International Journal of Scientific & Engineering Research Volume 3, Issue 7, June-2012 1

ISSN 2229-5518

Optimization of Specific Mechanical Energy Consumption of a Palm Nut-Pulp Separator Using Mathematical Programming Technique

Nwankwojike B. Nduka, Agunwamba C. Jonah, Ogbonnaya A. Ezenwa

Abstract

The influences of the driving power, P cake breaker speed, N c auger speed, N a and helix angle, of a palm nut-pulp separating machine on its

specific mechanical energy consumption, SE was evaluated and quantified in order to determine the optimal setting of these operational parameters at which the separator will operate with minimum energy consumption as well as maximum efficiency and throughput possible. This optimization was performed using mathematical programming modeling in which the devel oped SE model formed the objective function minimized, subject to the constraints of it efficiency, throughput and factor levels within which the operational parameters influence the responses si gnificantly. SE model analysis showed that the main effects of all the operational parameters provided strong primary contribution to the specific energy mechanical consumption of the

separator while the quadratic effects of the auger speed,

2 2

a and cake breaker speed c

and interactions of

N a N c , N a P,

N a,

N c P,

N c ,

N a N c ,

Pand

N a P

provided secondary effects to the response. The optimization results revealed that the palm nut-pulp

separator is more efficient and energy saving when operate at an optimal driving power, cake breaker speed, auger speed and h elix angle setting of

4.103kW (5.5Hp), 2821rpm, 2116rpm, and 450 for respectively. The machine performed with an average specific mechanical energy consumption of

16.41kJ/kg, efficiency of 95% and throughput of 900kg/h at this factor setting. This indicates 38.61% reduction in specific mechanical energy consumption of the separator, and increase in its efficiency and throughput by 1.06% and 3.72% respectively when compared with that of the factor

settings previously obtained from the graphical optimization of the machine.

Key words: Mathematical programming model, Operational parameters, Optimization, Palm nut-pulp separator, Specific mechanical energy consumption

Nomenclature

mo Total mass of the pulp and nuts separated, kg

m i Mass of digested mash input into the machine, kg

t Processing time, s

SE Specific Mechanical Energy Consumption, kJ/kg

Separating efficiency, %

TP Throughput, kg/h

N a Auger speed, rpm

Helix angle of the augers, 0

N c Cake breaker speed, rpm

P Mechanical power output of electric motor, W

1.0 Introduction

Palm nut-pulp separator is a machine developed for separating digested palm fruit cake into palm nut and pulp before pressing of the digested pulp for palm oil extraction in order to eliminate nut breakage and excessive loss of palm oil to pressed fibre in the mechanized palm fruit processing as proposed by [1]. Prior to the introduction of this new unit operation of nut-pulp separation in the mechanized palm fruit processing, the mash from oil palm fruits digestion process were usually pressed before the separation of the nuts and pressed fibre. Thus, the present day mechanized palm fruit processing is characterized by 9-22% nut breakage/crushing, 9-
11% palm oil loss to pressed fibre, palm oil and palm kernel
oil of undesired physiochemical properties and second pressing [2], [3], [4], [5]. The developed palm nut-pulp separator comprising a feed hopper, cake breaker, auger separator, electric motor, nut and pulp outlet chutes had its internal wall lined with score pad to ensure that the nuts neither break nor sustain internal injury as their hit the walls during cake breaking. The electric motor drives the auger shaft which in turn drives that of the cake breaker. The separation process starts with the slacking of the fairly compacted palm fruit mash from the digestion process as it falls from the hopper across the rotating cake breaker beaters (in the upper chamber of the machine) into the right end of the lower chamber of the machine by gravity, thereby detaching the entangled palm nuts from the digested pulp. The slacked mash is then separated into pulp and nuts as the auger conveys it from the right to the left end of lower chamber, the pulp escapes through the 2.5mm-wide slit into the pulp discharging chute, while the nuts (free of pulp) are conveyed and discharged to the nut chute through the 50mm-passage at the left end of the chamber [6].
Benefit cost analysis of incorporating this machine in a
semi-mechanized palm fruits processing at Umuahia, Nigeria showed total elimination of nut breakage during pressing, significant reduction in the processing time and cost, and improvement in the quantity and quality of palm oil and palm nuts extracted as well as profit [7]. Performance analysis of the

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separator showed 90.05% efficiency and throughput of
419.92kg/h with its design driving power, cake breaker speed,
auger speed and helix angle of 2.238kW, 730rpm, 730rpm and
450 respectively and also that these four operational parameters influence its efficiency and throughput [6], [8]. According to [8] the lower and upper levels of the limit within which these factors influence the performance of this separator significantly are 7.46-3.73kW, 2870-1900rpm, 2150-1425rpm and 25-450 for driving power, cake breaker speed, auger speed and helix angle respectively. Ref. [8] further evaluated and quantified the effects of these parameters on efficiency and throughput of this machine within this limit using the following response surface models.

Efficiency, (%):

because a machine/system may be very efficient in operation, but the application may not be economical if its SE is not relatively small with respect to its throughput. Thus,
minimization of specific mechanical energy consumption of processes and equipment remained one of the outstanding desires of present day researchers and designers [12], [13].
It was observed that the specific mechanical energy
consumption of this separator at its design throughput of
419.92kg/h is 19.23kJ/kg while that at a throughput of
867.69kg/h is 26.73kJ/kg. This revealed that this machine runs
at sub-optimal setting even though its throughput and efficiency of 867.69kg/h and 94% are higher because it consumes more energy per unit mass of digested palm fruit separated with this factors setting. This undesired observation is in agreement with the works of [9] and [14], which showed

9.6554  1.0484 10 2

N a  4.1728 10 Nc

that some industrial systems are being run at sub-optimal

 4.3204 103 P  6.5171101 1.0701105 N 2

settings even though each factor has been optimized
individually over time, thus finding the compromise optimum

 4.7150107 P2

6

 0.01342

 4.1738106

5

Na Nc

2

that does not optimize only one response become the major problem in industries. Also, optimal level of the factors

 1.016  10

7

N a P  7.3427 10

4

N a   0.0134

generated from the graphical plots of response surface models

 6.3164 10

Nc P  1.1780 10

Nc

(1)

(graphical optimization) is usually based on individual factor

Throughput, TP (kg/h):

TP  605 .8977  2.02  10

N a  3.787 10 c

pairs (two independent variables) versus one response [9]. It is
desired that this machine operates with maximum efficiency and throughput, and minimum specific energy consumption

 1.05 102 P  2.15

 3.521103 P

 2 10 4 N N

(2)

possible, thus the need for a multi-response optimization technique that will enable simultaneous evaluation of these three responses. In order to apply the multi-response
Ref. [8] used Response Surface Methodology (RSM) in the
performance analysis of this machine because the works of [9], [10] and [11] showed that the technique uses small number of experimental runs to quantify and optimize relationships among one or more measured responses under the influence of several variables. The driving power, cake breaker speed, auger speed and helix angle setting of 6.341kW, 2821.5rpm,
2113.75 rpm and 450 respectively were obtained using
exploration data tips of surface and contour plots of these
models as the optimal setting of these factors. The efficiency and throughput of the developed separator at this factor setting were predicted using the models at over 99.79% success and confirmed experimentally as 94% and 867.69kg/h respectively [8]. However, the influence of these factors on the effect specific mechanical energy consumption, SE of the palm nut-pulp separator was not assessed in the work despite the economic important of SE in the operation of engineering systems. Specific mechanical energy consumption is defined as the actual mechanical energy used in a system or process to produce a unit product [12]. Therefore, SE of the separator is the mechanical energy output of its motor used to separate a unit mass of digested palm fruit mash. Development of energy saving equipment is the one of the major international trend for production cost reduction in industries over the decades
optimization approach to this problem, it is of economic sense to quantify the relationship between the specific mechanical energy consumption of the separator and its operational parameter using a response surface model like the throughput and efficiency.

Optimization of a single response system is usually simple, but in most practical industrial researches/applications, multiple outputs that are interrelated in a way that improving one will cause deterioration of another such as finding settings which will increase yield and decrease the amount of scrap/rework and energy consumption represent opportunities for substantial financial gain in industries; rate versus consistency; strength versus expense are always the case [9], [14]. In multi objective optimizations, models are developed with the objective of improving all the responses of interest simultaneously [9], [11], [15]. From a mathematical point of view, the objective is to find the operating conditions or factor levels, x1, x2,…..,xk that maximize or minimize the system response variables Y1, Y2,…..Yk.. This requires some trade- offs in order to find the process operating conditions that are satisfactory for most (and hopeful all) responses. The four major techniques often used for optimization of response surface models include graphical (inspection of interpretation

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plots), path of steepest ascent/decent, desirability function and mathematical programming approaches [9]. Path of steepest
ascent approach is very useful for both single and multiple response cases when the responses exhibit adequate linear fit, while mathematical programming and desirability function approaches are adequately used for the optimization of higher order response surface models [9], [11], [16]. Mathematical programming technique is an outstanding tool for optimizing multiple outputs that are interrelated in a way that improving one will cause deterioration of another when one response can be chosen as the “primary” (or most important response) while bounds or targets can be defined on all other responses [9]. In the mathematical programming approach the primary response Yp is either desired to be maximized or minimized as expressed in Equations 3 or 4 respectively, subject to appropriate constraints of all other responses Y1, Y2,…..Yk as;

L xi U

Where xi constitutes the independent variables, L and U are the lower and upper limits of xi, and Ti is target or bound on each response Yi (i = 1, 2,…..n). Equations 3 and 4 are usually solved using software such as DRSALG (in the case of 2(dual) responses), Microsoft Excel, MATLAB and Design Expert. Base on these forgoing facts, this study aimed to develop a response model for the relationship between the specific mechanical energy consumption of the separator and its driving power, cake breaker speed, auger speed and helix angle and also determine the settings of these factors that will yield optimum efficiency, throughput and energy consumption of the separator using mathematical programming method.

Maximize:

Subject to:

Minimize:

Subject to:

Y p xi

Yi xi Ti

L xi U

Y p xi

Yi xi Ti

(3)

(4)

2.0 Materials and Methods

The values of specific mechanical energy consumption used in this investigation were computed from the experimental data (Table 1) conducted and used by [8] in the optimization of the efficiency and throughput of the palm nut-pulp separator.

TABLE 1

EXPERIMENTAL EVALUATION OF THE PALM NUT-PULP SEPARATOR BY RESPONSE SURFACE METHOD

Run.

Na

Nc

P

Separated

Time

TP

Order

(rpm)

(rpm)

(Watts)

(0)

Products

taken (s) (%

) (kg/h)

(kg)

1

1787.5

2385

5595

35

18.00

110.00

90.00

589.09

2

1425

1900

7460

25

16.39

108.00

81.95

546.33

3

1425

2870

7460

45

17.84

87.00

89.20

738.21

4

1425

1900

3730

45

15.95

132.00

79.75

435.00

5

1425

2870

7460

25

17.00

123.00

85.00

497.00

6

1425

2870

3730

25

16.16

253.00

80.80

229.94

7

2150

2870

3730

45

17.69

104.00

88.45

612.35

8

2150

1900

7460

25

16.51

90.00

82.55

660.40

9

2150

2870

3730

25

16.86

123.00

84.30

493.46

10

1787.5

2385

5595

35

18.00

110.00

90.00

589.09

11

2150

1900

3730

25

15.89

127.00

79.45

450.43

12

1425

1900

7460

45

16.50

74.00

82.50

807.50

13

2150

2870

7460

25

18.13

90.00

90.65

725.20

14

2150

2870

7460

45

18.50

85.68

92.50

777.31

15

1425

1900

3730

25

15.78

177.00

78.90

320.95

16

2150

1900

7460

45

17.09

84.00

85.48

732.43

17

1425

2870

3730

45

16.79

176.00

83.95

343.43

18

2150

1900

3730

45

16.27

104.00

81.35

563.19

19

1787.5

2385

5595

35

18.00

110.00

90.00

589.09

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The specific mechanical energy consumption as per each factor setting of this experimental plan/data was computed using the following relation:
pairs of interpretation plots (contour and three dimensional surface graphs) of the model were developed using version 7.5 of MATLAB software in order to explore and survey the
feasible region of the minimum SE of the separator for guidance during the iterative solution of multi-response

SEkJ / kg

Pt

1000 mo

(5)
model and trade-offs.
The developed SE model and those of the efficiency and
throughput (Equations 1 and 2) were simultaneously
Thereafter, version 16 of Minitab software was used for the
fitting and selection the response surface functions of the relationship between the specific mechanical energy consumption of palm nut-pulp separator and the four factors investigated. The model that best quantified the relationship between the factors and this response were selected by backward elimination method with the aid of model adequacy measures usually displayed by the software along with each fitted function. The adequacy of the selected model was also verified experimentally with six confirmation runs. The specific mechanical energy consumption of the separator at each combination of the variables was evaluated by feeding a
20kg of fresh digested palm fruit mash through the hopper
into the machine for separation into palm nut and pulp. The
processing time involved was taken using stop watch and the separated pulp and nuts weighed after each test and recorded. The SE of the machine was computed using equation (5) in each case, before comparing the actual experimental results with the predicted response (at α = 0.05) by computing the residuals and their percentage errors. The model adequacy measures used for the statistical verification of the fitted functions include regression analysis of model coefficients, analysis of variance (ANOVA) and lack-of-fit tests whilst residual diagnostic plots contains normal probability plots of residuals, histogram of residuals, dot plots of the residuals versus observation order and that of residuals versus fitted response. The calculated coefficients and equation of a good model must be significant (P-value < 0.05), lack-of-fit must be insignificant, various coefficients of determination, R2 and adjusted R2 values should be close to 1(100%) and SS of Error should be as small as possible (Steppan et al, 1998). Residual is the difference between the respective observed responses and their model predicted values. If a model is adequate, the points on the normal probability plots of the residuals should form a straight line. Small departure from the line in the normal probability plot is common, but a clearly “S” shaped
optimized using a non linear mathematical programming tool of the same software (MATLAB 7.5), the fmincon solver. A mathematical programming model was first formulated with the specific mechanical energy consumption function as the objective function to be minimized, subject to targets of more than 419.92kg/h and 90.05% placed on the throughput and efficiency of the machine. Since these two performance indicators are not desired to be less than these design values. In addition, bounds based on the high and low levels of the factors within which each influences the responses significantly as determined by [8] were placed on the factors. Thereafter, the formulated multi-response model was input into the fmincon solver for solution and further analysis/trade- offs before confirming the solution experimentally with four confirmation runs using the same procedure applied in the confirmation of the SE model.

3.0 Results and Discussion

The specific mechanical energy consumptions computed from the experimental trials/results of Table 1 are shown in Table 2. The run order and factor settings of Table 1 were retained in the Table 2 for clarity. Equation (6) is the final empirical model selected after inputing these computed SE response and their corresponding factor combinations into the Minitab software and examination of the adequacy measures and diagnostic plots of all the fitted functions for the response. The results from the confirmation tests of the developed SE model are shown in Table 3. This table revealed percentage error range between the actual and predicted value for specific mechanical energy consumption is between –1.30 and 2.48%. This indicates that the developed empirical SE model is reasonably accurate within 95% prediction and can be used for further analysis. Thus, the model revealed that the main effects of all the four operational parameters provided strong primary contribution to the specific energy mechanical consumption of the separator while the quadratic effects of the
curve indicates bimodal distribution of the residuals. Breaks
near the middle of this graph are also indications of
auger speed,

2

a and cake breaker speed

2

c and

abnormalities in the residual distribution. The plots of the
interactions of

N a N c , N a P,

N a,

N c P,

N c ,

residuals versus run order and that of residuals versus fitted
response should exhibit scatter feature without any obvious

N a N c ,

Pand N a P

provided secondary effects to the
pattern (i.e. structureless) while histogram of the residuals is expected to portray dumb-bell shape [9]. After fitting and selection of the best response surface function of the SE, six
response. The contour and 3D-surface plots of the SE model
are as presented in Fig. 1 to 6. The curvilinear profiles of these figures (Fig. 1-6) portray the quadratic nature of the SE model

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and the minimization required for the response is very obvious from the orientation of plots as desired. These plots also indicate that the optimal value of the specific mechanical
energy consumption of the separator falls between 11.89159 kJ/kg and 16.5708kJ/kg. The non-linear mathematical
programming model formed as per the procedure described in section 2 above which was used for determining the optimum value of the specific mechanical energy consumption of the
palm nut-pulp separator is also presented below.

TABLE 2

SPECIFIC MECHANICAL ENERGY CONSUMPTION OF THE PALM NUT-PULP SEPARATOR

SE  50.6  3.43Na

 2.68Nc

1.1102 P  1.02 9.74 104 N

2  5.38104 N 2

 5  10 5

N a N c  2  10

N a P  2.51  10

N a 8 10

N c P  1.31 10

N c

 1105 P

 7.91  10 7 N

N  4.65  10 8 N P

(6)

TABLE 3

CONFIRMATION TEST OF THE DEVELOPED SPECIFIC MECHANICAL ENERGY CONSUMPTION MODEL

S/No

Factors Settings

Separated products (kg)

Time

(s)

SE(kJ/kg)

Na

(rpm)

Nc

(rpm)

P (Watt)

(())

Palm nut

Digested pulp

Total output

Actual

Predicted

Residual

Error(%)

1

1425

1900

3730

45

3.85

12.10

15.95

132.00

30.87

30.39

0.48

1.56

2

2150

1900

3730

45

3.15

13.12

16.27

104.00

23.84

23.93

-0.09

-0.38

3

2150

2870

7460

25

3.98

14.15

18.13

90.00

37.03

37.01

0.02

0.05

4

1435

1915

3730

45

3.20

12.80

16.00

132.00

30.77

31.17

-0.40

-1.30

5

1435

1915

7460

25

3.60

12.80

16.40

107.00

48.67

48.27

0.40

0.82

6

2150

2870

4103

25

3.08

14.02

17.10

118.00

29.45

28.72

0.73

2.48

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Minimize SE:

TIIE MATIIEMAIICAL PROGRAMMING MODEL OF TIIE PALM NUT-PULP SEPARAWR

-50.6 -3.43Na + 2.68Nc + 1.1x 10-2 p + 1.02a +9.74x 10-4N- 5.38x 10-4 Nc 2 -5 X 10-5 NaNc- 2 X 10-6 NaP 2

-2.51 X w-4 N a a- 8 X w-G NCP -1.31 X w-) N c a -1X w-s Pa + 7.91 X w-7 N a N c a- 4.65 X w-s N a Pa

Subject to:

Non linear inequality constraints of 1790.05 and TP419.92;

9.6554-1.0484x 10-2 Na + 4.1728x 10-2 Nc +4.3204x 10-3 P +6.5171x 10-1a -1.0701x 10-5 Nc 2

-4.7150 xl0-7 P 2 -0.0134a 2 + 4.1738 xl0-6 NaN c +1.016 x10-6 NaP+ 7.3427 x10-5 Naa

+ 6.3164 X 10-7 NCP +1.1780 X 10-4 N c a90.05

4 3

605.8977-2.02 X 10-1Na -3.787x 10-1Nc +1.05 X 10-2 P- 2.15a + 2 X 10- Na Nc +3.521 X 10- Pa419.92

Linear inequality constraints of;

3.73:::; p:::; 7.46

19002 :::; Nc :::; 2870

1425 N a 2150

25 :::;a :::;45

1.5

1

0.5 x2 0

/ I Ill (

X=0.9

Y= 0.9

Level= 11.8959


25 30

20

20 u.J

(f)

-0.5

-1

-1.5

-1

15

0 1 10 x1

10

0

2

2

x2 -2 -2 x1

Fig. 1: Contour and 3D surface graph of SE versus auger and cake breaker speeds



1.5 30

1 40

0.5 25 30

u.J

(f)

Y=0.4 20

-0.5

Level= 13.7697 20

-1 -- - 2

-1.5

-1 0 1

15 2

x1 x3 -2 -2 x1

Fig. 2: Contour and 3D surface graph of SE versus auger speed and power

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1.5

1

0.5 x4 0

-0.5

-1

-1.5

X= 0.9

Y= 0.9

Level= 14.1603

-1 0 1 x1


26

24 30

22

20 20

18

10

16 2

14 0 x4

-2 -2

X: 0.9

Y : 0.9

Z: 14.16

2

0

x1

Fig. 3: Contour and 3D surface graph of SE versus auger speed and helix angle

1.5

1

0.5 x3 0

-0.5

-1

-1.5

X= 0.5

Y= 0.3

Level= 16.5708

-1 0 1

35

40

30

30

25

20

20 10

2

15

X: 0.5

Y : -0.3

Z: 16.57

2

0 0

x2 x3

-2 -2 x2

Fig. 4: Contour and 3D surface graph of SE versus cake breaker speed and power

1.5

1

0.5 x4 0

-0.5

-1

X= 0.9

Y= 0.9

Level= 13.6373


30 40

30

25

20

20 10

2

15 0

X: 0.9

Y : 0.9

Z: 13.64

2

0

-1.5

-1 0 1 x2

x4 -2 -2 x2

Fig. 5: Contour and 3D surface graph of SE versus cake breaker speed and helix angle

1.5

1

0.5 x4 0

-0.5

-1


30

25

20

40

30

20

10

2

IJSER © 2012 0

X: 0.4

Y : 0.9

Z: 15.09

2

0

-1.5

-1 0 1 x3

http://www.ijser.org

x4

-2 -2 x3

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Fig. 6: Contour and 3D surface graph of SE versus power and helix angle
The set of optimal solution obtained after inputing this optimization model into the fmincon solver of MATLAB
software is: Na= 2116.0701, Nc = 2821.0200, P = 4.1027, α =
44.9980, fval = 16.2904. The fval = 16.2904 in this solution set
represents the optimal value of the objective function (SE)
thus, solution is in agreement with the feasible region (11.89159-16.5708kJ/kg) identified from the SE model plots (Fig. 1-6). After all the necessary approximation (trade-offs) were made on this solution set in line with possible practical operational values, the separator was test runned with driving power, P = 4.103kW (5.5HP), cake breaker speed, Nc =
2821rpm, auger speed, Na = 2116rpm and helix angle of the
auger worm, α = 450. The experimental results for the verification of the solution of the optimization model are shown in Table 4.

. The confirmation results of the optimization showed that the palm nut-pulp separator performs with an average specific mechanical energy consumption of 16.41kJ/kg, efficiency of

95% and throughput of 900kg/h at driving power, cake
breaker speed, auger speed and helix angle setting of
4.103kW, 2821rpm, 2116rpm and 450 respectively. These experimental results indicate over 99% successful prediction
when compared with the multi-response model solution of
16.29035kJ/kg, 95.00005% and 900.43154kg/h for specific
mechanical energy consumption, efficiency and throughput
respectively. Thus, performance of the palm nut-
pulp separator with the operational parameters (factor) setting
determined in this multi-response optimization is better than its performance at both its design factor setting of 2.238kW,
730rpm, 730rpm and 450 for the driving power, cake breaker
speed, auger speed and helix angle respectively and that of
6.341kW, 2821.5rpm, 2113.75 rpm and 450 determined from
graphical optimization.
Recall that the separator performed with specific mechanical
energy consumption, efficiency and throughput 19.23kJ/kg,
419.92kg/h and 90.05% respectively at its design factor setting while its specific mechanical energy consumption, efficiency and throughput at the factor setting from graphical optimization are 26.73kJ/kg, 867.69kg/h and 94% respectively.

TABLE 3

CONFIRMATION TEST OF THE OPTIMIZATION RESULT

Test

Separated Products (kg)

Time

Taken

(s)

Responses

Palm Nut

Digested

Pulp

Total Output

SE(kJ/kg)

%

TP(kg/h)

1

3.96

15.05

19.01

76.00

16.40

95.05

900.47

2

4.02

14.96

18.98

76.00

16.43

94.90

877.06

3

3.98

15.02

19.00

76.00

16.41

95.00

900.00

4

4.00

15.01

19.01

76.00

16.40

95.05

900.47

Average

3.99

15.01

19.00

76.00

16.41

95.00

900.00

4.0 Conclusion and Recommendation

The palm nut-pulp separating machine is more efficient and energy saving when operates at an optimal driving power, cake breaker speed, auger speed and helix angle of 4.103kW (5.5Hp), 2821rpm, 2116rpm, and 450 for respectively. Thus, this factor setting constitutes the optimal operational parameters of the separator. It is therefore recommended that the machine should be operated at these factor settings and also that its replication should be based on these optimal factor setting to ensure optimum performance.

Acknowledgement

Funding received from National Mathematical Centre/Raw Materials Research and Development Council (NMC/RMRDC), Abuja, Nigeria through Mathematical Modeling of Processing Equipment grant for the year
2009/2010 is gratefully acknowledged.

References

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International Journal of Scientific & Engineering Research Volume 3, Issue 7, June-2012 9

ISSN 2229-5518

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Authors’ Information

Nwankwojike, Bethrand Nduka is a lecturer of Department of Mechanical Engineering, Michael Okpara University of Agriculture,Umudike, Nigeria. PH : +23480375178939

E-mail: jikeobodo@yahoo.com

Agunwamba, Chukwuemeka Jonah is the present Dean, Faculty of Engineering, University of Nigeria, Nsukka, Nigeria. PH : +2348035644561 E-mail: jcagunwamba@yahoo.com

Ogbonnaya, Ezenwa Alfred is the present Head of Department of Mechanical Engineering, Michael Okpara University of Agriculture,Umudike, Nigeria. PH : +2348037778406

E-mail: ezenwaogbonnaya@yahoo.com

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