GATE 2024 AG – Question 65
Fish fillets at−1°C are frozen in IQF air at−40°C. Characteristic dimension10 cm, density1200 kg/m³,printed conductivity2.5 W/(m²·K),convection coefficient100 W/(m²·K),latent heat300 kJ/kg. Treat as an infinite plate and find freezing time in minutes, to two decimals.
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Correct answer: MTA
Explanation
The official answer is **marks to all (MTA)**,which is retained for grading. For the conventional Plank calculation, interpret the conductivity unit as W/(m·K),the10 cm dimension as full plate thickness a, and−1°C as freezing temperature. Infinite-slab factors are P=1/2,R=1/8,so $$t=\frac{\rho L}{T_f-T_a}\left(\frac{Pa}{h}+\frac{Ra^2}{k}\right)=\frac{1200(300000)}{39}\left(\frac{.5(.1)}{100}+\frac{.125(.1)^2}{2.5}\right)=9230.769\ \mathrm s.$$ This is **153.85 min** under those assumptions. The source’s conductivity unit and characteristic-dimension interpretation are problematic; no numeric accepted range is invented for an MTA question.