Mathematical Modeling of Thin-Layer Drying Kinetics of Tomato Peels: Influence of Drying Temperature on the Energy Requirements and Extracts Quality

Abstract

Tomato drying implies high energy consumption due to the high moisture content, and limiting drying temperatures is necessary to avoid carotenoid degradation. To explain the mechanism of moisture transport through the material and to scale up the drying process, drying experiments are needed and supported by mathematical modeling. For the Rila tomato peel drying process, ten thin-layer mathematical models were formulated based on experimental data for six temperatures (50–75 °C) and validated by statistical analysis. Considering the slab geometry of the peels sample and Fick’s second law of diffusion model, the calculated effective moisture diffusivity coefficient values Deff varied between 1.01 × 10−9–1.53 × 10−9 m2/s with R2 higher than 0.9432. From the semi-theoretical models, Two-term presents the best prediction of moisture ratio with the highest R2 and lowest χ2 and RMSE values. Using the experimental data on extract quality (carotenoid content), two degradation models were formulated. Increasing the drying temperature from 50 °C to 110 °C, a degradation of 94% for lycopene and 83% for β-carotene were predicted. From the energy analysis, a specific energy consumption of 56.60 ± 0.51 kWh is necessary for hot-air drying of 1 kg of Rila tomato peel at 50 °C to avoid carotenoid degradation.

The Mathematical Modeling, Diffusivity, Energy, and Enviro-Economic Analysis (MD3E) of an Automatic Solar Dryer for Drying Date Fruits

“…E th,y = E th,D × N dy (35) Therefore, the ASD's annual thermal output (E th,y ) can be estimated by Equation (36).…”

“…Dried Product EMD, m 2 /s Ambawat et al [2] Moringa oleifera leaves 3.59 × 10 −10 -2.92 × 10 −10 Quality [35] Tomato 1.01 × 10 −9 -1.53 × 10 −9 Sandeepa and Rao [50] Sorghum Seeds 3.01 × 10…”

“…The mathematical modeling of the drying process under various operating circumstances is critical for creating models that may be used to regulate commercial-scale drying plants and improve the overall product quality [32]. Several mathematical models have been developed to study the drying properties of various products, for example, garlic slices [33], pearl millet [34], tomato [35][36][37][38][39][40], pumpkin slices [41], potato cubes [42], maize seeds [43], galangal [32], paddy grains [44], mint [7,45], onion [46], unbleached kraft pulpboard [47], apple [48], moringa oleifera leaves [2], kodo millet grains and fenugreek seeds [49], sorghum seeds [50], olive [51], black tea [52], and date fruit [53][54][55][56]. When evaluating the applicability of a mathematical model, higher values of R 2 and lower values of χ 2 , RMSE, and E% are generally considered more favorable [57][58][59].…”

“…Ambawat et al[2] Moringa oleifera leaves 3.59 × 10 −10 -2.92 × 10 −10 Quality[35] Tomato 1.01 × 10 −9 -1.53 × 10 −9 Sandeepa and Rao[50] Sorghum Seeds 3.01 × 10−10 -5.50 × 10 −10 Akpinar and Bicer [58] Strawberry 4.52 × 10 −10 -9.63 × 10 −10 Pahlavanzadeh et al [74] Grapes 2.4 × 10 −10 -6.22 × 10 −10 Lee and Hsieh [132] Strawberry 2.4 × 10 −9 -12.1 × 10 −9 Kaya et al [133] Quince 0.65 × 10 −10 -6.92 × 10 −10 Doymaz [134] Apricot 6.76 × 10 −10 -12.6 × 10 −10 Aghbashlo and Samimi-Akhijahani [135] Berberis 3.32 × 10 −10 -90 × 10 −10 Ruiz-Cabrera et al [136] Cactus pears 1.51 × 10 −10 -5.32 × 10 −10 T ˙IREK ˙I [137] Date fruit 1.53 × 10 −9 -1.74 × 10 −9Current study Date fruit 7.14 × 10 −12 -2.17 × 10 −11…”