Numerical modeling of infrared drying processes of apples

Abstract

Based on the known equations of heat balance, drying kinetics (Midilli model), and vitamin C degradation (first-order reaction with Arrhenius temperature dependence), a comprehensive mathematical model of heat and mass transfer for infrared drying of apples was adapted. The model was numerically implemented in Python language using NumPy and Matplotlib libraries. Comparative analysis of eight drying modes was carried out: continuous (300 and 500 W), intermittent with intermittency coefficients α = 0.67; 0.75; 0.80, oscillating (40–60°C), step-down (500 → 350 → 200 W), and combined (infrared heating 400 W combined with convection at 40°C). The initial moisture content was 6.0 kg kg, the final - 0.1 kg kg. It was found that the time to reach the target moisture content of 1.2 kg kg varied from 145 to 252 min. The maximum product temperature ranged from 42 to 68°C. Vitamin C preservation variesd from 2.1 to 18.2%. A complex efficiency index Q = 60·C t was introduced characterizing the percentage of vitamin C preserved per hour of drying. Q values ranged from 0.87 to 6.62. The intermittent mode 1:4 (α = 0.80) was identified as optimal providing Q = 6.62 with drying time 165 min, vitamin C preservation 18.2%, and maximum product temperature 42°C. It was found that increasing the intermittency coefficient α from 0.67 to 0.80 reduced the maximum product temperature by 6°C and increased vitamin C preservation by 6.7%. The obtained results may be used in the design of industrial drying equipment.