international journal of food

International Journal of Food Engineering

Volume 4, Issue 8 2008 Article 8

Mathematical Modeling of Thin Layer Drying Kinetics of Apple in Tunnel Dryer

Raj Kumar Goyal, Central Institute of Post Harvest Engineering and Technology Mujjeb O, Mar Athanasios

College For Advanced StudiesTiruvalla

Vinod Kumar Bhargava, Central Institute of Post Harvest Engineering and Technology

Recommended Citation:Goyal, Raj Kumar; O, Mujjeb; and Bhargava, Vinod Kumar (2008) "Mathematical Modeling of

Thin Layer Drying Kinetics of Apple in Tunnel Dryer," International Journal of FoodEngineering: Vol. 4 : Iss. 8, Article 8.Available at: http://www.bepress.com/ijfe/vol4/iss8/art8DOI: 10.2202/1556-3758.1233

©2008 Berkeley Electronic Press. All rights reserved.

http://www.bepress.com/ijfe/vol4/iss8/art8

Mathematical Modeling of Thin Layer Drying Kinetics of Apple in Tunnel Dryer

Raj Kumar Goyal, Mujjeb O, and Vinod Kumar Bhargava

Abstract

In this study, the drying kinetics of apple (control, blanching and blanching in 1% potassium meta bisulphate) in a tunnel dryer was studied at 50, 60, and 70°C air temperatures. The drying of apple slices occurred in a falling rate period. It was found that treated apple slices dried faster. Six thin layer-drying models were fitted to the experimental moisture ratio. Among the mathematical models evaluated, the logarithmic model satisfactorily described the drying behaviour of apple slices with high r2 values. The effective moisture diffusivity (Deff) of apple slices increased as the drying air temperature increased. The Deff values were higher for the treated samples than for the control.

KEYWORDS: apple, diffusivity, drying, mathematical models, tunnel dryer1. INTRODUCTION

The apples or seb (Malus pumila) are the most important and widely cultivated fruits of temperate regions. They have been successfully cultivated in India since the middle of 18th century both in the plains and hills of North India. It is now a commercial crop in the hilly areas of Kashmir, Kulu and Kumaon region of the country.

Fresh apples are considered moderate in energy value and low in protein, lipid, and vitamin content. Dried or dehydrated apples have a higher energy value per gram tissue due to the concentration of sugars (Lee and Mattick, 1989). Dried apples are convenient to handle, store and use (Somogyi and Luh, 1986). Under proper storage conditions they are almost immune to spoilage.

Drying and dehydration of fresh fruits and vegetables is one of the most energy-intensive processes in the food industry and promising method of reducing post harvest losses. Apart from the high-energy costs and legislation on pollution, sustainable and eco-friendly technologies have created greater demand for energy efficient drying processes in the food industry. Improving energy efficiency by only 1 % could result in an as much as 10% increase in profits (Beedie, 1995). However, food dehydration causes loss of volatiles and flavours, changes in colour and texture, and decrease in nutritional values. In simpler terms, technique of dehydration requires development of methods that minimize the adverse effects of processing.

Traditionally fruits and vegetables are dried in open sunlight, which is weather dependable and also prone to microbial and other contamination (Mathioulakis et al., 1998). To achieve consistent quality in dried product industrial dryers should be used. Industrial dryers are rapid and provide uniform, hygienic dried product (Abdelhaq & Labuza, 1987; Doymaz & Pala, 2002; Karathanos and Belessioutis, 1997). The drying rate can also be enhanced by pretreatments like blanching and sulphitation (Dabhade and Khedkar, 1980; Doymaz, 2004a). Pretreatments help in colour retention and improve storage stability by the preservative effects.

The drying kinetics of food is a complex phenomenon and requires simple representations to predict the drying behavior, and for optimizing the drying parameters. Recently studies have been done on drying kinetics of fruits and vegetables (Sabarez and Prince, 1999; Togrul and Pehlivan, 2002; Soysal, 2004; Doymaz, 2004b; Cao et al., 2004; Jain and Pathare, 2004, Goyal et al, 2006; Goyal et al., 2007). The studies found in the literature on drying of apple slices (Menges et al., 1997, sacilik and Elicin, 2006, Schultz et al., 2007, Wang et al., 2007) mainly show the effect of drying on shrinkage, change in colour under hot and microwave drying with apple pomace, golden apple and organic apple. Hence, the objectives of present study were to: (i) to study the drying kinetics of apple in a tunnel dryer as affected by various pre-treatments and (ii) to evaluate a time dependent model of drying process for predicting drying rates of apple.

2. MATERIALS AND METHODS

2.1. Raw material

Apple used for the drying experiments were purchased from local market, Ludhiana, India. Initial moisture content of apple was 584.93% d. b. and was determined by AOAC method no. 934.06 (AOAC, 2000). Good quality apple

o

were selected and stored in a refrigerator at 4 C until drying experiments. After 2hour stabilization at ambient temperature, homogenous samples (range between 150-160 g) were washed with tap water and hand peeled, and then cut into uniform slices (average thickness 3.5 ± 0.5 mm) using a hand operated slicer. Apple samples were subjected to three different pre-treatments (blanching, dipping in potassium metabisulphite and blanching with potassium metabisulphite) in order to prevent browning. In order to compare the effect of pre-treatments, the apple slices were also dried in their natural form, which was called untreated samples and were dried on the same day.

2.2. Pre-treatments

Apple slices were subjected to four different pre-treatments namely control, blanching, dipping in 1% KMS (potassium metabisulphite) and blanching with 1% KMS. Control was untreated or reference sample. Blanching of apple slices was carried out by dipping the sample in hot water (about 65°C for 5-6 minutes). For sulphitation 1% potassium metabisulphite (KMS) was used.

2.3. Drying equipment

The thin layer drying experiments were performed in a pilot plant cross-flow tunnel dryer (NSW-600, Narang Scientific works, New Delhi). The schematic diagram of the dryer is shown in figure 1. The dryer consisted of a tunnel, electrical heater, fan and a temperature controller (30-110°C, dry bulb temperature). The speed of the tunnel was fixed at 0.004 ms-1. The samples were dried in multiple passes in the dryer. It took 8 minutes for the trays to complete a single passage in the tunnel.

2.4. Drying procedure

Apple slices were dried with pre-treatments namely control (untreated samples), blanching, dipping in 1% KMS, and blanching with 1% KMS. Experiments were conducted at 50, 60, and 70°C. The relative humidity was in the range of 30-40% whereas room air temperature varies from 20-27 °C. After the dryer reached the set conditions, sliced samples (150 g) were uniformly spread in rectangular aluminium trays (size: 310 mm by 210 mm by 30 mm) and kept in the tunnel for drying. Moisture loss was recorded in 30 minutes intervals by a digital balance of 0.01 g accuracy (Scaltec instruments, Germany). The drying was continued until there was no large variation in the moisture loss. Experiments were replicated three times.

2.5. Mathematical modelling

Moisture ratio of the samples during drying was expressed by the following equation:M - M

MR =-----------^ (1)M0 - Me

Since the drying was conducted in the tunnel dryer, during drying, the samples were not exposed to uniform relative humidity and temperature continuously. So, the moisture ratio was simplified according to Pala et aL, (1996), Doymaz (2004a) and Goyal et al., (2007), and expressed as:

MMR =----- (2)

M 0

®7

Figure 1. Isometric diagram of tunnel dryer: (1) table; (2) drying chamber; (3) motor; (4) moving tunnel; (5) control panel; all

dimensions in mm

To select a suitable model for describing the drying process of apple slices, drying curves were fitted with six thin-layer drying equations. The moisture ratio models are presented in Table 1.

Table 1. Mathematical model given by various authorsEquation Name References

MR = exp (-kt) Newton Liu and Bakker-Arkema (1997), O'callaghan et al., (1971)

MR = exp (-ktn) Page Zhang and Litchfield (1991)

MR = exp (-(kt)n) Modified Page Overhults et al., (1973)

MR = a exp (-kt) Henderson and Pabis Henderson and Pabis (1961), Chinnman (1984)

MR = a exp (-kt)+c Logarithmic Yaldiz et al., (2001)MR = 1+ at + bt2 Wang and Singh Wang and Singh (1978)

(3)Goyal et al.: Thin Layer Drying Kinetics of Apple in Tunnel Dryer

Z ^exp,, -

MRwe l

)2

Z =

1 N

MBE = 1Z (MRpre, - MRexp, )N i=1

' 1 N

N ZKMRpre, - MRexp,i )

i=1

2.6. Moisture diffusivity

Fick' s diffusion equation for particles with slab geometry was used for calculation of effective moisture diffusivity. Since the apples were dried after slicing, the samples were considered of slab geometry. The equation is expressed as,

g

MR = —-exp n

Published by Berkeley Electronic Press, 2008

N - z

(4)

RMSE = (5)

t(6)

L2

Goyal et al.: Thin Layer Drying Kinetics of Apple in Tunnel Dryer

The effective diffusivity was calculated using method of slopes (Maskan et al., 2002; Doymaz, 2004b). The diffusion coefficient was typically calculated by plotting experimental drying data in terms of ln (MR) versus drying time.

RESULTS AND DISCUSSION

3.1 Drying behaviour of apple slices

The effect of treatment and the time taken to reach the final moisture content is presented in Table 2. The final moisture content of samples dried under different conditions ranged from 9% to 15% (d.b). It is evident that pre-treatments had effect on moisture movement from the

samples. In all the drying temperature selected, the sample blanched with 1%

KMS had shorter drying time than control, KMS and blanched samples. Similar results were reported in drying of apricots (Pala et al., 1996; Doymaz, 2004a), grapes (Doymaz & Pala, 2002) and mango (Goyal et al.,


7

3.

2006). The drying air temperature has also an important effect on drying of apple slices. At the higher temperature of 70°C, the drying time was less

International Journal of Food Engineering, Vol. 4 [2008], Iss. 8, Art. 8

http://www.bepress.com/ijfe/vol4/iss8/art8DOI: 10.2202/1556-3758.1233

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for control and blanched samples. Similar observations have been reported for drying of garlic slices (Madamba et al., 1996) and onion slices (Sarasvadia et al., 1999) and plum (Goyal et al., 2007).

Table 2. Drying time of raw apple slices

Sample Drying time (min) at different drying temperatures

50°C 60°C 70°CControl 330 300 270KMS 300 240 210Blanched 270 240 210Blanched with 1% KMS 240 210 180

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Effect of pre-treatment on drying curves of raw apple dried at 50, 60, 70 C are presented in figures 2-4. The drying curves show that the moisture ratio decreases continuously with drying time. During the initial period of drying, the drying rate was similar in all treatments. After the removal of surface moisture the drying rate of pre-treated samples was higher. Drying of apple slices occurred in falling rate period and no constant rate period was observed. The drying in falling rate


9

period indicates that, internal mass transfer has occurred by diffusion. Similar results have been reported for the drying studies on onion slices (Rapuas and Driscoll, 1995), apricots (Doymaz, 2004a), raw mango (Goyal et al., 2006) and tomato (Kingsly et al., 2007).

Time, min

Figure 2. Effect of pre-treatment on drying time at drying air temperature of 50°C



10



11

0 30 60 90 120 150 180 210 240 270 300 330Time, min

Figure 3. Effect of pre-treatment on

drying time at drying air

temperature of 60°C

Time, min

Figure 4. Effect of

pre-treatments on

drying time at

drying air

temperature of 70°C

3.2. Mathematical

modelling of drying

curves

The moisture ratio data of

raw apple slices dried at

different temperatures withdifferent pre-treatments were fitted into the thin layer models listed in Table 3.

2 2

The values of r , x , MBE and RMSE are summarised in Table 3.

In all cases, the value of r was greater than 0.90, indicating a good fit (Madamba et al., 1996; Erenturk et al., 2004). The values of r2 for the Page, Modified Page, Logarithmic and Wang and Singh model were above 0.99. But the Logarithmic model gave comparatively higher r values in all the drying treatments (0.9998), and also the x2 (0.023 x 10-3), MBE (0.010 x 10-3) and RMSE (0.0068) values were lower. Hence the logarithmic model may assume to represent the thin layer drying behaviour of apple slices. Sacilik and Elicin (2006) reported a similar result for organic apple slices.



12


Table 3.Results of statistical analyses on the thin layer drying of apple

Model Drying temperature

Treatment r2

x2 x io-3 MBE x 1 0-

3RMSE

Newton 50°C Control 0.9926 0.76 6.120 0.0263

Blanched 0.9646 4.71 6.600 0.0652

Dipped in 1% KMS 0.9861 1.59 4.891 0.0380

Blanched + 1% KMS 0.9636 4.84 6.250 0.0651

60°C Control 0.9739 2.99 6.060 0.0522

Blanched 0.9711 3.76 7.001 0.0578

Dipped in 1% KMS 0.9595 3.18 3.181 0.0670

Blanched + 1% KMS 0.9486 6.53 1.771 0.0755

70°C Control 0.9811 2.34 6.550 0.0459

Blanched 0.9684 4.53 8.711 0.0630

Dipped in 1% KMS 0.9833 2.11 5.930 0.0420

Blanched + 1% KMS 0.9688 4.66 8.731 0.0630

Page 50°C Control 0.9961 0.434 5.411 0.0190

Blanched 0.9982 0.260 0.351 0.0140

Dipped in 1% KMS 0.9990 0.117 3.050 0.0097

Blanched + 1% KMS 0.9968 0.478 5.442 0.0193

60°C Control 0.9929 0.898 7.990 0.0271

Blanched 0.9966 0.495 5.743 0.0196

Dipped in 1% KMS 0.9961 0.569 6.502 0.0210

Blanched + 1% KMS 0.9906 1.387 9.054 0.0320

70°C Control 0.9997 0.034 1.081 0.0052

Blanched 0.9994 0.100 1.562 0.0086

Dipped in 1% KMS 0.9966 0.448 5.113 0.0183

Blanched + 1% KMS 0.9984 0.282 4.163 0.0142

Modified 50°C Control 0.9961 0.434 5.411 0.0190

Page Blanched 0.9982 0.260 0.352 0.0140

Dipped in 1% KMS 0.9990 0.117 3.053 0.0097

Blanched + 1% KMS 0.9968 0.478 5.443 0.0193

60°C Control 0.9929 0.898 7.992 0.0271

Blanched 0.9966 0.495 5.741 0.0196

Dipped in 1% KMS 0.9961 0.569 6.504 0.0210

Blanched + KMS 0.9906 1.387 9.051 0.0320

70°C Control 0.9997 0.034 1.081 0.0052


13

Blanched 0.9994 0.100 1.562 0.0086

Dipped in 1% KMS 0.9969 0.448 5.112 0.0183

Blanched + 1% KMS 0.9984 0.282 4.163 0.0142

Henderson 50°C Control 0.9931 0.782 7.871 0.0255

& Pabis Blanched 0.9707 4.377 15.32 0.0590

Dipped in 1% KMS 0.9888 1.416 9.913 0.0340

Blanched + 1% KMS 0.9690 4.700 5.272 0.0605

60°C Control 0.9772 2.907 2.141 0.0480

Blanched 0.9750 3.708 14.44 0.0537

Dipped in 1% KMS 0.9666 4.890 13.78 0.0616

Blanched + 1% KMS 0.9554 6.608 12.91 0.0704

70°C Control 0.9844 2.188 12.28 0.0410

Blanched 0.9723 4.649 16.48 0.0590

Dipped in 1% KMS 0.9851 2.180 10.97 0.0405

Blanched + 1% KMS 0.9720 5.019 16.55 0.0598

Logarithmic 50 Control 0.9995 0.061 0.019 0.0068

Blanched 0.9935 0.280 0.069 0.0440

Dipped in 1% KMS 0.9979 0.291 0.028 0.0145

Blanched + 1% KMS 0.9911 1.570 0.011 0.0328

60 Control 0.9983 0.023 0.092 0.0131

Blanched 0.9934 1.140 0.010 0.0270

Dipped in 1% KMS 0.9967 0.550 0.027 0.0195

Blanched + 1% KMS 0.9984 0.270 0.028 0.0129

70 Control 0.9924 1.215 0.021 0.0291

Blanched 0.9998 0.860 0.031 0.0422

Dipped in 1% KMS 0.9987 0.214 0.043 0.0115

Blanched + 1% KMS 0.9913 2.176 0.083 0.0352

Wang 50°C Control 0.9918 0.930 6.722 0.0278

& Singh Blanched 0.9910 1.348 4.422 0.0328

Dipped in 1% KMS 0.9984 0.203 1.188 0.0128

Blanched + 1% KMS 0.9960 0.607 3.866 0.0217

60°C Control 0.9993 0.078 1.165 0.0079

Blanched 0.9985 0.213 2.136 0.0129

Dipped in 1% KMS 0.9981 0.275 3.201 0.0146

Blanched + 1% KMS 0.9988 0.177 1.188 0.1150

70°C Control 0.9963 0.512 2.001 0.0202

Blanched 0.9953 0.785 3.601 0.0240



14


Dipped in 1% KMS 0.9996 0.049 1.201 0.0060

Blanched + 1% KMS 0.9973 0.470 3.588 0.0180

3.3 Calculation of effective moisture diffusivity

The effective diffusivity was calculated using method of slopes (Maskan et al., 2002; Doymaz, 2004b). The values of moisture diffusivity were found to vary in range of 2.22 x 10-10 to 4.69 x 10-10

m2s-1 (Table 4), which was close to those of 1.42 x 10-

10 to 4.69 x 10-10 m2s-1 by Lazarides et al., (1997) for apple slices in the drying temperature range of 20-500C but slightly higher to those of 1.79 x 10-10 to 4.45 x 10-10 m2s-1 by Velic et al., (2004) for apple slices at a drying air temperature of 60°C with slice thickness of 5mm. The small difference among values could be due to the difference in varieties, drying equipment and other uncontrolled parameters. The effective diffusivity increases with increase in drying temperatures. These values are within the range of 10-9-10-11 m

2s-1

for drying of food materials (Maskan et al., 2002 and Akpinar et al., 2003) and


15

comparable with the reported values of 2.02 x 10-10 to 4.24 x 10-10 m2s-1

for garlic slices in a temperature range of 50-90°C (Madamba et al. 1996), with 2.32x 10-10 to 2.76x 10-10 m2s-1 for hot air drying of mulberry at 60-80°C (Maskan & Gogus, 1998), with 20.28 x 10-10

m2s-1 for hot air drying of paprika at 60°C (Ramesh et al., 2001), with 3.04 x 10-10 to 4.41 x 10-10 m2s-1

for hot air drying of plums at 5565 °C (Goyal et al., 2007). These values were consistent with the present estimated D e f f values for apple slices.

Table 4. Effective moisture diffusivity for drying of

apple slicesDrying Pre-treatments Deff (m2s-1) r2

temperature (°C)50 Control 2.22 x 10-10 0.9249

Dipped in 1% KMS 2.35 x 10-10 0.9338Blanched 3.11 x 10-10 0.9413Blanched + 1% KMS 3.34 x 10-10 0.9415

60 Control 2.42 x 10"1U 0.9016Dipped in 1% KMS 2.85 x 10-10 0.9101Blanched 2.99 x 10-10 0.9553Blanched + 1% KMS 3.07 x 10-10 0.9077

70 Control 2.95 x 10"1U 0.9859Dipped in 1% KMS 3.18 x 10-10 0.9207Blanched 4.19 x 10-10 0.9692



16




Blanched + 1% KMS 4.69 x 10-10 0.9513


17

CONCLUSION

The effect of temperature and pre-treatments on thin layer drying of apple slices in a tunnel drier was investigated. Increase in drying temperature from 50 to 70°C decreased the drying time from 330 to 270 min for control, 300 to 210 min for KMS treated, 270 to 210 min for blanched and 240 to 180 min for blanched with KMS samples. Thus apple slices blanched with 1% KMS have shorter drying time compared to other three samples. The entire drying process occurred in falling rate period and constant rate period was not observed. Six thin-layer equations were investigated for their suitability to describe the drying behaviour of apple slices. The Logarithmic model showed the best fit with high values for the coefficient of determination (0.9998) and low %2, MBE and RMSE values. The effective moisture diffusivity varied from 2.22 x 10-10 to 4.69 x 10-10 m2s-1 with higher values for treated samples.

Nomenclature

reduced chi-square empirical constants in drying models effective moisture diffusivity, m /s drying constant potassium meta bisulphite thickness of slice, mmoisture content at time t, kg moisture.kg-1 dry matter mean bias errorequilibrium moisture content, kg moisture.kg-1 dry matterinitial moisture content, kg moisture.kg-1 dry matterdimensionless moisture ratioexpected moisture ratiopredicted moisture rationumber of observationscoefficient of determinationroot mean square errordrying time, hnumber of drying constants

4. International Journal of Food Engineering, Vol. 4 [2008], Iss. 8, Art. 8


18

Xa, b, c, nDeff

kKMSLMMBE Me

Mo

MR MRe

MR

^-

exp

preNr2

RMSE tz



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international journal of food

Documents

berkeley electronic press

falling rate period

constant rate period

final moisture content

post harvest engineering

effective moisture diffusivity

hot air drying

drying air temperature