3. THE EFFECTS OF HOT-AIR DRYING METHODS ON THE DRYING OF
3.3 Results and Discussions
3.3.5 Mathematical modelling
71
The highest drying rate was found for OVD, which was 3% higher than MVD and 12% higher than OAD. This study finding clearly indicates that temperature, relative humidity and slice thickness had an influence in the drying rate. Constant drying conditions, such as those observed in OVD might not be suitable for drying 9 mm thick mango slices. Temperatures in MVD were more suitable, because a falling rate period was observed, during the drying process. It is clear that the use of OAD does not offer the best solution, because of the fluctuations in the drying rate, which may result in product quality losses.
72
ratio at the beginning of the drying period and the Lewis model over-predicts at the end of the drying period. Workneh and Oke (2012) made similar observations in microwave drying.
A comparison of the experimental and predicted moisture ratios in Figure 3.16 (a, b and c) shows that the Midilli et al. model provides the best correlation for drying mango slices, using OVD, OAD and MVD. Therefore, in the drying of mango slices, the model is representative of the drying data. Similar outcomes were observed in drying mangoes using a microwave oven (Nazmi et al., 2017), where Midilli et al. model was the best representative for predicting the moisture ratio. Similarly, the Abano et al. (2013) findings show that the Midilli et al. model has the best prediction in hot air drying of treated and untreated mangoes and that it is better than the Page model. Simal et al. (2005), Azoubel et al. (2010), Abano et al. (2013), Longhmanieh and Bakhoda (2013) found this model to be accurate when drying kiwis, bananas, mangoes and thyme leaves respectively.
73
Table 3.2 Statistical parameters of different drying models tried for the control mango samples of various thickness
Model Thickness (mm) Model constants 𝒙𝟐 𝑹𝟐 RMSE
k (hr-1) n a b
Lewis- OVD 3mm 0.5152 - - - 6.1147x10-7 0.9705 0.00072
6mm 0.3229 - - - 0.01094 0.9882 0.09924
9mm 0.1604 - - - 0.00057 0.9656 0.02245
Lewis- OAD 3mm 0.1199 - - - 1.0641x10-5 0.9413 0.00312
6mm 0.1151 - - - 0.00017 0.9972 0.01286
9mm 0.0777 - - - 3.1926x10-5 0.9643 0.00551
Lewis-VMD 3mm 0.3970 - - - 3.1606x10-6 0.9730 0.00154
6mm 0.1833 - - - 9.3369x10-6 0.9743 0.00911
9mm 0.1172 - - - 1.9517x10-5 0.9684 0.00425
Page-OVD 3mm 0.4406 1.2637 - - 0.00038 0.9803 0.01653
6mm 0.2211 1.3778 - - 0.02142 0.9856 0.13090
9mm 0.0733 1.5085 - - 0.00037 0.9954 0.01716
Page-OAD 3mm 0.0648 1.3099 - - 0.00197 0.9577 0.04050
6mm 0.0875 1.1330 - - 0.00049 0.9957 0.00049
9mm 0.0348 1.3273 - - 0.00177 0.9800 0.03998
Page-VMD 3mm 0.2773 1.4005 - - 0.00026 0.9910 0.01145
6mm 0.0983 1.3790 - - 0.00042 0.9907 0.01816
9mm 0.0607 1.3162 - - 0.00105 0.9815 0.03006
Henderson and Pabis-OVD 3mm 0.5306 - 1.0248 - 0.00032 0.9687 0.01343
6mm 0.3418 - 1.0461 - 0.01947 0.9862 0.12483
9mm 0.1749 - 1.0720 - 0.00054 0.9591 0.02040
Henderson and Pabis-OAD 3mm 0.1239 - 1.0254 - 0.00042 0.9388 0.01880
6mm 0.1202 - 1.0351 - 4.5775x10-5 0.9931 0.00626
9mm 0.0821 - 1.0453 - 0.00068 0.9603 0.02468
Henderson and Pabis-MVD 3mm 0.4111 - 1.0317 - 0.00058 0.9707 0.01705
6mm 0.1951 - 1.0545 - 0.00056 0.9701 0.02082
9mm 0.1238 - 1.0468 - 0.00062 0.9646 0.02311
Midilli et al.-OVD 3mm 0.4071 1.3348 0.9735 0 9.8458x10-5 0.9814 0.00649
6mm 0.1782 1.5255 0.9570 0 0.02177 0.9790 0.11431
9mm 0.0526 1.6314 1.6314 0 2.6825x10-5 0.9953 0.00386 Midilli et al.-OAD 3mm 0.0257 1.6962 0.9092 0 0.000106 0.9665 0.00839 6mm 0.0894 1.1251 1.0039 0 1.4651x10-6 0.9981 0.00102 9mm 0.9277 1.5806 0.9277 0 9.5974x10-5 0.9852 0.98520
Midilli et al.-MVD 3mm 0.2663 1.4287 0.9883 0 0 0.9913 0.00563
6mm 0.0817 1.4662 0.9704 0 5.9059x10-5 0.9916 0.00573
9mm 0.0395 1.4843 0.9466 0 0.00012 0.9842 0.00901
74
Table 3.3 Statistical parameters of different drying models tried for the lemon juice treated mango of various thickness
Model Thickness (mm) Model constants 𝒙𝟐 𝑹𝟐 RMSE
k (hr-1) n a b
Lewis- OVD 3mm 0.4783 - - - 0.00052 0.9633 0.02130
6mm 0.2714 - - - 0.00859 0.9689 0.08791
9mm 0.1634 - - - 0.00061 0.9647 0.02319
Lewis- OAD 3mm 0.1045 - - - 0.00066 0.9089 0.02449
6mm 0.1081 - - - 2.5591x10-5 0.9884 0.00487
9mm 0.0695 - - - 0.00194 0.9635 0.04297
Lewis-VMD 3mm 0.3934 - - - 1.7272x10-5 0.9694 0.00359
6mm 0.1989 - - - 1.7186x10-5 0.9827 0.00391
9mm 0.1213 - - - 1.0145x10-5 0.9774 0.00307
Page-OVD 3mm 0.3714 1.3724 - - 0.00037 0.9821 0.01634
6mm 0.2048 1.3889 - - 0.00059 0.9815 0.02166
9mm 0.0637 1.5573 - - 0.00043 0.9949 0.01822
Page-OAD 3mm 0.0282 1.6637 - - 0.00283 0.9550 0.04810
6mm 0.0072 1.1963 - - 0.00033 0.9901 0.01744
9mm 0.0334 1.2945 - - 0.00126 0.9772 0.03370
Page-MVD 3mm 0.2583 1.4675 - - 0.00026 0.9927 0.01140
6mm 0.1213 1.3078 - - 0.00029 0.9942 0.01523
9mm 0.0673 1.2852 - - 0.00013 0.9897 0.01078
Henderson and Pabis-OVD 3mm 0.4914 - 1.0381 - 0.00025 0.9614 0.01348
6mm 0.3236 - 1.0473 - 0.00028 0.9581 0.01486
9mm 0.1788 - 1.0763 - 0.00063 0.9577 0.02208
Henderson and Pabis-OAD 3mm 0.1139 - 1.0609 - 0.00037 0.9017 0.01761
6mm 0.1123 - 1.0297 - 0.00019 0.9824 0.01272
9mm 0.0732 - 1.0396 - 0.00035 0.9602 0.01785
Henderson and Pabis-MVD 3mm 0.4096 - 1.0376 - 0.00069 0.9665 0.01867
6mm 0.2093 - 1.0463 - 0.00052 0.9796 0.02107
9mm 0.1276 - 1.0439 - 0.00056 0.9741 0.02188
Midilli et al.-OVD 3mm 0.3369 1.4607 0.9722 0 6.8307x10-5 0.9832 0.00541 6mm 0.1643 1.5382 0.9584 0 5.0239x10-5 0.9836 0.00549 9mm 0.0512 1.6609 0.9708 0 3.0819x10-5 0.9959 0.00414 Midilli et al.-OAD 3mm 0.0077 2.2222 0.9138 0 7.9418x10-5 0.9662 0.00711 6mm 0.0559 1.2903 0.9659 0 3.1126x10-5 0.9932 0.00472 9mm 0.0166 1.5322 0.9351 0 5.9648x10-5 0.9818 0.00691
Midilli et al.-MVD 3mm 0.2475 1.4978 0.9883 0 0 0.9929 0.00548
6mm 0.0604 1.6372 0.8888 0 6.7893x10-6 0.9981 0.00194 9mm 0.0478 1.4193 0.9536 0 8.2897x10-5 0.9903 0.00769
75
(b) 6mm thickness (a) 3mm thickness
(c) 9mm thickness
0 0,2 0,4 0,6 0,8 1
0 5 10 15
Moisture ratio (dimensionless)
Time (hour)
treatment
Page-3mm Lemon juice treatment
Henderson and Pabis-3mm Lemon juice treatment Midilli-3mm Lemon juice treatment
Experimental-3mm Cotrol Lewis-3mm Control Page-3mm Control Henderson and pabis-3mm Control
Midilli-3mm Control
0 0,2 0,4 0,6 0,8 1 1,2
0 5 10 15
Moisture ratio (dimensionless)
Time (hour)
Experimental-6mm Lemon juice treatment
Lewis-6mm Lemon juice treatment
Page-6mm Lemon juice treatment
Henderson and Pabis-6mm Lemon juice treatment Midilli-6mm Lemon juice treatment
Experimental-6mm Cotrol Lewis-6mm Control Page-6mm Control Henderson and pabis-6mm Control
Midilli-6mm Control
0 0,2 0,4 0,6 0,8 1
0 5 10 15 20 25
Moisture raio (dimensionless
Time (hour)
treatment
Page-3mm Lemon juice treatment Henderson and Pabis-3mm Lemon juice treatment Midilli-3mm Lemon juice treatment
Experimental-3mm Cotrol Lewis-3mm Control Page-3mm Control Henderson and pabis-3mm Control
Midilli-3mm Control
Figure 3.13: Moisture ratio variation with drying time for (a) 3mm, (b) 6mm and (c) 9mm thickness mango dried in OAD
76
0 0,2 0,4 0,6 0,8 1
0 1 2 3 4 5
Moisture ratio (dimensionless
Time (hour)
Page-3mm Control Henderson and pabis-3mm Control
Midilli-3mm Control Experimental-3mm Lemon juice treatment
Lewis-3mm Lemon juice treatment
Page-3mm Lemon juice treatment
Henderson and pabis-3mm Control
Midilli-3mm Lemon juice treatment
0 0,2 0,4 0,6 0,8 1
0 2 4 6 8 10
Moisture ratio (dimensionless
Time (hour)
Page-6mm Control
Henderson and pabis-6mm Control Midilli-6mm Control
Experimental-6mm Lemon juice treatment
Lewis-6mm Lemon juice treatment Page-6mm Lemon juice treatment Henderson and pabis-6mm Control Midilli-6mm Lemon juice treatment
0 0,2 0,4 0,6 0,8 1 1,2
0 5 10 15
Moisture ratio (dimensionless)
Time (hour)
Experimental-9mm Lemon juice treatment
Lewis-9mm Lemon juice treatment
Page-9mm Lemon juice treatment
Henderson and pabis-9mm Lemon juice treatment Midilli-9mm Lemon juice treatment
Experimental-9mm Control Lewis-9mm Control Page-9mm Control Henderson and pabis-9mm Control
Midilli-9mm Control
Figure 3.14 Moisture ratio variation with drying time for (a) 3mm, (b) 6mm and (c) 9mm thickness mango dried in MVD (c) 9mm thickness
(b) 6mm thickness (a) 3mm thickness
77
0 0,2 0,4 0,6 0,8 1
0 1 2 3 4
Moisture raio (dimensionless)
Time (hour)
Lewis-3mm Control Page-3mm Control
Hendersn and Pabis-3mm Control Mdilli-3mm Control
Experimental-3mm Lemon juice treatment
Lewis-3mm Lemon juice treatment
Page-3mm Lemon juice treatment Henderson and pabis-3mm Lemon juice treatment
Midili-3mm Lemon juice treatment
0 0,2 0,4 0,6 0,8 1
0 1 2 3 4 5
Moisture ratio (dimensionless)
Time (hour)
Lewis-3mm Control Page-6mm Control Hendersn and Pabis-6mm Control
Mdilli-6mm Control Experimental-6mm Lemon juice treatment
Lewis-6mm Lemon juice treatment
Page-6mm Lemon juice treatment
Henderson and pabis-6mm Lemon juice treatment Midili-6mm Lemon juice treatment
0 0,2 0,4 0,6 0,8 1 1,2
0 2 4 6 8 10
Moisture ratio (dimensionless)
Time(hour)
Experimental-9mm Lemon juice treatment
Lewis-9mm Lemon juice treatment
Page-9mm Lemon juice treatment
Henderson and pabis-9mm Lemon juice treatment Midili-9mm Lemon juice treatment
Experimental-9mm Control Page-9mm Control Hendersn and Pabis-9mm Control
Midilli-9mm Control Lewis-9mm Control
Figure 3.15 Moisture ratio variation with drying time for (a) 3mm, (b) 6mm and (c) 9mm thickness mango dried in OVD (c) 9mm thickness
(a) 3mm thickness (b) 6mm thickness
78
(a) OVD (c) MVD
(b) OAD
Figure 3.16 Experimental vs. predicted moisture ratio of Midilli et al. model for (a) OVD, (b) OAD and (c) MVD
0 0,2 0,4 0,6 0,8 1 1,2
0 0,2 0,4 0,6 0,8 1 1,2
Predicted moisture ratio
Experimental moisture ratio
3mm-UN 3mm-TR 6mm-UN 6mm-TR 9mm-TR 9mm-TR Ideal trendline
0 0,2 0,4 0,6 0,8 1 1,2
0 0,2 0,4 0,6 0,8 1 1,2
Predicted moisture ratio
Experimental moisture ratio
3mm-UN 3mm-TR 6mm-UN 6mm-TR 9mm-TR 9mm-UN Ideal trendline
0 0,2 0,4 0,6 0,8 1 1,2
0 0,2 0,4 0,6 0,8 1 1,2
Predicted moisture ratio
Experimental moisture ratio
3mm-TR 3mm-UN 6mm-UN 6mm-TR 9mm-UN 9mm-TR Ideal trendline
79