Air Drying Kinetics of Potato Cylinders

ABSTRACT

An experimental air tunnel dryer was used to investigate the kinetics of moisture transport in potato cylinders (Solanum tuberasum). Acoordingly, the experimental results, represnting only falling-rate drying behaviour and hence. dehydration completely controlled by internal mass transfer, were interpreted on the basis of Fick's diffusional model for non-stedy state radial diffusion. The effects of air velocity and temperature on the drying rate were studied. with he temperature being the principal controlling factor. Analysis of the drying curves by the method of slopes resulted in a variable effective moisture diffusivity. Shrinkage as a function of moisture content under various drying conditions was investigated. The volumetric shrinkage of the samples was affected mainly by air velocity. whilst air temperature had a negligible effect. Good agreement was obtained between the experimental apparent density data and the predicted correlation.     

DIFFUSIONAL MODEL WITH AND WITHOUT SHRINKAGE DURING SALTED FISH MUSCLE DRYING

Abstract

The drying process of salted pieces of shark muscle (Carckarhinus limbatus) was accomplished using three air conditions (20 ^°C -40 %RH; 30 ^°C - 30 %RH; 40 ^°C - 45 %RH) and two air velocities (0.5 m/s; 3.0 m/s). Shrinkage of material during drying was correlated as a linear function between linear dimension and moisture content. The experimental drying data were obtained using both the diffusional model with moisture content parameter (considering no shrinkage) and the diffusional model with moisture concentration parameter (considering shrinkage). The values of effective diffusivity varied between 1.50×l0^?10m²/s and 2 85×l0^?10m²/s for drying process considering no shrinkage and between 0.87×l0^?10m²/s and 1.61×l0^?10m²/s for process considering shrinkage. The activation energy was calculated assuming an Arrhenius' type equation. The values were 17.94 KJ/mol with the air velocity of 0.5 m/s and 21.94 kJ/mol with the air velocity of 3,0 m/s for effective diffusivity without shrinkage. The values were 2.04 kJ/mol with the air velocity of 0.5 m/s and 16.12 kJ/mol with the air velocity of 3.0 m/s for effective diffusivity with shrinkage. These low activation energy values, calculated considering the shrinking effect, show that the side effects during drying reduces the effective diffusivity dependence on temperature     

Modelling and Simulation of a Direct Contact Rotary Dryer

ABSTRACT

A mathematical model able to predict solid and drying gas temperature and moisture content axial profiles along a direct contact rotary dryer was developed. The study was focused on the drying kinetics based on phenomenological models. Two different drying mechanisms in the decreasing drying rate period were tested: proponional to the unbound moisture content and moisture diffusion inside the particle. Experimental data collected in a pilot-scale direct contact rotary dryer was used to validate the model. Soya and fish meals were used as drying material.     

Convective drying of osmotically dehydrated apples described by three-dimensional numerical solution of the diffusion equation with analysis of water effective diffusivity spatial distribution

Abstract

This study presents two liquid diffusion models to represent the convective drying of apple, osmotically dehydrated in sucrose solution, cut into parallelepiped-shaped pieces. Model 1 considered water diffusivity and the volume of the slices with constant values. Model 2 considered water effective diffusivity and the dimensions of the slices as variable. The numerical solution of the three-dimensional diffusion equation in Cartesian coordinates was obtained through the finite volume method, with a fully implicit formulation and boundary condition of the third kind. Process parameters were estimated by an optimizer using experimental data. A spatial distribution analysis was carried out for water effective diffusivity and moisture content in the apple slices. The results showed that the concentration of the osmotic solution used in the pretreatment influenced the drying process and that the mathematical model that considered a variable diffusivity and shrinkage was more suitable to describe the experimental data.     

Principle and Applications of Drying Characteristic Functions

ABSTRACT

This article focuses on the concept of a ‘drying characteristic function,’ which is an effective way to correlate drying rate curves for convective drying of homogeneous nonporous, hygroscopic porous and non-hygroscopic porous materials. The characteristic function, obtained bv a certain transformation of a drying rate curve, is independent of drying conditions and hence characterizes the transport kinetics in the material. The principle and some applications of the functions are reviewed. The first application is estimation of dryinge rate curves. Because any drying rate curve can be transformed into the characteristic function and vice versa, the drying rate can be estimated for various drying conditions from a single drying experiment. Another aoolication is determination of the moisture diffusivity. Using the ‘flux ratio method’ an analytical expression of the characteristic function can be obtained for any aiven moisture diffusivity. The exprcssion enables one to determine the moisture diffusivity for a wide range of moisture content from a single drying experiment.     

A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

ABSTRACT

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

DYNAMIC SHRINKAGE AND VARIABLE PARAMETERS IN BAKKER-ARKEMA'S MATHEMATICAL SIMULATION OF WHEAT AND CANOLA DRYING

Abstract

The bulk volume shrinkage was linearly related to instantaneous grain moisture reduction. The shrinkage coefficient was found to be primarily a function of air relative humidity. The Bakker-Arkema's bulk grain drying model was modified to incorporate the shrinkage equation. A correction factor for thin layer drying equation was also introduced to reduce deviation between the experimental and simulated moisture content. The Bakker-Arkema model showed significant improvement due to these modifications.     

Determination of Moisture Diffusivity by Thermo-Gravimetric Analysis under Non-Isothermal Condition

Abstract:

In drying of solids, the diffusion model based on Fick's second law is usually applied to interpret the moisture migration within the solid. Then the temperature dependence of the moisture diffusivity, generally described by an Arrhenius-type equation, is obtained through the drying kinetics. In this article, a nonisothermal (linearly increasing temperature) procedure was used to determine the moisture diffusivity as a function of temperature with the complex optimization method, and the result was accessed by comparison with a classical isothermal procedure. All the experiments were conducted in a thermogravimetric analyzer (TGA) for accurately recording the mass loss from the sample and easily programming the heating profile.     

Shrinkage Characteristics of Potatos Dehydrated Under Combined Microwave and Convective Air Conditions

ABSTRACT

A study of the pysical structure and quality potatoes during microwave and air drying war undertaken. The effect of various experimental variables on volumetric shrinkage including microwove power levels, air temperature and velocity as well as sample geometry was investigated. In both microwave and air drying, the shrinkage of potatoes showed a linear behaviour in relation to different moisture content levels. Experimental data showedthat air velocity and microwave power had a major effect on the degree of shrinkage, also the shrinkage behaviour was independent of sample geometry and air temperature. The use of microwave produced smaller changer in volume (less shrinkage) and henee a better quality finished product.     

A New Correlation for the Estimation of Moisture Diffusivity in Corn Kernels from Drying Kinetics

ABSTRACT

The modelisation of cereal drying kinetics is more, and more often performed by the diffusion equation (Fick's law) Eor homogeneous materials rather than lumped or semi-empirical equations. The heterogeneity of the material is accounted for by the use of an effective diffusivity the prediction of which is essential for the determination of the functional relationship between diffusion coefficient and arain moisture content and temperature. For this dependence, the method of resolution may be analytical or numerical. In this study, the estimation of diffusion coefficient is based on drying curves obtained with arains in the ranae of initial moisture content of 18-509 and a temperature of 50:120??. The important result corresponds to the finding that the moisture diffusivity is a function not only of variabies of the state i.e. moisture content and temperature, but also of the initial moisture content as in the following : 'D = P4g X, exp(8 X ). AD and B are both dependent on temperature     

From Laboratory Experiments to Design of a Conveyor-Belt Dryer via Mathematical Modeling

Abstract

A conveyor-belt dryer for picrite has been modeled mathematically in this work. The necessary parameters for the system of equations were obtained from regression analysis of thin-layer drying data. The convective drying experiments were carried out at temperatures of 40, 60, 80, and 100°C and air velocities of 0.5 and 1.5 m/sec. To analyze the drying behavior, the drying curves were fitted to different semi-theoretical drying kinetics models such as those of Lewis, Page, Henderson and Pabis, Wang and Singh, and the decay models. The decay function (for second order reactions) gives better results and describes the thin layer drying curves quite well. The effective diffusivity was also determined from the integrated Fick's second law equation and correlated with temperature using an Arrhenius-type model. External heat and mass transfer coefficients were refitted to the empirical correlation using dimensionless numbers (J _h , J _D  = m · Re ⁿ ) and their new coefficients were optimized as a function of temperature. The internal mass transfer coefficient was also correlated as a function of moisture content, air temperature, and velocity.     

Diffusive Model with Variable Effective Diffusivity Considering Shrinkage for Hot-Air Drying of Lightly Salted Grass Carp Fillets

A diffusion model has been developed for predicting the change of moisture content in lightly salted grass carp fillets under the consideration of shrinkage and variable volumetric effective diffusivity. The established relationship between moisture content, temperature, and effective diffusivity validated the effectiveness of considering the variable volumetric effective diffusivity. The appearance of shrinkage during drying and the shrinkage coefficient have been determined for better predicting the variation of moisture content during drying to provide a thorough theoretical basis for industrial processes.     

A Simple Data Processing Approach for Drying Kinetics Experiments

A simple mathematical approach is proposed to be applied to drying kinetics raw data processing. The data collected in a drying experiment of powder cork under constant air drying conditions served as case study to present the methodology. Two functions (linear and third-degree polynomial) were used to fit solid moisture content in the constant drying rate and the falling rate periods. The drying rate curve was obtained by differentiation and the time at which the drying rate period's transition occurs was determined iteratively until virtually continuous functions were achieved. The critical moisture content was easily identified and two falling drying rate periods were detected.

The powder cork moisture decrease was also used to test several semiempirical models available in the literature. The Logarithmic, Midilli, and Page Modified I models were the ones that revealed the best correlations performance. When the methodology proposed was applied using these models, the critical moisture content was underpredicted.

The effective moisture diffusivity and the activation energy were also obtained for powder cork after the proposed mathematical approach has been applied on the raw data obtained in experiments performed at different air drying temperatures.     

Mathematical modeling and simulation of shrunk cylindrical material's drying kinetics—Approximation and application to banana

In the present work, a diffusion-based model was adopted to represent the convective drying behavior of cylindrical banana samples, taking into consideration the shrinkage along drying. The developed model simulated a significant number of situations resulting from the variations of some operating conditions. The temperatures tested were 50, 60, 67 and 70 °C, the air velocities were 3, 4 and 4.5 m/s and the relative humidity range of the drying air was from 3.5 to 11.5%. The calculated drying curves were compared to the experimental ones in order to determine apparent moisture diffusivity. An empirical equation was suggested, describing the apparent moisture diffusivity within the banana versus product temperature and local moisture content. A good agreement was found between experimental and calculated drying kinetics.     

Effective Diffusivity and Evaporative Cooling in Convective Drying of Food Material

This article presents mathematical models to simulate coupled heat and mass transfer during convective drying of food materials using three different effective diffusivities: shrinkage dependent, temperature dependent, and the average of those two. Engineering simulation software COMSOL Multiphysics was utilized to simulate the model in 2D and 3D. The simulation results were compared with experimental data. It is found that the temperature-dependent effective diffusivity model predicts the moisture content more accurately at the initial stage of the drying, whereas the shrinkage-dependent effective diffusivity model is better for the final stage of the drying. The model with shrinkage-dependent effective diffusivity shows evaporative cooling phenomena at the initial stage of drying. This phenomenon was investigated and explained. Three-dimensional temperature and moisture profiles show that even when the surface is dry, the inside of the sample may still contain a large amount of moisture. Therefore, the drying process should be dealt with carefully; otherwise, microbial spoilage may start from the center of the dried food. A parametric investigation was conducted after validation of the model.     

Determination of appropriate effective diffusivity for different food materials

Effective diffusivity is the most important key parameter needed in the analysis, design, and optimization of heat and mass transfer during food drying process. In general, two types of effective diffusivities are used to develop the mathematical modeling of food drying, namely, moisture-dependent effective diffusivity (MDED) and temperature-dependent effective diffusivity (TDED). However, no study has extensively investigated which effective diffusivity is more accurate in predicting drying kinetics. The main goal of this study is to determine the appropriate effective diffusivity for predicting the drying kinetics. Drying models were developed for different fruits and vegetables based on moisture-dependent and temperature-dependent effective diffusivities. COMSOL Multiphysics, a finite element-based engineering simulation software is used to solve the coupled heat and mass transfer equations. 3D moisture profiles were developed to investigate the spatial moisture distribution during drying. Extensive experimental investigation on five types of fruits and vegetables was conducted and results were compared with the simulated results. The experiments were repeated thrice, and the average of the moisture content at each value was used for constructing the drying curves. Close agreement between experimental and simulated results validates the models developed. It was observed that the moisture profile and temperature profile in case of MDED were more closely fitted with the experimental results. For all fruits and vegetables, the moisture ratio with MDED was significantly lower than moisture ratio with TDED. This finding confirms that the MDED is more accurate for predicting kinetics in food drying. Moreover, the moisture ratio of apple was lowest whereas pear showed the highest moisture ratio. On the other hand, carrot showed a considerably lower moisture ratio compared to potato.     

The Effect of Path Diffusion on The Effective Moisture Diffuslvlty in Carrot Slabs

ABSTRACT

In order to evaluate the effect of path diffusion on the average moisture diffusivity in carrot. drying curves for different shaves (slices and cylinders) and temperatures of 50, 60 and 70°C were ohtained takine into consideration the use of an average leneth of carrot sample (slice thickness or the cylinder radio). The. results showed significant differences betuecn radial and axial average diffusivities. Significant differences were also observed between core and annular diffusivity. The experimenta1 drying curves did not show enough evidence on the effect of drying temperature on the average moisture diffusivity.     

MOISTURE DIFFUSION IN GELATIN SLABS BY MODELING DRYING KINETICS

ABSTRACT

The aim of this work is to improve the knowledge concerning moisture mobility in gelatin slabs, through the evaluation of moisture diffusivity (function of temperature and moisture content) by modeling of drying kinetics

The first part of this work is devoted to the determination of the gel characteristics needed for a good modeling. Drying experiments were then carried out on a pilot drier according to a central composite design with 3 factors (temperature, moisture content and pH).

Moisture diffusivity was finally calculated by fitting a model to the drying experiments. The chosea model (a conventional diffusive model with variable diffusion coefficient, solved by finite difference calculations in a solid-related frame of coordinates) did not perfectly fit the experimental results. It especially under-estimates moisture gradients at the surface of the gel     

Effective Diffusivity Determination Considering Shrinkage by Means of Explicit Finite Difference Method

Drying data of salted shark (Carcharhinus limbatus) muscle pieces samples, dried in a convective dryer, by using three different air conditions and two different air velocities, were treated by Fick's second law. The shrinkage during drying process was considered as a linear function of sample moisture. The Fick's second law equation was numerically solved by the explicit finite difference method to obtain effective diffusivity, considering shrinkage and with and without simplification of moisture content profile. The experimental data fitted very well independently of the simplification introduced on the moisture content profile. The best fit was obtained by considering volumetric average of sample moisture content. The effective diffusivity values calculated considering the shrinkage varied from 0.72 to 2.20 × 10^?10 m²/s with the mean relative deviation modulus from 1.02 to 6.51%. The activation energy expressed in function of air temperature varied from 3.42 to 19.23 kJ/mol.     

SHRINKAGE OF APPLE DISKS DURING DRYING BY WARM AIR CONVECTION AND FREEZE DRYING

ABSTRACT

Volumetric and thickness shrinkage evaluated by direct measurement and n-heptane displacement were determined during convective and freeze drying of Golden delicious apples. For convective drying, the influence of blanching and diameter/thickness ratio of the apple disks used were analysed at different levels of moisture content under constant conditions. It was found that shrinkage of dried samples, both by convection and by freeze-drying, is anisotropic to a level which depends on sample geometry (ratio diameter/thickness) used. Blanching did not affect shrinkage results.

Based on results obtained a new model to predict bulk density of materials during drying is proposed, showing a better fit to experimental data than previous models reported in the literature. This model was further used to predict changes in apple porosity during drying.