Some Considerations in Modeling of Moisture Transport in Heating of Hygroscopic Materials

Hygroscopic materials are those in which the equilibrium pressure of water vapor changes with moisture content and temperature, such as food, soil or wood, etc. Heat and moisture transports are coupled in heating of hygroscopic materials. One of the major links between temperature and moisture changes is water evaporation. There have been different formulations on modeling of evaporation in the past. A typical approach (Model 1 in this article) is to equate the evaporation rate to the rate of local moisture loss. The first part of this paper illustrates that such an approach is physically incorrect based on fundamental conservation relationships. A conservation-based coupled heat and moisture transfer model (Model 2) is presented here based on previous multiphase transport models. It shows that total evaporation rate over the entire material is included in Model 1 while the local evaporation rate is not. The situations when Model 1 may or may not generate large errors are discussed. The second part of this article completes the modeling of evaporation using Model 2. Two types of formulations are given depending on the phase equilibrium of moisture in the hygroscopic materials. When phase equilibrium between water and vapor is assumed for any location at any time, vapor pressure is provided as known variables. In a nonequilibrium approach, evaporation rate needs to be provided. The latter poses numerical difficulties near the material surface, which arises from the possibility that equilibrium state may have a large change near the surface. Further discussions were made on the physical and numerical considerations in using both approaches.     

Effect of moisture content on mechanical properties,thermal and structural stability and extrudate texture of poly(vinyl chloride)/wood sawdust composites

Mechanical properties and thermal and structural changes of poly(vinyl chloride) (PVC)/wood sawdust composites were assessed with respect to the effect of moisture content, varying from 0.33 to 3.00 % by weight in the composite, for three different wood sawdust contents. The swell ratio and texture characteristics of the composite extrudates were also evaluated. Unique explanations were given to describe changes in the composite properties in terms of molecular interactions between PVC, cellulosic sawdust and moisture, such as dipole–dipole interactions, interfacial defects and bonding, fibre swelling, and moisture evaporation. The results suggest that at low moisture content the tensile modulus decreased and elongation at break of the composites increased with moisture content, the effect being reversed for high moisture content. Tensile strength decreased with increasing moisture content up to 1–2 %, and then unexpectedly increased at higher moisture contents. The effect of moisture content on flexural properties of the composite was similar to that on tensile properties. Impact strength of the composites was considerably improved with moisture content at low sawdust contents (16.7 wt%), and was independent of the moisture content at higher sawdust contents (28.6 and 37.5 wt%). A decrease in decomposition temperature with an increase in polyene content was evidenced with increasing moisture content, while the glass transition temperature did not change with varying moisture content. The extrudate swell ratio increased with the shear rate but remained unaffected by moisture content. The bubbling and peeling‐off in the composite extrudate occurred as a result of the evaporation of water molecules and the application of a high shear rate. Copyright © 2004 Society of Chemical Industry     

Finite Element Analysis of a Moving Boundary Value Problem

A finite element formulation and the solution of a set of nonlinear coupled heat and mass transfer equations for a two-phase system with a moving evaporation interface is presented. The interface condition takes into account the moisture transfer balance at the moving boundary. The finite element results were compared with existing results for a single phase system for model validation. In the two-phase system, the movement of evaporation front has an appreciable effect on the temperature and moisture distribution inside the porous medium during drying. The effect of the nondimensional heat of vapourization parameter γ on the evaporation front, temperature and moisture distribution in porous medium was studied. The higher the value of γ, the slower is the movement of the evaporation front. The temperature decreased and the moisture content increased as the nondimensional vapourization parameter γ increased. This model has potential applications in studying the heat and mass transfer characteristics in food and biomaterials.     

单颗粒褐煤高温烟气干燥过程数值模拟

褐煤干燥对于提高其品质具有重要意义。为了模拟高温烟气干燥这一高温差、变温差非稳态传热传质过程中褐煤内水分蒸发过程,采用有限体积法建立了一维球坐标系下蒸发界面向内迁移的单颗粒褐煤干燥数学模型,并利用该模型分析了初始烟气温度和颗粒粒径对单个褐煤颗粒干燥特性的影响。模型模拟结果与实验结果对比表明二者变化趋势一致,所建模型能较好地反映出高温烟气干燥过程中褐煤内水分蒸发过程。结果表明,初始烟气温度越高,颗粒粒径越小,蒸发界面向内迁移速度越快,水分脱除越快,干燥时间越短;蒸发界面平均迁移速度均与初始烟气温度和颗粒粒径呈线性关系;在初始烟气温度700℃下,较短的停留时间使得颗粒表面温度未达到挥发分析出温度,本研究中不同粒径褐煤颗粒在干燥过程中基本没有挥发分的析出。     

Variability in Transport Properties Regarding Drying Behavior for Blackbutt Timber in New South Wales

Variability is a key issue in the processing of many biological materials, in this case the drying of hardwood timber. This article reports the measurements of variability of the diffusion coefficient (a transport property), the initial moisture content, and the basic density that are relevant to the drying of blackbutt, Eucalyptus pilularis Sm, from northern New South Wales in Australia. The diffusion coefficient was quantified using a mathematical model solving Fick's second law of diffusion for mass transfer, and Fourier's law for heat transfer. The initial moisture content and the basic density were measured using experimental procedures. Specifically, within-tree and between-tree variations are reported. The coefficients of variation of the initial moisture contents and final moisture contents are 0.24 and 0.19, respectively, for within-tree variability. A similar result was found for the amount of between-tree variability. Compensating differences in the diffusion coefficients of the timber boards were a significant reason for the small dispersion of final moisture contents, despite the large variation in initial moisture contents.

An analysis of variance showed that some timber properties were affected by the board positions within trees and between trees. Circumferential and radial effects were significant for the within-tree variability of most transport properties. Moreover, principal components analysis suggested that timber boards with low densities have high initial moisture contents and high diffusion coefficients. A potential reason is that if there is less wood material per unit volume (lower density), then there is more space to be occupied by water (higher initial moisture content), and there is also less resistance to the diffusive transport of moisture (higher diffusion coefficients).     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D_eff) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D_eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

Effect of moisture on sewage sludge combustion temperature profile and heavy metal leaching

Moisture is the most important parameter affecting sewage sludge treatment efficiency and cost. In this article, the effect of moisture on sewage sludge combustion temperature profile and heavy metal leaching behavior has been experimentally studied. The temperature profiles inside the sludge pellet were recorded, and the volume shrinkage was obtained by image processing method. Results revealed that combustion rate and burnout of sludge strongly depends on moisture content and there exists an optimal moisture content for sludge incineration with respect to best combustion performance and minimum heavy metal leaching. The enlarged pore size may account for this moisture rate, that is, 48% for the sludge studied. During combustion, the shrinkage rate varied from 15 to 25%, and it was found to be proportional with moisture content. The cross-section image of burning sludge pellet illustrated that during the drying and combustion stage, the moisture evaporation was running parallel with the decomposition of volatile that was burned out in the vicinity of the sludge surface. Measured temperature profiles indicate that effect of volatile combustion on inner temperature profile was ignorable. A mathematic model taking sludge volume shrinkage into consideration has been developed to predict sludge central and surface temperature during combustion.     

Effects of material parameters on the diffusion and sorption properties of wood‐flour/polypropylene composites

Composites of wood in a thermoplastic matrix (wood–plastic composites) are considered a low maintenance solution to using wood in outdoor applications. Knowledge of moisture uptake and transport properties would be useful in estimating moisture‐related effects such as fungal attack and loss of mechanical strength. Our objectives were to determine how material parameters and their interactions affect the moisture uptake and transport properties of injection‐molded composites of wood‐flour and polypropylene and to compare two different methods of measuring moisture uptake and transport. A two‐level, full‐factorial design was used to investigate the effects and interactions of wood‐flour content, wood‐flour particle size, coupling agent, and surface removal on moisture uptake and transport of the composites. Sorption and diffusion experiments were performed at 20°C and 65 or 85% relative humidity as well as in water, and diffusion coefficients were determined. The wood‐flour content had the largest influence of all parameters on moisture uptake and transport properties. Many significant interactions between the variables were also found. The interaction between wood‐flour content and surface treatment was often the largest. The diffusion coefficients derived from the diffusion experiments were different from those derived from the sorption experiments, suggesting that different mechanisms occur. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 752–763, 2007     

Influence of drum inlet air conditions on drying process in a domestic tumble dryer

This study examines how the inlet air temperature, relative humidity, and flow rate influence the textile drying process in an open cycle tumble dryer. An experimental setup was prepared by connecting a domestic tumble dryer to an external system for controlled heating, humidification, and transport of air. Experiments were conducted by drying cotton textiles (8?kg dry mass) at different air inlet conditions. On the basis of measured data, correlations for determination of the total drying time, the moisture evaporation rate during the constant drying rate, and the area-mass transfer coefficient were developed. The process in the drum was modeled by using an established moisture evaporation model, based on sorption isotherms. A commonly used and a recently reported sorption isotherm for cotton were used with the model. Agreement between calculated and measured drying curves was better in case of the commonly used sorption isotherm, but final moisture content was better predicted by the recently reported sorption isotherm.     

Variability in Transport Properties Regarding Drying Behavior for Blackbutt Timber in New South Wales

ABSTRACT

Variability is a key issue in the processing of many biological materials, in this case the drying of hardwood timber. This article reports the measurements of variability of the diffusion coefficient (a transport property), the initial moisture content, and the basic density that are relevant to the drying of blackbutt, Eucalyptus pilularis Sm, from northern New South Wales in Australia. The diffusion coefficient was quantified using a mathematical model solving Fick's second law of diffusion for mass transfer, and Fourier's law for heat transfer. The initial moisture content and the basic density were measured using experimental procedures. Specifically, within-tree and between-tree variations are reported. The coefficients of variation of the initial moisture contents and final moisture contents are 0.24 and 0.19, respectively, for within-tree variability. A similar result was found for the amount of between-tree variability. Compensating differences in the diffusion coefficients of the timber boards were a significant reason for the small dispersion of final moisture contents, despite the large variation in initial moisture contents.

An analysis of variance showed that some timber properties were affected by the board positions within trees and between trees. Circumferential and radial effects were significant for the within-tree variability of most transport properties. Moreover, principal components analysis suggested that timber boards with low densities have high initial moisture contents and high diffusion coefficients. A potential reason is that if there is less wood material per unit volume (lower density), then there is more space to be occupied by water (higher initial moisture content), and there is also less resistance to the diffusive transport of moisture (higher diffusion coefficients).     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D _eff ) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D _eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

DETERMINATION OF THE EVAPORATION OF WATER DURING WOOD DRYING BY MEANS OF HEAT FLUX MEASUREMENT

Since the only measured value that is derived from the wood for controlling the kiln drying process is the mean moisture content, it is essential to develop new techniques for the measurement of additional process parameters. When the drying rate, which could be such an additional parameter, is seen in conjunction with other process variables, conclusions on the instantaneous drying behaviour of the wood are possible. A simple and practical way for determining the drying rate is based on the relationship between the drying rate and the heat-flux for evaporation. A measurement of the heat-flux by means of a heat-flux sensor allows the calculation of the drying rate.     

Solidification by Convective Drying of Particle Layer Wetted with Dilute Agar Gel

Abstract:

Solidified porous slab is formed through convective drying of glass particle layer wetted with aqueous dilute agar gel. Measured critical mean moisture content increases with increasing initial moisture or agar content. The agar gel moves in viscous flow caused by capillary pressure during drying. A new drying model based on the receding evaporation plane model is proposed. Drying period is divided into surface and internal evaporation periods. Wet slab consists of dried and wet zones during the internal evaporation period, while the wet slab consists of wet zone only during the surface evaporation period. In the new model, the evaporation rate from the wet zone in the internal drying period is estimated with the linear driving force (LDF) approximation in the field of adsorption engineering. Critical moisture content, that is, mean moisture content between the surface and internal periods, is estimated with a mass balance on the surface. Simulated results by the new drying model with reasonable fitting parameters agree very well with measured drying data.     

Examining the Suitability of the Reaction Engineering Approach (REA) to Modeling Local Evaporation/Condensation Rates of Materials with Various Thicknesses

The reaction engineering approach (REA) is examined here to investigate its suitability as the local evaporation rate to be used in multiphase drying. For this purpose, REA is first implemented to model the convective drying of materials with various thicknesses. The relative activation energy, as the fingerprint of REA, generated from one size of a material is used to model the convective drying of the same material with different thicknesses. Because the results indicate that REA parameters can model the drying of materials with various thicknesses, REA can be scaled down to describe the local evaporation rate (at the microscale as affected by local composition and temperature). The relative activation energy is used to describe the global drying rate in modeling the local evaporation rate. REA is combined with a system of equations of conservation of heat and mass transfer in order to yield the spatial reaction engineering approach (S-REA) as a nonequilibrium multiphase drying model. By using S-REA, the spatial profiles of moisture content, concentration of water vapor, temperature, and local evaporation rate can be generated, which can assist in comprehending the transport phenomena.     

Solidification by Convective Drying of Particle Layer Wetted with Dilute Agar Gel

Solidified porous slab is formed through convective drying of glass particle layer wetted with aqueous dilute agar gel. Measured critical mean moisture content increases with increasing initial moisture or agar content. The agar gel moves in viscous flow caused by capillary pressure during drying. A new drying model based on the receding evaporation plane model is proposed. Drying period is divided into surface and internal evaporation periods. Wet slab consists of dried and wet zones during the internal evaporation period, while the wet slab consists of wet zone only during the surface evaporation period. In the new model, the evaporation rate from the wet zone in the internal drying period is estimated with the linear driving force (LDF) approximation in the field of adsorption engineering. Critical moisture content, that is, mean moisture content between the surface and internal periods, is estimated with a mass balance on the surface. Simulated results by the new drying model with reasonable fitting parameters agree very well with measured drying data.     

Microwave-Vacuum Drying of Wood: Model Formulation and Verification

Based on the mechanism of moisture and heat transfer in wood during microwave-vacuum drying (MVD), a one-dimensional mathematical model to describe the process of wood MVD was established and verified by experiments in this research. The results showed that the process of MVD of wood experienced three distinct periods: (1) accelerating rate with rapid warming-up drying period, (2) a constant temperature and constant rate drying period, and (3) a heating-up with falling rate drying period. Compared with conventional hot air drying, the total drying process is almost governed by a constant rate period in vacuum-microwave drying of wood. The predicted temperature and moisture content in wood match well with the experimental data, the square of the relevant coefficient of the values of simulation and test is above 0.9, and the simulation precision of the change rule of the moisture is higher than that of the temperature.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING, PART I: MODEL DEVELOPMENT AND PREDICTIONS

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

A mathematical description of thermal decomposition and spontaneous ignition of wood slab under a truncated-cone heater

A mathematical model of thermal decomposition together with the flammability limit is proposed to describe the pyrolysis and spontaneous ignition of wood slab subjected to the radiation from a truncated-cone heater. The prominent physical and chemical phenomena were considered in the model, involving heat transfer in a solid, heat consumed by thermal decomposition reactions, the evaporation of moisture, re-radiation from pore surfaces inside a solid and so on. The numerical solution allows the prediction of in-depth temperature profiles, evolution of volatiles, variation of thermal conductivity, apparent mass loss (solid conversion) and ignition time. The different densities for wood species and effect of moisture content and grain orientation on thermal conductivity are also considered in the model, producing a good prediction of surface temperatures. This gives birth to the reasonable prediction on ignition time of wood by employing fixed surface temperature (400 °C) as ignition criterion. However, the analysis of constituent fractions for the species associated with the multi-components kinetic scheme should be included in the mathematical model to give a more precise prediction on the apparent mass loss of solid.     

DETERMINATION OF THE EVAPORATION OF WATER DURING WOOD DRYING BY MEANS OF HEAT FLUX MEASUREMENT

ABSTRACT

Since the only measured value that is derived from the wood for controlling the kiln drying process is the mean moisture content, it is essential to develop new techniques for the measurement of additional process parameters. When the drying rate, which could be such an additional parameter, is seen in conjunction with other process variables, conclusions on the instantaneous drying behaviour of the wood are possible. A simple and practical way for determining the drying rate is based on the relationship between the drying rate and the heat-flux for evaporation. A measurement of the heat-flux by means of a heat-flux sensor allows the calculation of the drying rate.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART I: MODEL DEVELOPMENT AND PREDICTIONS

ABSTRACT

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.