Various air speeds of 2.5m/s, 3.0m/s, 3.5m/s and 4.0m/s at constant thickness were used to study the effects of drying sir speed on the drying rate as given in Figures 4.56 to 4.63. The numerical data is shown in Table A.9-A.18. It was seen that increase in air speed leads to a relative increase in the drying rate at the initial time of drying before decreasing for both balanced and unbalanced yam samples. After a drying time of 60 minutes, the drying rate was seen to be 0.566, 0.565,
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 100 200 300 400 500 600
Drying rate
Time (mins)
2mm 4mm 6mm
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 100 200 300 400 500 600
Drying rate
Time (mins)
2mm 4mm 6mm
162
0.494 and 0.277 g/g.min for drying air speeds of 2.5, 3.0, 3.5 and 4.0 m/s respectively. Nicholas (2012) reported an increase in drying rate as air speed increases from 1.8 to 3.8 m/s. Mirzaee et al (2009) reported a similar trend.
It is apparent that the drying rate is higher at the beginning of the drying process and decreases continuously with the drying time for both the convective dryer and the solar dryer. Mirazaee et al, (2009) reported the same trend. According to Wankhade et al (2012), the drying rate goes on decreasing witha decrease in moisture content. The rate of drying also has an important effect on the quality of dried food products.
Figure 4. 56:Variation of drying rateat different air speeds for drying unblanched water yam using convective dryer
Figure 4. 57:Plot of drying rateagainst time at different air speeds for drying of unblanched aerial yam using convective dryer
0 1 2 3
0 50 100 150 200 250 300 350
Drying rate
Time (mins)
2.0 m/s 2.5 m/s 3.0 m/s 3.5 m/s 4.0 m/s
0 1 2 3 4 5
0 50 100 150 200 250 300 350
Drying rate
Time (mins)
2.0 m/s 2.5 m/s 3.0 m/s 3.5 m/s 4.0 m/s
163
Figure 4. 58:Plot of drying rate against time at different air speeds for drying of blanched water yam using convective dryer
Figure 4. 59: Plot of drying rate against time at different air speeds for drying of blanched aerial yam using convective dryer
Figure 4. 60: Plot of drying rate against time at different air speeds for drying of unblanched water yam using solar dryer
-0.5 0 0.5 1 1.5 2 2.5
0 100 200 300 400
Drying Rate (g/g min)
Time (mins)
2.0 m/s 2.5 m/s 3.0 m/s 3.5 m/s 4.0 m/s
0 0.5 1 1.5 2
0 100 200 300 400
Drying Rate g/g min)
Time (mins)
2.0 m/s 2.5 m/s 3.0 m/s 3.5 m/s 4.0 m/s
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
0 100 200 300 400 500 600
Drying rate
Time (mins)
0.5m/s 1.0m/s 1.5m/s 2.0m/s 2.5m/s
164
Figure 4. 61:Plot of drying rate against time at different air speeds for drying of unblanched aerial yam using solar dryer
Figure 4. 62:Plot of drying rate against time at different air speeds for drying of blanched water yam using solar dryer
Figure 4. 63:Plot of drying rate against time at different air speeds for drying of blanched aerial yam using solar dryer
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0 100 200 300 400 500 600
Drying rate
Time (mins)
0.5m/s 1.0m/s 1.5m/s 2.0m/s 2.5m/s
0 0.1 0.2 0.3 0.4 0.5 0.6
0 100 200 300 400 500
Drying rate
Time (mins)
0.5m/s 1.0m/s 1.5m/s 2.0m/s 2.5m/s
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
0 100 200 300 400 500
Drying rate
Time (mins)
0.5m/s 1.0m/s 1.5m/s 2.0m/s 2.5m/s
165 4.6.3 Effect of Temperature on Drying Rate
Temperature is one of the factors that affect the drying rate. Various temperatures of 40, 50, 60 and 70 oC were used to investigate the effect of temperature on the drying rate for convective dryer at constant airspeed and slice thickness of 2.5 m/s and 2.0 mm, respectively. The effects of temperature on the drying rate were given in Figures 4.64 to 4.67, and the numerical data is shown in Table A.1-A.8. It is seen that increase in temperature increases the rate of drying. This is attributed to increased evaporation of water both on the surface and in the products due to the increased temperature (Junling et al, 2008). As the drying process continues, less free water on the surface of the product is available and hence, the drying rate starts to decrease for both the blanched and unblanched yam samples. The high drying rate at high drying temperature could be due to more heating energy which speeds up the movement of water molecules and results in higher moisture diffusivity within the yam samples (Junling et al, 2008).
The curve of the drying rate did not give a perfect curve probably because of the nature of the drying products and the diffusion mechanism inside the products as the drying progresses.
Divine et al (2013) obtained similar drying rate curve against temperature.
Figure 4. 64: Effect of temperature on drying rate for drying of unblanched water yam using convective dryer
-0.5 0 0.5 1 1.5 2 2.5 3
0 50 100 150 200 250 300 350 400
Drying rate
Time (mins)
40 oC 50 oC 60 oC 70 oC
166
Figure 4. 65:Effect of temperature on drying rate for drying of unblanched aerial yam using convective dryer
Figure 4. 66: Effect of temperature on drying rate for drying of blanched water yam using convective dryer
Figure 4. 67: Effect of temperature on drying rate for drying of blanched aerial yam using convective dryer.
-0.5 0 0.5 1 1.5 2 2.5 3 3.5
0 50 100 150 200 250 300 350 400
Drying rate
Time (mins)
40 oC 50 oC 60 oC 70 oC
0 0.5 1 1.5 2
0 100 200 300 400 500
Drying Rate (g/g min)
Time (mins)
40 oC 50 oC 60 oC 70 oC
0 0.5 1 1.5 2
0 100 200 300 400 500
Drying Rate (g/g min)
Time (mins)
40 oC 50 oC 60 oC 70 oC
167 4.7Drying Kinetic Models
Seven moisture ratio kinetic models were tested using regression methods for both water yam and aerial yam as presented in Tables 4.10 and 4.11. The acceptability of the drying models was determined by the correlation coefficient first and then by the root mean square error (RMSE) and the others. To select the best model for describing the drying curve, the criteria is that the value of correlation coefficient (R2) should be high while the RMSE should be low.
It was seen from the statistical error indices in Table 4.10 and the plotted graphs (Figs. 4.68 and 4.69) that the best model for the water yam under the given drying conditions was the Logarithmic model with correlation coefficient of 0.9995. This is followed by Page/ Weibull models.
For the aerial yam, it was observed from the statistical error indices in Table 4.11 and the plotted graphs that the best model for the aerial yam under the given drying conditions was the Logarithmic model with correlation coefficient of 0.9991. This was followed by Page models.
This time, the Weibull model performed badly. Therefore, only the Logarithmic model plots are presented in Figures 4.68a and 4.68b. The plots of other kinetic models are given in appendix C.
168
Figure 4. 68a: Variation of experimental and Logarithmic model based predicted moisture ratio with time for drying of water yam
Figure 4. 68b: Variation of experimental and Logarithmic model based predicted moisture ratio with time for drying of aerial yam
Table 4. 10: The Kinetic models and their Statistical Error indicators for the unblanched Water Yam dried at heater temp of 40 oC
Model Model Name Coeffs. R2 RMSE MBE MABE Corr.
169
Coef.
𝜒 = exp −𝑘𝑡 Newton k=0.005442 0.9719 0.0482 0.0024 0.0413 0.9925 𝜒 = exp −𝑘𝑡𝑛 Page k = 0.01804
n = 0.771
0.9943 0.0218 -0.0042 0.0179 0.9973
𝜒 = exp − 𝜅𝑡 𝑛 Page modified 𝜅=0.0055 n = 0.771
0.9943 0.0218 -0.0042
0.0179 0.9973
𝜒 = 𝑎exp −𝑘𝑡 Henderson et Pabis
a = 0.9492 k = 0.005074
0.9791 0.0416 -0.0066
0.0351 0.9905
𝜒 = 1 + 𝑎𝑡 + 𝑏𝑡2 Wang et Singh a = -0.005025 b = 7.735e-06
0.9819 0.0387 0.0125 0.0336 0.9944
𝜒
= 𝑎exp −𝑘𝑡 + c
Logarithmic a =0.8222 c =0.1699 k =0.008579
0.9995 0.0062 -0.0000 0.0052 0.9998
𝜒 = exp − 𝑡 𝛽
𝛼
Weibull 𝛼 = 0.771 𝛽 =182.7
0.9943 0.0218 -0.0042 0.0179 0.9973
Table 4. 11:The Kinetic models and their Statistical Error indicators for the Unblanched Aerial Yam dried at heater temp of 40 oC
Model Model Name Coeffs. R2 RMSE MBE MABE Corr.
Coef.
𝜒 = exp −𝑘𝑡 Newton k=0.006789 0.974
0.0486
-0.0006
0.0421
0.9945
170 𝜒 = exp −𝑘𝑡𝑛 Page k =0.02171
n =0.7709
0.9949
0.0215
-0.0038
0.0178 0.9975 𝜒
= exp − 𝜅𝑡 𝑛
Page modified 𝜅=0.0070 n =0.7709
0.9949
0.0215
-0.0038
0.0178 0.9975 𝜒 = 𝑎exp −𝑘𝑡 Henderson et
Pabis
a = 0.942 k = -0.00627
0.9819
0.0406 -0.0089
0.0339 0.9922 𝜒
= 1 + 𝑎𝑡 + 𝑏𝑡2
Wang et Singh a = -0.005648 b =9.049e-06
0.9716
0.0508
0.0181 0.0446 0.9924 𝜒
= 𝑎exp −𝑘𝑡 + c
Logarithmic a =0.8521 c =0.1286 k =0.009626
0.9991
0.0093
0.0000
0.0069 0.9995 𝜒
= exp − 𝑡 𝛽
𝛼
Weibull 𝛼 = 9.375 𝛽 =1.152
-1.5340
0.4806 -0.3864
0.3864 0.4483
Since the Logarithmic Kinetic models best correlated the experimental data, it was selected for modeling the moisture ratio kinetics of the rest of the experimental data at different temperatures.
The Logarithmic Kinetic models at different temperatures were evaluated and presented in Table 4.12a. For the unblanched yam samples (Table 4.12a), the best correlation coefficient (0.9991) was obtained at 40oC for both water yam and aerial yam. For blanched samples (Table 4.12b),
171
the best correlation coefficient (0.9993) for drying water yam was obtained at 50oC while for drying aerial yam, 0.9989 was obtained at 60oC.
Table 4. 12:TheLogarithmic Kinetic models and their Statistical Error indicators for the unblanched Yams dried at different heater temp.
Temp [o] Coeffs. R2 RMSE MBE MABE Corr. Coef.
40 a =0.8521
c =0.1286 k =0.009626
0.9991 0.0093
0.0000
0.0069 0.9995
172 Water
Yam
50 a =0.9465
c =0.09586 k =0.01228
0.9957 0.0224 0.0000 0.0184 0.9978
60 a =1.029
c =-0.01255 k =0.0188
0.9988 0.0132 0.0000 0.0115 0.9994
a = 0.0088T + 0.5, c = - 0.00038T2 + 0.031T - 0.5, k = 1.9e-05T2 - 0.0015T + 0.038
Arial Yam
40 a =0.8521
c =0.1286 k =0.009626
0.9991 0.0093
0.0000
0.0069 0.9995
50 a =0.903
c =0.1252 k =0.01425
0.9979 0.0149 0.0000 0.0106 0.9990
60 a =0.9153
c =0.09962 k =0.02521
0.9985 0.0130 0.0000 0.0110 0.9992
a= - 0.00019T2 + 0.022T + 0.26, c = - 0.00011T2 + 0.0096T - 0.08, k = 3.2e-05T2- 0.0024T + 0.054
Table 4. 13:TheLogarithmic Kinetic models and their Statistical Error indicators for the Blanched Yams dried at different heater temp.
Water Yam
Temp [o] Coeffs. R2 RMSE MBE MABE Corr. Coef.
40 a =0.8381
c =0.1057 k =0.01086
0.9952 0.0200 0.0000 0.0150 0.9976
50 a =0.9483 0.9993 0.0088 0.0000 0.0064 0.9997
173 c =0.1539
k =0.02254
60 a =0.9488
c =0.02008 k =0.03371
0.9981 0.0146 0.0000 0.0112 0.9991
a = - 0.00055T2 + 0.06T - 0.7, c = - 0.00091T2 + 0.087T - 1.9, k= 0.0011T - 0.035 Arial
Yam
40 a =1.353
c =0.04775 k =0.01052
0.9973 0.0245 0.0000 0.0139 0.9986
50 a =1.262
c =0.1252 k =0.02413
0.9980 0.0200 0.0000 0.0171 0.9990
60 a =1.277
c =0.1332 k =0.02656
0.9989 0.0150 0.0000 0.0132 0.9995
a = 0.00053T2 - 0.057T + 2.8, c = - 0.00035T2 + 0.039T - 0.96 k= - 5.6e-05T2 + 0.0064T - 0.16
4.8 Finite Element Analysis