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Automatic feeder productivityTable 1 and Figs. 4, 5 and 6 show the automatic feeder productivity as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the automatic feeder productivity increases with increasing feed pellets size, air flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the automatic feeder productivity significantly increased from 11.16 to 13.87 (by 19.54%) kg min−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the automatic feeder productivity significantly increased from 11.02 to 14.03 (by 21.45%) kg min−1, while the automatic feeder productivity significantly increased from 3.33 to 21.46 (by 84.48%) kg min−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 1 Automatic feeder productivity at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 4Automatic feeder productivity at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 5Automatic feeder productivity at different feed pellet sizes and air flow rates.Full size imageFigure 6Automatic feeder productivity at different rotational speeds of screw and flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to increase the automatic feeder productivity from 3.04 to 3.79, 6.23 to 8.92, 11.86 to 14.10, 15.27 to 18.94 and 19.42 to 23.62 kg min−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the automatic feeder productivity increased from 3.04 to 19.42, 3.16 to 21.36 and 3.79 to 23.62 kg min−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 4.From statistical analysis, there were no significant different between feed pellets sizes 1 and 2 on the automatic feeder productivity, meanwhile, there were significant differences between feed pellets size 3 and sizes 1 and 2 on the productivity. Regarding the effect of air flow rate, there were significant differences between air flow rates on the automatic feeder productivity, the same trend was happened with the effect of rotational speed of screw on productivity. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 1.Regarding the effect of feed pellet size and air flow rate on the automatic feeder productivity, the results indicate that the automatic feeder productivity increases with increasing the feed pellets size and flow rate. It increased from 9.53 to 12.37, 11.23 to 13.82 and 12.73 to 15.43 kg min−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the automatic feeder productivity increased from 9.53 to 12.73, 11.16 to 13.92 and 12.37 to 15.43 kg min−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 5.The results also indicate that the automatic feeder productivity increased from 2.26 to 4.54, 6.39 to 8.90, 11.76 to 14.56, 15.25 to 18.68 and 19.44 to 23.45 kg min−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the automatic feeder productivity increased from 2.26 to 19.44, 3.19 to 21.50 and 4.54 to 23.45 kg min−1 at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 6.Multiple regression analysis was carried out to obtain a relationship between the automatic feeder productivity as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ Pr_{actual} = – 8.457 + 1.354PS + 0.301FR + 0.025RS{text{ R}}^{{2}} = 0.98{ ,} $$
(13)
where PS is the feed pellets size, mm; FR is the air flow rate, m3 min−1; RS is the rotational speed of screw, rpm.This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Automatic feeder efficiencyTable 2, Figs. 7, 8 and 9 show the automatic feeder efficiency as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that, when the feed pellets size increased from 1 to 3 mm, the automatic feeder efficiency significantly increased from 65.30 to 82.14 (by 20.50%) %. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the automatic feeder efficiency significantly increased from 62.58 to 85.07 (by 26.44%) %, while the automatic feeder efficiency significantly increased from 61.58 to 78.69 (by 21.74%) % when the rotational speed of screw increased from 180 to 900 rpm.Table 2 Automatic feeder efficiency at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 7Automatic feeder efficiency at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 8Automatic feeder efficiency at different feed pellet sizes and air flow rates.Full size imageFigure 9Automatic feeder efficiency at different rotational speeds of screw and air flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to increase the automatic feeder efficiency from 55.79 to 69.41, 57.10 to 81.78, 72.48 to 86.13, 69.96 to 86.81 and 71.19 to 86.58% at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the automatic feeder efficiency increased from 55.79 to 71.19, 57.98 to 78.29 and 69.41 to 86.58% at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 7.The statistical analysis showed that the differences between the obtained data of automatic feeder efficiency due to the effect of feed pellets size (A) and air flow rate (B) were significant. Regarding the effect of rotational speed of screw, there were significant differences between rotational speeds of screw 1, 2 and 3, meanwhile, there were no significant differences between rotational speeds of screw 3, 4 and 5. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 2.Regarding the effect of feed pellet size and air flow rate on the automatic feeder productivity, the results indicate that the automatic feeder efficiency increases with increasing the feed pellets size and flow rate. It increased from 53.91 to 70.69, 65.23 to 81.19 and 76.78 to 94.54% for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the automatic feeder efficiency increased from 53.91 to 76.78, 63.14 to 83.89 and 70.69 to 94.54% at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 8.The results also indicate that the automatic feeder efficiency increased from 41.37 to 83.28, 58.53 to 81.54, 71.85 to 84.96, 69.88 to 85.59 and 71.27 to 85.98% at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the automatic feeder efficiency increased from 41.37 to 71.27, 58.53 to 80.82 and 83.28 to 85.98% at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 9.Increasing the parameters seams to increase the productivity but regarding the efficiency, results show that the efficiency increases with increasing this parameter at (540 rpm) started to be constant and 720–900 rpm decreased in all treatments under study (Figs. 7, 9). It is concluded that efficiency with the parameters increased, became constant and decreased.Multiple regression analysis was carried out to obtain a relationship between the automatic feeder efficiency as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ eta = 9.566 + 8.417PS + 2.249FR + 0.025RS{text{ R}}^{{2}} = 0.89{ ,} $$
(14)
where this equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Specific energy consumptionTable 3, Figs. 10, 11 and 12 show the specific energy consumption of automatic feeder as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the specific energy consumption of automatic feeder decreases with increasing feed pellets size, air flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the specific energy consumption of automatic feeder significantly decreased from 8.93 to 6.74 (by 24.52%) W h kg−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the specific energy consumption of automatic feeder significantly decreased from 10.83 to 5.42 (by 49.95%) W h kg−1, while the specific energy consumption significantly decreased from 9.08 to 6.55 (by 27.86%) W h kg−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 3 Specific energy consumption at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 10Specific energy consumption at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 11Specific energy consumption at different feed pellet sizes and air flow rates.Full size imageFigure 12Specific energy consumption at different rotational speeds of screw and air flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to decrease the specific energy consumption from 9.87 to 7.94, 9.18 to 7.63, 9.14 to 7.30, 8.65 to 6.63 and 7.79 to 4.20 W h kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the specific energy consumption decreased from 9.87 to 7.79, 9.42 to 7.65 and 7.94 to 4.20 W h kg−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 10.From statistical analysis, there were no significant differences between feed pellets sizes 1 and 2 on the specific energy consumption, meanwhile, there were significant differences between feed pellets size 3 and 1 and 2 on the specific energy consumption. Regarding the effect of air flow rate, there were significant differences between air flow rates and specific energy consumption. Regarding the effect of rotational speed of screw, there were significant differences between rotational speeds of screw 1, 2, 4 and 5 on the specific energy consumption, meanwhile, there were no significant differences between rotational speeds of screw 2 and 3 on the specific energy consumption. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 3.Regarding the effect of feed pellet size and air flow rate on the specific energy consumption, the results indicate that the specific energy consumption decreases with increasing the feed pellets size and flow rate. It decreased from 12.05 to 9.07, 8.81 to 6.56 and 5.92 to 4.59 W h kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the specific energy consumption decreased 12.05 to 5.92, 11.37 to 5.75 and 9.07 to 4.59 W h kg−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 11.The results also indicate that the specific energy consumption decreased from 12.31 to 6.18, 11.43 to 5.63, 11.21 to 5.63, 10.38 to 5.21 and 8.81 to 4.46 W h kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the specific energy consumption decreased from 12.31 to 8.81, 8.75 to 6.37 and 6.18 to 4.46 W h kg−1 at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown Fig. 12.
Multiple regression analysis was carried out to obtain a relationship between the specific energy consumption of automatic feeder as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ SEC = 20.045 – 1.095PS – 0.541FR – 0.003RS{text{ R}}^{{2}} = 0.92 , {.} $$
(15)
This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Total costs of automatic feederTable 4, Figs. 13, 14 and 15 show the total cost of automatic feeder as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the total cost of automatic feeder decreases with increasing feed pellets size, flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the total cost of automatic feeder significantly decreased from 0.15 to 0.11 (by 26.27%) EGP kg−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the total cost of automatic feeder significantly decreased from 0.16 to 0.09 (by 43.75%) EGP kg−1, while the total cost of automatic feeder significantly decreased from 0.16 to 0.10 (by 37.50%) EGP kg−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 4 Total cost of automatic feeder at different feed pellets sizes, air flow rate and rotational speeds of screw.Full size tableFigure 13Total cost of automatic feeder at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 14Total cost of automatic feeder at different feed pellet sizes and air flow rates.Full size imageFigure 15Total cost of automatic feeder at different rotational speeds of screw and air flow rate.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to decrease the total cost of automatic feeder from 0.18 to 0.14, 0.16 to 0.12, 0.15 to 0.11, 0.13 to 0.09 and 0.12 to 0.08 EGP kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the total cost of automatic feeder decreased from 0.18 to 0.12, 0.17 to 0.10 and 0.14 to 0.08 EGP kg−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 13.From statistical analysis, there were no significant differences between feed pellets sizes 1 and 2 on the total cost of automatic feeder, meanwhile, there were significant differences between feed pellets size 3 and 1 and 2 on the total cost of automatic feeder. Regarding the effect of air flow rate, there were significant differences between air flow rates and specific energy consumption. Regarding the effect of rotational speed of screw, there were no significant differences between rotational speeds of screw 1 and 2, also 3 and 4 on the total cost of automatic feeder, meanwhile, there were significant differences between rotational speeds of screw 2 and 3 on the total cost of automatic feeder.Regarding the effect of feed pellet size and flow rate on the total cost of automatic feeder, the results indicate that the total cost of automatic feeder decreases with increasing the feed pellets size and air flow rate. It decreased from 0.18 to 0.13, 0.16 to 0.11 and 0.10 to 0.08 EGP kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the total cost of automatic feeder decreased from 0.18 to 0.10, 0.16 to 0.10 and 0.13 to 0.08 EGP kg−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 14.The results also indicate that the total cost of automatic feeder decreased from 0.22 to 0.11, 0.18 to 0.10, 0.16 to 0.10, 0.13 to 0.09 and 0.12 to 0.07 EGP kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the total cost of automatic feeder decreased from 0.22 to 0.12, 0.16 to 0.11 and 0.11 to 0.07 EGP kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 15.
Multiple regression analysis was carried out to obtain a relationship between the total costs of automatic feeder as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:$$ TC = 0.315 – 0.020PS – 0.006FR – 8.8 times 10^{ – 5} RS{text{ R}}^{{2}} = 0.87{,} $$
(16)
where: TC is the total cost of automatic feeder, EGP kg−1.This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw. More