aptitude are smaller but reliably-scoring fixed blocks (15 marks each here) that reward systematic formula recall over deep domain knowledge.
Numerically heavy sections. Section 4 (Soil & Water Conservation Engineering) and Section 6 (Agricultural Process Engineering) each carry multiple multi-step numerical problems (earthwork/grid-levelling, USLE soil-loss, freeze-drying, psychrometrics) — these reward careful unit-tracking and formula memorisation (Hooghoudt, Wismer–Luth, Chilton–Colburn analogy, USLE) more than conceptual recall.
Linked and common-data questions cluster in the applied sections (farm power/traction, food-process drying) — expect these paired questions to test the same underlying formula twice, so an error in the first half of a pair is costly (no credit on the second, per the paper's own marking rules).
Weak-confidence flags in this solved set (Q.19 interpretation ambiguity resolved via cross-checking against the printed options; Q.41 and Q.51 not fully pinned) point to two areas — grid/levelling earthwork conventions, and falling-rate drying diffusivity derivations — worth extra practice with fully-worked reference solutions, since the formula convention used by examiners for these topics is not always the first one a textbook presents.
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