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

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Experimental and Numerical Investigations of Moisture
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
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.

Key Words:
Drying; Finite element method; Moisture diffusion; Pistachio nut


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.
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):

time step, t and a given set of nodal values, { }i
a set
div(D?X ) , in the domain of grain, ? ,t > 0 (1)
i +
of nodal moisture values {X } 1 were obtained and stored.

The results of formulation used to model drying of a
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

step t
? was 1s.
, at the nut surface,
,t > 0 (2)

= h ( X ? X )
Thin layer drying data of pistachio nuts. The pistachio

nuts were sliced for thin layer drying. The experiments were
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
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,
? >0 (3)
N ]
? ? X
? X ? ?X ?
continued until the moisture content (w.b.%) of the sample
? ? = 0
? ? ?r
?z ? ?t ?
was reduced to 5%. The average moisture content of the

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
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
nuts only a quarter of pistachio nut was modeled.

Consequently, a finite element computer code for predicting
K {X }
? • ?
+ C ? X ? ? F = 0 ( )
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

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
? K +
? X
X n + F ( )
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


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

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%

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


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
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. Agric., 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

Cereal Chem., 77: 708?13
Segerlind, L.J., 1984. Applied Finite Element Analysis, 2nd Edition. John
Wiley and Sons, New York

Casada, M.E. and J.H. Young, 1994. Model for heat and moisture transfer in
Sacilik, K., R. Keskin and A.K. Elicin, 2006. Mathematical modelling of
arbitrarily shaped two- dimensional porous media. Trans. ASAE, 37:
solar tunnel drying of thin layer organic tomato. J. Food Eng., 73:
Cnossen, A.G. and T.J. Siebenmorgen, 2000. The glass transition
Sokhansanj, S. and D.M. Bruce, 1987. A conduction model to predict grain
temperature in rice drying and tempering: Effect on milling quality.
temperature in grain drying simulation. Trans. ASAE, 30: 1181–4
Trans. ASAE, 23: 1661–7
Wu, B., W. Yang and C.A. Jia, 2004. Three-dimensional Numerical
Ertekin, C. and O. Yaldiz, 2004. Drying of eggplant and selection of a
simulation of Transient Heat and Mass Transfer inside a Single Rice
suitable thin layer drying model. J. Food Eng., 63: 349–59
Kernel during the Drying Process. Bio-systems Eng., 87: 191–200
Fortes, M., M.R. Okos and J.R. Barrett, 1981. Heat and mass transfer
Yang, W., C. Jia, T.J. Siebenmorgen and A.G. Cnossen, 2000. Intra–kernel
analysis of intra-kernel wheat drying and re-wetting. J. Agric. Eng.
moisture gradients and glass transition temperature in relation to
Res., 26: 109–25
head rice yield variation during heated air drying of rough rice. In:
Gaston, A.L., R.M. Abalon and S.A. Giner, 2002. Wheat drying kinetics.
P.J.A.M. Kerkhof, W.J. Coumans and G.D. Mooiweer (eds.), Proc.
Diffusivities for sphere and ellipsoid by finite element. J. Food Eng.,
12th Int’l Drying Symp. Osium IDS2000, P: 069. 28–31 August.
52: 313–22
Elsevier Science. Noordwijkerhout, The Netherlands
Haghighi, K. and L.J. Segerlind, 1988. Modeling simultaneous heat and
Yang, W., C. Jia, T.J. Siebenmorgen and A.G. Cnossen, 2003. Relationship
mass transfer in an isotropic sphere- a finite element approach.
of kernel moisture content gradients and glass transition temperatures
Trans. ASAE, 31: 629–37
to head rice yield. Bio-systems Eng., 85: 467–76
Haghighi, K., J. Irudayaraj, R.L. Stroshine and S. Sokhansanj, 1990. Grain

kernel drying simulation using the finite element method. Trans.
(Received 29 November 2006; Accepted 13 December 2006)
ASAE, 33: 1957–65