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

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.     

DETERMINATION OF MOISTURE DIFFUSIVITY OF RED DELICIOUS APPLE TISSUES BY THERMOGRAVIMETRIC ANALYSIS

ABSTRACT

Moisture diffusivity is an important parameter needed in the analysis, design and optimization of drying processes for food and other materials. Published data on moisture diffusivities of food materials are scarce and, sometimes, inconsistent due to a lack of a precise and repeatable experimental technique. Most experimental data are limited to low and moderate drying temperature (<70°C), whereas in the food industry hot air of up to 100°C is usually used in the falling rate period to speed up the drying processes. In this study, the effective moisture diffusivities of Red Delicious apple tissues were determined from drying curves produced with a Perkin Elmer thermogravimetric analyzer, using the slope method. The experiments were conducted at lour temperatures 60, 80, 100 and 120°C. Two well defined falling rate periods were observed. The effective moisture diffusivity, for the four temperature levels ranged from 3.2 × 10^?7 to 7.9 × 10^?8 m²/s for the first falling rate period and 3.8 × 10^?8 to 4.7 × 10^?8 m²/s for the second falling rate period. The temperature dependence of the effective diffusivity can be described with an Arrhenius-type equation.     

干燥过程热质传递的简化模型

对多孔介质体积平均理论进行简化,得到简化的热质传递干燥模型,用一个理论式表达模型中有效扩散系数。对香蕉片千燥的研究表明,模型的预测值与实验结果相     

DETERMINATION OF MOISTURE DIFFUSIVITY AND BEHAVIOR OF TOMATO CONCENTRATE DROPLETS DURING DRYING IN AIR

ABSTRACT

The drying mechanism and diffusion coefficient of water in spherical droplets (1.73 – 2.08 mm diameter) of tomato concentrates were successfully interpreted and modelled by using Fick's law. Solids content of the initial concentrate (5–15% w/w), and drying temperature (60^° – 100^° C) were varied but the drying air was kept at constant velocity and humidity.

The effective moisture diffusivity was estimated from the drying rate curves and expressed by an Arrhenius relation. Further, it was observed that case hardening has a large effect on the diffusion process causing the effective diffusional distance and the rate of moisture accumulation in the hardened crust to vary with the moisture content, according to a sorption controlled mechanism.     

DETERMINATION METHOD OF VARIABLE DIFFUSION COEFFICIENTS OF HYGROSCOPIC MATERIAL FROM DRYING RATE CURVES OF THE SINGLE PARTICLE

ABSTRACT

The concentration dependency of diffusion coefficients of hygroscopic materials can usually only be calculated by cumbersome experimental techniques.

Taking the diffusion rate in the fictious steady state with the same mean moisture concentration as in the regular regime of the drying process of a spherical hygroscopic particle (which means the drying period not influenced by initial moisture distributions) into account, a simple method is proposed to estimate the dependency of diffusion coefficients on the moisture concentration for hygroscopic materials from drying rate curves of the single particle.     

A SHORT-CUT METHOD FOR DETERMINING CONCENTRATION DEPENDENT DIFFUSIVITY IN LIQUID FOODS AND POLYMER SOLUTIONS FROM REGULAR REGIME DRYING CURVES

A simple method for determining concentration (water or solvent content) dependent diffusivity in liquid foods and polymer solutions from the regular regime drying curve was developed on the basis of the power-law diffusion model. The method was first tested to the drying data generated from numerical solutions of the diffusion equation with various types of concentration dependent diffusivities. The present method was found to be very simple yet accurate compared with the previous methods. Then, the drying rates of various sugar solutions experimentally obtained were analyzed on the basis of the present method to determine the moisture content dependent diffusivities.     

A SHORT-CUT METHOD FOR DETERMINING CONCENTRATION DEPENDENT DIFFUSIVITY IN LIQUID FOODS AND POLYMER SOLUTIONS FROM REGULAR REGIME DRYING CURVES

A simple method for determining concentration (water or solvent content) dependent diffusivity in liquid foods and polymer solutions from the regular regime drying curve was developed on the basis of the power-law diffusion model. The method was first tested to the drying data generated from numerical solutions of the diffusion equation with various types of concentration dependent diffusivities. The present method was found to be very simple yet accurate compared with the previous methods. Then, the drying rates of various sugar solutions experimentally obtained were analyzed on the basis of the present method to determine the moisture content dependent diffusivities.     

AN ASSESSMENT OF THE USE OF CHARACTERISTIC DRYING CURVES FOR THE HIGH-TEMPERATURE DRYING OF SOFTWOOD TIMBER

ABSTRACT

An explicit assessment has been carried out, using the experimental data of Pang (1994), of the applicability of the concept of a characteristic drying curve to the drying of Pinus radiata softwood timber. This concept has been used recently by Pang and Keey (1994) and Nijdam and Key (1996) when investigating the expected drying behaviour of a complete stack of timber. The concept appears to be applicable over the range of wet-bulb depressions which are common inside the stacks of timber, supporting its use in kiln-wide analysis of drying behaviour.     

REGULAR REGIME ANALYSIS AND MOISTURE DIFFUSIVITY IN WOOD

ABSTRACT

The Regular Regime analysis, introduced by Schoeber in 1976, enables the determination of concentration dependent diffusivities from a single desorption experiment. A study on theoretical and practical aspects of this analysis is presented here. The theoretical background of the method is treated. Efforts have been made to simplify the calculation procedures by compacting and clarifying some complicated relationships. The calculation has become simple, straightforward and easy to use in practice. A stepwise procedure is given.

The Regular Regime analysis has been applied to wood specimens (Norway spruce). The moisture diffusivities are compared with those obtained from a Stationary Flux method. The observed differences are discussed. Also attention is paid to some problems in the application of the Regular Regime analysis.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

CONVECTIVE-AIR DRYING KINETICS OF OSMOTICALLY PRE-TREATED BLUEBERRIES

Abstract

The second stage convective drying behavior of osmo-dehydrated blueberries was evaluated in a forced-air cabinet dryer (temperature: 50°C, relative humidity: 14%, air velocity: 0.6 m/s) with a cross-flow tray arrangement. Fick's second law of unsteady state diffusion was used to model the air drying kinetics. The results showed that the convective-air drying of the blueberries occurred in two falling rate periods. The effective diffusion coefficients, D_eff, during the first falling rate period ranged from 1.19 × 10^?10 m²/s to 2.14 × 10^?10 m²s and ranged from 4.04 × 10^?11 m²/s to 1.32 × 10^?10 m²/s during the second falling rate period. Among the pre-treatment conditions, the temperature and sucrose concentration during osmotic dehydration significantly (p < 0.05) influenced the air drying time, while the effect of contact time was not significant (p > 0.05).     

DETERMINATION OF MASS DIFFUSIVITY COEFFICIENT OF SWEET POTATO

Abstract

Using Luikov's heat and mass transfer equations and a finite element formulation, the drying process of an anisotropic biological product (sweet potato) was investigated. The model was used to determine the coefficients of heat and mass transfer, the mass diffusivity normal and parallel to the fibers of sweet potato samples. These parameters were estimated by minimizing the deviation of experimental data and numerical predictions.

Laboratory experiments with three different configurations were conducted to measure the temperature and moisture content of sweet potato samples during drying. Numerical simulation showed good agreement with the measured values.     

ADSORPTION DRYING OF CORN IN ZEOLITE GRANULES USING A ROTARY DRUM

ABSTRACT

This study was conducted to evaluate the potential of a natural zeolite (chabazite) as the particulate medium for grain drying. The granular zeolite was heated in an electric oven and mixed with grain corn. Drying experiments were conducted in a rotary batch dryer equipped with a computer and a data acquisition and control unit simulating an adiabatic process. Five initial medium temperatures (140, 160, 180, 200, and 220 °C) were used. Drying curves for grain corn and the values of effective diffusivity are reported. The amount of moisture removed and     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

DETERMINATION AND INTERPRETATION OF THE CRITICAL MOISTURE CONTENT (C.M.C.) AND THE INTERNAL MOISTURE CONTENT PROFILE DURING THE CONSTANT DRYING RATE PERIOD.

Abstract

In this study, the critical moisture content ( CMC. ) and the internal moisture content profiles during the constant rate period were determined experimentally for several conditions of convective drying of plaster. The experimental CMC values obtained allow us to validate the theoretical model of prediction of this parameter presented by KEEY [1] and SUZUKI [2] for drying rates higher than 3×10^?4 kg/(m².s) and to determine the equivalent moisture difliisivity at the external surface of plaster which was found to be equal to 3.9 × 10^?9 m²/s On the other hand, expressions of the internal humidity profiles were determined without solving the second FICK's law and were found to be same that the ones obtained by KEEY [1] for thick products and KRJSCHER and KROLL [3] for thin products by solving this law. The moisture diffusivity at the surface previously obtained was used in these equations to predict the internal humidity profiles during the constant rate period Comparison between theoretical predictions and experimental humidity profiles obtained on plaster shows a quite good agreement.     

COMBINED MICROWAVE AND SPOUTED BED DRYING OF DICED APPLES: EFFECT OF DRYING CONDITIONS ON DRYING KINETICS AND PRODUCT TEMPERATURE

ABSTRACT

The influence of microwave power (0 to 8.0 W/g, dry basis) and hot air temperature (25°C to 95 °C) on drying rate and product temperature of diced apples (from 31 % to 5% moisture content, dry basis) in a laboratory microwave and spouted-bed combined dryer was investigated. Product temperature initially increased sharply to a plateau about 12 to 15°C above the spouted bed air temperature at a microwave input power 6.4 W/g. This temperature remained almost constant thereafter. Uniform microwave heating was achieved as evidenced by uniform product color and product temperature. Drying rates increased with increasing spouted-bed air temperature or microwave power level, But higher microwave power caused more darkening of the product. Drying of the diced apples in the microwave and spouted bed drying system exhibited two falling rates periods. The influence of air temperature on effective moisture diffusivity followed an Arrhenius type equation. The activation energies were 23.7 kJ/mol and 26.7 kJ/mol for the first and second falling rate periods, respectively.     

COMBINED MICROWAVE AND SPOUTED BED DRYING OF DICED APPLES: EFFECT OF DRYING CONDITIONS ON DRYING KINETICS AND PRODUCT TEMPERATURE

The influence of microwave power (0 to 8.0 W/g, dry basis) and hot air temperature (25°C to 95 °C) on drying rate and product temperature of diced apples (from 31 % to 5% moisture content, dry basis) in a laboratory microwave and spouted-bed combined dryer was investigated. Product temperature initially increased sharply to a plateau about 12 to 15°C above the spouted bed air temperature at a microwave input power 6.4 W/g. This temperature remained almost constant thereafter. Uniform microwave heating was achieved as evidenced by uniform product color and product temperature. Drying rates increased with increasing spouted-bed air temperature or microwave power level, But higher microwave power caused more darkening of the product. Drying of the diced apples in the microwave and spouted bed drying system exhibited two falling rates periods. The influence of air temperature on effective moisture diffusivity followed an Arrhenius type equation. The activation energies were 23.7 kJ/mol and 26.7 kJ/mol for the first and second falling rate periods, respectively.     

A SEMI-THEORETICAL MODEL FOR THE DRYING OF THUMPSON SEEDLESS GRAPES

In this paper, the usefulness of a mathematical model based on equations describing the diffusional phenomena which are variable with time, is developed and discussed in relation to serve as a model for experimental data of drying of Thompson seedless grapes.

This model represents more closely the drying curves tested, than the classic diffusion model normally utilized to analize drying processes     

A SIMULATION MODEL FOR TIMBER DRYING CHECKED BY MEASUREMENTS AT TECHNICAL KILNS

ABSTRACT

A physically based simulation program for timber drying, which predicts the integral drying course, the profiles of moisture content, and internal stress during drying, was checked by data from technical drying runs. A data logging system served to record the data sets from several drying runs at diverse kilns. The comparison of model predictions and measured data led to the following conclusions: The integral drying course, i.e. time dependence of the average moisture content, can be well precalculated in quantity. Calculations of the moisture profiles were found to be right in tendency, but not in accuracy. Stress calculation by means of a visco-elastic Burger model leads to results correct in tendency, but to high in comparison with measured data.

To improve the stress calculation mechano-sorptive creep by models of Salin and Ranta-Maunus were tested. The calculation of these models corresponded with measurements from laboratory experiments. The simulation program is estimated to be applicable for further calculations of energy demand and costs in drying.     

A DIFFUSION MODEL WITH A MOISTURE DEPENDENT DIFFUSION COEFFICIENT FOR PARBOILED RICE

A mathematical model describing moisture migration by diffusion in a solid sphere with variable diffusion coefficient is proposed. An analytical expression for dependence of the diffusion coefficient with moisture content was derived based on the assumption that the activation energy for diffusion varies linearly with the desorption energy.

The expression for moisture dependence of diffusion coefficient was used to simulate drying of parboiled rice in the temperature range 50-90°C. The mathematical model shows good agreement between observed and predicted drying rate curves.