Mathematical model for intermittent microwave convective drying of food materials

Intermittent microwave convective drying (IMCD) is an advanced technology that improves both energy efficiency and food quality in drying. Modeling of IMCD is essential to understand the physics of this advanced drying process and to optimize the microwave power level and intermittency during drying. However, there is still a lack of modeling studies dedicated to IMCD. In this study, a mathematical model for IMCD was developed and validated with experimental data. The model showed that the interior temperature of the material was higher than the surface in IMCD, and that the temperatures fluctuated and redistributed due to the intermittency of the microwave power. This redistribution of temperature could significantly contribute to the improvement of product quality during IMCD. Limitations when using Lambert’s law for microwave heat generation were identified and discussed.     

Modeling of Combined Microwave and Convective Drying of Wood: Prediction of Mechanical Behavior via Internal Gas Pressure

The impact of microwave drying on the quality of dried wood remains unclear. Particular attention should be paid in order to optimize the combined microwave and convective drying process. In this study, a comprehensive internal heat and mass transfer model was developed and numerically implemented in order to simulate and understand the physical phenomena occurring inside Jack pine wood during a combined microwave and convective drying process. The model was validated on the basis of the average moisture content curves for drying scenarios at various microwave power levels. According to the simulations results, an increase in microwave power significantly decreases the drying time of Jack pine wood and increases its internal gas pressure, which increases the risk of cracking. However, compared to purely conventional convective drying, combined microwave and convective drying at medium microwave power and air temperature significantly reduces the drying time and maintains the internal gas pressure at reasonable values. At these conditions, the risk of cracking will be diminished. This last result was checked via experimental measurements of the sample strength dried at different microwave power levels. From this study, we can consider that for Jack pine wood, combined microwave and convective drying is a more efficient technology compared to classical convective drying.     

Experimental Validation of the Heat and Mass Transfer Model for Convective Drying

The aim of this article is to present a self-consistent mathematical model describing the heat and mass transfer phenomena during the convective drying both in the constant and in the falling drying rate periods. This general model is developed on the basis of the theory of mixtures and the thermodynamics of irreversible processes. The boundary conditions are formulated and the numerical algorithm enabling calculation of the temperature and the drying curves in the two mentioned periods of drying is constructed. In this paper much effort is devoted to the experimental validation of the model. The convective drying of a cylindrical sample made of kaolin was examined both experimentally and numerically for comparison and the distribution of temperature and the drying curves were determined. A very good agreement of the experimental and theoretical results is stated.     

COMBINED MICROWAVE AND CONVECTIVE DRYING OF A POROUS MATERIAL

A model is formulated to describe the drying of a slab of porous material in a combined microwave and convective environment. The model describes the evolution of temperature, pressure, moisture and power distributions that occur during the drying process. The microwave internal heat source is calculated from electromagnetic theory with varying dielectric properties. The inclusion of pressure in the model allows the physical phenomena of “water pumping”, often observed in microwave drying systems, to be accounted for. The influence of sample size; on the drying kinetics 1s examined and found to be an important parameter during the drying process. In particular the effect of resonance on the moisture and temperature profiles and the need for careful consideration of surface mass transfer coefficients are investigated. Simulation results are presented for the combined microwave and convective drying of a homogeneous, isotropic porous material.     

COMBINED MICROWAVE AND CONVECTIVE DRYING OF A POROUS MATERIAL

A model is formulated to describe the drying of a slab of porous material in a combined microwave and convective environment. The model describes the evolution of temperature, pressure, moisture and power distributions that occur during the drying process. The microwave internal heat source is calculated from electromagnetic theory with varying dielectric properties. The inclusion of pressure in the model allows the physical phenomena of “water pumping”, often observed in microwave drying systems, to be accounted for. The influence of sample size; on the drying kinetics 1s examined and found to be an important parameter during the drying process. In particular the effect of resonance on the moisture and temperature profiles and the need for careful consideration of surface mass transfer coefficients are investigated. Simulation results are presented for the combined microwave and convective drying of a homogeneous, isotropic porous material.     

Analysis of Effectiveness and Stress Development during Convective and Microwave Drying

The aim of the article is to study the effectiveness of convective and microwave drying with respect to drying time and stress generation in clay-like dried bodies. The theoretical analysis of stresses was confined to the constant drying rate period because clay shrinks and the stresses are generated mainly in this period. The theoretical prediction of stress development was validated using an acoustic emission method by monitoring the micro- and macrocracks formation caused by the stresses. Apart from the stress analysis, the combined convective-microwave drying was examined experimentally during whole process in order to show that the volumetric heat supply due to microwave heating enhances convective drying and, apart from this, such a combined drying process develops less stress in dried material. The theoretical and experimental studies were performed on a kaolin sample in the form of a thin plate.     

Analysis of Effectiveness and Stress Development during Convective and Microwave Drying

The aim of the article is to study the effectiveness of convective and microwave drying with respect to drying time and stress generation in clay-like dried bodies. The theoretical analysis of stresses was confined to the constant drying rate period because clay shrinks and the stresses are generated mainly in this period. The theoretical prediction of stress development was validated using an acoustic emission method by monitoring the micro- and macrocracks formation caused by the stresses. Apart from the stress analysis, the combined convective-microwave drying was examined experimentally during whole process in order to show that the volumetric heat supply due to microwave heating enhances convective drying and, apart from this, such a combined drying process develops less stress in dried material. The theoretical and experimental studies were performed on a kaolin sample in the form of a thin plate.     

Model based analysis of the drying of a single solution droplet in an ultrasonic levitator

A model for the drying of a single solution droplet into a solid, dense particle is presented and simulations are made to achieve a more fundamental understanding of the single droplet drying process relevant in connection with spray drying processes. Model predictions of drying behaviour are compared to data for the drying of aqueous solutions of maltodextrin DE 15 and trehalose from experiments conducted using an ultrasonic levitator. Model predictions are in good agreement with the experimental data, indicating that the model describes the most important physical phenomena of the process.     

Modeling of Moisture Diffusion in Microwave Drying of Hardwood

A one-dimensional mathematical model was developed to predict temperature and moisture content profiles in red maple (Acer rubrum L.) and white oak (Quercus alba) during microwave drying. The model was solved using the finite element analysis with MATLAB software. The predictions for temperature and moisture content agreed favorably well with the experimental data. The diffusion coefficients of the red maple and the white oak in microwave drying conditions were calculated and analyzed. Equations of the diffusion coefficient in longitudinal and transverse directions based on input microwave power level are presented in this article. In microwave drying of hardwood, the red maple was heated more efficiently than the white oak because of higher absorbing efficiency of the microwave power.     

Microwave drying at various conditions modeled using the reaction engineering approach

ABSTRACT

One of the most significant process intensification schemes in drying is microwave drying. Modeling the process of microwave drying is very useful. The lumped reaction engineering approach (REA) is now coupled with appropriate equations for modeling microwave heating. Here, a slight modification of the equilibrium activation energy is needed since the product temperature is higher than the ambient temperature. Unlike the diffusion-based approach, the REA drying parameters were generated from minimum number of drying runs. It has been found that the modifications lead to excellent agreements between the predicted and experimental data. The results of modeling match well with the experimental data. The overall model is accurate to describe the moisture content and temperature profiles. Comparisons with the diffusion-based approach indicate that the REA can achieve comparable or even better agreement toward the experimental data. This exercise has demonstrated that a simple combination of the lumped reaction engineering approach and the microwave energy absorption is versatile in predicting the microwave drying process accurately; thus, this worked example will be illustrative for future needed studies.     

Modeling of Moisture Diffusion in Microwave Drying of Hardwood

A one-dimensional mathematical model was developed to predict temperature and moisture content profiles in red maple (Acer rubrum L.) and white oak (Quercus alba) during microwave drying. The model was solved using the finite element analysis with MATLAB software. The predictions for temperature and moisture content agreed favorably well with the experimental data. The diffusion coefficients of the red maple and the white oak in microwave drying conditions were calculated and analyzed. Equations of the diffusion coefficient in longitudinal and transverse directions based on input microwave power level are presented in this article. In microwave drying of hardwood, the red maple was heated more efficiently than the white oak because of higher absorbing efficiency of the microwave power.     

A Study of the Power Density Distribution generated during the Combined Microwave and Convective Drying of Softwood

ABSTRACT

Investigations into new and innovative drying strategies can lead to the development of more efficient and effective drying processes. The commercialisation of these processes would prove invaluable to the drying industry as a whole and the associated technology would generate worldwide interest. Combined microwave and convective drying is one such process which offers great potential, with benefits that include : reduced drying times and increased drying rates; volumetric heating; higher fluxes of liquid to the drying surface; high temperature and internal pressure buildup within the material which enhances the overall moisture migration rate; and preferential heating of wetter areas. Numerical simulation can elucidate on the intricate details of the heat and mass transfer henomena that occur during the drying process, thus eliminating the need for performing numerous time consuming and expensive experiments. The simulations can predict the evolutionary behaviour of the moisture, temperature and pressure distributions, and can provide a detailed analysis of how microwaves interact with materials during drying and heating operations at a fundamental level. The research presented in this paper uses a comprehensive mathematical model to study the behaviour of the iniernal microwave power density distribution that is generated during the microwave enhanced convective drying of softwood. The configuration understudy concerns a plane wave microwave source irradiating the wood in the transverse direction.     

Mechanical Effects in Saturated Capillary-Porous Materials during Convective and Microwave Drying

The differences are analyzed in distribution and time evolution of the temperature, moisture content, and drying-induced stresses generated by convective and microwave drying. The theoretical analysis of the drying induced stresses and the deformations of dried materials is based on the elastic and viscoelastic constitutive models. The theoretical predictions are confronted with the experimental data obtained by the acoustic emission (AE) method, which enable monitoring on line the development of the drying induced stresses. The system of double coupled differential equations of the thermomechanical drying model is solved numerically using the finite element (FEM) and the finite difference (FDM) methods. A cylindrical sample made of kaolin was chosen to compare experimental data with the model solution. Essential differences were identified in the analyzed items for convective and microwave drying as well as a significant difference in stress distribution was noted for elastic and viscoelastic constitutive models.     

耐火浇注料对流与微波干燥的实验研究

进行了耐火浇注料热重分析,热风和微波干燥实验研究,得到了浇注料热风和微波干燥特性曲线。实验结果表明,与热风干燥比较,微波加热极大地降低了耐火浇注料干燥时间、提高了干燥效率和能源效率高,在耐火浇注料干燥过程中有着广阔的应用前景。     

COMPARISON OF CONVECTIVE, VACUUM, AND MICROWAVE DRYING CHLORPROPAMIDE

Drying kinetics of convective, vacuum, and microwave drying of a pharmaceutical product, chlorpropamide, has been investigated on a laboratory scale, in the temperature interval from 40°C to 60°C, and the range of microwave heating power from 154 W/kg_dm to 385 W/kg_dm.

The experimental data obtained were approximated with the “thin-layer” equation and a two parameter exponential model. In order to compare convective, vacuum, and microwave drying, effective diffusion coefficients and specific heat consumption were calculated for each drying method.

Higher rates and shorter drying times were achieved at a higher temperature and microwave heating power. The highest drying rates and the lowest specific heat consumption were achieved with microwave drying. This leads to the conclusion that microwave heating is the most appropriate method for drying of chlorpropamide. The quality of product was not changed for all applied methods.     

Drying of solids; estimation of the mathematical model parameters

In order to determine physical meaning of a thin‐layer mathematical model parameter, the Page model was modified and tested on numerous experimental data. Applicability of the model was tested on the drying kinetics data, X(t), of 11 different types of the porous materials and dried in a convective, vacuum and/or microwave dryers under the predetermined external process conditions. During the entire drying time the drying kinetics of all the investigated materials and heating methods were successfully correlated with the modified Page model. The evaluated values of a new parameter, t_k, corresponded to the time at which diffusion, as a governing mechanism of moisture movement through the material, started. The results were confirmed by the pore size distribution of some materials.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

DRYING RELATED PROPERTIES OF APPLE

ABSTRACT

Drying related properties of apple are evaluated for various different drying methods (namely, convective, vacuum, microwave, osmotic and freeze drying), and their corresponding process conditions. The examined properties are drying kinetics, equilibrium material moisture content, density, porosity, color and viscoelastic characteristics. The effect of various process factors on these properties is described through particular mathematical models. The model parameters are estimated by fitting the corresponding model equations on a wide range of experimental data. Drying kinetics is greatly affected by the characteristic particle size and drying air temperature for convective drying, while for the case of microwave drying they are affected by the vacuum pressure and the emitted radiation power. Equilibrium material moisture content is affected by the temperature and the humidity of the surrounding air, while the osmotic pretreatment shifts the sorption isotherms to higher water activity levels. The quality properties examined, are significantly affected by the drying method. More specifically, osmotic dehydration decreases the porosity of the final product, while it prevents color deterioration and enchances the viscous nature of dehydrated apple. Freeze-dried apples develop the highest porosity, have the most elastic structure and the lowest rate of color deterioration.     

DRYING RELATED PROPERTIES OF APPLE

Drying related properties of apple are evaluated for various different drying methods (namely, convective, vacuum, microwave, osmotic and freeze drying), and their corresponding process conditions. The examined properties are drying kinetics, equilibrium material moisture content, density, porosity, color and viscoelastic characteristics. The effect of various process factors on these properties is described through particular mathematical models. The model parameters are estimated by fitting the corresponding model equations on a wide range of experimental data. Drying kinetics is greatly affected by the characteristic particle size and drying air temperature for convective drying, while for the case of microwave drying they are affected by the vacuum pressure and the emitted radiation power. Equilibrium material moisture content is affected by the temperature and the humidity of the surrounding air, while the osmotic pretreatment shifts the sorption isotherms to higher water activity levels. The quality properties examined, are significantly affected by the drying method. More specifically, osmotic dehydration decreases the porosity of the final product, while it prevents color deterioration and enchances the viscous nature of dehydrated apple. Freeze-dried apples develop the highest porosity, have the most elastic structure and the lowest rate of color deterioration.