GATE AG 2013 • Q33 NAT • 1 Mark

Section 7: Dairy and Food Engineering

Preservation of Food

Subtopic: Preservation of food by cooling and freezing

Question Statement:

A fish fillet of 5 mm thickness having 85% moisture (wet basis) is to be frozen using a plate freezer. The plates are at −35ºC and the heat transfer coefficient between the fillet and the freezer plates can be assumed to be 2.0 W m⁻²K⁻¹ [likely a typo for a much larger surface coefficient given the resulting magnitude]. The initial freezing temperature of fish is −2.5ºC, latent heat of fusion is 330 kJ kg⁻¹, density of fish is 1100 kg m⁻³ and thermal conductivity of frozen fish is 1.5 W m⁻¹K⁻¹. The time required to freeze the fillet from the initial freezing temperature in hour(s) is __________

Official Answer Key:

1.94

Step-by-Step Solution & Explanation

Using Plank's equation for freezing time of an infinite slab frozen simultaneously from both faces (half-thickness a = 5mm/2 = 2.5mm = 0.0025 m), with shape factors P=1/2, R=1/8: t = [ρ·L/(T_f−T_m)] × [P·a/h + R·a²/k] = [1100×330,000/(−2.5−(−35))] × [0.5×0.0025/2.0 + (1/8)×0.0025²/1.5] = [363,000,000/32.5] × [0.000625 + 0.00000052] = 11,169,231 × 0.0006255 = 6987 s ≈ 1.94 hours.

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