24
Special Issue December 2015 INTERNATIONAL JOURNAL OF HUMANITIES AND CULTURAL STUDIES ISSN 2356-5926 http://www.ijhcs.com/index.php/ijhcs/index Page 783 The study of parameters that affect on drying process of Aloevera Gel using microwave method and the examination of the consistency of mathematical models Kinetic compared with experimental results Mohammad Ebrahim Kaveh, .Islamic Azad University, Damghan Branch, Damghan, Iran Mohammad Samipourgiri* Associate professor, Islamic Azad University, North Tehran Branch, Tehran, Iran *Corresponding author email: [email protected] Abstract The main purpose of drying food is increase the shelf life of the final product. There are different methods of drying food. Each of these methods has their own advantages and applications. Increasing concerns about product quality and production costs has interested researchers to examine the use of microwave technology for drying. Drying by microwave is a quick dewatering technique. Short processing time in drying by microwave, improve product quality and flexibility in the production of a wide range of dried products are as the advantages of microwave drying, especially for putrefying products. In this study the possibility of using the microwave oven for drying aloe vera and effective drying parameters were evaluated. Experiments were done in three powers (0.25, 0.50 and 0.75 watts) and in the range 2 to 50 minutes. In these study curves of drying by kinetic mathematical models of Henderson and Pabys, binomial, Wong and Singh, Henderson and "reformed Pabys" and February, which are widely used for biological substances and the majority of food items, was fitted. To determine the most appropriate mathematical model to describe the behavior of drying, fitness of 5 mathematical models by determining the determination coefficient 2 R and the total mean square error (MSE) was evaluated. In this method, firstly a mathematical intended model is selected, then based on the amount of moisture absorption and equilibrium model relationship an objective function was define to optimization and after optimization, optimized constants of mathematical model was obtained intended as functions of operating parameters. The results of the fitness of models showed that the mathematical model of Henderson and "Pabys modified " and binomial were highly adapted to the laboratory data. Keywords Microwave Method, Aloe Vera, Kinetics Mathematical Models, Henderson And Pabys, Binomial, Wong And Singh, Henderson And «Reformed Pabys ", February.

The study of parameters that affect on drying process of

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 783

The study of parameters that affect on drying process of Aloevera Gel

using microwave method and the examination of the consistency of

mathematical models Kinetic compared with experimental results

Mohammad Ebrahim Kaveh,

.Islamic Azad University, Damghan Branch, Damghan, Iran

Mohammad Samipourgiri*

Associate professor, Islamic Azad University, North Tehran Branch, Tehran, Iran

*Corresponding author email: [email protected]

Abstract

The main purpose of drying food is increase the shelf life of the final product. There are

different methods of drying food. Each of these methods has their own advantages and

applications. Increasing concerns about product quality and production costs has interested

researchers to examine the use of microwave technology for drying. Drying by microwave is

a quick dewatering technique. Short processing time in drying by microwave, improve

product quality and flexibility in the production of a wide range of dried products are as the

advantages of microwave drying, especially for putrefying products. In this study the

possibility of using the microwave oven for drying aloe vera and effective drying parameters

were evaluated. Experiments were done in three powers (0.25, 0.50 and 0.75 watts) and in

the range 2 to 50 minutes. In these study curves of drying by kinetic mathematical models of

Henderson and Pabys, binomial, Wong and Singh, Henderson and "reformed Pabys" and

February, which are widely used for biological substances and the majority of food items,

was fitted. To determine the most appropriate mathematical model to describe the behavior

of drying, fitness of 5 mathematical models by determining the determination coefficient 2R

and the total mean square error (MSE) was evaluated. In this method, firstly a mathematical

intended model is selected, then based on the amount of moisture absorption and equilibrium

model relationship an objective function was define to optimization and after optimization,

optimized constants of mathematical model was obtained intended as functions of operating

parameters. The results of the fitness of models showed that the mathematical model of

Henderson and "Pabys modified " and binomial were highly adapted to the laboratory data.

Keywords Microwave Method, Aloe Vera, Kinetics Mathematical Models, Henderson

And Pabys, Binomial, Wong And Singh, Henderson And «Reformed Pabys ", February.

Page 2: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 784

Introduction

Plants from the beginning of history have been considered as one of the most important

sources of food and medicine. Aloe vera plant with the scientific name Aloe Barbadensis, is a

native African plant, a perennial Plant, drought-resistant with fleshy and water leaves and

contain inside colorless gel and is owned by Lilies family which has historically been used

for a variety of therapeutic purposes (1).Clinical studies have documented that drug's active

ingredients are in the gel and green part of aloe vera leaves (2). In recent years a lot of study

has been done about the medicinal properties of aloe vera gel and has achieved very

significant results, causing the gel of the plant has many uses in the pharmaceutical and food

industries. Very diverse drug-like effects such as skin wound and lesions healing (3), effects

of anti-mutation and anti-cancer (4), anti-bacterial(5) and … have been attributed to it. Food

products of it include a variety of beverages and other routinely world-wide used products

(6).

Human beings from the beginning of in parallel effort for daily sustenance have been always

thinking about food storage and preservation. To maintain and preserve food from

contamination and infectious agents by taking into account the type of pollution, different

methods are used. Based on the type of food, physical and chemical properties of food

products and the length of storage time and economic aspects and technology for any type,

specific method is used.

Among the various food preservation techniques, the use of heat is important and has long

been used (7). Thermal effect in preventing three types of biological, chemical and physical

corruption is effective. Drying fruits and vegetables is one of the oldest and most widely

known methods for food preservation and the most important process to maintain the quality

of the food. The main objective in drying agricultural products, reducing humidity to the

extent that they be stable in the long term that with reduction of microbial enzyme activity

and reduce the speed of chemical reactions, increase product shelf life and with a significant

reduction in weight and volume facilitate the cost of packaging, storage and transportation of

it (8).

Drying is not only a simple process to reduce the moisture of product, appearance and color

characteristics of dried food depend on drying method. Texture of the final product is one of

the most important traits of fruits and vegetables. Physical changes include shrinkage,

swelling, crystallization and chemical and biochemical changes include color, texture, odor

and other properties of food. Drying can also reduce the quality of food and the nutritional

value and can cause irreversible structural damage in food. The aim of designing drying

equipment is minimizing these adverse changes that will be realized by choosing suitable

conditions for drying food (9).

There are various ways of drying for agricultural products, including the method of drying by

oven at low temperatures, drying at high temperatures, osmotic drying, drying with

microwaves, and drying with different rays(10-12). Each of mentioned methods has its own

advantages and disadvantages. The most common methods of drying food products is the use

of hot air in which heat transfer to interior of nutrient is limited, energy efficiency is lowed,

and longer time is required for drying(13). One of the ways in which a lot of attention has

been paid over the last decade, is drying using microwave radiation .In the microwave

Page 3: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 785

method because heat transfer is not done by conduction and heat is made in the whole context

of food, therefore, the heat transfer rate is faster than other drying methods and the damage

and burning surface parts of food is prevented. (14-16)

Today microwave drying due to higher performance and lower power consumption is

employed as an alternative to the old method of drying (2004 Lillard et. al).The researchers

have introduced the microwave method as a way to early preparation and as a way for drying

fruit (Meskavi, 2007; Najafi, 2011).

Microwaves rays are a category of electromagnetic radiation with long wavelength

(frequency 300-3000 MHz).When the waves pass through the tissues of food, polar

molecules such as water and salts are vibrated, and this vibration causes conversion of

microwave energy to heat. In addition, microwaves rays unlike X-rays and gamma rays are

unable to break chemical bonds and damage to the molecules of food. Two important

mechanisms that explain generation of heat in the material that is placed in a microwave field

are ionic polarization and dipole rotation (Moytiga et al., 2005) and (17-19) usual drying

method is combined with common and conventional heating. The first commercial

advertisement of use of microwave energy in foods processing, was the final drying of potato

chips. Drying with microwaves is used in spices, tomato paste, rice wild, snacks and pieces of

bacon. There are egregious differences between conventional mechanisms of drying process

and using microwave, because microwaves can penetrate the skin of dry foods to achieve not

evaporated moisture (Modget, 1989).

The study of aloe vera gel qualitative parameters has been done indifferent temperature

conditions with warm air velocity with and without air re-circulation to reduce waste output.

The results showed that with increasing temperature, the samples showed less resistance to

color change. (20)

Microwave is a quick method for drying food that its energy is comparable to the methods of

drying with hot air. In microwave drying removing moisture is faster and also because

microwave energy concentration, the microwave system only 20 to 35% compared to other

methods of drying needs for space (21).

The main purpose of this study firstly was demonstration the effectiveness of microwave

technology in drying Aloe Vera. In addition to this, identification and examining the effective

and optimized parameters of microwave system to plan a semi-industrial pilot reactor in the

next phase of research is also very important. In general, use of microwaves in the food

industry for drying is developing. In fact, the microwave has been the emergence of a new

method which is different with the use of physical and chemical phenomena and conventional

drying methods (Chamat et al., 2011).

Given reviewing the literature, it seems that this study is the first research experience in the

field of kinetic modeling of Aloe Vera gel drying. Major research in this sphere has been

merely laboratory. Because of the soft structure and bright color, aloe vera gel drying process

can mainly be confronted with a fundamental flaw- bruising. This research could help us

understand the factors affecting the success of the aloe vera gel drying process using

microwave.

Page 4: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 786

The feasibility of using microwave for drying aloe vera gel and the study of factors affecting

of drying process of product is very important. The aim of this study was to investigate

effects of temperature and time of drying and microwave source power on drying aloe vera

gel and finally, the best model and the optimum conditions for maximum efficiency after

fitness by kinetic mathematical models of Henderson and Pabys, binomial, Wang and Singh,

Henderson and "modified Pabys" and February were presented.

Materials and methods

After preliminary studies done on the performance of microwave waves and identifying

structures that microwave performance on it is optimized, aloe vera as a material with a soft

structure in order to investigate the role of microwaves in these studies has not been

considered. The reason for this choice is traced in several factors:

1. The financial advantage: According to economic analysis, it seems that the

comparative advantage derived from the dried aloe vera is much preferred than

similar products (Table 1).

Table 1The world price of dried products (from websites Alibaba.com)

Product Name Range of world price

(dollars)

Dried apple 5-12

Melon 8-16

Pineapple 8-20

orange 5-15

Aloe Vera 10-30

2. Darkening of dried aloe vera in drying processes: In drying processes due to the white

color of Aloe Vera, the final product due to oxidation, would be discolored and brown.

According to previous studies using microwave technology as a pretreatment method can

prevent discoloration of the product (Fernandes et al., 2008).

3.The absence of extensive studies around the topic of this article: Another reason for

choosing this material has been the lack of extensive research in this area. According to

reviewing the literature it seems that this is the first research study to calculate the optimal

conditions to applying microwave radiation for drying fruit of aloe vera. The Majority

research in this area is associated with the laboratory methods that due to lack of proper care

can’t be used to optimize radiation conditions.

4.The need for industrial and applied research in the field of microwave and its application in

drying Aloe Vera.

Page 5: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 787

5. Having a suitable plant structure for being impressionable from microwave: Due to the

porous and soft structure, use a microwave oven for drying of the product can be considered

appropriate. The reason for this is requirement to be lower radiation and thus save energy

consumption.

In this study, aloe plant leaf samples were collected from the local market. After separating

gel part of plant leaf, was cut to desired thickness and the initial moisture content of the

samples was calculated. The system used is home microwave system which has the setting of

the amount of input energy. Due to the chosen topic, in this study which is related to

optimizing discussion the use of energy analysis systems seems necessary. The system used

in this study, has been a probe (generator) with a maximum power of 2000 watts and

optimized frequency of 22 kHz, which its mechanical wave generator is piezoelectric type.

Kind of generator is probe and radiation conducted directly. In order to compare the obtained

results from the drying process, using microwave waves, digital scale with accuracy of at

least one-tenth g was used.

The process of testing

In this study, a large number of equal-sized slices of aloe vera have been used to perform

tests. Since the project variables are time and light (radiation) power, so in order to maintain

equal conditions for all experiments an aloe vera plant has been used. In short, the tests can

be outlined as follows:

1.Preparation of Aloe Vera

2.After preparation of aloe vera plant leaf sample and separation of the gel and intended part

of leaf, it was cut to the desired thickness and with the same size and then Aloe Vera samples

have been placed in an oven at a specified temperature and were ready to dry (this process at

different temperatures were repeated: 50, 60, 70 and 80 ° C). In the end, the initial moisture

content of the samples was calculated.

3. Using a digital scale, with accuracy of tenth of a gram the samples were weighed, and

photographed from the original form of it.

4. In two different series of experiments (variable microwave power and constant exposure

time) and (fixed microwave power and variable exposure time) tests were performed.

5.After each round the wave radiation was photographed and samples weight was recorded

and moisture ratio of product was calculated.

Moisture Measuring

Initial moisture of the samples (based on wet weight) using method of AOAC04 / 931 and by

placing the samples in an oven at 105 ° C for 18 hours and using the following formula was

calculated (Doymaz, 2012; Minayeeet al. ,2008; Hosseini-Ziba, 1990).

Equation (1)

Page 6: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 788

100).(

in

outin

w

wwbwMC

Modeling of drying

For kinetics mathematical modeling of mass drying thin texture of aloe vera from proportion

of moisture during the drying the mass has been used. The proportion of moisture,

considering the initial moisture, balance moisture and mass moisture at any time during

drying was calculated by Equation 2.

Equation (2)

e

ed

MM

MMMR

0

Where ، dM is the mass moisture at current moment in dry basis, eM is balance moisture and

0M is initial moisture of the product mass. The left side of the equation indicates proportion

of moisture which determines the drying process. Based on conducted studies, in products

that have high moisture during drying equation (2) would be simple in the form of equation

(3).

Equation (3)

0M

MMR d

Curve models of Aloe Vera drying based recommended models by researchers who have

worked in this field were selected and are presented in Table 2. The achieved moisture

proportion during testing with 5 models from standard models drying of thin layer

agricultural products largely are used for biological materials and most food products, were

compared. These equations are derived from relationship between changes in moisture and

drying time.

Table 2 Regression models of drying of mass thin layer used in modeling

Model

name Model* Source

1 Henderson and Pabys )exp( ktaMR [15]

2 binomial )-exp()-exp( 10 tkbtkaMR

[17]

3 Wong and Singh 21 btatMR [19]

4 Henderson and

[20] )exp()exp()exp( htcgtbktaMR

Page 7: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 789

"reformed Pabys"

5 February MR=a0+a1×cos(x×w)+b1×sin(x×w)+

a2×cos(2×x×w) + b2×sin(2×x×w) [21]

*M: Moisture (d.b.), t: time (min) and a, b and c, the coefficients of h, g, k and m, fixed

models

To determine the most appropriate mathematical model to describe the behavior of drying,

fitness of 5 mathematical models by determining the coefficient of determination 2R and the

total mean square error (MSE) was evaluated.

In this method, firstly an intended mathematical model is selected then based on the amount

of moisture absorption and equilibrium model relationship, a targeted function is defined to

optimize that after the optimization, the optimized constants of intended mathematical model

are obtained as functions of operating parameters.

Calculation of the total square error (the sum of squared error) for each model:

After finding the optimal constants for each equilibrium model, absorption values at all

experimental points based on the calculation and with absorption values were compared at

the same experimental points. This comparison with quantity of mean relative error SSE (sum

of squared errors) was performed (Eq. 4).

Equation 4 2ˆ YySSE i

The yiis experimental results and Ŷ is modeling results.

In this study, the feasibility of using microwave method for drying aloe vera and effective

parameters on drying were evaluated. Experiments in three powers (0.25, 0.50 and 0.75

watts) and in the range of 5 to 50 minutes were done (Table 3).

Table 3 Changes change in input parameters of network

50-2 Time (min)

25/0, 50/0, 75/0 wavelength

In this study, three sets of data from laboratory results in different powers of microwave

device including the relationship between changes in moisture and drying time was obtained

and with the results of 5 fitness of 5 different mathematical models were compared. Based on

evaluation of models, Henderson and "modified Pabys", February and binominal have the

Page 8: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 790

highest value of (R2) and the lowest value of (SSE) among the other models and showed

better results.

As is clear in Figs. 1 to 15, the results obtained from fitness of models show that the

mathematical model of Henderson and "Pabys reformed" were highly adapted to the

experimental results.

The results of mathematical modeling

1. The first category of results (time 2 to 50 minutes and power of 0/75)

Constant coefficients such as (a.b.c.n), using experimental data related to kinetics of aloe vera

drying and with curve fitness tool has been estimated in MATLAB software.

X1=Time

Y1=Proportion of moisture

1-1. Henderson and Pabys

f(x) = a*exp(b*x) Model

a = 58.66 (54.98, 62.33)

b = -0.02063 (-0.02361, -0.01766) Coefficients

SSE: 46.6

R-square: 0.9683

Adjusted R-square: 0.9648

RMSE: 2.275

Error

Page 9: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 791

Figure 1 The adaptation of the first category of experimental results with the model of

Henderson and Pabys

1-2. Binomial model

f(x) = a*exp(b*x) + c*exp(d*x) Model

a = 13.77 (1.274, 26.27)

b = -0.1674 (-0.5275, 0.1928)

c = 51.16 (36.13, 66.18)

d = -0.01647 (-0.02426, -0.008686)

Coefficients

SSE: 22.19

R-square: 0.9849

Adjusted R-square: 0.9784

RMSE: 1.78

Error

Figure 2 The adaptation of the first category of experimental results with the binomial model

1-3. Wang and sink models

f(x) = p1*x^2 + p2*x + p3 Model

p1 = 0.01162 (0.003919, 0.01931)

p2 = -1.311 (-1.718, -0.9046) Coefficients

Page 10: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 792

p3 = 59.59 (55.21, 63.98)

SSE: 41.81

R-square: 0.9716

Adjusted R-square: 0.9645

RMSE: 2.286

Error

Figure 3 The adaptation of the first category of experimental results with the Wang

and sink model

1-4. Henderson and "modified Pabys" model

f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-

b2)/c2)^2) + a3*exp(-((x-b3)/c3)^2) Model

a1 = 31.18 (-2.05e+09, 2.05e+09)

b1 = 3.427 (-4.502e+06, 4.502e+06)

c1 = 1.448 (-4.449e+07, 4.449e+07)

a2 = -7.192 (-826.9, 812.6)

b2 = 23.75 (-216.1, 263.6)

c2 = 17.63 (-632.2, 667.5)

a3 = 48.33 (-528.6, 625.3)

Coefficients

Page 11: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 793

b3 = 4.861 (-1027, 1037)

c3 = 51.11 (-1206, 1308)

SSE: 5.564

R-square: 0.9962

Adjusted R-square: 0.9811

RMSE: 1.668

Error

Figure 4 The adaptation of the first category of experimental results with the Henderson and

"modified Pabys" model

1-5. February Model

f(x) = a0 + a1*cos(x*w) + b1*sin(x*w) +

a2*cos(2*x*w) + b2*sin(2*x*w) Model

a0 = 1.015e+09 (-5.812e+14, 5.812e+14)

a1 = -1.353e+09 (-7.748e+14, 7.748e+14)

b1 = -5.245e+07 (-2.252e+13, 2.252e+13)

a2 = 3.379e+08 (-1.936e+14, 1.936e+14)

b2 = 2.622e+07 (-1.126e+13, 1.126e+13)

w = 0.0003024 (-43.3, 43.3)

Coefficients

Page 12: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 794

SSE: 16.98

R-square: 0.9885

Adjusted R-square: 0.9769

RMSE: 1.843

Error

Figure 5 The adaptation of the first category of experimental results with the February model

2. The second category of results (Time of 2 to 50 minutes and wave power of 0/5)

X1=Time

Y1=Proportion of moisture

2-1. Henderson and Pabys model

f(x) = a*exp(b*x) Model

a = 67.65 (63.32, 71.97)

b =-0.02246 (-0.0256, -0.01932) Coefficients

SSE: 62.28

R-square: 0.9708

Adjusted R-square: 0.9675

RMSE: 0.2733

Error

Page 13: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 795

Figure 6The adaptation of the second category of experimental results with the model of

Henderson and Pabys

2-2. Binomial model

f(x) = a*exp(b*x) + c*exp(d*x) Model

a = 22.55 (11.76, 33.34)

b = -0.3242 (-0.5958, -0.05254)

c = 60.3 (55.78, 64.81)

d = -0.01865 (-0.02112, -0.01619)

Coefficients

SSE: 7.934

R-square: 0.9963

Adjusted R-square: 0.9947

RMSE: 1.065

Error

Page 14: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 796

Figure 7 The adaptation of the seconf category of experimental results with the binomial

model

2-3. Wang and sing models

f(x) = p1*x^2 + p2*x + p3 Model

p1 = 0.01448 (0.00542, 0.02353)

p2 = -1.603 (-2.081, -1.124)

p3 = 68.55 (63.39, 73.71)

Coefficients

SSE: 57.9

R-square: 0.9728

Adjusted R-square: 0.966

RMSE: 2.69

Error

Page 15: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 797

Figure 8 The adaptation of the second category of experimental results with the Wang and

sink model

2-4. Henderson and "modified Pabys" model

f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-

b2)/c2)^2) + a3*exp(-((x-b3)/c3)^2) Model

a1 = 28.83 (-26.33, 84)

b1 = -2.686 (-17.44, 12.07)

c1 = 8.044 (-2.726, 18.81)

a2 = 49.42 (26.43, 72.42)

b2 = -2.116 (-55.05, 50.82)

c2 = 55.46 (3.204, 107.7)

a3 = 21.75 (-1.847e+08, 1.847e+08)

b3 = 47.45 (-1.846e+05, 1.847e+05)

c3 = 1.672 (-3.179e+06, 3.179e+06)

Coefficients

SSE: 0.2804

R-square: 0.9999

Adjusted R-square: 0.9993

RMSE: 0.3744

Error

Page 16: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 798

Figure 9 The adaptation of the second category of experimental results with the Henderson

and "modified Pabys" model

2-5. February Model

Figure 10 The adaptation of the second category of experimental results with the February

model

3. The first category of results (time 2 to 50 minutes and power of 0/75)

f(x) = a0 + a1*cos(x*w) + b1*sin(x*w) +

a2*cos(2*x*w) + b2*sin(2*x*w) Model

a0 = 6.763e+08 (-2.74e+13, 2.74e+13)

a1 = -9.015e+08 (-3.653e+13, 3.653e+13)

b1 = 2.102e+07 (-6.388e+11, 6.388e+11)

a2 = 2.252e+08 (-9.129e+12, 9.13e+12)

b2 = -1.051e+07 (-3.194e+11, 3.193e+11)

w = -0.0007582 (-7.681, 7.679)

Coefficients

SSE: 6.187

R-square: 0.9971

Adjusted R-square: 0.9942

RMSE: 1.112

Error

Page 17: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 799

X3=Time

Y3=Relative humidity

3-1. Henderson and Pabys model

f(x) = a*exp(b*x) Model

a = 63.66 (60.14, 67.18)

b = -0.02194 (-0.02463, -0.01925) Coefficients

SSE: 41.67

R-square: 0.9772

Adjusted R-square: 0.9746

RMSE: 2.152

Error

Figure 11 The adaptation of the third category of experimental results with the Henderson

and Pabys model

3-2. Binomial model

f(x) = a*exp(b*x) + c*exp(d*x) Model

a = 24.4 (-15.17, 63.97)

b = -0.5577 (-1.455, 0.3395)

c = 59.38 (55.28, 63.47)

Coefficients

Page 18: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 800

Figure 12 The adaptation of the third category of experimental results with binomial model

3-3. Wang and sink models

f(x) = p1*x^2 + p2*x + p3 Model

p1 = 0.01505 (0.009149, 0.02095)

p2 = -1.568 (-1.88, -1.256)

p3 = 65.17 (61.81, 68.53)

Coefficients

SSE: 24.57

R-square: 0.9865

Adjusted R-square: 0.9832

RMSE: 1.752

Error

Figure 13 The adaptation of the third category of experimental results with Wang and Singh

model

3-4. Henderson and "modified Pabys" model

f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-

b2)/c2)^2) + a3*exp(-((x-b3)/c3)^2) Model

a1 = 2.39e+17

b1 = -159.8

c1 =26.3

a2 = 0

b2 = -146.6

Coefficients

d = -0.01956 (-0.02206, -0.01707)

SSE: 10.84

R-square: 0.9941

Adjusted R-square: 0.9915

RMSE: 1.244

Error

Page 19: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 801

c2 = 0.7847

a3 = 3002 (-2.773e+06, 2.779e+06)

b3 = -430.6 (-9.307e+04, 9.221e+04)

c3 = 216.9 (-2.117e+04, 2.16e+04)

SSE: 12.05

R-square: 0.9934

Adjusted R-square: 0.967

RMSE: 2.455

Error

Figure 14 The adaptation of the third category of experimental results with Henderson and

modified Pabys" model

3-5. February Model

f(x) = a0 + a1*cos(x*w) + b1*sin(x*w) +

a2*cos(2*x*w) + b2*sin(2*x*w) Model

a0 = 4.658e+07 (-3.419e+12, 3.419e+12)

a1 = -6.207e+07 (-4.557e+12, 4.557e+12)

b1 = 2.229e+06 (-1.227e+11, 1.227e+11)

a2 = 1.548e+07 (-1.138e+12, 1.138e+12)

b2 = -1.113e+06 (-6.133e+10, 6.133e+10)

Coefficients

Page 20: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 802

w = -0.00115 (-21.11, 21.11)

SSE: 16.7

R-square: 0.9908

Adjusted R-square: 0.9817

RMSE: 1.828

Error

Figure 15 The adaptation of the third category of experimental results with February model

Table 4 summarizes the results obtained from the use of fitness of mathematical models and

their compatibility with experimental data has been collected. As previously mentioned,

Henderson and "modified Pabys" model, binomial and February have the highest valueof (R2)

and the lowest value of (SSE) among the other models and showed better results and

mathematical model of Henderson and "modified Pabys " had the most conformity with the

experimental results.

Table 4Constants of the fitness of used mathematical models with neural networks and their

compatibility with the experimental results

Wave power 25/0 50/0 75/0

model name R2 SSE R

2 SSE R

2 SSE

Henderson

and Pabys 9683/0 6/46 9708/0 28/62 9772/0 67/41

Binomial 9849/0 19/22 9963/0 934/7 0/9941 84/10

Wang and

sink 9716/0 81/41 9728/0 9/57 9865/0 57/24

Page 21: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 803

February 9885/0 98/16 9971/0 187/6 9908/0 7/16

Henderson

and

modified

Pabys

9962/0 564/5 9999/0 2804/0 9934/0 05/12

Conclusion

Choose an appropriate method for drying aloe vera can be led to improve the final quality of

the product. The main purpose of drying products with higher storage capacity is lower cost

of packaging and transportation costs. Choose an appropriate method for drying can lead to

improve the final quality of the product.

The inner part of the aloe vera leaf green which is separated from shell been is called aloe

vera gel. In recent years the use of this gel in the cosmetic industry and in the formulation of

food has increased extensively. Aloe Vera is from Lilies family. More than 98-99 percent

aloe gel is composed of water and 60 percent of it’s solids is polysaccharide.

Today use of computer models due to higher accuracy and speed than many classical,

experimental and laboratory methods, in many developed countries has been taken into

consideration and is used in industries. One of the important issues that researchers and

scientists of decision-making are faced with is the selection of the influencing variables on

the output model. Because of the limitations of the present study do not allow all the

identified variables for the decision and prediction the model that is designed to this purpose

be used, and on the other hand since all identified variables will not necessarily have the

appropriate effect on output, therefore, the adoption of procedures for screening incoming

data to decision-making and prediction based on the logic of mathematical models is very

important.

In this study, the feasibility of using microwave method for drying aloe vera and effective

parameters on drying were evaluated. Experiments in three powers (0.25, 0.50 and 0.75

watts) and in the range of 5 to 50 minutes were done (Table 3).

The results of the fitness of models show that the mathematical model of Henderson and

"modified Pabys" and Binomial model have the best results in compliance with experimental

results and Henderson mathematical model and "modified Pabys" was highly adapted to the

experimental results. The results of the model is partly resembles to result of work Arentark

(2007).

Also, designed experiments in this study could also answer the following questions:

1. Is there any optimal time to microwave radiation for drying slices of aloe vera?

Page 22: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 804

Due to the sharp increase in the drying rate during the period of sample warming in the

microwave method, it is inferred, consecutive doing of this method in a short time can lead to

a product with confident moisture.

2. Is the microwave power can have an important role in accelerating drying fruit of aloe

vera?

Drying speed in microwave method for sun dried samples in the same moisture values (about

22 percent based on dry weight)is 10 times more than displacement method. In addition, the

maximum speed of drying in the microwave method is much more than displacement

method.

In addition, in all three microwave powers, the time required to reduce the equal value

without the dimensionless, is 2.8 times less than the time needed to reduce moisture, in

displacement method.

Considering the drying time, the effective rate of moisture penetration and indexes of color, it

seems that the microwave method is optimal method under controlled conditions.

3. What is the maximum power in which drying process is done without creating a

negative impact on the appearance of slices of Aloe Vera?

Though effective rate of moisture penetration in higher power level is greater, too much

drying reduces product quality.

4. Can the microwave method, be used as the primary method for drying aloe veraor is a

way to primary preparation of drying process?

Considering the sharp increase in the drying rate during the period of sample warming in the

microwave method, it is inferred, consecutive doing of this method in a short time can lead to

a product with confident moisture.

Of course, the process of economic study is a research necessity in this field. Also examining

the combined drying process and qualitative experiments of the final product showed that the

use of microwave energy as final drying process can have different important and desirable

aspects and this method can improve significantly qualitative parameters such as color,

rehydration and including the amount of vitamin C as well as reducing drying time.

5. If you use the microwave as the main method for drying aloe vera, what effect of

oven temperature during the preparation of the initial drying process on the drying

process?

The oven temperature has a direct impact on the speed of drying of sample.

Page 23: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 805

References

Lawless, J. and Allan. J., 2000. Aloe vera––natural wonder cure. London: Harper Collins

Publishers.

Reynolds T. Aloes; The genus Aloe. Medicinal and Aromatic plants-Industrial Profile. s,

2004.

Choi SW, Son BW, Son YS, Park YI, Lee SK, Chung MH. The wound-healing effect of a

glycoprotein fraction isolated from aloe vera. Br J Dermatol. 2001; 145(4): 535-45.

Snežana S. Anti-genotoxic effect of aloe veragelR on the mutagenic action of ethyl

methanesulfonate. Arch Biol Sci. 2007; 59(3): 223-6.

Rabe T, van Staden J. Antibacterial activity of South African plants used for medicinal

purposes. J Ethnopharmacol. 1997;56(1):81-7.

Pugh N, Ross SA, Elsholy MA, Pasco DS. Characterisation of Aloeride, a new high-

molcular-weight polysaccharidefrom Aloe vera with potent immune stimulatory activity.

JAgric Food Chem 2001; 49(2): 1030-40.

Maskan, M. 2000. Microwave/air and microwave finish drying of banana. Journal of Food

Engineering.,44: 71-78.

Akpinar, K., Bicer, Y., and Cetinkay, F. 2006. Modelling of thin layer drying of parsley

leaves in a convective dryer and under open sun. Journal of Food Engineering, 3: 308-315.

Maskan, M. 2001. Drying shrinkage and rehydration characteristics of kiwi fruits during hot

air and microwavedrying. Journal of Food Engineering 35: 267-280.

AOAC. (2002). Official Methods ofAnalysis. 17th Ed. Association of Official Analytical

Chemists. Gaithersburg. Maryland.USA.

Stroshine, R. and Hamann, D. (1994).Physical properties of agricultural material and food

products. West Lafayette: Dept of Agricultural Engineering Purdue University USA.

Kubilay, V. Hasim, K. Serkan, S. (2006). A Study on Some Chemical and Physico-Mechanic

Properties of Three Sweet Cherry Varieties. Journal of Food Engineering.74:568–575.

Zyrjany, L., Tavakolipour, h., In 2010. The study of banana production possibility by using a

combination of hot air and microwave drying method. Journal of Food Science and

Technology Research, 6 (1), 0.58-67

Alibas, I. 2007. Microwave, air and combined microwave–air-drying parameters pumpkin

slice. Journal of Food Science and Technology, 8: 1445-145.

Abbasi, S. and S. Rahimi, 2007. Microwave and it application in food industries Sonboleh.,

20(163): 28-29.

Mertens, B. and D. Knorr. 1992. Developments of non thermal processes for food

preservation. FoodTechnology., 46(5): 124-133.

Prothon., Funebo, T., Kidman, S. and M., Langton. 2001. Effects of combinated Osmotic and

Microwave Dehydration of Apple on Texture, Microstructure and Rehydration

Characteristics. Lebensm-Wiss, u-Techno. 34: 95-101.

Maskan, M. 2001. Drying, shrinkage and rehydration characteristics of kiwifruits during hot

air and microwave drying. Journal of Food Engineering. 48: 177-182.

Page 24: The study of parameters that affect on drying process of

Special Issue

December 2015

INTERNATIONAL JOURNAL OF HUMANITIES AND

CULTURAL STUDIES ISSN 2356-5926

http://www.ijhcs.com/index.php/ijhcs/index Page 806

Funebo, T. Kidman, S and M., Langton. 2000. Microwave heat treatment of apple before air

dehydration effects on physical properties and microstructure, Journal of Food Engineering

46: 173-182.

Adabi, M.A, Mousavi Seyedi, Kalantari, d., Taghizadeh, A., 2016 , The investigation of some

changes to the qualitative properties of aloe vera gel in re-circulation of warm air drying

method (desiccant), Journal of Food Science and Technology, Issue 54, Volume 13, 85-93.

Crank J. 1975. Mathematics of diffusion (2nd ed.) London: Oxford University Press. 414 pp.