- Email: [email protected]
Drying kinetics of prickly pear fruit (Opuntia ficus indica)
Journal of Food Engineering 61 (2004) 173–179 www.elsevier.com/locate/jfoodeng
Drying kinetics of prickly pear fruit (Opuntia ficus indica) S. Lahsasni a, M. Kouhila b
b,*
, M. Mahrouz a, J.T. Jaouhari
b
a Unit e de Chimie Agroalimentaire (LCOA), Facult e des Sciences Semlalia, BP 2390, Marrakech, Morocco Laboratoire d’Energie Solaire et Plantes Aromatiques et M edicinales, Ecole Normale Sup erieure, BP 2400, Marrakech, Morocco
Received 24 October 2002; accepted 12 March 2003
Abstract The present work examines the effect of drying air conditions on drying kinetics of the prickly pear fruit in a convective solar drier operating with an auxiliary heating system under air controlled conditions. Moreover, the prickly pear fruits are sufficiently dried in the ranges between 32 and 36 °C of ambient air temperature, 50–60 °C of drying air temperature, 23–34% of relative humidity, 0.0277–0.0833 m3 /s of drying air flow rate and 200–950 W/m2 of solar radiation. The results verified with good reproducibility that drying air temperature is the main factor in controlling the drying rate and the experimental drying curves show only a falling rate period. The expression of the drying rate equation is determined empirically from the characteristic drying curve. Eight different thin layer drying models were compared according to their coefficients of determination to estimate solar drying curves. The two-term model was found to satisfactorily describe the solar drying curves of prickly pear fruit with a correlation coefficient (r) of 0.9999. The constants and coefficients of this model could be explained by the effect of drying air temperature with a correlation coefficient (r) of 1.0000. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Characteristic drying curve; Drying curves; Modeling; Prickly pear fruit; Solar dryer
1. Introduction The cactus pear (prickly pear) grows in all parts of the American continent, from southern Canada to Patagonia, and in the course of time has been cultivated in different areas of Europe, particularly in the Mediterranean countries, as well as in Africa and Australia. Many different species of Opuntia are grown in Mexico for fruit production whereas in Italy and the Mediterranean region in general, Opuntia ficus indica is cultivated. Thanks to its ability to adapt to different environmental conditions, the cactus pear grows in plains, coastal regions, plateaus and among diverse vegetation. A common feature of the areas where the plant grows is a more or less marked degree of aridity to which the plant has adapted thanks to its CAM photosynthetic metabolism (Feitosa-Teles, 1977). Prickly pear fruit is a fleshy, and polyspermic unilocular berry. The major components of the fruit pulp are 85% of water, 10–15% of carbohydrates, and substantial amounts of vitamin C, 0.025–0.030% (Gurrieri et al.,
2000). Its nutritional value lies essentially in its glucose and fructose content (6–8%) (Habibi, Mahrouz, & Vignon, 2002). The level of ascorbic acid is moderate (0.023%); and acidity is low (0.06%). The prickly pear can be used in many ways in diverse sectors, utilizing different parts of the plant. In the food sector, besides consumption of the fresh fruit, jams, alcoholic, soft drinks, syrups, candied fruit, and flour can be produced from the plant and oil extracted from the seeds. The vegetable stems (cladode) and fruits of prickly pear are useful to treat diabetes, high blood cholesterol levels, inflammation and obesity (Galati, Monforte, Tripodo, dÕAquino, & Mondello, 2001; Park, Kahng, Lee, & Shin, 2001). The objectives of the study were to determine the effect of drying air temperature and air flow rate on the drying kinetics of the prickly pear fruit, and to select the best mathematical model for the drying curves.
2. Materials and methods 2.1. Materials
*
Corresponding author. Tel.: +212-44-34-07-89; fax: +212-44-3422-87. E-mail address: [email protected] (M. Kouhila). 0260-8774/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00084-0
The prickly pear fruit used in the drying experiments was grown in the region of Bengrir (near the town of
174
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Nomenclature CDC characteristic drying curve ðdM=dtÞ0 initial drying rate (kg water/(kg dry matter min)) dM=dt drying rate at any time of drying (kg water/ (kg dry matter min)) Dv drying air flow rate (m3 /s) Exp experiment f dimensionless drying rate M moisture content at any time of drying (kg water/kg dry matter) Mf final moisture content (kg water/kg dry matter) Me equilibrium moisture content (kg water/kg dry matter)
Marrakech). Harvest period was between June and October 2002. Marrakech is situated 140 km east of the Atlantic, north of the High Atlas. Its geographic coordinates are 8° 20 west, 31° 370 north and 463 m over the sea level. Summer in Marrakech is hot and dry while winter is temperate and humid with occasional rains (Idlimam, Kaoua, Alem, & Daguenent, 1994). The experimental apparatus consists of an indirect forced convection solar dryer with a solar air collector, an auxiliary heater, a circulation fan and a drying cabinet as shown in Fig. 1. The solar air collector had dimensions of 1 m by 2.5 m. A corrugated galvanised iron sheet painted black was used as an absorber plate for absorbing the incident solar radiation. It was oriented southward under the collector angle of 31°. This angle
Fig. 1. Schematic representation of the solar dryer. (1) Solar collector; (2) direction of fan; (3) fan; (4) direction of aspiration; (5) control-box; (6) auxiliary heating system; (7) shelves; (8) drying cabinet; (9) recycling air; (10) control foot; (11) exit of air; (12) humidity probes; (13) thermocouples.
MR M0 N n r Rh Sr t T v
moisture ratio initial moisture content (kg water/kg dry matter) number of observations number of constants correlation coefficient relative humidity (%) standard error drying time (min) drying air temperature (°C) reduced chi-square
was fixed by the control foot. A glass and plastic sheet was used as a transparent cover for the air heater to prevent the top heat losses. The frame was made of wood. The drying cabinet was constructed with insulted walls (dimensions, 1.40 m (length), 0.5 m (width), and 0.90 m (depth)) and has 10 shelves. A centrifugal ventilator (0.0833 m3 /s; 80 mm CE, 220 V) connected to the north side of the drying cabinet provides a maximum air velocity of 1.7 m/s and allowed to vary the drying air flow rate from 0.0227 to 0.0833 m3 /s. The circulation fan to supply fresh air has a power of 0.1 kW. The auxiliary heater has a power of 4 kW. It was connected to the inlet of control box. 2.2. Experimental procedure The drying materials were cut in the bits of 1 0.1 g weight. The major diameter and length were 0.5 0.01 cm, and 2 0.03 cm, respectively. The loading density of the drying trays was 3 kg/m2 for prickly pear fruit. In the experiments, the 2nd and 10th shelves were not selected for the efficient utilisation of drying air. However, the samples were uniformly spread evenly on a drying tray that was then placed on the first shelf of the drying cabinet. The heated air enters the drying cabinet below the trays and flowed upwards trough the samples. The amounts of solar radiation were measured with KipZonen solarmeter. Temperature measurements and recordings at different points in the solar dryer were made by Cr–alumel thermocouples (0.2 mm diameter) connected to a data-logger enabling 0.1 °C accuracy and the outlet temperatures were measured with thermometer. The relative humidities were measured by capacitance sensors. These values were determined by probes Humicolor 2%. A digital weighing apparatus (0.001 g) measures the mass loss of the product during the drying process.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
2.3. Fitting of the solar drying curves Nine experiments of prickly pear fruit were performed by using the solar drying at T ¼ 50, 55, and 60 °C, and Dv ¼ 0:0227, 0.0556, and 0.0833 m3 /s which correspond to the average velocity of drying air in the drying cabinet 0.5667, 1.1333 and 1.7 m/s, respectively. The solar drying curves were fitted with eight different moisture ratio equations (Table 1) (Basunia & Abe, 2001; Hassan & Hobani, 2000; Jayas, Cenkowski, Pabis, & Muir, 1991; Mujumdar, 1987; Togrul & Pehlivan, 2002; Yaldiz & Ertekin, 2001; Yaldiz, Ertekin, & Uzun, 2001). The moisture ratio MR can be calculated as: MR ¼
M Me M0 Me
ð1Þ
It is particularly emphasized that the correlation coefficient r is one of the primary criteria to select the best equation to account for the variation in the solar drying curves of the dried samples (Midilli & Kucuk, 2003). In addition to r, the reduced chi-square (v2 ) was used to determine the best of the fit (Togrul & Pehlivan, in press). Chi-square can be calculated as: PN ðMRexp;i MRpre;i Þ2 2 ð2Þ v ¼ i¼1 N n where MRexp;i is the ith experimental moisture ratio, MRpre;i the ith predicted moisture ratio, N the number of observations and, n the number of constants. Table 1 Mathematical models applied to the drying curves Model name
Model
Newton Page Modified Page Henderson and Pabis Logarithmic Two-term Two-term exponential Wang and Singh
MR ¼ expðktÞ MR ¼ expðktn Þ MR ¼ expððktÞn Þ MR ¼ a expðktÞ MR ¼ a expðktÞ þ c MR ¼ a expðk0 tÞ þ b expðk1 tÞ MR ¼ a expðktÞ þ ð1 aÞ expðkatÞ MR ¼ 1 þ at þ bt2
175
In this study, the relationship between the drying air temperature and the coefficients of the best suitable model was also determined. In order to determine the most suitable model for prickly pear fruit, MarquardtLevenberg non-linear optimisation method, using the computer program ‘‘curve Expert 3.1’’ was used.
3. Results and discussion The solar drying experiments were carried out during the period of June and July 2002 in Marrakech, Morocco. Each experiment started at 8:30 a.m. and continued until 6:00 p.m. A total of nine drying experiments were run at different air conditions. During the experiments, solar radiation changed between 200 and 950 W/m2 , ambient air temperature ranged from 32 to 36 1 °C, ambient air relative humidity from 23 to 34 2%, inlet drying air temperature from 50 to 60 0:1 °C, and drying air flow rate from 0.0227 to 0:0833 0:002 m3 /s. The initial moisture content of the prickly pear fruit ranged from 5.9719 to 4.9336 kg water per kg dry matter and was reduced to the final moisture content which varies from 0.0722 to 0.0297 kg water per kg dry matter (Table 2). 3.1. Determination of the drying curves Fig. 2 shows the hourly variation of the measured solar radiation of a typical summer day (23 June 2002). The moisture content versus drying time and the drying rate versus moisture ratio are shown in Figs. 3 and 4, respectively. The constant rate period is absent in the solar drying of prickly pear fruit. The drying process took place in the falling rate period. Drying rate decreases continuously with diminishing moisture ratio. These results are in agreement with the observations of earlier researchers (Bellegha, Amami, Farhat, & Kechaou, 2002; Kouhila, 2001). Drying during the falling rate period is so governed by water diffusion in the solid. This is a complex mechanism involving water in both liquid and vapour states, which is very often
Table 2 Drying conditions during experiments in the solar dryer Experiment number
Dv 0:002 (m3 /s)
Inlet T 0:1 (°C)
Outlet Rh 2 (%)
M0 (kg/kg dry matter)
Me (kg/kg dry matter)
Mf (kg/kg dry matter)
t (min)
1 2 3 4 5 6 7 8 9
0.0227 0.0227 0.0227 0.0556 0.0556 0.0556 0.0833 0.0833 0.0833
50 55 60 50 55 60 50 55 60
42 46 38 38 31 36 32 35 30
5.4302 5.9719 5.5468 5.2920 4.9336 4.9702 5.4034 5.4778 5.4484
0.2536 0.4026 0.2317 0.2375 0.2067 0.2221 0.2106 0.2239 0.1948
0.0722 0.0679 0.0411 0.0297 0.0535 0.0410 0.0348 0.0384 0.0407
476 315 265 425 272 225 285 225 195
176
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
3.2. Influence of temperature and air flow rate
800 600 400 200 0 6
8
10
12
14
16
18
20
Time (h)
Moisture content (kg water/kg dry matter)
Fig. 2. Variation of solar radiation vs. time during a typical summer day in Marrakech.
6 Exp. 1
5
Exp. 2 Exp. 3
4
Exp. 4 Exp. 5
3
Exp. 6 Exp. 7
2
Exp. 8 Exp. 9
1 0 0
100
200
300
400
500
Drying time (min)
In order to study the effect of air conditions, it was observed that the main factor influencing drying kinetics is the drying air temperature, as noted in other studies (Belghit, Kouhila, & Boutaleb, 2000; Kechaou, Bagane, Maalej, & Kapseu, 1996; Kouhila, Kechaou, Otmani, Fliyou, & Lahsasni, 2002). Thus, a higher drying air temperature produced a higher drying rate and consequently the moisture ratio decreased (Fig. 5). This is due to the increase of the air heat supply rate to the product and the acceleration of water migration inside the prickly pear fruit. The drying rate does not vary a lot as a function of air flow rate which seems to have a less important effect than the drying air temperature (Fig. 6), as noted in other studies (Kouhila, 2001; Kouhila et al., 2002).
Drying rate (kg water/(kg dry matter.min))
Global radiation (W/m2)
1000
8
6
Exp. 7 (T=50˚C, Dv=0.0833 m 3/s) Exp. 8 (T=55˚C, Dv=0.0833 m 3/s) Exp. 9 (T=60˚C, Dv=0.0833 m 3/s)
4
2
0 0.0
0.2
0.6
0.8
1.0
Fig. 5. Variation of drying rate with temperature during drying of prickly pear fruit.
7
Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5 Exp. 6 Exp. 7 Exp. 8 Exp. 9
6 5 4 3 2 1 0 0.0
0.2
0.4
0.6
0.8
1.0
Moisture ratio
Fig. 4. Variation of drying rate as a function of moisture ratio.
characterised by a so-called Ôeffective diffusivityÕ (Al Hodali, 1997). These results indicated that diffusion is the most likely physical mechanism governing moisture movement in the prickly pear fruit.
Drying rate (kg water/ kg dry matter. min)
Drying rate (kg water/(kg dry matter.min))
0.4
Moisture ratio
Fig. 3. Variation of moisture content as a function of drying time.
6
4
Exp. 1 (T=50˚C. Dv=0.0227 m 3/s) Exp. 4 (T=50˚C. Dv=0.0556 m 3/s) Exp. 7 (T=50˚C. Dv=0.0833 m 3/s)
2
0 0.0
0.2
0.4
0.6
0.8
1.0
Moisture ratio Fig. 6. Variation of drying rate with air flow rate during drying of prickly pear fruit.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
3.3. Determination of the characteristic drying curve
where f is the dimensionless drying rate. More details about the experiments and the instruments used for determined Me may be found elsewhere (Lahsasni, Kouhila, Mahrouz, & Kechaou, 2002; Lahsasni, Kouhila, Mahrouz, & Fliyou, 2003). The Van Meel transformation is applied for determining the characteristic drying curve of prickly pear fruit. Experimental drying data are plotted in Fig. 8 to represent f ¼ f ðMRÞ. This figure shows that all drying curves obtained with the moisture ratio and dimensionless drying rate, for the different tested conditions, fall into a tight band, indicating that the effect of variation in different conditions is small over the range tested. The correlation coefficient (r) was one of the primary criteria for selecting the best equation to define the prickly pear fruit characteristic drying curve. In addition
Equilibrium moisture content (kg water/kg dry matter)
100
Experimental data at T=50˚C 80 60
1.0
Dimensionless drying rate
Models have been developed by which the analysis of drying process of several products and air conditions may be carried out based on only few laboratory drying experiments. For example, using Van MeelÕs concept (1958) of the characteristic drying curve, it is possible to present the drying rate curves of a given product, obtained under different air conditions by a single normalized drying rate curve. This curve can be used to generalize data for drying kinetics of prickly pear fruit in a solar dryer with an auxiliary heating system. Kechaou (2000) and Kouhila (2001) used simply the initial moisture content (M0 ) and the equilibrium moisture content (Me ) derived from desorption data (Fig. 7) to obtain moisture ratio and initial drying rate ðdM=dtÞ0 to normalize the drying rate as follows: dM dt f ¼ ð3Þ dM dt 0
177
Exp. 1-9 CDC
0.8 0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
Fig. 8. Characteristic drying curve of prickly pear fruit.
to r, the statistical parameter standard error (Sr ) was used to determine the goodness of fitting. Marquardt-Levenberg non-linear optimization method, using the computer program ‘‘Curve Expert 3.1’’ was used to find the best equation for the prickly pear fruit characteristic drying curve: f ¼ 0:03112 þ 0:7159 MR þ 0:2226 MR2
ð4Þ
The criterion used to evaluate goodness of fit was the standard error (Sr ¼ 0:076) and the correlation coefficient (r ¼ 0:969). 3.4. Modelling of the drying curves Table 3 presents the drying constants and the values of r and v-square of the eight models (see Table 1). Generally r and v-square values were changed between 0.9963 and 0.9999 and 6.6800 104 and 1.0159 105 . From Table 3, the two-term model gave the best results in fitting the experimental data resulting from the convective solar drying of prickly pear fruit with an r of 0.9999 and v2 of 1.0159 105 . Consequently, it can be said that the two-term model could sufficiently define the convective solar drying of prickly pear fruit. The coefficients of the accepted model (Eq. (5)) for the convective solar drying of prickly pear fruit were determined by Marquardt-Levenberg non-linear optimization method. The degree 2 polynomial function have shown the highest values of r and the lowest values of Sr . These coefficients are expressed as follows: MR ¼ a expðk0 tÞ þ b expðk1 tÞ
40
ð5Þ
where
20
a ¼ 2:9205 þ 0:1117T 0:0011T 2 0 0.0
1.0
Moisture ratio
0.2
0.4
0.6
0.8
Equilibrium relative humidity Fig. 7. Desorption isotherm of prickly pear fruit.
1.0
k0 ¼ 1:1619 0:0439T þ 0:0004T b ¼ 2:3099 0:0547T þ 0:0005T
ð6Þ
2
ð7Þ
2
ð8Þ 5
k1 ¼ 0:0764 þ 0:0027T 2:1658 10 T
2
ð9Þ
178
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Table 3 Modelling of moisture ratio according to drying time for prickly pear fruit Model
Coefficients
r
v2
Newton Page Modified Page Henderson and Pabis Logarithmic Two-terma
k ¼ 0:0070 k ¼ 0:0043; n ¼ 1:1147 k ¼ 0:0060; n ¼ 1:1838 a ¼ 1:0329; k ¼ 0:0070 a ¼ 1:2346; k ¼ 0:0052; c ¼ 0:2337 a ¼ 0:0013; k0 ¼ 0:0182; b ¼ 1:0125; k1 ¼ 0:0069 a ¼ 1:6283; k ¼ 0:0097 a ¼ 0:0061; b ¼ 1:0463 105
0.9963 0.9991 0.9963 0.9978 0.9998 0.9999
5.5666 104 1.5061 104 6.6800 104 3.9400 104 2.3945 105 1.0159 105
0.9993 0.9995
1.1457 104 8.2798 105
Two-term exponential Wang and Singh
This model gives the best results for prickly pear fruit in a convective solar dryer.
The four expressions (Eqs. (6)–(9)) predicted well the moisture ratio (MR) at three drying temperatures 50, 55, and 60 °C for the prickly pear fruit. The relationship between coefficients of two-term model and drying air temperatures was very significant, with an r of 1 and Sr of 0 so that the moisture content of prickly pear fruit at any time during the drying process could be estimated. This result can be noted consequently from Figs. 9–11,
1.0 3 Exp. 3 (T=60˚C, Dv=0.0227 m /s) Two term model
0.8
Moisture ratio
a
0.6 0.4 0.2
1.0 0.8
Moisture ratio
0.0
Exp. 1 (T=50˚C, Dv=0.0227 m 3/s) Two term model
0
100
150
200
Drying time (min) 0.6
Fig. 11. Experimental data of moisture ratio versus drying time fitted with two-term model.
0.4 0.2 0.0 0
100
200
300
400
Drying time (min) Fig. 9. Experimental data of moisture ratio versus drying time fitted with two-term model.
1.0
0.6 0.4 0.2 0.0 0
50
100
150
which compare experimental data with predicted values. As these expressions are purely empirical, they would hold good only for similar drying conditions of drying materials (weight 1 0.1 g, diameter 0.5 0.01 cm, length 2 0.03 cm), dryer capacity (3 kg/m2 of prickly pear fruit by tray), drying air temperatures (50–60 °C), and drying air flow rates (0.0227–0.0833 m3 /s) considered in this study. 4. Conclusions
Exp. 2 (T=55˚C, Dv=0.0227 m 3/s) Two term model
0.8
Moisture ratio
50
200
Drying time (min) Fig. 10. Experimental data of moisture ratio versus drying time fitted with two-term model.
From the drying kinetics study of prickly pear fruit, it is observed that only the falling rate period exists. Also, drying air temperature is the main factor influencing the drying kinetics. The drying rate increases with a higher drying air temperature and higher drying air flow rate. The characteristic drying curve is obtained and the expression of the drying rate equation is determined. According to these results, the two-term drying model could adequately describe the thin layer drying behavior of prickly pear fruit with an r of 0.9999 and v2 of 1.0159 105 . When the effect of the drying air temperature of the two-term model was examined, the resulting model gave an r of 1 and Sr of 0.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Acknowledgements This study was partially financed by the CNRST (Morocco) for a project PROTARS III (Ref. D12/34) on Solar Drying and Quality of Medicinal and Aromatic plants.
References Al Hodali, R. (1997). Numerical simulation of an agricultural foodstuffs drying unit using solar energy and adsorption process. Ph.D. Thesis, Universite Libre de Bruxelles, Belgium, 309 p. Basunia, M. A., & Abe, T. (2001). Thin layer solar drying characteristics of rough rice under natural convection. Journal of Food Engineering, 47, 295–301. Belghit, A., Kouhila, M., & Boutaleb, B. C. (2000). Experimental study of drying kinetics by forced convection of aromatic plants. Energy Conversion and Management, 44(12), 1303–1321. Bellegha, S., Amami, E., Farhat, A., & Kechaou, N. (2002). Drying kinetics and characteristic drying curve of Lightly Salted Sardine (Sardinella Aurita). Drying Technology, 20(7), 1523–1534. Feitosa-Teles, F. F. (1977). Nutrient analysis of prickly pear. Ph.D. Thesis, University of Arizona, Tucson, 157 p. Galati, E. M., Monforte, M. T., Tripodo, M. M., dÕAquino, A., & Mondello, M. R. (2001). Antiulcer activity of Opuntia ficus indica (L.) Mill. (Cactaceae): ultrastructural study. Journal of Ethnopharmacology, 76(1), 1–9. Gurrieri, S., Miceli, L., Lanza, M. L., Tomaselli, F., Bonomo, P. R., & Rizzarelli, E. (2000). Chemical characterization of Sicilian prickly pear (Opuntia ficus indica) and perspectives for the storage of its juice. Journal of Agricultural and Food Chemistry, 48, 5424–5431. Habibi, Y., Mahrouz, M., & Vignon, M. (2002). Isolation and structure of D -xylans from pericarp seeds of Opuntia ficus-indica prickly pear fruits. Carbohydrate Research, 337, 1593–1598. Hassan, B. H., & Hobani, A. I. (2000). Thin layer drying of dates. Journal of Food Process Engineering, 23, 177–189. Idlimam, A., Kaoua, M., Alem, L., & Daguenent, M. (1994). Etude experimentale du rayonnement solaire a Marrakech. In Comptes techniques de dimensionnement des systemes energetiques solaires, Actes du colloque international, Perpignan, France.
179
Jayas, D. S., Cenkowski, S., Pabis, S., & Muir, W. E. (1991). Review of thin layer drying and wetting equations. Drying Technology, 9(3), 551–588. Kechaou, N., Bagane, M., Maalej, M., & Kapseu, C. (1996). Approche empirique de la cinetique du sechage des dattes. Sciences des Aliments, 16, 593–606. tude theorique et experimentale du processus de Kechaou, N. (2000). E tat, sechage de produits agro-alimentaires, These de Doctorat dÕE Faculte des Sciences de Tunis, Tunisie, 192 p. Kouhila, M. (2001). Etude experimentale et theorique de cinetiques de sechage convectif partiellement solaire des plantes medicinales et aromatiques (Menthe, Verveine, Sauge et Eucalyptus) de la region de Marrakech, These de Doctorat dÕEtat, Universite Cadi Ayyad de Marrakech, Morocco, 170 p. Kouhila, M., Kechaou, N., Otmani, M., Fliyou, M., & Lahsasni, S. (2002). Experimental study of sorption isotherms and drying kinetics of Moroccan Eucalyptus Globulus. Drying Technology, 20(10), 2027–2039. Lahsasni, S., Kouhila, M., Mahrouz, M., & Kechaou, N. (2002). Experimental study and modelling of adsorption and desorption isotherms of prickly pear peel (Opuntia ficus indica). Journal of Food Engineering, 55(3), 201–207. Lahsasni, S., Kouhila, M., Mahrouz, M., & Fliyou, M. (2003). Moisture adsorption–desorption isotherms of prickly pear cladode (Opuntia ficus indica) at different temperatures. Energy Conversion and Management, 44(6), 923–936. Midilli, A., & Kucuk, H. (2003). Mathematical modeling of thin layer drying of pistachio by using solar energy. Energy Conversion and Management, 44(7), 1111–1122. Mujumdar, A. S. (1987). Handbook of industrial drying. New York: Marcel Dekker. Park, E. H., Kahng, J. H., Lee, S. H., & Shin, K. H. (2001). An antiinflammatory principle from cactus. Fitoterapia, 72(3), 288–290. Togrul, T. I., & Pehlivan, D. (2002). Mathematical modeling of solar drying of apricot in thin layers. Journal of Food Engineering, 55, 209–216. Togrul, T. I., & Pehlivan, D. (in press). Modeling of drying kinetics of single apricot. Journal of Food Engineering. Van Meel, D. A. (1958). Adiabatic convection batch drying with recirculation of air. Chemical Engineering Science, 9, 36–44. Yaldiz, O., & Ertekin, C. (2001). Thin layer solar drying of some vegetables. Drying Technology, 19(3), 583–597. Yaldiz, O., Ertekin, C., & Uzun, H. I. (2001). Mathematical modeling of thin layer solar drying of sultana grapes. Energy, 26, 457–465.
Drying kinetics of prickly pear fruit (Opuntia ficus indica) S. Lahsasni a, M. Kouhila b
b,*
, M. Mahrouz a, J.T. Jaouhari
b
a Unit e de Chimie Agroalimentaire (LCOA), Facult e des Sciences Semlalia, BP 2390, Marrakech, Morocco Laboratoire d’Energie Solaire et Plantes Aromatiques et M edicinales, Ecole Normale Sup erieure, BP 2400, Marrakech, Morocco
Received 24 October 2002; accepted 12 March 2003
Abstract The present work examines the effect of drying air conditions on drying kinetics of the prickly pear fruit in a convective solar drier operating with an auxiliary heating system under air controlled conditions. Moreover, the prickly pear fruits are sufficiently dried in the ranges between 32 and 36 °C of ambient air temperature, 50–60 °C of drying air temperature, 23–34% of relative humidity, 0.0277–0.0833 m3 /s of drying air flow rate and 200–950 W/m2 of solar radiation. The results verified with good reproducibility that drying air temperature is the main factor in controlling the drying rate and the experimental drying curves show only a falling rate period. The expression of the drying rate equation is determined empirically from the characteristic drying curve. Eight different thin layer drying models were compared according to their coefficients of determination to estimate solar drying curves. The two-term model was found to satisfactorily describe the solar drying curves of prickly pear fruit with a correlation coefficient (r) of 0.9999. The constants and coefficients of this model could be explained by the effect of drying air temperature with a correlation coefficient (r) of 1.0000. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Characteristic drying curve; Drying curves; Modeling; Prickly pear fruit; Solar dryer
1. Introduction The cactus pear (prickly pear) grows in all parts of the American continent, from southern Canada to Patagonia, and in the course of time has been cultivated in different areas of Europe, particularly in the Mediterranean countries, as well as in Africa and Australia. Many different species of Opuntia are grown in Mexico for fruit production whereas in Italy and the Mediterranean region in general, Opuntia ficus indica is cultivated. Thanks to its ability to adapt to different environmental conditions, the cactus pear grows in plains, coastal regions, plateaus and among diverse vegetation. A common feature of the areas where the plant grows is a more or less marked degree of aridity to which the plant has adapted thanks to its CAM photosynthetic metabolism (Feitosa-Teles, 1977). Prickly pear fruit is a fleshy, and polyspermic unilocular berry. The major components of the fruit pulp are 85% of water, 10–15% of carbohydrates, and substantial amounts of vitamin C, 0.025–0.030% (Gurrieri et al.,
2000). Its nutritional value lies essentially in its glucose and fructose content (6–8%) (Habibi, Mahrouz, & Vignon, 2002). The level of ascorbic acid is moderate (0.023%); and acidity is low (0.06%). The prickly pear can be used in many ways in diverse sectors, utilizing different parts of the plant. In the food sector, besides consumption of the fresh fruit, jams, alcoholic, soft drinks, syrups, candied fruit, and flour can be produced from the plant and oil extracted from the seeds. The vegetable stems (cladode) and fruits of prickly pear are useful to treat diabetes, high blood cholesterol levels, inflammation and obesity (Galati, Monforte, Tripodo, dÕAquino, & Mondello, 2001; Park, Kahng, Lee, & Shin, 2001). The objectives of the study were to determine the effect of drying air temperature and air flow rate on the drying kinetics of the prickly pear fruit, and to select the best mathematical model for the drying curves.
2. Materials and methods 2.1. Materials
*
Corresponding author. Tel.: +212-44-34-07-89; fax: +212-44-3422-87. E-mail address: [email protected] (M. Kouhila). 0260-8774/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00084-0
The prickly pear fruit used in the drying experiments was grown in the region of Bengrir (near the town of
174
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Nomenclature CDC characteristic drying curve ðdM=dtÞ0 initial drying rate (kg water/(kg dry matter min)) dM=dt drying rate at any time of drying (kg water/ (kg dry matter min)) Dv drying air flow rate (m3 /s) Exp experiment f dimensionless drying rate M moisture content at any time of drying (kg water/kg dry matter) Mf final moisture content (kg water/kg dry matter) Me equilibrium moisture content (kg water/kg dry matter)
Marrakech). Harvest period was between June and October 2002. Marrakech is situated 140 km east of the Atlantic, north of the High Atlas. Its geographic coordinates are 8° 20 west, 31° 370 north and 463 m over the sea level. Summer in Marrakech is hot and dry while winter is temperate and humid with occasional rains (Idlimam, Kaoua, Alem, & Daguenent, 1994). The experimental apparatus consists of an indirect forced convection solar dryer with a solar air collector, an auxiliary heater, a circulation fan and a drying cabinet as shown in Fig. 1. The solar air collector had dimensions of 1 m by 2.5 m. A corrugated galvanised iron sheet painted black was used as an absorber plate for absorbing the incident solar radiation. It was oriented southward under the collector angle of 31°. This angle
Fig. 1. Schematic representation of the solar dryer. (1) Solar collector; (2) direction of fan; (3) fan; (4) direction of aspiration; (5) control-box; (6) auxiliary heating system; (7) shelves; (8) drying cabinet; (9) recycling air; (10) control foot; (11) exit of air; (12) humidity probes; (13) thermocouples.
MR M0 N n r Rh Sr t T v
moisture ratio initial moisture content (kg water/kg dry matter) number of observations number of constants correlation coefficient relative humidity (%) standard error drying time (min) drying air temperature (°C) reduced chi-square
was fixed by the control foot. A glass and plastic sheet was used as a transparent cover for the air heater to prevent the top heat losses. The frame was made of wood. The drying cabinet was constructed with insulted walls (dimensions, 1.40 m (length), 0.5 m (width), and 0.90 m (depth)) and has 10 shelves. A centrifugal ventilator (0.0833 m3 /s; 80 mm CE, 220 V) connected to the north side of the drying cabinet provides a maximum air velocity of 1.7 m/s and allowed to vary the drying air flow rate from 0.0227 to 0.0833 m3 /s. The circulation fan to supply fresh air has a power of 0.1 kW. The auxiliary heater has a power of 4 kW. It was connected to the inlet of control box. 2.2. Experimental procedure The drying materials were cut in the bits of 1 0.1 g weight. The major diameter and length were 0.5 0.01 cm, and 2 0.03 cm, respectively. The loading density of the drying trays was 3 kg/m2 for prickly pear fruit. In the experiments, the 2nd and 10th shelves were not selected for the efficient utilisation of drying air. However, the samples were uniformly spread evenly on a drying tray that was then placed on the first shelf of the drying cabinet. The heated air enters the drying cabinet below the trays and flowed upwards trough the samples. The amounts of solar radiation were measured with KipZonen solarmeter. Temperature measurements and recordings at different points in the solar dryer were made by Cr–alumel thermocouples (0.2 mm diameter) connected to a data-logger enabling 0.1 °C accuracy and the outlet temperatures were measured with thermometer. The relative humidities were measured by capacitance sensors. These values were determined by probes Humicolor 2%. A digital weighing apparatus (0.001 g) measures the mass loss of the product during the drying process.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
2.3. Fitting of the solar drying curves Nine experiments of prickly pear fruit were performed by using the solar drying at T ¼ 50, 55, and 60 °C, and Dv ¼ 0:0227, 0.0556, and 0.0833 m3 /s which correspond to the average velocity of drying air in the drying cabinet 0.5667, 1.1333 and 1.7 m/s, respectively. The solar drying curves were fitted with eight different moisture ratio equations (Table 1) (Basunia & Abe, 2001; Hassan & Hobani, 2000; Jayas, Cenkowski, Pabis, & Muir, 1991; Mujumdar, 1987; Togrul & Pehlivan, 2002; Yaldiz & Ertekin, 2001; Yaldiz, Ertekin, & Uzun, 2001). The moisture ratio MR can be calculated as: MR ¼
M Me M0 Me
ð1Þ
It is particularly emphasized that the correlation coefficient r is one of the primary criteria to select the best equation to account for the variation in the solar drying curves of the dried samples (Midilli & Kucuk, 2003). In addition to r, the reduced chi-square (v2 ) was used to determine the best of the fit (Togrul & Pehlivan, in press). Chi-square can be calculated as: PN ðMRexp;i MRpre;i Þ2 2 ð2Þ v ¼ i¼1 N n where MRexp;i is the ith experimental moisture ratio, MRpre;i the ith predicted moisture ratio, N the number of observations and, n the number of constants. Table 1 Mathematical models applied to the drying curves Model name
Model
Newton Page Modified Page Henderson and Pabis Logarithmic Two-term Two-term exponential Wang and Singh
MR ¼ expðktÞ MR ¼ expðktn Þ MR ¼ expððktÞn Þ MR ¼ a expðktÞ MR ¼ a expðktÞ þ c MR ¼ a expðk0 tÞ þ b expðk1 tÞ MR ¼ a expðktÞ þ ð1 aÞ expðkatÞ MR ¼ 1 þ at þ bt2
175
In this study, the relationship between the drying air temperature and the coefficients of the best suitable model was also determined. In order to determine the most suitable model for prickly pear fruit, MarquardtLevenberg non-linear optimisation method, using the computer program ‘‘curve Expert 3.1’’ was used.
3. Results and discussion The solar drying experiments were carried out during the period of June and July 2002 in Marrakech, Morocco. Each experiment started at 8:30 a.m. and continued until 6:00 p.m. A total of nine drying experiments were run at different air conditions. During the experiments, solar radiation changed between 200 and 950 W/m2 , ambient air temperature ranged from 32 to 36 1 °C, ambient air relative humidity from 23 to 34 2%, inlet drying air temperature from 50 to 60 0:1 °C, and drying air flow rate from 0.0227 to 0:0833 0:002 m3 /s. The initial moisture content of the prickly pear fruit ranged from 5.9719 to 4.9336 kg water per kg dry matter and was reduced to the final moisture content which varies from 0.0722 to 0.0297 kg water per kg dry matter (Table 2). 3.1. Determination of the drying curves Fig. 2 shows the hourly variation of the measured solar radiation of a typical summer day (23 June 2002). The moisture content versus drying time and the drying rate versus moisture ratio are shown in Figs. 3 and 4, respectively. The constant rate period is absent in the solar drying of prickly pear fruit. The drying process took place in the falling rate period. Drying rate decreases continuously with diminishing moisture ratio. These results are in agreement with the observations of earlier researchers (Bellegha, Amami, Farhat, & Kechaou, 2002; Kouhila, 2001). Drying during the falling rate period is so governed by water diffusion in the solid. This is a complex mechanism involving water in both liquid and vapour states, which is very often
Table 2 Drying conditions during experiments in the solar dryer Experiment number
Dv 0:002 (m3 /s)
Inlet T 0:1 (°C)
Outlet Rh 2 (%)
M0 (kg/kg dry matter)
Me (kg/kg dry matter)
Mf (kg/kg dry matter)
t (min)
1 2 3 4 5 6 7 8 9
0.0227 0.0227 0.0227 0.0556 0.0556 0.0556 0.0833 0.0833 0.0833
50 55 60 50 55 60 50 55 60
42 46 38 38 31 36 32 35 30
5.4302 5.9719 5.5468 5.2920 4.9336 4.9702 5.4034 5.4778 5.4484
0.2536 0.4026 0.2317 0.2375 0.2067 0.2221 0.2106 0.2239 0.1948
0.0722 0.0679 0.0411 0.0297 0.0535 0.0410 0.0348 0.0384 0.0407
476 315 265 425 272 225 285 225 195
176
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
3.2. Influence of temperature and air flow rate
800 600 400 200 0 6
8
10
12
14
16
18
20
Time (h)
Moisture content (kg water/kg dry matter)
Fig. 2. Variation of solar radiation vs. time during a typical summer day in Marrakech.
6 Exp. 1
5
Exp. 2 Exp. 3
4
Exp. 4 Exp. 5
3
Exp. 6 Exp. 7
2
Exp. 8 Exp. 9
1 0 0
100
200
300
400
500
Drying time (min)
In order to study the effect of air conditions, it was observed that the main factor influencing drying kinetics is the drying air temperature, as noted in other studies (Belghit, Kouhila, & Boutaleb, 2000; Kechaou, Bagane, Maalej, & Kapseu, 1996; Kouhila, Kechaou, Otmani, Fliyou, & Lahsasni, 2002). Thus, a higher drying air temperature produced a higher drying rate and consequently the moisture ratio decreased (Fig. 5). This is due to the increase of the air heat supply rate to the product and the acceleration of water migration inside the prickly pear fruit. The drying rate does not vary a lot as a function of air flow rate which seems to have a less important effect than the drying air temperature (Fig. 6), as noted in other studies (Kouhila, 2001; Kouhila et al., 2002).
Drying rate (kg water/(kg dry matter.min))
Global radiation (W/m2)
1000
8
6
Exp. 7 (T=50˚C, Dv=0.0833 m 3/s) Exp. 8 (T=55˚C, Dv=0.0833 m 3/s) Exp. 9 (T=60˚C, Dv=0.0833 m 3/s)
4
2
0 0.0
0.2
0.6
0.8
1.0
Fig. 5. Variation of drying rate with temperature during drying of prickly pear fruit.
7
Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5 Exp. 6 Exp. 7 Exp. 8 Exp. 9
6 5 4 3 2 1 0 0.0
0.2
0.4
0.6
0.8
1.0
Moisture ratio
Fig. 4. Variation of drying rate as a function of moisture ratio.
characterised by a so-called Ôeffective diffusivityÕ (Al Hodali, 1997). These results indicated that diffusion is the most likely physical mechanism governing moisture movement in the prickly pear fruit.
Drying rate (kg water/ kg dry matter. min)
Drying rate (kg water/(kg dry matter.min))
0.4
Moisture ratio
Fig. 3. Variation of moisture content as a function of drying time.
6
4
Exp. 1 (T=50˚C. Dv=0.0227 m 3/s) Exp. 4 (T=50˚C. Dv=0.0556 m 3/s) Exp. 7 (T=50˚C. Dv=0.0833 m 3/s)
2
0 0.0
0.2
0.4
0.6
0.8
1.0
Moisture ratio Fig. 6. Variation of drying rate with air flow rate during drying of prickly pear fruit.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
3.3. Determination of the characteristic drying curve
where f is the dimensionless drying rate. More details about the experiments and the instruments used for determined Me may be found elsewhere (Lahsasni, Kouhila, Mahrouz, & Kechaou, 2002; Lahsasni, Kouhila, Mahrouz, & Fliyou, 2003). The Van Meel transformation is applied for determining the characteristic drying curve of prickly pear fruit. Experimental drying data are plotted in Fig. 8 to represent f ¼ f ðMRÞ. This figure shows that all drying curves obtained with the moisture ratio and dimensionless drying rate, for the different tested conditions, fall into a tight band, indicating that the effect of variation in different conditions is small over the range tested. The correlation coefficient (r) was one of the primary criteria for selecting the best equation to define the prickly pear fruit characteristic drying curve. In addition
Equilibrium moisture content (kg water/kg dry matter)
100
Experimental data at T=50˚C 80 60
1.0
Dimensionless drying rate
Models have been developed by which the analysis of drying process of several products and air conditions may be carried out based on only few laboratory drying experiments. For example, using Van MeelÕs concept (1958) of the characteristic drying curve, it is possible to present the drying rate curves of a given product, obtained under different air conditions by a single normalized drying rate curve. This curve can be used to generalize data for drying kinetics of prickly pear fruit in a solar dryer with an auxiliary heating system. Kechaou (2000) and Kouhila (2001) used simply the initial moisture content (M0 ) and the equilibrium moisture content (Me ) derived from desorption data (Fig. 7) to obtain moisture ratio and initial drying rate ðdM=dtÞ0 to normalize the drying rate as follows: dM dt f ¼ ð3Þ dM dt 0
177
Exp. 1-9 CDC
0.8 0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
Fig. 8. Characteristic drying curve of prickly pear fruit.
to r, the statistical parameter standard error (Sr ) was used to determine the goodness of fitting. Marquardt-Levenberg non-linear optimization method, using the computer program ‘‘Curve Expert 3.1’’ was used to find the best equation for the prickly pear fruit characteristic drying curve: f ¼ 0:03112 þ 0:7159 MR þ 0:2226 MR2
ð4Þ
The criterion used to evaluate goodness of fit was the standard error (Sr ¼ 0:076) and the correlation coefficient (r ¼ 0:969). 3.4. Modelling of the drying curves Table 3 presents the drying constants and the values of r and v-square of the eight models (see Table 1). Generally r and v-square values were changed between 0.9963 and 0.9999 and 6.6800 104 and 1.0159 105 . From Table 3, the two-term model gave the best results in fitting the experimental data resulting from the convective solar drying of prickly pear fruit with an r of 0.9999 and v2 of 1.0159 105 . Consequently, it can be said that the two-term model could sufficiently define the convective solar drying of prickly pear fruit. The coefficients of the accepted model (Eq. (5)) for the convective solar drying of prickly pear fruit were determined by Marquardt-Levenberg non-linear optimization method. The degree 2 polynomial function have shown the highest values of r and the lowest values of Sr . These coefficients are expressed as follows: MR ¼ a expðk0 tÞ þ b expðk1 tÞ
40
ð5Þ
where
20
a ¼ 2:9205 þ 0:1117T 0:0011T 2 0 0.0
1.0
Moisture ratio
0.2
0.4
0.6
0.8
Equilibrium relative humidity Fig. 7. Desorption isotherm of prickly pear fruit.
1.0
k0 ¼ 1:1619 0:0439T þ 0:0004T b ¼ 2:3099 0:0547T þ 0:0005T
ð6Þ
2
ð7Þ
2
ð8Þ 5
k1 ¼ 0:0764 þ 0:0027T 2:1658 10 T
2
ð9Þ
178
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Table 3 Modelling of moisture ratio according to drying time for prickly pear fruit Model
Coefficients
r
v2
Newton Page Modified Page Henderson and Pabis Logarithmic Two-terma
k ¼ 0:0070 k ¼ 0:0043; n ¼ 1:1147 k ¼ 0:0060; n ¼ 1:1838 a ¼ 1:0329; k ¼ 0:0070 a ¼ 1:2346; k ¼ 0:0052; c ¼ 0:2337 a ¼ 0:0013; k0 ¼ 0:0182; b ¼ 1:0125; k1 ¼ 0:0069 a ¼ 1:6283; k ¼ 0:0097 a ¼ 0:0061; b ¼ 1:0463 105
0.9963 0.9991 0.9963 0.9978 0.9998 0.9999
5.5666 104 1.5061 104 6.6800 104 3.9400 104 2.3945 105 1.0159 105
0.9993 0.9995
1.1457 104 8.2798 105
Two-term exponential Wang and Singh
This model gives the best results for prickly pear fruit in a convective solar dryer.
The four expressions (Eqs. (6)–(9)) predicted well the moisture ratio (MR) at three drying temperatures 50, 55, and 60 °C for the prickly pear fruit. The relationship between coefficients of two-term model and drying air temperatures was very significant, with an r of 1 and Sr of 0 so that the moisture content of prickly pear fruit at any time during the drying process could be estimated. This result can be noted consequently from Figs. 9–11,
1.0 3 Exp. 3 (T=60˚C, Dv=0.0227 m /s) Two term model
0.8
Moisture ratio
a
0.6 0.4 0.2
1.0 0.8
Moisture ratio
0.0
Exp. 1 (T=50˚C, Dv=0.0227 m 3/s) Two term model
0
100
150
200
Drying time (min) 0.6
Fig. 11. Experimental data of moisture ratio versus drying time fitted with two-term model.
0.4 0.2 0.0 0
100
200
300
400
Drying time (min) Fig. 9. Experimental data of moisture ratio versus drying time fitted with two-term model.
1.0
0.6 0.4 0.2 0.0 0
50
100
150
which compare experimental data with predicted values. As these expressions are purely empirical, they would hold good only for similar drying conditions of drying materials (weight 1 0.1 g, diameter 0.5 0.01 cm, length 2 0.03 cm), dryer capacity (3 kg/m2 of prickly pear fruit by tray), drying air temperatures (50–60 °C), and drying air flow rates (0.0227–0.0833 m3 /s) considered in this study. 4. Conclusions
Exp. 2 (T=55˚C, Dv=0.0227 m 3/s) Two term model
0.8
Moisture ratio
50
200
Drying time (min) Fig. 10. Experimental data of moisture ratio versus drying time fitted with two-term model.
From the drying kinetics study of prickly pear fruit, it is observed that only the falling rate period exists. Also, drying air temperature is the main factor influencing the drying kinetics. The drying rate increases with a higher drying air temperature and higher drying air flow rate. The characteristic drying curve is obtained and the expression of the drying rate equation is determined. According to these results, the two-term drying model could adequately describe the thin layer drying behavior of prickly pear fruit with an r of 0.9999 and v2 of 1.0159 105 . When the effect of the drying air temperature of the two-term model was examined, the resulting model gave an r of 1 and Sr of 0.
S. Lahsasni et al. / Journal of Food Engineering 61 (2004) 173–179
Acknowledgements This study was partially financed by the CNRST (Morocco) for a project PROTARS III (Ref. D12/34) on Solar Drying and Quality of Medicinal and Aromatic plants.
References Al Hodali, R. (1997). Numerical simulation of an agricultural foodstuffs drying unit using solar energy and adsorption process. Ph.D. Thesis, Universite Libre de Bruxelles, Belgium, 309 p. Basunia, M. A., & Abe, T. (2001). Thin layer solar drying characteristics of rough rice under natural convection. Journal of Food Engineering, 47, 295–301. Belghit, A., Kouhila, M., & Boutaleb, B. C. (2000). Experimental study of drying kinetics by forced convection of aromatic plants. Energy Conversion and Management, 44(12), 1303–1321. Bellegha, S., Amami, E., Farhat, A., & Kechaou, N. (2002). Drying kinetics and characteristic drying curve of Lightly Salted Sardine (Sardinella Aurita). Drying Technology, 20(7), 1523–1534. Feitosa-Teles, F. F. (1977). Nutrient analysis of prickly pear. Ph.D. Thesis, University of Arizona, Tucson, 157 p. Galati, E. M., Monforte, M. T., Tripodo, M. M., dÕAquino, A., & Mondello, M. R. (2001). Antiulcer activity of Opuntia ficus indica (L.) Mill. (Cactaceae): ultrastructural study. Journal of Ethnopharmacology, 76(1), 1–9. Gurrieri, S., Miceli, L., Lanza, M. L., Tomaselli, F., Bonomo, P. R., & Rizzarelli, E. (2000). Chemical characterization of Sicilian prickly pear (Opuntia ficus indica) and perspectives for the storage of its juice. Journal of Agricultural and Food Chemistry, 48, 5424–5431. Habibi, Y., Mahrouz, M., & Vignon, M. (2002). Isolation and structure of D -xylans from pericarp seeds of Opuntia ficus-indica prickly pear fruits. Carbohydrate Research, 337, 1593–1598. Hassan, B. H., & Hobani, A. I. (2000). Thin layer drying of dates. Journal of Food Process Engineering, 23, 177–189. Idlimam, A., Kaoua, M., Alem, L., & Daguenent, M. (1994). Etude experimentale du rayonnement solaire a Marrakech. In Comptes techniques de dimensionnement des systemes energetiques solaires, Actes du colloque international, Perpignan, France.
179
Jayas, D. S., Cenkowski, S., Pabis, S., & Muir, W. E. (1991). Review of thin layer drying and wetting equations. Drying Technology, 9(3), 551–588. Kechaou, N., Bagane, M., Maalej, M., & Kapseu, C. (1996). Approche empirique de la cinetique du sechage des dattes. Sciences des Aliments, 16, 593–606. tude theorique et experimentale du processus de Kechaou, N. (2000). E tat, sechage de produits agro-alimentaires, These de Doctorat dÕE Faculte des Sciences de Tunis, Tunisie, 192 p. Kouhila, M. (2001). Etude experimentale et theorique de cinetiques de sechage convectif partiellement solaire des plantes medicinales et aromatiques (Menthe, Verveine, Sauge et Eucalyptus) de la region de Marrakech, These de Doctorat dÕEtat, Universite Cadi Ayyad de Marrakech, Morocco, 170 p. Kouhila, M., Kechaou, N., Otmani, M., Fliyou, M., & Lahsasni, S. (2002). Experimental study of sorption isotherms and drying kinetics of Moroccan Eucalyptus Globulus. Drying Technology, 20(10), 2027–2039. Lahsasni, S., Kouhila, M., Mahrouz, M., & Kechaou, N. (2002). Experimental study and modelling of adsorption and desorption isotherms of prickly pear peel (Opuntia ficus indica). Journal of Food Engineering, 55(3), 201–207. Lahsasni, S., Kouhila, M., Mahrouz, M., & Fliyou, M. (2003). Moisture adsorption–desorption isotherms of prickly pear cladode (Opuntia ficus indica) at different temperatures. Energy Conversion and Management, 44(6), 923–936. Midilli, A., & Kucuk, H. (2003). Mathematical modeling of thin layer drying of pistachio by using solar energy. Energy Conversion and Management, 44(7), 1111–1122. Mujumdar, A. S. (1987). Handbook of industrial drying. New York: Marcel Dekker. Park, E. H., Kahng, J. H., Lee, S. H., & Shin, K. H. (2001). An antiinflammatory principle from cactus. Fitoterapia, 72(3), 288–290. Togrul, T. I., & Pehlivan, D. (2002). Mathematical modeling of solar drying of apricot in thin layers. Journal of Food Engineering, 55, 209–216. Togrul, T. I., & Pehlivan, D. (in press). Modeling of drying kinetics of single apricot. Journal of Food Engineering. Van Meel, D. A. (1958). Adiabatic convection batch drying with recirculation of air. Chemical Engineering Science, 9, 36–44. Yaldiz, O., & Ertekin, C. (2001). Thin layer solar drying of some vegetables. Drying Technology, 19(3), 583–597. Yaldiz, O., Ertekin, C., & Uzun, H. I. (2001). Mathematical modeling of thin layer solar drying of sultana grapes. Energy, 26, 457–465.