Intermittent Drying of Mango Tissues ... - ACS Publications

Ind. Eng. Chem. Res. 2011, 50, 1089–1098

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Intermittent Drying of Mango Tissues: Implementation of the Reaction Engineering Approach Aditya Putranto,† Zongyuan Xiao,‡ Xiao Dong Chen,*,†,‡ and Paul A. Webley† Department of Chemical Engineering, Monash UniVersity, Clayton Campus, Victoria 3800, Australia, and Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen UniVersity, Xiamen 361005, People’s Republic of China

A drying model is very useful for design and evaluation of dryer performance. A good drying model should be simple, accurate, robust, and favorable for quick decision-making in industries. For sustainable processing and product technology objectives, intermittent drying is conducted to minimize energy consumption and achieve better quality of products. In this paper, the reaction engineering approach (REA) is applied innovatively for modeling the intermittent drying of mango tissues. The equilibrium activation energy and the heat balance are implemented according to the corresponding drying condition in each section. Prediction of surface temperature is also incorporated because the sample dimensions are rather thick. Results of modeling reveal that the REA describes both moisture content and temperature profile very well. This has shown further success of the REA to model drying under time-varying mode. In addition, the modeling itself is still proven to be simple and only requires short computational time. This makes future applications for solving industrial problems very promising. 1. Introduction Drying is a process to remove water from materials involving simultaneous heat and mass transfer. A drying model is very useful for assisting in the design of dryer and evaluation of dryer performance including troubleshooting and optimization. A number of drying models was proposed which can be classified into empirical and mechanistic models. The empirical ones have advantages of simple mathematical formulation and solution but they cannot capture the physics of the drying process.1-9 The models are also not appropriate for prediction of various drying conditions since they are only valid for the conditions being tested. On the other hand, the mechanistic models are derived from drying phenomena so that the physics of drying can be described. However, the models are represented as partial differential equations which require a long time for computation.10-17 The useful drying models are the ones which can capture the major physics of the drying process, but they should also be accurate, simple, and robust as well as require only a short computational time favorable for quick decision-making in industries. It is recognized that drying is an energy-intensive process as heat needs to be supplied for water evaporation. Due to problems of climate change and energy issues, a practice of sustainable processing should be applied in the drying process. Schemes should be proposed to minimize energy consumption, but they should be favorable for product quality and not alter drying kinetics significantly. One of the possible schemes is intermittent drying by supplying different heat inputs during drying or exposing materials being dried to different drying conditions along the drying time. It was shown that applying a time-varying temperature profile resulted in the reduction of the effective drying time so that energy consumption can be minimized.18-20 Application of a square-wave temperature profile was shown to reduce the effective drying time appreciably and result in * To whom correspondence should be addressed. E-mail: xdc@ xmu.edu.cn. † Monash University. ‡ Xiamen University.

similar final moisture content.19 Saving of effective drying time of 25, 48, and 61% was also revealed by intermittent drying with a fraction of the heating time to total drying time of 0.25, 0.5, and 0.67.18 Intermittency of infrared drying was indeed reported to greatly reduce effective drying time.22 Similarly, application of pulsed microwave drying increased the energy efficiency.21 In addition, improvement of product quality can be achieved by intermittent drying.18,21,23,24 Application of a fraction of the heating time to a total drying time of 0.25, 0.5, and 0.67 reduced nonenzymatic browning by 45.7 33.6, and 25.6%, respectively, as well as reduced the ascorbic acid loss by 11.6, 9.1, and 7.4%, respectively, compared to continuous drying at 35 °C.17 A higher amount of β-carotene in squash could be preserved by tempering the drying rather than by conventional continuous drying.24 Less fissuring and cracking were observed by tempering of a rice kernel as a result of better moisture distribution.23 Time varying heat input was also shown to minimize cracking of kaolin because of a smaller value of stress applied, while drying kinetics was not affected significantly.25 Several drying models have been proposed to describe the intermittent drying kinetics.18-20,26-29 A combination of Darcy liquid flow and vapor diffusion was employed to model intermittent drying of potatoes, and good agreement toward experimental data was indicated.18-20 A simple empirical model involving a drying constant, surface mass-transfer coefficient, and equilibrium moisture content was implemented.28 Baini and Langrish29 applied empirical, diffusion, and CDRC (characteristics drying rate curve) models to describe the intermittent drying of banana tissues. It was revealed that the empirical model could not match with the experimental data while the diffusion model described the process reasonably well. It was analyzed that CDRC seemed unable model the intermittent drying because this could not be simply represented as constant and falling rate period. In addition, Vaquiro et al.16 employed a diffusion model, and a reasonable agreement toward experimental data was shown. It can be examined that the mechanistic based models can describe the drying kinetics well. However, as mentioned before,

10.1021/ie101504y  2011 American Chemical Society Published on Web 12/07/2010

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Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011

they need long computational time as they are represented in partial differential equations and several sets of drying experiments are required to generate the diffusivity as a function of moisture content and/or temperature. Due to the accuracy and robustness of the reaction engineering approach (REA) to model various convective drying of food and nonfood products,30-36 it is worthwhile to apply the REA for intermittent drying. This study is aimed to investigate the effectiveness and accuracy of the reaction engineering approach to model intermittent drying of mango tissues with side length of 2.5 cm (rather thick samples). The accuracy of the REA is validated toward published experimental data.16 It is expected that the REA can describe the intermittent drying well following the robustness of the REA shown previously. The outline of this paper is as follow: the REA is briefly reviewed first followed by brief experimental details, modeling, and application of the REA on intermittent drying of mango tissues.

The drying rate of a material can be expressed as ms

dX ) -hmA(Fv,s - Fv,b) dt

where ms is the dried mass of thin layer material (kg), t is time (s), X is the moisture content on a dry basis (kg · kg-1), Fv,s is the vapor concentration at the material-air interface (kg · m-3), Fv,b is the vapor concentration in the drying medium (kg · m-3), hm is the mass-transfer coefficient (m · s-1), and A is the surface area of the material (m2). hm is determined on the basis of the established Sherwood number correlations for the geometry and flow condition of concern or established experimentally for the specific drying conditions involved. The surface vapor concentration (Fv,s) can be scaled against saturated vapor concentration (Fv,sat.) using the following equation:37,38 Fv,s ) exp

2. Brief Review of the Reaction Engineering Approach The reaction engineering approach is an application of chemical reactor engineering principles to model drying kinetics.37,38 The REA is represented in the form of the ordinary differential equations with respect to time. The similarities and differences between the classical CDRC method and REA were discussed in detail by Chen.38 The REA was shown to be accurate and robust to model drying of various thin layer or small food materials. For instance, modeling of drying of aqueous lactose solution droplet showed that the average absolute difference of weight loss profile was about 1% of the initial weight, while that of the temperature profile was only about 1.2 °C.33 Application of REA to model drying of cream and whey protein concentrate showed an average absolute difference of weight profile of 1.9 and 2.1%, respectively, while that of temperature was about 3 and 1.9 °C for cream and whey protein concentrate, respectively.34 Modeling of skim milk and whole milk powder by REA was also robust and accurate.31 The REA has also been implemented in CFD (computational fluid dynamics) based simulations to predict performance of a spray drier.39-41 CFD simulation using REA can predict the outlet air temperature and the outlet particle moisture content reasonably well compared to the experimental data. In addition, the REA was also implemented to predict the evaporation zone, drying rate, trajectory of particles, and deposition of particles in the spray dryer.39 Two-dimensional and three-dimensional application of CFD implementing the REA as drying kinetics were conducted.40,41 Results of 2D simulation matched well with pilot plant data. Wall boundary conditions affected significantly the particle trajectories, while distribution of particles in dryers and particle residence time are also influenced by particle size.40 In addition, 3D simulation indicated that nonlinear central jet oscillations and promotion of turbulence near the air/liquid inlet, while turbulence was dampened, occurred in main dryer chamber as a result of the presence of a discrete phase.41 The REA has been applied to model drying of nonfood products. The REA was implemented to model a thin layer of a mixture of poly(vinyl alcohol) (PVA)/glycerol/water, and good agreement toward published experimental data was revealed.36 The REA has been attempted to model infrared heating drying of a mixture of polymer solution by introducing a new concept of maximum activation energy (∆Ev,b) as a function of the final product temperature and absolute humidity. Good agreement toward published experimental data was also revealed.36

(1)

(

)

-∆Ev Fv,sat.(T) RT

(2)

where ∆Ev represents the additional difficulty of removing moisture from the material beyond the free water effect, which is moisture content (X) dependent. T is the temperature of the material being dried, and Fv,sat. for water can be estimated with the following equation: Fv,sat. ) 4.844 × 10-9(T - 273)4 - 1.4807 × 10-7(T - 273)3 +

2.6572 × 10-5(T - 273)2 - 4.8613 × 10-5(T - 273) + 8.342 × 10-3 (3)

where T is temperature (K) on the basis of the summarized data.42 The mass balance (eq 1) is then expressed as ms

[ ( )

]

-∆Ev dX ) -hmA exp Fv,sat. - Fv,b dt RT

(4)

∆Ev is determined experimentally by placing the parameters required for eq 4 in its rearranged form:

[(

∆Ev ) -RT ln -ms

) ]

dX 1 + Fv,b /Fv,sat. dt hmA

(5)

where dX/dt is experimentally determined. The dependence of activation energy on moisture content on a dry basis X can be normalized as ∆Ev ) f(X - Xb) ∆Ev,b

(6)

where f is a function of water content difference, ∆Ev,b is the “equilibrium” activation energy representing the maximum ∆Ev under relative humidity (RHb) and temperature of the drying air (Tb): ∆Ev,b ) -RTb ln(RHb)

(7)

Xb is the equilibrium moisture content on a dry basis corresponding to RHb and Tb (K) which can be related to one another through the equilibrium isotherm of the same material. The REA parameters for drying of a material can be obtained from a particular drying experiment and can then be applied in other different drying conditions since the activation energy would collapse to the same profiles in these cases.31,33,38 The REA parameters should be generated from the material with similar initial moisture content since the activation energies are dependent on the initial moisture content near the start.31,38 The

Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011 16

Table 1. Schemes of Intermittent Drying of Mango Tissues

drying air period of first period of resting period of second temperature (°C) heating (s) (at 27 ( 1.6 °C) (s) heating (s) 45 55 65

16 200 9 480 7 800

10 800 10 800 10 800

36 360 33 720 16 200

relative activation energy essentially describes the internal behavior of materials during drying. The representation of the relative activation energy as a function of moisture content difference indicated in eq 6 makes this flexible for various drying conditions.31,37,38 3. Experimental Details The experimental data of drying of mango tissues are derived from Vaquiro et al.16 For better understanding, the experimental details are summarized and reviewed in this section. The samples of mango tissues were cubes with side length of 2.5 cm. The initial moisture content and temperature are 9.3 kg · kg-1 and 10.8 °C, respectively. The laboratory drier was described in Sanjuan et al.43 During drying the weight of the sample and the center temperature were recorded. The drying air temperature and air velocity were controlled at preset values by PID control algorithms, while air humidity was maintained constant during drying. The intermittency is created by a heating and resting period listed in Table 1. During the resting period, the samples stay at an environment with ambient temperature of 27 ( 1.6 °C and relative humidity of 60%.16 Determination of density, thermal conductivity, heat capacity, equilibrium moisture content, and shrinkage of samples being dried is shown in the Appendix. The cube sample was suspended during drying to allow the sample to receive heat from all directions so that an equivalent one-dimensional problem could be set up.16,44 4. Modeling of Intermittent Drying of Mango Tissues Using the Reaction Engineering Approach For modeling using the REA, the mass balance shown in eq 4 is applied by implementing surface temperature. This results in

ms

[ ( )

1091

]

-∆Ev dX ) -hmA exp Fv,sat.(Ts) - Fv,b dt RTs

(8)

where Ts is the surface temperature (K). Because the dimensions of samples are rather thick, the temperature inside the sample may not be uniform, and thus prediction of the sample temperature profile is necessary. Chen38 proposed the simple parabolic approximation represented as T ) To +

(

Ts - T o L2

)

x2

(9)

where To is the center temperature (K), L is the half-length of the slab (m), and x is the axial position (m). Since the lumped heat balance represented as the average temperature (Tav) is applied, the surface (Ts) and center temperatures (To) need to be expressed as a function of average temperature (Tav) and drying air temperature (Tb). Tav) is evaluated from

∫

L

Tav )

0

T(x) dx

(10)

L

Heat balance at the surface can be written as h(Tb - Ts) ) k

( dTdx )

x)L

+ |Nv |∆Hv

(11)

where h is the convective heat-transfer coefficient (W · m-2 · K-1), k is the thermal conductivity of samples (W · m-1 · K-1), Nv is the evaporation flux (kg · m-2 · s-1), and ∆Hv is the vaporization heat (J · kg-1). Equation 11 indicates that, at the surface, heat received by convection is balanced by conduction and heat for vaporization of water. The models which do not require the heat of evaporation at the boundary (x ) L) are spatial multiphase drying models in which the local evaporation term is applied to link the transfer of water between liquid and vapor phases.45-47 It was explained that the models should incorporate the evaporation term at the surface if the models do not implement the local evaporation rate in the spatial heat and mass balance.45-47 In this paper, the REA is applied as a global (bulk) evaporation rate. The heat of evaporation needs to be incorporated at the boundary condition, as shown by eq 11 for prediction of the surface temperature. By combining eqs 10 and 11, the surface and center temperature can be expressed as

(

Ts ) Tav +

L hL hL T - |Nv |∆Hv / 1 + 3k b 3k 3k

)(

1 1 ( 23 - 2 + (2hL/3k) ) - 2 + (2hL/3k ( hL3k T

To ) Tav

b

)

(12)

- |Nv |∆Hv

L 3k

)

(13) These expressions can be generalized by incorporating the equivalent radius of the sample.44 For cubes, the side length is the equivalent radius.48 The relative activation energy derived from continuous convective drying of mango tissues can be written as

Figure 1. Relative activation energy of convective drying of mango tissues at air velocity of 4 m · s-1, drying air temperature of 55 °C, and air humidity of 0.0134 kg of H2O · (kg of dry air)-1.

∆Ev ) -9.92 × 10-4(X - Xb)3 + 9.74 × 10-3(X - Xb)2 ∆Ev,b 0.101(X - Xb) + 1.053 (14)

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Figure 2. Moisture content profile of mango tissues during intermittent drying at drying air temperature of 45 °C and resting at 27 °C.

Figure 3. Temperature profile of mango tissues during intermittent drying at drying air temperature of 45 °C and resting at 27 °C.

Only one set of experimental data needed to generate the relative activation energy derived from convective drying of mango tissues at drying air temperature of 55 °C.16 The good agreement between fitted and experimental activation energy is shown by R2 ) 0.997 and revealed in Figure 1. The predictions of the surface temperature and the relative activation energy represented in eqs 12 and 14 have been implemented to model continuous convective drying of mango tissues at various drying air temperature, and very good agreement toward experimental data was revealed. When benchmarking toward a diffusion model implemented by Vaquiro et al.,16 the REA gave comparable and even better results.49 For modeling of intermittent drying, the relative activation energy (∆Ev/∆Ev,b) shown in eq 14 is combined with the equilibrium activation energy written in eq 14. It is highlighted that the equilibrium activation energy (∆Ev,b) is evaluated according to the corresponding drying air temperature and absolute humidity in each section of drying. The heat balance of convective drying of mango tissues can be written as49


d(mCpTav) dX ≈ hA(Tb - Ts) + ms ∆HV dt dt

(15)

For intermittent drying, the heat balance is employed according to the drying air temperature in each section. The mass and heat balances indicated in eqs 8 and 15, respectively, are solved simultaneously to yield the profile of moisture content and average temperature of mango tissues, while the center temperature is evaluated by eq 13. 5. Results and Discussions 5.1. Modeling of Intermittent Drying of Mango Tissues. Figures 2-7 show the results of modeling of intermittent drying of mango tissues using the REA. For intermittent drying at drying air temperature of 45 °C, the REA describes both the moisture content and temperature profile very well. A very good agreement is observed between experimental and predicted data. Similar results are also revealed for intermittent drying at drying air temperatures of 55 and 65 °C. The predicted moisture content and temperature match well with the experimental data. The good predictions of moisture content and temperature profile are revealed by R2 and RMSE shown in Table 2.

A benchmark toward modeling proposed by Vaquiro et al.16 employing a diffusion model was conducted, and it is revealed that the REA gives comparable or even better results. Modeling proposed by Vaquiro et al.16 showed a kink of the temperature profile at the beginning of drying; which was not observed by modeling using the REA. In addition, the underestimation of the moisture content profile at the last period of drying at drying condition of 65 °C is not revealed by the REA, as shown by modeling by Vaquiro et al.16 It can be said that the REA is accurate for modeling intermittent drying of mango tissues although the REA is represented in a lumped model. This is because the relative activation energy (∆Ev/∆Ev,b) implemented allows the natural transition along the drying time according to the drying scheme as revealed in Figure 8. The relative activation energy keeps increasing during drying, indicating the increase of difficulty to remove water from materials. This increases significantly during the heating period, while this only increases slightly during the resting period. This natural transition during drying is not observed by empirical models and CDRC (characteristics drying rate curve).29 It was revealed that the empirical models could not model the intermittent drying of banana tissues well. It was also analyzed that CDRC might not be able to handle


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Table 2. R and RMSEof Intermittent Drying of Mango Tissues


drying air temperature (°C)

R2X

R2T

RMSE X

RMSE T

45 55 65

0.998 0.998 0.998

0.996 0.997 0.997

0.083 0.087 0.082

0.483 0.554 0.686

Therefore, this has extended the application of the REA significantly to model not only continuous drying but also intermittent drying of rather thick samples. This reveals further success of the REA following the success of modeling continuous drying of a thin layer of food and nonfood materials.30-36 Although the results of modeling are accurate and robust, the simplicity of the modeling is still proven and only a short computational time is required. 5.2. Analysis of Surface Temperature, Surface Relative Humidity, and Saturated and Surface Vapor Concentration during Intermittent Drying. Analysis of surface temperature, surface relative humidity, and saturated and surface water vapor concentration during intermittent drying will assist for determining the appropriate cycle conditions, i.e., the length of drying and resting periods to minimize energy and final moisture content. The following paragraphs discuss these of the intermittent drying of mango tissues. The reaction engineering approach is applied here and combined with several equations to yield a profile of the surface temperature, surface relative humidity, saturated vapor concentration, and surface vapor concentration. The saturated vapor concentration and surface temperature are evaluated by eqs 3 and 12. In addition, the surface relative humidity is evaluated by RHs ) exp


( ) -∆Ev RTs

(16)

where RHs is surface relative humidity. The surface vapor concentration is calculated by eq 2. The profile of surface relative humidity is shown in Figure 9. It decreases during the heating period while it increases during resting, representing the increase of the surface moisture content. In addition, Figure 10 indicates the profiles of surface temperature and saturated vapor concentration during intermittent drying at drying air temperature of 65 °C. The profiles of saturated vapor concentration follow the trend of surface temperature. It increases in the first section, decreases in the second section, and increases again in the third section.


this since the drying rate of intermittent drying could not be represented simply as a linear and exponential decreasing drying rate.29

Figure 8. Relative activation energy profile of mango tissues during intermittent drying at drying air temperature of 65 °C and resting at 27 °C.

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However, the profile of surface vapor concentration is different from that of saturated vapor concentration as revealed in Figures 11 and 12 because the profile of surface vapor concentration is affected by both surface temperature and surface relative humidity. It is apparent that the surface vapor concentration increases in the very early part of drying because of the increase of surface temperature, followed by the decrease due to the decrease of surface relative humidity. During the initial part of the resting period, the surface vapor concentration increases significantly as the surface relative humidity increases dramatically. This is followed by the decrease of the surface vapor concentration because of the low surface temperature, leading to the decrease of saturated vapor concentration. At the second heating period, the surface vapor concentration continues to decrease as the surface relative humidity decreases. This analysis is in agreement with Baini and Langrish29 applying a diffusion model for intermittent drying of banana tissues. It was revealed that during the resting period the surface temperature decreased while the surface moisture content increased initially as a result of the initial increase of the surface relative humidity. It can be analyzed that during the resting period at drying time higher than around 12 000 s, the surface vapor concentration has reached flat profiles. It means there is actually no point

Figure 11. Surface and saturated vapor concentration profile of mango tissues during intermittent drying at drying air temperature of 65 °C and resting at 27 °C.

Figure 12. Surface vapor concentration and surface temperature profile of mango tissues during intermittent drying at drying air temperature of 65 °C and resting at 27 °C.

Figure 9. Surface relative humidity profile of mango tissues during intermittent drying at drying air temperature of 65 °C and resting at 27 °C.

Figure 10. Saturated vapor concentration and surface temperature profile of mango tissues during intermittent drying at drying air temperature of 65 °C and resting at 27 °C.

in extending the resting period until 18 600 s. The resting period could be shortened and followed by a subsequent heating period. Similarly, during the second heating period, the surface vapor concentration profile has nearly flattened after the drying time around 25 000 s. The heating time could be shortened also followed by a subsequent resting period for achieving higher surface vapor concentration. From the above analysis, it seems that a cycle with higher frequency would give better results. Simulation of intermittent drying at drying air temperature of 45 °C with each heating and resting period (at 27 °C) of 4000 s and total drying time of 64 000 s (total heating time at 45 °C of 32 000 s) was conducted to illustrate these profiles of this scheme. Results of simulation including the profiles of moisture content, surface temperature, surface relative humidity, and saturated and surface temperature are presented in Figures 13-17. It can be seen that the trend of surface relative humidity and saturated and surface vapor concentration are similar to those that have been discussed in the previous paragraphs. Nevertheless, no flat profile of surface vapor concentration is shown during the resting period, which means resting is not conducted under prolonged time. It is also observed that the final moisture content is similar to that of intermittent drying of mango tissues at 45 °C using the scheme listed in Table 1,16 although the total


Figure 13. Moisture content profile of intermittent drying of mango tissues with heating (at drying air temperature of 45 °C) and resting period each for 4000 s.

Figure 14. Saturated vapor concentration and surface temperature profile of intermittent drying of mango tissues with heating (at drying air temperature of 45 °C) and resting period each for 4000 s.

heating time of this scheme is lower. The total heating time of this scheme is 32 000 s while that at 45 °C listed in Table 116 is 52 560 s. The total drying time of this scheme (64 000 s) is also similar to that at 45 °C listed in Table 116 (62 650 s). Because the heating time is lower while the total drying time and the final moisture content are not significantly altered, from a sustainable processing perspective, it is beneficial to apply such a cycle. This is because the energy cost can be minimized while the objective to obtain a similar target moisture content can be achieved. 5.3. Analysis of Biot and Chen-Biot Number. To show the “gentle” prediction of the distribution of temperature within the sample compared with a small object, the Biot number is commonly used to assess the temperature gradient inside materials. Both the conventional Biot number (Bi) and Chen-Biot number (Ch_Bi) are calculated to investigate the temperature gradient inside mango tissues during drying modeled by REA. For nonevaporative process, the thermal Biot number (Bi) is defined as the ratio of internal heat-transfer resistance due to conduction to external heat transfer due to convection. It is expressed as hx Bi ) k where x is the characteristic length (m).

(17)

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Figure 15. Surface vapor concentration and surface temperature profile of intermittent drying of mango tissues with heating (at drying air temperature of 45 °C) and resting period each for 4000 s.

Figure 16. Surface and saturated vapor concentration profile of intermittent drying of mango tissues with heating (at drying air temperature of 45 °C) and resting period each for 4000 s.

Figure 17. Surface vapor concentration and surface relative humidity profile of intermittent drying of mango tissues with heating (at drying air temperature of 45 °C) and resting period each for 4000 s.

For evaporative processes, Chen50 and Chen and Peng51 proposed that the evaporation effect should be incorporated for the evaluation of the thermal Biot number. The Chen-Biot number is written as

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Figure 18. Biot number (Bi) and Chen-Biot number (Ch_Bi) profiles of intermittent drying of mango tissues at drying air temperature of 45 °C.

Figure 20. Bi and Ch_Bi profiles of intermittent drying of mango tissues at drying air temperature of 55 °C.

The REA is shown to be accurate and robust to model both moisture content and temperature, while it maintains the advantages of simple mathematical modeling and fast computational purposes. When benchmarking toward the diffusion model implemented by Vaquiro et al.,16 the REA gives comparable or even better results. A thorough analysis of profiles of surface temperature, surface relative humidity, and saturated and surface vapor concentration was conducted to assist the determination of appropriate scheme for achieving minimized energy consumption. Therefore, this work has extended substantially the application of the REA for modeling intermittent drying of samples with rather thick dimensions. Application of the REA for modeling infrared heating or microwave drying under intermittent mode would be interesting and will be conducted in the near future. Acknowledgment Figure 19. Bi and Ch_Bi profiles of intermittent drying of mango tissues at drying air temperature of 55 °C.

Ch_Bi ) Bi -

Nv∆Hvx (Tb - Ts)k

(18)

The Bi and Ch_Bi of mango tissues of intermittent drying of mango tissues at drying air temperatures of 45, 55, and 65 °C are presented in Figures 18-20. It is indicated that Ch_Bi is much lower than Bi as a result of the second term of RHS taking into account the evaporation. This reveals the temperature gradient inside the sample is not large. Unlike the profiles of Bi increasing at the end of drying, those of Ch_Bi are more complex because of effects of evaporation flux and temperature difference between drying air temperature and surface temperature during drying indicated also by Patel and Chen.52 However, at a last period of drying, the temperature difference gets lower, and this does not result in practical problems in modeling.

A.P. acknowledges ALAS (Australian Leadership Award Scholarship). Appendix: Determination of Properties of Mango Tissues16,44,53-57 Fw ) 997 + 3.14 × 10-3T - 3.76 × 10-3T2

(B1)

where Fw is density of water (kg · m-3), T is sample temperature (°C), and Fs ) 1599 - 0.31T

(B2)

where Fs is density of solids (kg · m-3). kw ) 0.571 × 10-3 + 1.76 × 10-6T - 6.7 × 10-9T2

(B3) where kw is thermal conductivity of water.

6. Conclusion The reaction engineering approach (REA) has been implemented innovatively in this study for modeling of intermittent drying of mango tissues. The relative activation energy derived from continuous convective drying is applied and combined with the equilibrium activation energy as well as the heat balance according to the corresponding drying conditions in each section.

ks ) 0.201 × 10-3 + 1.39 × 10-6T - 4.33 × 10-9T2

(B4) where ks is thermal conductivity of solids. 1 w 1-w ) + F Fw Fs

(B5)

Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011 -3

where F is sample density (kg · m ), w is mass fraction of water (by weight). k)

kwFsX + ksFw FsX + Fw

(B6)

where k is sample thermal conductivity and X is moisture content on dry basis (kg · kg-1). w)

X 1+X

Cp,water ) -2 × 10-9T5 + 4.39 × 10-6T4 3.56 × 10-3T3 + 1.4327T2 - 285.6T + 26779.6

(B7)

where Cp,water is specific heat of water (J · kg-1 · K-1) (here, T given in kelvin). Cp,s ) -3.9 × 10-3T3 + 0.13T2 + 30T + 650

(B8)

where Cp,s is the specific heat of solid (J · kg-1 · K-1; T in °C). Cp,mix ) wCp,water + (1 - w)Cp,s

(B9)

where Cp,mix is the specific heat of the sample (J · kg-1 · K-1), x is the mass fraction of water (by weight) Xe ) 0.112

CGKGRH (1 - KGRH)(1 + (CG - 1)KGRH)

(B10) CG ) CG0 exp

(

KG ) KG0 exp

( 7005 RT )

∆HvMw - 56596 RT

(B11)

)

(B12)

where Xe is the equilibrium moisture content (kg · kg-1), R ) 8.314 J · mol-1 · K-1, RH is relative humidity of air, T is in kelvin, Mw is molecular weight of water (kg · kmol-1), and ∆Hv is vaporization enthalpy of water (kJ · kg-1). The shrinkage model is expressed as Sb )

Fw + FsX Fw + FsX0

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ReceiVed for reView July 14, 2010 ReVised manuscript receiVed October 19, 2010 Accepted November 15, 2010 IE101504Y

Intermittent Drying of Mango Tissues ... - ACS Publications

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