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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
74
THERMAL KINETICS OF THIN LAYER DRYING OF INDIAN
GOOGEBERRY OR ANOLA FLAKS (PHYLLANTHUS EMBLICA)
Dinesh Kumar1
, Dr. L.P. Singh2
, Dr. Anil Kumar Singh3
1
Research Scholar, Dept. of Mechanical Engg. SHIATS-DU,Allahabad
2
Assistant Professor, MED, SHIAT-DU, Allahabad
3
Associate Professor, Dept. of Mechanical Engg. and Principal (I/C),
Lok Nayak Jai Prakash Institute of Technology Chapra- 841302 (Bihar), India
ABSTRACT
The aonla (Phyllanthus emblica), a fruit rich in vitamin-C, has high medicinal importance in
human life. Drying of aonla in the form of flakes and powder is one of the widely used methods of
its preservation. Thermal kinetics during drying a hygroscopic material in thin layer, the moisture
ratio is calculated by the Half Life Time Method. The experiment was conducted at an average
velocity of 0.48m/s, relative humidity 35% and temperature in the range from 40 to 750
C. Comparing
the experimental values with the predicted values using Newton’s Model, Page Model, Modified
Page Model on the basis of Root Mean Square Error (RMSE), chi-square(χ2
) and Efficiency (EF),
RMSE and χ2
were found lowest and EF .RMSE lay between 0.0382 and 0.0094, reduced χ2
between 0.000132 and 0.00761 and EF between 0.9598 and 0.9985.Thus, this thermal kinetic model
can be used to predict the moisture of the aonla at any drying instant during thin layer drying
process with reasonable accuracy.
Keywords: Aonla (Phyllanthus Emblica), Drying, Drying Kinetics, Hygroscopic Material, Half Life
Time Method, Indian Gooseberry.
1. INTRODUCTION
Drying, one of the most energy-intensive and thermal processes is used for storage and
processing of cereal grains in chemical and food industries. Whereas dehydration is the removal of
moisture to a very low moisture content, nearly a dry-bone condition [16], the basic objective of
drying a food fruit is the removal of moisture to a level, which would prevent the growth of moulds
and insects that normally cause spoilage [6], yet retaining the germination capacity.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 7, July (2014), pp. 74-79
© IAEME: www.iaeme.com/IJMET.asp
Journal Impact Factor (2014): 7.5377 (Calculated by GISI)
www.jifactor.com
IJMET
© I A E M E
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
75
A large amount of energy is consumed in a drying process every year all over the world.
Therefore understanding the thermal kinetics during drying process is necessary in establishing
design requirements for an energy- efficient drying system. Drying may be accomplished by
adsorption, mechanical separation, vaporization, chemical means or a combination of two or more of
the above methods. In this paper, only artificial drying of hygroscopic fruits using heated air as a
drying medium will be considered.
When a hygroscopic material is exposed to a particular environment for a long time, the grain
adsorbs or desorbs moisture depending on whether its vapour pressure is less or greater than that of
the environment. The flow ceases when the two vapour pressures become equal and the grain is said
to have reached equilibrium moisture content (EMC), the EMC depends on the variety and maturity
of the grain and the humidity and temperature conditions of the environment. Since determination of
EMC, (Me) requires separate experiment for the material under consideration, a few researchers
have suggested use of another simpler definition of moisture ratio MR=M/Mo in place of
(M-Me)/ (Mo-Me). Lewis proposed a model analogous to Newton’s Law of cooling.
)( eMMk
dt
dM
−−= (1.1)
The thin layer drying experiment was conducted with air of given humidity and temperature.
Moisture content, M during drying, was taken on dry basis. The moisture ratio M/Mo was calculated
from the moisture content (% d.b.). The thermal kinetics during drying the relationship between
moisture ratios and drying instants was determined. Based on the Lewis proposal, seven models were
proposed by researchers.
2. EXPERIMENTAL SET-UP AND PROCEDURE
The experimental set up consist of three main units: Humidification chamber, Air heating
system, and drying unit. The humidification chamber was constructed of galvanized iron sheet in two
cylindrical parts, which were joined together by means of an airtight flange-joint. The lower part of
the humidification chamber is of 0.3 m diameter and 1 m height. A float valve is employed in order
to maintain a desired level of water in the lower portion of the chamber. An overhead water tank
supplies water to the chamber. The air suction pipe, 3 m long and 106 mm in diameter, is connected
to the humidification chamber through an orifice meter just above the water level. The lower part of
the humidification chamber is also provided with a water level indicator, a drain valve, two 2-kW
electric immersion heaters, a water pump and a 12 mm diameter perforated spray tube.
Fig 1: Thin Layer Drying Unit
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
76
2.1 Preparation of the fruit samples
A batch of 50 kg of Aonla fruits was obtained from aonla tree. The fruit was cleaned, sorted
and graded before it was used for the experiment. The fruit samples at the desired moisture were
obtained by adding calculated amounts of distilled water to the fruit and then sealed in separate bags.
The samples were kept at 278 K in a refrigerator for a week to enable the moisture to become
uniformly distributed throughout the material. Before starting a test, the required quantity of the
fruit was taken out of the refrigerator and was allowed to warm up to the room temperature. The initial
moisture contents and the equilibrium moisture content and time taken for this change are recorded and the
values of M/Mo from experimental observation are calculated.
2.2 Thin-layer drying
To obtain thermal kinetics during drying the desired values of velocity, temperature and
relative humidity of the drying air, airflow rate and energy supplied to the water-heater and air
heaters were suitably adjusted. It was ensured that the system achieved steady state conditions; it
was only after about one hour that the drying experiments could be started. About 1kg of Aonla
flakes was weighed and distributed uniformly in a thin-layer, one flake high, in each of the drying
pans. The drying pans were then placed on the openings in the base plate in the exposure chamber.
As the drying continued, the samples were weighed periodically. The duration between
two consecutive weighing was 6 min during the first hour and 12 min thereafter. As the drying
proceeded, the drying rate decreased. The time interval beyond 12h of drying was increased
to 30 min. The drying was continued until the weight difference between two consecutive readings
of a drying sample was negligible The experimental observations were obtained for the following
conditions: Initial moisture content was about 35%, Average air velocity of drying air 0.48m/s, Drying
air temperature : 323, 333, 338 343, 348, 353 & 358K with two dew-point temperatures
(approximately 293 and 303 K).
3. METHOD OF SOLUTION
To determine the thermal kinetics of drying thin layer, an Analytical determination of drying
coefficient “k” by Half Life Method.
The drying equations used by researchers [11, 21] were of the following type
kt
eo
e
Ae
MM
MM
MR −
=
−
−
= (3.1)
By plotting the value of natural log of experimental MR against drying time for a given
drying air temperature, they found the plot to be a straight line, the slopes gives the drying
coefficient and the intercept the natural logarithmic value of the shape factor for the temperature
under consideration. It is assumed that the types of equation remain the same when the definition of
Moisture Ratio is changed to MR=M/Mo and therefore, MR becomes
MR=M/Mo = A e -kt
(3.2)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
77
Fig 2: Semi log plot of Moisture Ratio vs Drying
The value of “k” can be determined analytically by the half-life Method. Half –life period is
the time of one-half response in a drying process and can be defined as the number of hours
necessary to obtain a moisture ratio of one-half. Using the experimental results on drying of Aonla
obtained in the present work, with drying air at 500
C, drying time at which MR is half, (i.e. ½) can
be found by linear interpolation at 4 and 8 hours
Fig 3: Graph for Drying Coefficient
Using the values of drying coefficient k and shape factor A for various drying temperatures
the correlation are found as given below
k = 0.0267e0.0243T
and A = 2.4095T-0.2325
y = 0.026e0.024x
R² = 0.988
0.08
0.1
0.12
0.14
0.16
0.18
0.2
40 45 50 55 60 65 70 75 80
"K"Values
Temperatures degree C
Drying coefficient K
K
Expon…
-10.0
-9.0
-8.0
-7.0
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
0 10 20 30 40 50
LnMoistureRaio
Time , (hrs)
Semilog plot of moisture ratio Vs drying time
ln MR at 50 ln MR at 55 ln MR at 60
ln MR at 65 ln MR at 70 ln MR at 75
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
78
thus the drying equation
teT
M
M
MR T
o
)0267.0(exp)4095.2( 0243.02325.0
−=





= −
Where t is the drying time in hours, and T is the drying air temperature in 0
C.
4. MODELS FOR THE DRYING OF AONLA FLAKES
There are No of Mathematical models as Newton Model ; MR = exp(-kt ) , Page Model;
MR=exp(-ktn
),Modified Page Model; MR = exp [( -kt ) n
]etc. From Page Model; MR=exp (-ktn
),
the values of χ2
, RMSE and EF for various values of empirical constant (n) at a given drying air
temperature 500
C, it was found that the value n=1 has maximum EF (efficiency) and minimum
RMSE value shown in Curvefittingcriteriaforsemi-theoreticalthinlayerdryingmodelforthe dryingofaonla.
Fig 4: Graph of RMES & EF vs Temperature based on Modified Page Model
4.1 Summary
For values of RMSE and EF (Efficiency) Page Model & Modified Page Model are equal
from 50 to 750
C (higher temperature) where as the value of χ2
is different for air
temperatures above 650
C onwards. RMSE values for Page Model varies from 0.0067 to 0.0766.
Fig 4: Graph of RMES & EF vs Temperature based on Page Model
Value of RMES & EF Vs Temerature based on Modified Page Model at
Exp. Temp. 50C
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
Temperature(oC)
ValueofRMES
0.80
0.85
0.90
0.95
1.00
EF(Efficiency)
RMES
EF
Value of RMES and EF Vs Temperature based on Page Model at
Experiment Temp. 50C
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
Temperature(oC)
ValueofRMES
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
Valueofefficiency(EF)
RMES
EF
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME
79
5. CONCLUSIONS
For modeling and numerical approach of thermal kinetics during drying the hygroscopic
material, the experimental moisture content data were used on the dry weight basis.
The drying models, namely Newton’s Model, Page Model, and Modified Page Model etc.
were compared on the basis of their statistical coefficients such as Root Mean Square Error RMSE,
chi-square and Efficiency EF to see how close the predicted values were to experimental one.
7. REFERENCES
[1] Akpinar K, Bicer Y. & Yildiz C. Thin layer drying of red pepper. Food Engineering 2003;
59(1): 99-104.
[2] Akpinar K, Midilli A. & Bicer Y. Experimental investigation of drying behavior and
conditions of pumpkin slice via a cyclone-type dryer. Food Engineering, 2003b; 83(14):
1480-1486.
[3] Ayenseu, A. Dehydration of food crops using a solar dryer with convective heat flow. Solar
Energy, 1997; 594-6): 121-126.
[4] Babbit J, Barre. On differential equation of diffusion. Can. J: Res. Sec. A18: 419-474, 1949.
[5] Bajgai T R, Hashinaga F. Application of high electric field on the shelf life extension of
embolic fruit (Phyllanthus Emblica L.). Food Engineering2006; 74(06):308-313.
[6] Brooker D B, Bakker Arkema F W and Hall C W. Drying Cereal Grains. Westport Conn.
U. S. A: The AVI PUB. Co. Inc., 1974.
[7] Chhinnan M S. and Young J H. A study of diffusion equations describing moisture
movement in peanut pods. Transaction of the ASAE 1977; 20(4): 749-753.
[8] Chhinnan M S. Evaluation of selected mathematical models for describing thin-layer drying
of in-shell pecans. Transactions of the ASAE 1984; 27: 610-615.
[9] Chittenden D H. and Hustruild A. Determining drying constants for shelled corn.
Transactions of the ASAE 1968; 9(1): 52-55.
[10] Dandamrongrak R. Young G. & Mason R. Evaluation of various pre-treatments for the
dehydration of banana and selection of suitable drying models. Food Engineering 2002;
95:139-146.
[11] Demir V, Gun ham T. et al. A Mathematical modeling and determination of some quality
parameters of air-dried bay leaves. Biosystems Engineering 2004; 88(3):325-335.
[12] Doymaz I. Drying kinetics of white mulberry, Food Engineering 2004c; 61(3): 341-346.
[13] Dutta S K, Nema V K and Bharadwaj R K. Thermal properties of gram. Agricultural
Engineering 1988b; 39: 269-275.
[14] Dutta S K, Nema V K and Bharadwaj R K. Physical properties of gram. Agricultural
Engineering 1988a; 39: 259-268.
[15] Henderson S M and Pabis S. Grain Drying Theory IV: The effect of airflow rate on drying
index. Agricultural Engineering Research 1962; 7(2): 85-89.
[16] Henderson S M. Progress in developing the thin layer drying equation. Transaction of the
ASAE 1974; 17(6): 1167-1168.
[17] Hussain A, Chen C S. and Whitney L F. Simultaneous heat and mass diffusion in biological
materials. Agric. Engg. Res. 1973; 18(4): 3443-354.
[18] Singh, L.P., Choudhry V. and Upadhyay, R. K., “Drying Characteristics of a Hygroscopic
Material in a Fabricated Natural Convective Solar Cabinet Drier”, International Journal of
Mechanical Engineering & Technology (IJMET), Volume 4, Issue 3, 2013, pp. 299 - 305,
ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.

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THERMAL KINETICS OF THIN LAYER DRYING OF INDIAN GOOGEBERRY OR ANOLA FLAKS (PHYLLANTHUS EMBLICA)

  • 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 74 THERMAL KINETICS OF THIN LAYER DRYING OF INDIAN GOOGEBERRY OR ANOLA FLAKS (PHYLLANTHUS EMBLICA) Dinesh Kumar1 , Dr. L.P. Singh2 , Dr. Anil Kumar Singh3 1 Research Scholar, Dept. of Mechanical Engg. SHIATS-DU,Allahabad 2 Assistant Professor, MED, SHIAT-DU, Allahabad 3 Associate Professor, Dept. of Mechanical Engg. and Principal (I/C), Lok Nayak Jai Prakash Institute of Technology Chapra- 841302 (Bihar), India ABSTRACT The aonla (Phyllanthus emblica), a fruit rich in vitamin-C, has high medicinal importance in human life. Drying of aonla in the form of flakes and powder is one of the widely used methods of its preservation. Thermal kinetics during drying a hygroscopic material in thin layer, the moisture ratio is calculated by the Half Life Time Method. The experiment was conducted at an average velocity of 0.48m/s, relative humidity 35% and temperature in the range from 40 to 750 C. Comparing the experimental values with the predicted values using Newton’s Model, Page Model, Modified Page Model on the basis of Root Mean Square Error (RMSE), chi-square(χ2 ) and Efficiency (EF), RMSE and χ2 were found lowest and EF .RMSE lay between 0.0382 and 0.0094, reduced χ2 between 0.000132 and 0.00761 and EF between 0.9598 and 0.9985.Thus, this thermal kinetic model can be used to predict the moisture of the aonla at any drying instant during thin layer drying process with reasonable accuracy. Keywords: Aonla (Phyllanthus Emblica), Drying, Drying Kinetics, Hygroscopic Material, Half Life Time Method, Indian Gooseberry. 1. INTRODUCTION Drying, one of the most energy-intensive and thermal processes is used for storage and processing of cereal grains in chemical and food industries. Whereas dehydration is the removal of moisture to a very low moisture content, nearly a dry-bone condition [16], the basic objective of drying a food fruit is the removal of moisture to a level, which would prevent the growth of moulds and insects that normally cause spoilage [6], yet retaining the germination capacity. INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME: www.iaeme.com/IJMET.asp Journal Impact Factor (2014): 7.5377 (Calculated by GISI) www.jifactor.com IJMET © I A E M E
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 75 A large amount of energy is consumed in a drying process every year all over the world. Therefore understanding the thermal kinetics during drying process is necessary in establishing design requirements for an energy- efficient drying system. Drying may be accomplished by adsorption, mechanical separation, vaporization, chemical means or a combination of two or more of the above methods. In this paper, only artificial drying of hygroscopic fruits using heated air as a drying medium will be considered. When a hygroscopic material is exposed to a particular environment for a long time, the grain adsorbs or desorbs moisture depending on whether its vapour pressure is less or greater than that of the environment. The flow ceases when the two vapour pressures become equal and the grain is said to have reached equilibrium moisture content (EMC), the EMC depends on the variety and maturity of the grain and the humidity and temperature conditions of the environment. Since determination of EMC, (Me) requires separate experiment for the material under consideration, a few researchers have suggested use of another simpler definition of moisture ratio MR=M/Mo in place of (M-Me)/ (Mo-Me). Lewis proposed a model analogous to Newton’s Law of cooling. )( eMMk dt dM −−= (1.1) The thin layer drying experiment was conducted with air of given humidity and temperature. Moisture content, M during drying, was taken on dry basis. The moisture ratio M/Mo was calculated from the moisture content (% d.b.). The thermal kinetics during drying the relationship between moisture ratios and drying instants was determined. Based on the Lewis proposal, seven models were proposed by researchers. 2. EXPERIMENTAL SET-UP AND PROCEDURE The experimental set up consist of three main units: Humidification chamber, Air heating system, and drying unit. The humidification chamber was constructed of galvanized iron sheet in two cylindrical parts, which were joined together by means of an airtight flange-joint. The lower part of the humidification chamber is of 0.3 m diameter and 1 m height. A float valve is employed in order to maintain a desired level of water in the lower portion of the chamber. An overhead water tank supplies water to the chamber. The air suction pipe, 3 m long and 106 mm in diameter, is connected to the humidification chamber through an orifice meter just above the water level. The lower part of the humidification chamber is also provided with a water level indicator, a drain valve, two 2-kW electric immersion heaters, a water pump and a 12 mm diameter perforated spray tube. Fig 1: Thin Layer Drying Unit
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 76 2.1 Preparation of the fruit samples A batch of 50 kg of Aonla fruits was obtained from aonla tree. The fruit was cleaned, sorted and graded before it was used for the experiment. The fruit samples at the desired moisture were obtained by adding calculated amounts of distilled water to the fruit and then sealed in separate bags. The samples were kept at 278 K in a refrigerator for a week to enable the moisture to become uniformly distributed throughout the material. Before starting a test, the required quantity of the fruit was taken out of the refrigerator and was allowed to warm up to the room temperature. The initial moisture contents and the equilibrium moisture content and time taken for this change are recorded and the values of M/Mo from experimental observation are calculated. 2.2 Thin-layer drying To obtain thermal kinetics during drying the desired values of velocity, temperature and relative humidity of the drying air, airflow rate and energy supplied to the water-heater and air heaters were suitably adjusted. It was ensured that the system achieved steady state conditions; it was only after about one hour that the drying experiments could be started. About 1kg of Aonla flakes was weighed and distributed uniformly in a thin-layer, one flake high, in each of the drying pans. The drying pans were then placed on the openings in the base plate in the exposure chamber. As the drying continued, the samples were weighed periodically. The duration between two consecutive weighing was 6 min during the first hour and 12 min thereafter. As the drying proceeded, the drying rate decreased. The time interval beyond 12h of drying was increased to 30 min. The drying was continued until the weight difference between two consecutive readings of a drying sample was negligible The experimental observations were obtained for the following conditions: Initial moisture content was about 35%, Average air velocity of drying air 0.48m/s, Drying air temperature : 323, 333, 338 343, 348, 353 & 358K with two dew-point temperatures (approximately 293 and 303 K). 3. METHOD OF SOLUTION To determine the thermal kinetics of drying thin layer, an Analytical determination of drying coefficient “k” by Half Life Method. The drying equations used by researchers [11, 21] were of the following type kt eo e Ae MM MM MR − = − − = (3.1) By plotting the value of natural log of experimental MR against drying time for a given drying air temperature, they found the plot to be a straight line, the slopes gives the drying coefficient and the intercept the natural logarithmic value of the shape factor for the temperature under consideration. It is assumed that the types of equation remain the same when the definition of Moisture Ratio is changed to MR=M/Mo and therefore, MR becomes MR=M/Mo = A e -kt (3.2)
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 77 Fig 2: Semi log plot of Moisture Ratio vs Drying The value of “k” can be determined analytically by the half-life Method. Half –life period is the time of one-half response in a drying process and can be defined as the number of hours necessary to obtain a moisture ratio of one-half. Using the experimental results on drying of Aonla obtained in the present work, with drying air at 500 C, drying time at which MR is half, (i.e. ½) can be found by linear interpolation at 4 and 8 hours Fig 3: Graph for Drying Coefficient Using the values of drying coefficient k and shape factor A for various drying temperatures the correlation are found as given below k = 0.0267e0.0243T and A = 2.4095T-0.2325 y = 0.026e0.024x R² = 0.988 0.08 0.1 0.12 0.14 0.16 0.18 0.2 40 45 50 55 60 65 70 75 80 "K"Values Temperatures degree C Drying coefficient K K Expon… -10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 0 10 20 30 40 50 LnMoistureRaio Time , (hrs) Semilog plot of moisture ratio Vs drying time ln MR at 50 ln MR at 55 ln MR at 60 ln MR at 65 ln MR at 70 ln MR at 75
  • 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 78 thus the drying equation teT M M MR T o )0267.0(exp)4095.2( 0243.02325.0 −=      = − Where t is the drying time in hours, and T is the drying air temperature in 0 C. 4. MODELS FOR THE DRYING OF AONLA FLAKES There are No of Mathematical models as Newton Model ; MR = exp(-kt ) , Page Model; MR=exp(-ktn ),Modified Page Model; MR = exp [( -kt ) n ]etc. From Page Model; MR=exp (-ktn ), the values of χ2 , RMSE and EF for various values of empirical constant (n) at a given drying air temperature 500 C, it was found that the value n=1 has maximum EF (efficiency) and minimum RMSE value shown in Curvefittingcriteriaforsemi-theoreticalthinlayerdryingmodelforthe dryingofaonla. Fig 4: Graph of RMES & EF vs Temperature based on Modified Page Model 4.1 Summary For values of RMSE and EF (Efficiency) Page Model & Modified Page Model are equal from 50 to 750 C (higher temperature) where as the value of χ2 is different for air temperatures above 650 C onwards. RMSE values for Page Model varies from 0.0067 to 0.0766. Fig 4: Graph of RMES & EF vs Temperature based on Page Model Value of RMES & EF Vs Temerature based on Modified Page Model at Exp. Temp. 50C 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 Temperature(oC) ValueofRMES 0.80 0.85 0.90 0.95 1.00 EF(Efficiency) RMES EF Value of RMES and EF Vs Temperature based on Page Model at Experiment Temp. 50C 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 Temperature(oC) ValueofRMES 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Valueofefficiency(EF) RMES EF
  • 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 7, July (2014), pp. 74-79 © IAEME 79 5. CONCLUSIONS For modeling and numerical approach of thermal kinetics during drying the hygroscopic material, the experimental moisture content data were used on the dry weight basis. The drying models, namely Newton’s Model, Page Model, and Modified Page Model etc. were compared on the basis of their statistical coefficients such as Root Mean Square Error RMSE, chi-square and Efficiency EF to see how close the predicted values were to experimental one. 7. REFERENCES [1] Akpinar K, Bicer Y. & Yildiz C. Thin layer drying of red pepper. Food Engineering 2003; 59(1): 99-104. [2] Akpinar K, Midilli A. & Bicer Y. Experimental investigation of drying behavior and conditions of pumpkin slice via a cyclone-type dryer. Food Engineering, 2003b; 83(14): 1480-1486. [3] Ayenseu, A. Dehydration of food crops using a solar dryer with convective heat flow. Solar Energy, 1997; 594-6): 121-126. [4] Babbit J, Barre. On differential equation of diffusion. Can. J: Res. Sec. A18: 419-474, 1949. [5] Bajgai T R, Hashinaga F. Application of high electric field on the shelf life extension of embolic fruit (Phyllanthus Emblica L.). Food Engineering2006; 74(06):308-313. [6] Brooker D B, Bakker Arkema F W and Hall C W. Drying Cereal Grains. Westport Conn. U. S. A: The AVI PUB. Co. Inc., 1974. [7] Chhinnan M S. and Young J H. A study of diffusion equations describing moisture movement in peanut pods. Transaction of the ASAE 1977; 20(4): 749-753. [8] Chhinnan M S. Evaluation of selected mathematical models for describing thin-layer drying of in-shell pecans. Transactions of the ASAE 1984; 27: 610-615. [9] Chittenden D H. and Hustruild A. Determining drying constants for shelled corn. Transactions of the ASAE 1968; 9(1): 52-55. [10] Dandamrongrak R. Young G. & Mason R. Evaluation of various pre-treatments for the dehydration of banana and selection of suitable drying models. Food Engineering 2002; 95:139-146. [11] Demir V, Gun ham T. et al. A Mathematical modeling and determination of some quality parameters of air-dried bay leaves. Biosystems Engineering 2004; 88(3):325-335. [12] Doymaz I. Drying kinetics of white mulberry, Food Engineering 2004c; 61(3): 341-346. [13] Dutta S K, Nema V K and Bharadwaj R K. Thermal properties of gram. Agricultural Engineering 1988b; 39: 269-275. [14] Dutta S K, Nema V K and Bharadwaj R K. Physical properties of gram. Agricultural Engineering 1988a; 39: 259-268. [15] Henderson S M and Pabis S. Grain Drying Theory IV: The effect of airflow rate on drying index. Agricultural Engineering Research 1962; 7(2): 85-89. [16] Henderson S M. Progress in developing the thin layer drying equation. Transaction of the ASAE 1974; 17(6): 1167-1168. [17] Hussain A, Chen C S. and Whitney L F. Simultaneous heat and mass diffusion in biological materials. Agric. Engg. Res. 1973; 18(4): 3443-354. [18] Singh, L.P., Choudhry V. and Upadhyay, R. K., “Drying Characteristics of a Hygroscopic Material in a Fabricated Natural Convective Solar Cabinet Drier”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 3, 2013, pp. 299 - 305, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.