# Experimental and Numerical Investigations of Moisture Diffusion in Pistachio Nuts during Drying with High Temperature and Low Relative Humidity

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INTERNATIONAL JOURNAL OF AGRICULTURE & BIOLOGY

1560–8530/2007/09–3–412–415

http://www.fspublishers.org

**Experimental and Numerical Investigations of Moisture**

Diffusion in Pistachio Nuts during Drying with High

Temperature and Low Relative Humidity

SHAHIN RAFIEE1, ALI JAFARI, MEHDI KASHANINEJAD† AND MAHMOUD OMID

Diffusion in Pistachio Nuts during Drying with High

Temperature and Low Relative Humidity

*Faculty of Biosystem Engineering, University of Tehran, P.O. Box 4111, Postal Code 31587-11167, Karaj, Iran*

†

*Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran*

1Corresponding author's e-mail: [email protected]

**In this study, a numerical solution based on finite element (FE) is adopted to simulate the mass distribution inside a pistachio**

ABSTRACT

ABSTRACT

nut (cv. Ohadi). It was found that the FE solution of the diffusive moisture transfer equation could improve nut-drying

simulation of axisymmetric bodies. An axisymmetric linear triangular element with two degree of freedom per node was used

to discretize the pistachio nut in the model. A thin layer pistachio nut was dried at two drying air temperatures of 55 and 70°C

under constant air velocity and relative humidity and moisture content was measured every minute. The simulation data were

tested using values obtained from thin layer drying experiments. Comparison showed that the simulation program gave good

prediction for moisture content variations during the drying process. Results showed that there was no constant-rate drying

period and the whole drying process occurs during the falling rate period. The moisture distribution inside the individual

pistachio nuts was predicted using the model at five selected periods of 5, 10, 20, 50 and 100 min with drying air temperatures

of 55 and 70°C. The results showed that distribution of the moisture content inside kernels was non-uniform. The moisture

content at the center and surface of kernels reduced slowly and very rapidly respectively.

**Drying; Finite element method; Moisture diffusion; Pistachio nut**

Key Words:

Key Words:

INTRODUCTION

INTRODUCTION

*et al.*, 2003). Therefore, it is important to examine the

internal behavior of a single nut in order to improve the

Artificial drying is one of the most important stages of

drying process and product quality. Because of the small

pistachio nut processing. Many theoretical and experimental

size of kernels, internal changes in temperature and moisture

studies have been conducted to describe the drying process

cannot easily be measured. Computer simulation is a

of agricultural products (Ertekin & Yaldiz, 2004; Sacilik

*et*

powerful tool for achieving this goal. The increasing

*al.*, 2006). Luikov developed a mathematical model for

development of special professional software had a great

describing the drying of porous media (Husain

*et al*., 1972).

impact on the design of dryers and quality evaluation of

Some researchers, while applied Luikov's model to grain

agricultural products. Much work has been done to simulate

drying (Nemenyi

*et al.,*2000) concluded that consideration

the temperature, moisture content and stress distributions

of the coupling effects of temperature and moisture in the

inside single grain kernels (Cnossen & Siebenmorgen,

analysis of grain drying is not required for engineering

2000; Jia

*et al.*, 2000; Perdon

*et al.*, 2000; Yang

*et al.*, 2000,

practice (Husain

*et al.,*1973). Jia

*et al.*(2000) combined

2003; Wu

*et al*., 2004), but there is no information about

Luikov’s model and considered the effects of thermal

simulation of moisture diffusion in pistachio nut.

behavior of grain, internal temperature and moisture

Ohadi variety is one of the major pistachio nut

gradients, which increased the drying simulation accuracy.

varieties that is grown in Iran. Therefore, this cultivar was

Fortes

*et al.*(1981) proposed a model for grain drying,

selected in this study. In this study, the simulation of Ohadi

which assumed that the liquid form of moisture diffused to

variety drying was modified by the experimental data of the

the outer boundary of the kernel and evaporated on the

thin layer drying and mass transfer within pistachio nut

surface of the grain. This assumption was supported by

during drying. The moisture content distribution inside the

wheat drying experiments in other studies (Sokhansanj &

kernel at five selected times (5, 10, 20, 50 & 100 min) under

Bruce, 1987). However, some assumptions, such as constant

drying air temperatures of 55 and 70°C was simulated.

diffusion coefficient and material properties for simplifying

calculations could affect the simulation accuracy.

**MATERIALS AND METHODS**

The drying behavior, as described by moisture,

temperature and stress distributions inside a kernel during

For pistachio nut drying simulation, the Fick’s

drying and the quality traits of individual grain kernels

diffusive equation describing the mass transfer process was

affect the overall quality of the grain dried in a dryer (Yang

applied (Jia

*et al*., 2000):

MOISTURE DIFFUSION IN PISTACHIO NUTS UNDER VARYING ENVIRONMENTS /

*Int. J. Agri. Biol., Vol. 9, No. 3, 2007*

*X*

?

?

=

time step,

*t*and a given set of nodal values, { }

*i*

*X*

a set

*div*(

*D*?

*X*) , in the domain of grain, ?

*,t*> 0 (1)

*i*+

*t*

?

of nodal moisture values {

*X*} 1 were obtained and stored.

The results of formulation used to model drying of a

Where

pistachio nut can be compared with experimental data. The

X is the moisture content (d.b.); D is the diffusion

differential equation for mass transfer (Equation 1) can

coefficient (m2/s); and t is time (s). The following initial

predict the moisture distribution within the nut.

(IC) and boundary (BC) conditions were used:

The pistachio nut was modeled with a two-

**IC: X = X**

?

dimensional axisymmetric finite element grid. Each grid

i, in the domain of nut,

,

*t*= 0

consisted of 1600, 3-node elements, 861 nodes and time

BC:

?

*X*

?

step

*t*

? was 1s.

?

, at the nut surface,

*,t*> 0 (2)

*D*

=

*h*(

*X*?

*X*)

*m*

*s*

*e*

?

*n*

**Thin layer drying data of pistachio nuts.**The pistachio

**Where**

nuts were sliced for thin layer drying. The experiments were

X

conducted at two different drying air temperatures (55 &

i, Xs and Xe are initial, surface and equilibrium

moisture content of the nuts, respectively. In equation (2),

70ºC). Throughout the experiments the air velocitiy and

h

relative humidity (RH) were maintained at 1.5 m/s and 5%,

m is surface moisture transfer coefficient and n is outward

normal at the nut surface. Using a 2D Galerkin's model in

respectively. To reduce experimental errors, each test was

performed in triplicate. The ambient, up-stream and down-

cylindrical coordinate (r, ? , z) (Segerlind, 1984), equation

stream dry bulb temperatures, air relative humidity, air

1 was rewritten as:

velocity and sample weight were continuously monitored

and the data were recorded every 60s (Fig. 1). Drying was

[

, at the nut surface,

*t*

*,*

? >0 (3)

*N*]

2

2

?

*T*

? ?

*X*

?

*X*? ?

*X*?

?

?

*D*

+

?

*d*

continued until the moisture content (w.b.%) of the sample

?

?

?

?

?

? ? = 0

2

2

? ? ?

*r*

?

*z*? ?

*t*?

was reduced to 5%. The average moisture content of the

**Where**

samples during each weighing period was calculated, based

[

on the initial mass and final moisture content of the samples.

*N*] is the shape function matrix and r and z are

After each drying experiment, the samples were oven-dried

cylindrical components. In conventional drying, the surface

at 103 ± 2ºC to determine the moisture content

of the nut exchanges heat with the environment via

(Kashaninejad & Tabil, 2004).

convection, while the internal part of the nut is heated by

conduction. For modeling a mathematical mass transfer in

nut, it was assumed that liquid diffusion of moisture to the

**RESULTS AND DISCUSSION**

outer boundaries of the nut and evaporation only at the

Equation (5) was solved numerically in order to

surface of nut. After some mathematical steps and replacing

predict moisture distributions within the pistachio nuts

the notation ? , with the two-dimensional space, A, the

during drying. Nodal moisture values were calculated

following system of first-order differential equations can be

during drying. Because of inherent symmetry of pistachio

written:

nuts only a quarter of pistachio nut was modeled.

Consequently, a finite element computer code for predicting

*K*{

*X*}

? • ?

+

*C*?

*X*? ?

*F*= 0 ( )

4

the moisture fields inside a quarter of pistachio nut was

? ?

developed using Fortran-90 language. Good agreements

were observed when the output of the model was compared

**Where**

to the experimental data. The Mean Relative Deviation

K is the global moisture conductance matrix, C is the

between simulation values for modified moisture diffusivity

global moisture capacitance matrix and F the load vector.

and experimental thin layer drying at drying air

The forward difference method is used to approximate{

*X*},

temperatures of 55 and 70°C, were 0.0824 and 0.1039,

therefore equation (4) is rewritten as:

respectively. This confirmed that simulated results were

very close to experimental data. Similar results have been

?

*C*?

reported by other researches for wheat (Jia

*et al.*, 2000;

*n*+1

*C*

?

*K*+

?

*X*

=

*X n*+

*F*( )

5

?

?

Gaston

*t*?

?

*t*

*et al.*, 2002), peanut (Casada & Young, 1994),

maize (Jia

*et al.*, 1996) and rough rice (Yang

*et al*.,

2000, 03).

A computer program for a two-dimensional transient

Drying rates of pistachio nut at 55 and 70°C drying air

field problem such as the one described by equation (5) was

temperature were also calculated (Fig. 2 & 3). A closer look

written by Segerlind (1984). The effect of moisture content

at the results shown in these figures reveals that there is no

for each time step was modified for use of axially

constant-rate drying period and all the drying processes

symmetric triangular elements. This new program first

occur during the falling rate period. During the first 20 min

solves equation (5) for given initial nodal values. For every

the simulated values for drying air temperature of 55°C was

413

RAFIEE

*et al*. /

*Int. J. Agri. Biol., Vol. 9, No. 3, 2007*

**Fig. 1. Diagram of thin layer dryer**

that the predicted values were lower than the experimental

values. Drying decreased rapidly for the first 15 min and

was slowed down thereafter.

From the practical point of view, it is important to

know the temperature and moisture distributions of nuts

during drying, because combinations of moisture and

temperature gradients would produce greater stress levels in

nut. In order to examine the moisture and thermal stresses in

details, it is imperative to find the temperature and moisture

distributions of nuts (Fortes

*et al.,*1981; Haghighi &

Segerlind, 1988). Fig. 4 and 5 show the moisture content

distributions inside the nuts at five selected times (5, 50,

100, 200 & 400 min) under drying air temperatures of 55

and 70°C, respectively. At initial stage of drying, nut’s

**Fig. 2. Variation of drying rate with drying time and**

surface moisture content was decreased quickly and then

**initial moisture content of 59.13% (d.b.), T = 55**°

**C**

**Fig. 4. Moisture distributions inside pistachio nuts at**

**and RH = 5%**

**selected drying times for X**

**i= 59.13% (d.b.), T = 55**°

**C**

**and RH = 5%**

**°**

Fig. 3. Variation of drying rate with drying time and

initial moisture content of 55.28% (d.b.), T = 70

Fig. 3. Variation of drying rate with drying time and

initial moisture content of 55.28% (d.b.), T = 70

**C**

**and RH = 5%**

**Fig. 5. Moisture distributions inside pistachio nuts at**

**selected drying times for Xi = 55.28% (d.b.), T = 70**°

**C**

and RH = 5%

and RH = 5%

a bit higher than the experimental values and this trends was

reversed afterwards. Similar trends during the first 25 min

were shown for the drying air temperature of 70°C and after

414

MOISTURE DIFFUSION IN PISTACHIO NUTS UNDER VARYING ENVIRONMENTS /

*Int. J. Agri. Biol., Vol. 9, No. 3, 2007*

slowly. But nut’s center moisture content in first stage was

Husain, A., C.C. Sun and J.T. Clayton, 1973. Simultaneous heat and mass

constant and then decreased. The moisture distribution for

diffusion in biological materials.

*J. Agric. Eng. Res*., 18: 343–54

Husain, A., C.S. Chen, J.T. Clayton and L.F. Whitney, 1972. Mathematical

different drying times was reported within a single kernels

simulation of heat and mass transfer in high–moisture foods.

*Trans.*

of wheat (Jia

*et al.,*2000), maize (Nemenyi

*et al.,*2000) and

*ASAE,*15: 732–6

barley (Haghighi

*et al.,*1990).

Jia, C., D. Sun and C. Cao, 2000. Mathematical simulation of temperature

and moisture fields within a grain kernel during drying.

*Drying*

**CONCLUSIONS**

*Technol*., 18: 1305–25

Jia, C, Y. Li, D. Liu and C. Cao, 1996. Mathematical simulation of the

moisture content distribution within a maize kernel during

The simulated moisture content of the pistachio nut’s

tempering.

*Trans. Chinese Soc. Agric. Eng*., 12: 147–51

center showed that the times to reach 10% moisture content

Kashaninejad, M. and L.G. Tabil, 2004. Drying characteristics of purslane

(from initial moisture content at drying air temperatures of

(

*Portulace oleraceae*L.).

*Drying Technol*., 22: 2183–200

55 & 70ºC) were 1660 and 640 min, respectivly. The

Nemenyi, M., I. Czaba, A. Kovacs and T. Jani, 2000. Investigation of

simultaneous heat and mass transfer within the maize kernels during

moisture content distribution of the pistachio nut’s surface

drying.

*Comp. Elec. Agr*ic., 26: 123–35

becomes dry very rapid and that of nut’s center is slow.

Perdon, A.A., T.J. Siebenmorgen and A. Mauromoustakos, 2000. Glassy

Therefore, it cause wide moisture gradient in the nut.

state transition and rice drying, Development of a brown rice state

diagram.

*Cereal Chem*., 77: 708?13

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