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. 2019 Apr 4;9:5625. doi: 10.1038/s41598-019-42016-0

Table 3.

Parameters and statistical results of thin-layer mathematical models for the moisture rate of the Refractance Window drying process.

Model and equation Temperature Carrier material Parameter SS RMSE R2 Adj R2
Lewis 333 K With kd = 0.000397 20.485 0.811 0.682 0.670
MR = exp (−kd t)61 Without kd = 0.0204 25.000 0.699 0.884 0.873
343 K With kd = 0.0224 6.011 0.056 0.975 0.973
Without kd = 0.0252 48.199 0.142 0.879 0.868
353 K With kd = 0.0269 0.056 0.022 0.993 0.992
Without kd = 0.0332 53.135 0.141 0.909 0.901
Page 333 K With kd = 0.067 0.019 0.027 0.987 0.986
MR = exp (−kd tn)62 n = 0.740
Without kd = 0.00257 23.458 0.727 0.899 0.889
n = 1.32
343 K With kd = 0.0746 0.169 0.018 0.992 0.992
n = 0.7013
Without kd = 8.345E-08 0.018 0.027 0.993 0.992
n = 4.3697
353 K With kd = 0.0207 0.106 0.018 0.993 0.993
n = 1.0684
Without kd = 0.00257 1.968 0.405 0.757 0.735
n = 1.32
Henderson & Pabis 333 K With a = 0.905 6.204 0.042 0.971 0.970
MR = a exp(−kd t)63 kd = 0.0213
Without a = 1.2122 0.053 0.305 0.866 0.854
kd = 0.0241
343 K With a = 0.8958 2.915 0.041 0.966 0.964
kd = 0.0197
Without a = 1.1973 43.453 0.110 0.867 0.854
kd = 0.029
353 K With a = 1.0188 0.053 0.018 0.993 0.992
kd = 0.0272
Without a = 1.1657 4.633 0.128 0.903 0.894
kd = 0.0373
Logaritmic 333 K With a = 0.9008 9.868 0.038 0.973 0.972
MR = a exp (−kd t) + c64 kd = 0.0246
c = 0.0318
Without a = 1.8749 2.617 0.305 0.898 0.889
kd = 0.0101
c = −0.7257
343 K With a = 0.8659 0.391 0.029 0.982 0.981
kd = 0.0303
c = 0.1004
Without a = 1.4758 13.000 0.099 0.886 0.875
kd = 0.0174
c = −0.321
353 K With a = 1.0242 0.063 0.018 0.993 0.992
kd = 0.0267
c = −0.0078
Without a = 1.2645 8.848 0.120 0.910 0.902
kd = 0.0293
c = −0.1197
Two terms exponential 333 K With a = 0.2463 3.225 0.032 0.985 0.984
MR = a exp (−kd t) + (1 − a) exp (−kd a t)65 kd = 0.0755
Without a = 2.4621 26.000 0.866 0.946 0.941
kd = 0.0381
343 K With a = 0.2481 1.615 0.029 0.987 0.986
kd = 0.0699
Without a = 2.4602 25.012 0.074 0.940 0.935
kd = 0.0455
353 K With a = 1.4949 0.008 0.018 0.993 0.992
kd = 0.0317
Without a = 2.5047 1.545 0.070 0.971 0.968
kd = 0.061
Diffusion approximation 333 K With a = −0.0267 19.713 0.053 0.971 0.970
MR = a exp(−kd t) + (1 − a)exp (−K b t)66 kd = 0.0068
b = 3.0378
Without a = 1.2767 40.000 0.866 0.889 0.879
kd = 0.0185
b = 0.9013
343 K With a = 0.5237 0.113 0.016 0.993 0.994
kd = 0.0121
b = 5.343
Without a = 0 0.382 0.121 0.879 0.868
kd = 0.0219
b = 1.1534
353 K With a = 0 0.009 0.019 0.993 0.992
kd = 0.0226
b = 1.1859
Without a = 0.000 0.238 0.309 0.909 0.901
kd = 0.02512
b = 1.3215
Midilli 333 K With a = 0.999 0.019 0.027 0.987 0.986
MR = a exp(−kd tn) + bt67 kd = 0.0215
n = 0.741
b = 0.000
Without a = 1.016 8.945 0.058 0.981 0.978
kd = 1.4169E-7
n = 3.141
b = 0.0001
343 K With a = 1.00519 0.166 0.018 0.992 0.992
kd = 0.067
n = 0.6978
b = 0
Without a = 0.9715 0.017 0.026 0.992 0.991
kd = 5.33E-06
n = 4.2102
b = 4.1595E-14
353 K With a = 1.0069 0.008 0.018 0.993 0.993
kd = 0.07609
n = 1.0598
b = 0.000
Without a = 0.997 0.070 0.308 0.996 0.994
kd = 7.144E-06
n = 3.4433
b = 0.000107
Verma 333 K With a = 0.604 0.017 0.025 0.989 0.988
MR = a exp (−kd 0 t) + (1 − a) exp (−kd 1 t)68 kd 0 = 0.0149
kd 1 = 0.0789
Without a = 4.823 1.075 0.866 0.878 0.867
kd 0 = 0.00295
kd 1 = 0.0016
343 K With a = 0 43.971 0.536 0.775 0.761
kd 0 = 0.00295
kd 1 = 0.0016
Without a = 8.0139 0.283 0.104 0.885 0.874
kd 0 = 0.0094
kd 1 = 0.008007
353 K With a = 1.9784 0.008 0.018 0.993 0.992
kd 0 = 0.0212
kd 1 = 0.0168
Without a = 14.6764 0.859 0.309 0.911 0.903
kd 0 = 0.01654
kd 1 = 0.01570
kd 2 = 0.037

SS = Sum of squares, RSME = Root mean squared error, R2 = R-squared, Adj R2 = Adjusted R-squared.