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This is the author’s version of a work that was submitted/accepted for pub-lication in the following source:

Kumar, Chandan, Karim, Azharul, Joardder, Mohammad Uzzal Hossain, & Miller, Graeme (2012) Modeling heat and mass transfer process during convection drying of fruit. In The 4th International Conference on Compu-tational Methods (ICCM2012), Crowne Plaza, Gold Coast, Australia. This file was downloaded from: http://eprints.qut.edu.au/55423/

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Copyright 2012 Please consult the author.

Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source:

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The 4th International Conference on Computational Methods (ICCM2012), Gold Coast, Australia www.ICCM-2012.org

November 25-27, 2012, Gold Coast, Australia www.ICCM-2012.org

Modeling Heat and Mass Transfer Process during Convection Drying of Fruit

C. Kumar*, A. Karim, M.U.H. Joardder,G.J. Miller Science and Engineering Faculty

Queensland University of Technology, Brisbane, Queensland, Australia *Corresponding author: chandan.kumar@student.qut.edu.au Abstract

Fruit drying is a process of removing moisture to preserve fruits by preventing microbial spoilage. It increase shelf life, reduce weight and volume thus minimizing packing, storage, and transportation cost and enable storage of food under ambient environment. But, it is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the material. In this background, the aim of this paper to develop a mathematical model to simulate coupled heat and mass transfer during convective drying of fruit. This model can be used predict the temperature and moisture distribution inside the fruits during drying. Two models were developed considering shrinkage dependent and temperature dependent moisture diffusivity and the results were compared. The governing equations of heat and mass transfer are solved and a parametric study has been done with Comsol Multiphysics 4.3. The predicted results were validated with experimental data.

Keywords: Drying, Heat and mass transfer, Modeling, Comsol-Multyphysics

Introduction

Drying is one of the oldest and most cost-effective means of preservation of grains, crops and foods of all varieties(Askari, Emam-Djomeh et al. 2006). Fruits and vegetables contain approximately 80% moisture so they are classified as highly perishable (Orsat, Yang et al. 2007). Therefore, 1.3 billion tons of food is lost annually due to lack of proper processing which is one third of global food production(Gustavsson, Cederberg et al. 2011). Drying has a great potential in process food industries as it is perhaps the oldest, most common and most diverse of chemical engineering and operation for food preservation. However, drying is an energy intensive process as it usually requires hot air as heating medium to allow simultaneous heat and mass transfer between the drying air and material being dried. Moreover quality of food degrades during drying. A good drying model is essential for optimization of this process for reducing energy consumption and improving product quality. Several drying model have been proposed to describe drying kinetics. Most of them are empirical which do not help toward optimization because they cannot able to capture the real physics behind drying and are only applicable for specific operating conditions. The diffusion based model can capture well the physics during drying (Chou, Chua et al. 2000; Chua, Mujumdar et al. 2003). However they are presented in terms of partial differential equations which have constant those changes with temperature and moisture content. Most of the diffusion models consider constant thermal conductivity, specific heat, constant diffusion coefficient and constant heat and mass transfer coefficients although the does changes as drying process. The objective of the present study is to develop a mathematical model considering variable material properties. Two models were developed and compared based on temperature and shrinkage dependent effective moisture diffusivity. The model consist of coupled heat conduction and mass diffusion equations which were solved numerically using finite element method through the use of COMSOL Multiphysics 4.3.

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Mathematical Model: Problem formulation:

Figure 1 represent schematic diagram of food drying showing both transport of heat and mass. This transport process of heat experience two different distinct occurrences: (1) an increase in food temperature towards air temperature due to inward flux of heat and (2) a decrease in temperature due to outward heat flux because of evaporation (Barati and Esfahani 2011)

Figure 1. Schematic diagram of heat and mass transfer during drying of food material In this study experimental data of banana cylinder drying from Karim and Hawlader (2005a) are used to validate the model. Figure 2 shows the actual geometry and simplified 2D axisymmetric geometry used for modeling. Due to axial symmetry only one quarter of a planer intersection was considered for simulation.

Figure 2. (a) Actual geometry of the banana slice and (b) Simplified 2D axisymmetric model domain.

In developing the model the following assumption were made: (1) Moisture movement and heat transfer are one dimensional (2) No chemical reaction takes place during drying.

Governing Equations: Mass transfer equations: Heat Transfer equation:

Mass flux

Energy, moisture convected away

Air Flow Energy in from air

Heat flux FOOD 36mm 4mm 18mm 2mm Axis of Symmetry (a) (b)

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Initial and Boundary conditions:

Initial moisture content, kg/kg dry basis, Initial temperature Heat transfer boundary conditions:

At open boundary:

At symmetry and other boundary: Mass transfer boundary conditions:

At open boundary:

At symmetry and other boundaries: Input Parameters of the model:

However the specific heat and thermal conductivity are not considered as constant, the following equations of moisture dependent specific heat and thermal conductivity of banana were used (Bart-Plange, Addo et al. 2012).

1742 75 . 24 811 . 0 2 − + = w w s M M C (1) 120 . 0 006 . 0 + = w s M K (2)

The model developed for air velocity and 600C as data for this drying condition available in graph as well as tabulated form (Karim and Hawlader 2005b).

Shrinkage and temperature dependent effective diffusivity Calculation:

Crank (1975) and Fish (1958) presented effective diffusion coefficient as a function of moisture content for product undergoing shrinkage during drying. In this study the following equation were used to incorporate shrinkage dependent diffusivity.

2 0      = b b D D eff ref (3)

Thickness ratio obtained by the following equation

      + + = s w s w w M M b b ρ ρ ρ ρ 0 0 (4)

Temperature dependent diffusivity was obtained from Arrhenius type relationship with the temperature with the following equation.

Heat and mass transfer coefficient calculation:

Average heat transfer coefficient is calculated from the following equation (Mills 1995) for laminar and turbulent flow respectively:

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As Fourier’s law and Fick’s law are identical in mathematical form the analogy is used to find mass transfer coefficient. Nusselt number and Prandtle number is replaced by Sherwood number and Schmidt number respectively as following relationship:

Where , and

Results and discussion:

The temperature evolution of the material is shown in Figure 3 for drying air temperature 600C and velocity 0.5m/s. It is evident that the predicted temperatures for both model agreed reasonably well with those experimental data.

Figure 3. Temperature profile obtained for experimental and simulation with shrinkage and temperature dependent diffusivity (for T=600C and V=0.5m/s)

Figure 4 represents the moisture content with drying time. It shows that temperature dependent moisture diffusivity closely agrees with the experimental moisture content data whereas the shrinkage dependent diffusivity initially shows faster drying rate. This is may be due to the fact that shrinkage dependent diffusivity starts simulation with reference diffusivity and decrease with time. So initially evaporation is too high because of higher diffusion coefficient which causes more deviation from experimental data. So from this it could be said that to consider temperature dependent diffusivity is better for simulation of drying. Baini and Langrish (2007) also recommended using temperature dependent diffusivity which is also reflected from the simulation. They reported that shrinkage reduce diffusion path length which increases diffusivity on the other

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hand it reduces capillary which decrease diffusion. So shrinkage has two opposite effect on diffusion coefficient which are likely to cancel each other.

Figure 4. Moisture profile obtained for experimental and simulation with shrinkage and temperature dependent diffusivity (T=600C and V=0.7m/s).

Temperature and moisture distribution inside the food at any time during the drying can easily be obtained from the simulation. For the sake of brevity, only temperature and moisture distribution at 300 minutes for temperature dependent moisture diffusivity model presented in figure 5.

Figure 5: (a) Temperature and (b) Moisture distribution inside the food after 300 minutes of drying at T=600C and V=0.3m/s.

(a)

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However from the figure 5a it is observable that the temperature gradient is not significant inside the material because the thickness of the material is very small in the simulation. It is also clear from figure 5 that the temperature and moisture flux are opposite in direction.

Parametric Analysis: After validation of the model it is very easy to do parametric analysis in COMSOL Multiphysics with its parametric sweep option. The following figure 6 and 7 shows moisture and temperature evolution for 40, 50 and 600C with air velocity 0.7m/s.

Figure 6. Moisture content for different air temperature for velocity 0.7m/s

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From the figure 6 it is easily concluded that the as the drying air temperature increases drying rate increases, for example, it takes approximately 750,450 and 300 minutes to reach a moisture content value 0.5kg/kg dry basis for drying air temperature 40, 50 and 60 0C respectively.

Conclusion:

In this work a mathematical model for heat and mass transfer during has been developed with COMSOL Multiphysics 4.3. Moisture dependent specific heat and thermal conductivity and temperature dependent diffusivity were considered. The model is validated against experimental data and then a distribution of moisture and temperature distribution were presented as well as a parametric study has been conducted.

The proposed model can easily be implemented by additional multi-physics effect such as microwave and can readily extended to allow for full three dimensional geometries by using COMSOL flexible features.

Nomenclature

b Half thickness Greek Letters

Moisture Concentration Density,

Specific heat, Dynamic viscosity,

Diffusivity, Dimensionless Number

Constant of Integration, Reynolds Number

Activation Energy of diffusion of water, Nusselt number Latent heat of evaporation of water, Smidth Number

Heat transfer Coefficient, Sherwood number

Mass transfer Coefficient, Prandtl number

Thermal conductivity, Subscripts

Characteristics length a/air air

M Moisture content w Water/wet basis

Heat source or sink s Solid or material

gas constant, eff effective

Reaction rate ref Reference

Absolute temperature b Banana/bulk

Velocity of surface (m/s) 0 Initial

Velocity of air, e equilibrium

References:

Askari, G. R., Z. Emam-Djomeh, et al. (2006). "Effects of Combined Coating and Microwave Assisted Hot-air Drying on the Texture, Microstructure and Rehydration Characteristics of Apple slices." Food Science and Technology International 12 (1): 39-46

Baini, R. and T. A. G. Langrish (2007). "Choosing an appropriate drying model for intermittent and continuous drying of bananas." Journal of Food Engineering 79(1): 330-343.

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Barati, E. and J. A. Esfahani (2011). "Mathematical modeling of convective drying: Lumped temperature and spatially distributed moisture in slab." Energy 36(4): 2294-2301.

Bart-Plange, A., A. Addo, et al. (2012). "THERMAL PROPERTIES OF GROS MICHEL BANANA GROWN IN GHANA." ARPN Journal of Engineering and Applied Sciences 7(4).

Chou, S. K., K. J. Chua, et al. (2000). "On the Intermittent Drying of an Agricultural Product." Food and Bioproducts Processing 78(4): 193-203.

Chua, K. J., A. S. Mujumdar, et al. (2003). "Intermittent drying of bioproducts––an overview." Bioresource Technology

90(3): 285-295.

Crank, J. (1975). The Mathematics of Diffusion. Oxford, UK, Clarendon Press.

Fish, B. P. (1958). Diffusion and thermodynamics of water in potato starch gel, London: Society of Chemical Industry. Gustavsson, J., C. Cederberg, et al. (2011). "Global food losses and food waste."

Karim, M. A. and M. N. A. Hawlader (2005a). "Mathematical modelling and experimental investigation of tropical fruits drying." International Journal of Heat and Mass Transfer 48(23-24): 4914-4925.

Karim, M. A. and M. N. A. Hawlader (2005b). "Drying characteristics of banana: theoretical modelling and experimental validation." Journal of Food Engineering 70(1): 35-45.

Mills, A. F. (1995). Basic Heat and Mass Transfer, Massachusetts: Irwin.

Orsat, V., W. Yang, et al. (2007). "Microwave-Assisted Drying of Biomaterials." Food and Bioproducts Processing

References

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