Subtopic: Preservation of food by cooling and freezing
Question Statement:
A long cylindrical piece of meat having a diameter of 0.02 m containing 80% moisture is being frozen with air at −30 °C. Initial temperature of the meat is −2.5 °C (freezing point). The heat transfer coefficient of the freezer unit is 20 W m⁻² K⁻¹. If density of the unfrozen meat is 1050 kg m⁻³ and the thermal conductivity of the frozen meat is 1.025 W m⁻¹ K⁻¹, the latent heat of fusion for water is 335 kJ kg⁻¹, shape factors P and R are (1/4) and (1/16) respectively, the freezing time is
Options:
(A) 0.158 h
(B) 0.373 h
(C) 0.464 h
(D) 2.12 h
Official Answer Key:
C
Step-by-Step Solution & Explanation
Plank's equation: t = (ρL/(T_f−T_a))·[P·a/h + R·a²/k], where a is the characteristic dimension (radius for an infinite cylinder, a=0.01 m). ρL = 1050×335,000 = 3.518×10⁸ J/m³ (using whole-density × latent heat, standard Plank convention). ΔT = −2.5−(−30) = 27.5 K. t = (3.518×10⁸/27.5)×[(0.25×0.01/20) + (0.0625×0.01²/1.025)] = 1.279×10⁷×[1.25×10⁻⁴+6.10×10⁻⁶] = 1.279×10⁷×1.311×10⁻⁴ = 1677 s = ≈0.466 h ≈ 0.464 h.
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