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Drying characteristics of tomatoes
Journal of Food Engineering
14 (1991) 259-268
Drying Characteristics of Tomatoes M. N. A. Hawlader,”
M. S. Uddin, b* J. C. Ho u & A. B. W. Teng a
“Mechanical and Production Engineering Department, bChemical Engineering Department, Faculty of Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 05 11 (Received 20 June 1990; revised version received 20 November accepted 2 1 November 1990)
1990;
ABSTRACT
In this investigation, the drying characteristics of tomatoes have been studied under various operating conditions. A drier was built for expen’ments under controlled conditions. Experiments were conducted with different air temperatures and flow velocities to determine the drying characteristics of tomato. A diffusion model was used to study the drying of sliced tomato specimens. Shrinkage was observed and this effect was taken into account in the basic diffusion model through the use of a power law expression that related apparent shrinkage to moisture content. Analysis of experimental data yielded correlations between the flective diffusivity and both temperature and air velocity. An equation was also developed to estimate the drying time to reach a particular moisture level.
INTRODUCTION The lack of proper processing causes considerable damage and wastage of seasonal crops in many tropical countries. Drying is a common form of food preservation and allows food to be kept for a longer period than would otherwise have been possible. For the purpose of storage, the moisture content of a crop must be reduced to a reasonably low level immediately after harvest in order to prevent the growth of mould and also to stop bacterial action. During the drying process, a reduction in moisture content occurs by evaporation, where the latent heat of evaporation is provided by the *To whom correspondence
should be addressed. 259
Journal
of Food
Engineering
0260-8774/91/$03.50
Publishers Ltd. England. Printed in Great Britain
- 0
1991
Elsevier
Science
260
M. N.A. Hawiader, M. S. U&in, J. C. Ho, A. B. W. Teng
drying medium. For the same humidity, the drying potential of a medium increases with the increase in temperature of the medium. Many foodstuffs have been dried successfully and these include various fruits, vegetables and meats (Holdsworth, 1986). In the tropics tomatoes are available throughout the year. In the temperate regions it is a seasonal crop and, hence, there is surplus in one season and shortage in another. Currently, tomatoes are preserved in the form of ketchup, paste and juice. Many methods (Ginnette et al., 1963; Lazar et al., 1956; Kaufman et al., 195 5) are available for drying tomatoes but conventional air drying is considered expensive due to the high moisture content in the fruits. Drying of tomatoes in the sun has been practised in many countries (Gupta & Nath, 1984; Bassuoni & Tayeb, 1982). Tomato is considered to be rather complex with an inner wall structure resembling a fibrous material while the pulpous areas containing the seeds resemble a non-porous material; it is considered to be hygroscopic. Existing literature (Mujurndar, 1987; van Arsdel & Copley, 1963) has defined a generalized drying curve that includes a constant drying rate region and falling rate regions. However, not all materials follow this pattern. For some, only the falling rate regions are observed. A substance undergoes a constant drying rate when a film of water is freely available at the drying surface for evaporation into the drying medium. This drying rate is similar to that of a pool of water evaporating into air. It is dependent upon the air temperature, air humidity and heat transfer to the water. The falling rate regions are indicative of an increased resistance to both heat and mass transfer and occur when the surface water no longer exists and water to be evaporated comes from within the structure and must be transported to the surface. With different falling rate regions the possibility exists of drying rates being affected by changes in structure, such as case hardening and shrinkage. In this analysis, a simple diffusion model based on Fick’s second law of diffusion is considered for the transport mechanisms of the falling rate regions and is given by the following equation: i?W
a2W
-D--
ax2
(1)
where w = moisture contents (g water/g dry mass); t = time (s); x = length (m); D = diffusion coefficient for moisture in solids (m*/s).
261
Drying characterhics of tomatoes
In this model, the diffusion coefficient D serves as a measure of the drying rate. The determination of its value under various drying conditions for a given specimen is a major objective of this report. Considering a slice of tomato as a flat plate of thickness L drying on both sides and under the given boundary conditions of t=O;OIxlL;w=w, t>O;x=O,L;
w=w e
the following solution exists in the absence of any external resistances (Rao & Rizvi, 1986): w-w, _=wo-w,
8
m c l n2.=,(2n-1)
-(2n-I)‘9 1
where w, and w, represent the equilibrium and initial moisture content, respectively. In eqn (2), it is assumed that the sample temperature and thickness are constant during drying. Equilibrium moisture content of a sample being dried depends upon the structure and type of material, and the moisture content of the air. When air is recirculated in a drier there might be considerable change in air humidity during the process and hence a constant value of equilibrium moisture content cannot be assumed. In such cases, sorption isotherms for that food system are required for drying calculations. However, the equilibrium moisture content for the conditions of drying in the present study is considered negligible (Uddin et al., 1990). Also for conditions where L is small and t is large, the terms in the summation series in eqn (2) corresponding to II > 1 are small. Under these conditions the following approximation can be made ln(w/wo)=ln(8/n2)-n2Dt/L2
(3)
Equation (3) shows that the diffusion coefficient D can be measured from the slope of the plot of m( w/wJ against t or t/L2. The approach described here is a simplified one and the diffusivity measured would be a ‘lumped value, called effective diffusivity, incorporating factors that were not considered separately but would affect the drying characteristics. Nonetheless, the model would provide a consistent measure of the effective diffusivity for the specimen under given drying conditions. The measurement of the effective diffusivity would thus allow for a quantitative study of the drying characteristics in relation to controlled experimental variables such as air flow and temperature.
M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
262
In this paper the drying characteristics of tomatoes are investigated under controlled laboratory conditions. The effects of flow rate and temperature of the drying medium have been investigated in detail.
MATERIALS
AND METHODS
In order to determine the influence of temperature and flow velocity on the drying of tomato, a cabinet drier was built which included a 12 kW heater, a blower and a temperature controller. Test specimens were placed on trays made of wire mesh. Temperature could be varied by varying the input power to the different banks of heater elements. The air flow rate was varied by controlling the inlet opening of the blower. The desired temperature was maintained by a thermal controller. Temperatures were measured by thermocouples at different locations in the test rig and recorded on a chart recorder. The air flow rate was measured by a rotating vane anemometer at regular intervals. The humidity of the air was measured with a sling hygrometer and readings were taken at different times of the day to obtain an average value. Fresh, ripe tomatoes of Malaysian variety, each weighing in the range of 90-120 g, were used in the experiments. Fourteen to sixteen pieces of sliced tomatoes of approximately 5 mm thickness placed on a wire mesh tray were dried under conditions given in Table 1. The average diameter, number of pieces and the total weight of the tray and the specimens were recorded. Once the desired conditions were achieved in the drier, the tray with the specimens was inserted into the cabinet drier and a timer was switched on. The door of the drier was properly sealed to prevent air leakage. At regular intervals, the tray was taken out of the drier, weighed and returned to the drier. The mass and the corresponding drying time were then recorded. Drying continued until the mass of the specimen reached approximately 10% of its initial value. After the completion of TABLE 1 Variables Considered in the Experiments Specimen Thickness: 5 mm Air velocity (m/s)
Air temperature CC)
40 50 60 70 80
o-4 0.4 0.4
1.0 0.7
1.0 1.(I
1.4
1.8 1.8 1.8 1% 1.8
Drying characteristicsof tomatoes
263
drying, the specimens were dried in an oven at 105°C for at least 24 h during which the specimens were checked for constant mass to determine if the fully dry condition had been reached. The final dry mass was then recorded. The experiment was repeated at different temperatures and air flow rates and the results were recorded.
RESULTS AND DISCUSSION The results obtained from experiments and analyses are presented in this section. Correlations have been developed for the effective diffusion coefficient and the drying time in terms of flow velocity and the temperature of the drying medium. Figure 1 shows the variation of mass in a sample during drying. With the increase in temperature of the drying medium, the drying potential increases and the moisture removal rate increases. This is shown in Fig. 1 over the temperature range 60-80°C for the same air flow rate. Similar effects were obtained when the flow rate was increased at constant temperature. Figure 2 shows the variation in drying rate as a function of moisture content with air velocity and temperature as variables. For the given experimental conditions, the samples did not show any constant rate of drying. This implied that a fihn of water did not exist at the surface of the specimens and whatever water reached the surface from within the body of the specimen evaporated almost immediately. Higher temperature and
Drying time 1mini
Fig. 1.
Total mass versus drying time at: .-
l,6O”C, 0.4 m/s;
0,
8O”C, O-4 m/s; q, 8o”C,
264
M. IV.A. Hawlader, M. S. LJddin, J. C. Ho, A. B. W. Teng
velocity increased the drying potential for the transport of moisture and, hence, the drying rate increased. To determine the effective diffusivity, the experimental values of ln( w/wO) were plotted against t/L 2, as shown in Fig. 3. The slope of the curve is a measure of the effective diffusivity. It can be seen that the variation is non-linear on a semi-log plot. All the experimental values show a similar behaviour. The non-linear nature of the curve could be due to changes in specimen temperature. Although the external air temperature was constant, equilibrium between the specimen and the air would not have necessarily existed. Existing literature (Alzamora et al, 1980) and measurements during the experi-
Moisture Content (g/g dry)
Fig. 2.
Drying rate versus moisture content at: l, 60°C. 0.4 m/s; 60°C. 1% m/s.
.
5
Ia
15
t/L2(mm/mmZ)
Fig. 3.
Plot of ln( w/w”) versus ( t/L ?) (eqn (3)).
0,
WC, 0.4 m/s; q,
1 2a
265
Drying characteristicsof tomatoes
ments indicate that the actual temperature of the specimen increased as drying continued but it remained below the dry bulb temperature of the air. The increase in the slope of the curve and, hence, the effective diffusivity could be attributed to this increase in temperature. In eqn (3), the thickness L was assumed constant throughout the drying process. However, in the experiment, the tomato specimens did not maintain this initial thickness but shrank as they dried. The reduction in thickness was more than the decrease in diameter of the specimen. This disproportionate shrinkage was probably due to the way the specimens were cut. This was evident from the observations and the photographs of the tomato specimens taken at different stages of drying and implies an increased sample rigidity in the radial direction. An increase in temperature of the specimen increases the diffusion coefficient whereas the shrinkage and hardening evident during the experiment would decrease it. The actual nature of the curve would depend upon the relative magnitude of these opposing effects. If the shrinkage effect is taken into account and a modified thickness L’ is used, it might be possible to replace the curve by a straight line. The temperature of the specimen and the shrinkage effect are considered to be related to moisture content of the specimen. Assuming the diameter to be constant, the reduced thickness L’ was related to the moisture content by the following equation (Uddin et al., 1990): L’/L =( m,/m,)” where
(4)
m, = total mass of the specimen at drying time t (g) total mass (g) L = initial thickness of the specimen (mm)
m, = original
A value of n = 0.14 was found which resulted in almost a straight line for the experimental conditions when hr( w/we) was plotted against t/L ‘2, as shown in Fig. 4. The index II = 0.14 probably represents the combined effects of both the specimen temperature and shrinkage. The magnitude of the index would depend on the characteristics of the substance. A value of n = 0 would imply no shrinkage while a value of n = 1 would indicate that the volume shrinkage is equal to the volume of water lost. Table 2 shows the effective diffusion coefficients for the various experimental conditions considered in this project. The dependence of the effective diffusion coefficient on the temperature of the drying medium and flow velocity was investigated in greater detail and the following empirical equation was derived: D = 1.67 x lop8 Do exp( - 3024/T)
(m*/s)
(5)
M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
266
-I 0
20
IO
30
I
t/C*fmin/mm2)
Fig. 4.
Plot of ln( w/wO) versus (t/L ‘*) (shrinkage corrected).
TABLE 2 Effective Diffusion Coefficients Air temperature 0
40 40 40 50 60 60 60 60 60 70 80 80 80
Air velocity
D@sivity x lOi
(mls)
(m’ls)
@4 1.0 1.8 1.8 0.4 0.7 1.0 1.4 1.8 1.8 0.4 1,o 1,8
l-52 2.20 3.03 4.73 3.22 5.07 4.57 6-75 6.75 7.93 5.40 8.27 9.12
where D, = exp( 1.022 X V0’5 + 4.477) T= temperature of the medium (K) V= flow velocity (m/s) As discussed earlier, the effective diffusion coefficient D was obtained from the plot of ln( w/wO) versus t/L’*. For In( w/wO)> - 4 or w/w0 a#proximately greater than 2%, the equation for the plot was ln( W/W(J= Kt /LIZ
(6)
Drying characteristics of tomatoes
where
267
K = slope of the curve Lf I ~(~~pm,)o.”
Here m, is the total mass of the specimen at time t. The determination of moisture content w requires a knowledge of the final dry mass. The final dry mass, based on the number of tests conducted in this study, was found to be approximately equal to 5% of the total original mass and the ratio w /wOis given by m, - 0.0 5 m, W/W0
=
0*95m,
Substituting eqn (7) into eqn (6) gives
(8)
100
50
Orymg time(mml
Fig. 5.
Comparison of predicted drying time with experimental values at 60°C and 1-O analytical results (eqn (8)). m/s: *, experimental values; -,
Drying time (min)
Fig. 6.
Comparison of predicted drying time with experimental values at 80°C and l”8 analytical results (eqn (8)). m/s: + , experimental values; -,
268
M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
The comparison of the experimental results are agree fairly well with the that eqn (8) will predict taken into account.
predicted drying time, using eqn (8), and the shown in Figs 5 and 6. The predicted values experimental results and lead to the conclusion the diffusivity during drying when shrinkage is
REFERENCES Alzamora, S. M., Chirife, J., Viollaz, P. & Vaccarezza, L. M. (1980). Heat and mass transfer during air drying of avocado. In Drying ‘80, Vol. 1: Developments in Drying, ed. A. S. Mujumdar. Hemisphere Publishing, New York, pp. 247-54. Bassuoni, A. M. A. & Tayeb, A. M. ( 1982). Solar drying of tomatoes in the form of sheets. In Proceedings of Third International Drying Symposium, Vol. 1, ed. J. C. Ashworth, Birmingham, UK, 3-15 September 1982. Drying Research Ltd, Wolverhampton, pp. 385-9. Ginnette, L. F., Graham, R. P., Miers, J. C. & Morgan, A. I., Jr (1963). Tomato powder by foam-mat drying. Food Technology, 17,8 11. Gupta, R. G. & Nath, N. (1984). Drying of tomatoes. Journal of Food Science and Technology, 21,372-6.
Holdsworth, S. D. ( 1986). Advances in the dehydration of fruits and vegetables. In Concentration and Drying of Food, ed. D. MacCarthy. Elsevier Applied Science Publishers, London, pp. 293-303. Kaufman, V. F., Wong, F., Taylor, D. H. & Talburt, W. ( 1955). Problems in the production of tomato juice powder. Food Technology 9,120. Lazar, M. E., Brown, A. M., Smith, G. S., Wong, S. F. & Lindquist, F. E. ( 1956). Experimental production of tomato powder by spray drying. Food Technology, 10, 129. Mujumdar, A. S. (1987). Handbook of Industrial Drying. Marcel Dekker, New York. Uddin, M. S., Hawlader, M. N. A. & Rahman, M. S. ( 1990). Evaluation of drying characteristics of pineapple in the production of pineapple powder. J. Food ProcessingandPreservation,
14,375-91.
Rao, M. A. & Rizvi, S. S. H. (1986). Engineering Properties of Food. Marcel Dekker, New York. van Arsdel, W. B. & Copley, M. J. (1963). Food Dehydration. AVJ Publishing, Westport, Connecticut.
14 (1991) 259-268
Drying Characteristics of Tomatoes M. N. A. Hawlader,”
M. S. Uddin, b* J. C. Ho u & A. B. W. Teng a
“Mechanical and Production Engineering Department, bChemical Engineering Department, Faculty of Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 05 11 (Received 20 June 1990; revised version received 20 November accepted 2 1 November 1990)
1990;
ABSTRACT
In this investigation, the drying characteristics of tomatoes have been studied under various operating conditions. A drier was built for expen’ments under controlled conditions. Experiments were conducted with different air temperatures and flow velocities to determine the drying characteristics of tomato. A diffusion model was used to study the drying of sliced tomato specimens. Shrinkage was observed and this effect was taken into account in the basic diffusion model through the use of a power law expression that related apparent shrinkage to moisture content. Analysis of experimental data yielded correlations between the flective diffusivity and both temperature and air velocity. An equation was also developed to estimate the drying time to reach a particular moisture level.
INTRODUCTION The lack of proper processing causes considerable damage and wastage of seasonal crops in many tropical countries. Drying is a common form of food preservation and allows food to be kept for a longer period than would otherwise have been possible. For the purpose of storage, the moisture content of a crop must be reduced to a reasonably low level immediately after harvest in order to prevent the growth of mould and also to stop bacterial action. During the drying process, a reduction in moisture content occurs by evaporation, where the latent heat of evaporation is provided by the *To whom correspondence
should be addressed. 259
Journal
of Food
Engineering
0260-8774/91/$03.50
Publishers Ltd. England. Printed in Great Britain
- 0
1991
Elsevier
Science
260
M. N.A. Hawiader, M. S. U&in, J. C. Ho, A. B. W. Teng
drying medium. For the same humidity, the drying potential of a medium increases with the increase in temperature of the medium. Many foodstuffs have been dried successfully and these include various fruits, vegetables and meats (Holdsworth, 1986). In the tropics tomatoes are available throughout the year. In the temperate regions it is a seasonal crop and, hence, there is surplus in one season and shortage in another. Currently, tomatoes are preserved in the form of ketchup, paste and juice. Many methods (Ginnette et al., 1963; Lazar et al., 1956; Kaufman et al., 195 5) are available for drying tomatoes but conventional air drying is considered expensive due to the high moisture content in the fruits. Drying of tomatoes in the sun has been practised in many countries (Gupta & Nath, 1984; Bassuoni & Tayeb, 1982). Tomato is considered to be rather complex with an inner wall structure resembling a fibrous material while the pulpous areas containing the seeds resemble a non-porous material; it is considered to be hygroscopic. Existing literature (Mujurndar, 1987; van Arsdel & Copley, 1963) has defined a generalized drying curve that includes a constant drying rate region and falling rate regions. However, not all materials follow this pattern. For some, only the falling rate regions are observed. A substance undergoes a constant drying rate when a film of water is freely available at the drying surface for evaporation into the drying medium. This drying rate is similar to that of a pool of water evaporating into air. It is dependent upon the air temperature, air humidity and heat transfer to the water. The falling rate regions are indicative of an increased resistance to both heat and mass transfer and occur when the surface water no longer exists and water to be evaporated comes from within the structure and must be transported to the surface. With different falling rate regions the possibility exists of drying rates being affected by changes in structure, such as case hardening and shrinkage. In this analysis, a simple diffusion model based on Fick’s second law of diffusion is considered for the transport mechanisms of the falling rate regions and is given by the following equation: i?W
a2W
-D--
ax2
(1)
where w = moisture contents (g water/g dry mass); t = time (s); x = length (m); D = diffusion coefficient for moisture in solids (m*/s).
261
Drying characterhics of tomatoes
In this model, the diffusion coefficient D serves as a measure of the drying rate. The determination of its value under various drying conditions for a given specimen is a major objective of this report. Considering a slice of tomato as a flat plate of thickness L drying on both sides and under the given boundary conditions of t=O;OIxlL;w=w, t>O;x=O,L;
w=w e
the following solution exists in the absence of any external resistances (Rao & Rizvi, 1986): w-w, _=wo-w,
8
m c l n2.=,(2n-1)
-(2n-I)‘9 1
where w, and w, represent the equilibrium and initial moisture content, respectively. In eqn (2), it is assumed that the sample temperature and thickness are constant during drying. Equilibrium moisture content of a sample being dried depends upon the structure and type of material, and the moisture content of the air. When air is recirculated in a drier there might be considerable change in air humidity during the process and hence a constant value of equilibrium moisture content cannot be assumed. In such cases, sorption isotherms for that food system are required for drying calculations. However, the equilibrium moisture content for the conditions of drying in the present study is considered negligible (Uddin et al., 1990). Also for conditions where L is small and t is large, the terms in the summation series in eqn (2) corresponding to II > 1 are small. Under these conditions the following approximation can be made ln(w/wo)=ln(8/n2)-n2Dt/L2
(3)
Equation (3) shows that the diffusion coefficient D can be measured from the slope of the plot of m( w/wJ against t or t/L2. The approach described here is a simplified one and the diffusivity measured would be a ‘lumped value, called effective diffusivity, incorporating factors that were not considered separately but would affect the drying characteristics. Nonetheless, the model would provide a consistent measure of the effective diffusivity for the specimen under given drying conditions. The measurement of the effective diffusivity would thus allow for a quantitative study of the drying characteristics in relation to controlled experimental variables such as air flow and temperature.
M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
262
In this paper the drying characteristics of tomatoes are investigated under controlled laboratory conditions. The effects of flow rate and temperature of the drying medium have been investigated in detail.
MATERIALS
AND METHODS
In order to determine the influence of temperature and flow velocity on the drying of tomato, a cabinet drier was built which included a 12 kW heater, a blower and a temperature controller. Test specimens were placed on trays made of wire mesh. Temperature could be varied by varying the input power to the different banks of heater elements. The air flow rate was varied by controlling the inlet opening of the blower. The desired temperature was maintained by a thermal controller. Temperatures were measured by thermocouples at different locations in the test rig and recorded on a chart recorder. The air flow rate was measured by a rotating vane anemometer at regular intervals. The humidity of the air was measured with a sling hygrometer and readings were taken at different times of the day to obtain an average value. Fresh, ripe tomatoes of Malaysian variety, each weighing in the range of 90-120 g, were used in the experiments. Fourteen to sixteen pieces of sliced tomatoes of approximately 5 mm thickness placed on a wire mesh tray were dried under conditions given in Table 1. The average diameter, number of pieces and the total weight of the tray and the specimens were recorded. Once the desired conditions were achieved in the drier, the tray with the specimens was inserted into the cabinet drier and a timer was switched on. The door of the drier was properly sealed to prevent air leakage. At regular intervals, the tray was taken out of the drier, weighed and returned to the drier. The mass and the corresponding drying time were then recorded. Drying continued until the mass of the specimen reached approximately 10% of its initial value. After the completion of TABLE 1 Variables Considered in the Experiments Specimen Thickness: 5 mm Air velocity (m/s)
Air temperature CC)
40 50 60 70 80
o-4 0.4 0.4
1.0 0.7
1.0 1.(I
1.4
1.8 1.8 1.8 1% 1.8
Drying characteristicsof tomatoes
263
drying, the specimens were dried in an oven at 105°C for at least 24 h during which the specimens were checked for constant mass to determine if the fully dry condition had been reached. The final dry mass was then recorded. The experiment was repeated at different temperatures and air flow rates and the results were recorded.
RESULTS AND DISCUSSION The results obtained from experiments and analyses are presented in this section. Correlations have been developed for the effective diffusion coefficient and the drying time in terms of flow velocity and the temperature of the drying medium. Figure 1 shows the variation of mass in a sample during drying. With the increase in temperature of the drying medium, the drying potential increases and the moisture removal rate increases. This is shown in Fig. 1 over the temperature range 60-80°C for the same air flow rate. Similar effects were obtained when the flow rate was increased at constant temperature. Figure 2 shows the variation in drying rate as a function of moisture content with air velocity and temperature as variables. For the given experimental conditions, the samples did not show any constant rate of drying. This implied that a fihn of water did not exist at the surface of the specimens and whatever water reached the surface from within the body of the specimen evaporated almost immediately. Higher temperature and
Drying time 1mini
Fig. 1.
Total mass versus drying time at: .-
l,6O”C, 0.4 m/s;
0,
8O”C, O-4 m/s; q, 8o”C,
264
M. IV.A. Hawlader, M. S. LJddin, J. C. Ho, A. B. W. Teng
velocity increased the drying potential for the transport of moisture and, hence, the drying rate increased. To determine the effective diffusivity, the experimental values of ln( w/wO) were plotted against t/L 2, as shown in Fig. 3. The slope of the curve is a measure of the effective diffusivity. It can be seen that the variation is non-linear on a semi-log plot. All the experimental values show a similar behaviour. The non-linear nature of the curve could be due to changes in specimen temperature. Although the external air temperature was constant, equilibrium between the specimen and the air would not have necessarily existed. Existing literature (Alzamora et al, 1980) and measurements during the experi-
Moisture Content (g/g dry)
Fig. 2.
Drying rate versus moisture content at: l, 60°C. 0.4 m/s; 60°C. 1% m/s.
.
5
Ia
15
t/L2(mm/mmZ)
Fig. 3.
Plot of ln( w/w”) versus ( t/L ?) (eqn (3)).
0,
WC, 0.4 m/s; q,
1 2a
265
Drying characteristicsof tomatoes
ments indicate that the actual temperature of the specimen increased as drying continued but it remained below the dry bulb temperature of the air. The increase in the slope of the curve and, hence, the effective diffusivity could be attributed to this increase in temperature. In eqn (3), the thickness L was assumed constant throughout the drying process. However, in the experiment, the tomato specimens did not maintain this initial thickness but shrank as they dried. The reduction in thickness was more than the decrease in diameter of the specimen. This disproportionate shrinkage was probably due to the way the specimens were cut. This was evident from the observations and the photographs of the tomato specimens taken at different stages of drying and implies an increased sample rigidity in the radial direction. An increase in temperature of the specimen increases the diffusion coefficient whereas the shrinkage and hardening evident during the experiment would decrease it. The actual nature of the curve would depend upon the relative magnitude of these opposing effects. If the shrinkage effect is taken into account and a modified thickness L’ is used, it might be possible to replace the curve by a straight line. The temperature of the specimen and the shrinkage effect are considered to be related to moisture content of the specimen. Assuming the diameter to be constant, the reduced thickness L’ was related to the moisture content by the following equation (Uddin et al., 1990): L’/L =( m,/m,)” where
(4)
m, = total mass of the specimen at drying time t (g) total mass (g) L = initial thickness of the specimen (mm)
m, = original
A value of n = 0.14 was found which resulted in almost a straight line for the experimental conditions when hr( w/we) was plotted against t/L ‘2, as shown in Fig. 4. The index II = 0.14 probably represents the combined effects of both the specimen temperature and shrinkage. The magnitude of the index would depend on the characteristics of the substance. A value of n = 0 would imply no shrinkage while a value of n = 1 would indicate that the volume shrinkage is equal to the volume of water lost. Table 2 shows the effective diffusion coefficients for the various experimental conditions considered in this project. The dependence of the effective diffusion coefficient on the temperature of the drying medium and flow velocity was investigated in greater detail and the following empirical equation was derived: D = 1.67 x lop8 Do exp( - 3024/T)
(m*/s)
(5)
M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
266
-I 0
20
IO
30
I
t/C*fmin/mm2)
Fig. 4.
Plot of ln( w/wO) versus (t/L ‘*) (shrinkage corrected).
TABLE 2 Effective Diffusion Coefficients Air temperature 0
40 40 40 50 60 60 60 60 60 70 80 80 80
Air velocity
D@sivity x lOi
(mls)
(m’ls)
@4 1.0 1.8 1.8 0.4 0.7 1.0 1.4 1.8 1.8 0.4 1,o 1,8
l-52 2.20 3.03 4.73 3.22 5.07 4.57 6-75 6.75 7.93 5.40 8.27 9.12
where D, = exp( 1.022 X V0’5 + 4.477) T= temperature of the medium (K) V= flow velocity (m/s) As discussed earlier, the effective diffusion coefficient D was obtained from the plot of ln( w/wO) versus t/L’*. For In( w/wO)> - 4 or w/w0 a#proximately greater than 2%, the equation for the plot was ln( W/W(J= Kt /LIZ
(6)
Drying characteristics of tomatoes
where
267
K = slope of the curve Lf I ~(~~pm,)o.”
Here m, is the total mass of the specimen at time t. The determination of moisture content w requires a knowledge of the final dry mass. The final dry mass, based on the number of tests conducted in this study, was found to be approximately equal to 5% of the total original mass and the ratio w /wOis given by m, - 0.0 5 m, W/W0
=
0*95m,
Substituting eqn (7) into eqn (6) gives
(8)
100
50
Orymg time(mml
Fig. 5.
Comparison of predicted drying time with experimental values at 60°C and 1-O analytical results (eqn (8)). m/s: *, experimental values; -,
Drying time (min)
Fig. 6.
Comparison of predicted drying time with experimental values at 80°C and l”8 analytical results (eqn (8)). m/s: + , experimental values; -,
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M. N. A. Hawlader, M. S. Uddin, J. C. Ho, A. B. W. Teng
The comparison of the experimental results are agree fairly well with the that eqn (8) will predict taken into account.
predicted drying time, using eqn (8), and the shown in Figs 5 and 6. The predicted values experimental results and lead to the conclusion the diffusivity during drying when shrinkage is
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