Carrot slices of 2 mm thickness are freeze dried from initial free moisture content 80% (wet basis) to final free moisture content 2% (wet basis). Mass density of fresh carrot is 1100 kg m⁻³. Thermal conductivity of dried layer is 0.005 W m⁻¹K⁻¹. Latent heat of sublimation at −35°C is 2840 kJ kg⁻¹, product surface temperature is −5°C. Total drying time in hour is
Options:
(A) 1.2
(B) 2.3
(C) 3.2
(D) 5.4
Official Answer Key:
B
Step-by-Step Solution & Explanation
Freeze drying is modelled as a receding sublimation front conducting heat through the dried (porous) layer: t = ρ₀·ΔX·L_s·L²/(2·k·ΔT), where L is the half-thickness (drying assumed from both exposed faces), ΔX = 0.80−0.02 = 0.78 (mass fraction of ice removed per unit fresh volume), ΔT = −5−(−35) = 30°C. L = 0.002/2 = 0.001 m. Ice-equivalent mass to remove per m³ = 1100×0.78 = 858 kg/m³. t = 858×2,840,000×(0.001)²/(2×0.005×30) = 8122 s = 2.26 h ≈ 2.3 h.
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