Mass Transfer from Wooden Surfaces and Internal Moisture Non-Equilibrium

ABSTRACT

The transfer of moisture from a wooden surface and the corresponding mass transfer coefficient in relation to the heat transfer coefficient are considered. Experimental data are reviewed that show that the mass transfer coefficient often is one order of magnitude smaller than what could be expected from the analogy between heat and mass transfer. The nature of this deviation and its influence on wood drying models is discussed. It has been suggested by Wadsö.that moisture flow inside the wood exhibits non–Fickian behaviour and that this may be due to a slow desorptiodabsorption by the wood fibre. A model is thus developed where the normal assumption of internal local equilibrium between the vapour and bound phases is replaced by a mass transfer resistance. The model is applied to one–dimensional moisture flow in a body of finite thickness and solved analytically. Numerical values calculated with the model are analysed in order to establish whether “apparent” non–Fickian behaviour of the kind observed could be explained by such a model. It is also analysed whether the model could explain an apparent decreased mass transfer coefficient at the surface.     

Some Considerations In Simulation Of Superheated Steam Drying Of Softwood Lumber

ABSTRACT

A mathematical model for high-temperature drying of softwood lumber with moist air has been modified and extended to simulate wood drying with superheated steam. In the simulation, differences between the two types of drying are considered, these include: external heat and mass transfer processes and calculation of equilibrium moisture content. The external mass transfer coefficient in the perheated steam drying was found to be much higher than that in the moist air drying, however, the heat ransfer coefficients for these two cases were of the same order. The predicted drying curves and wood temperatures from the superheated steam drying model were compared with experimental data and there was close agreement. Further studies will apply the model to development of commercial drying schedules for wood drying with superheated steam.     

Mathematical model of heat and moisture transfer in alder birch wood during the thermo-vacuum treatment and its application in the quantitative control of the wood color

High-temperature heat treatment (HTHT) is an effective method for improving the wood dimensional stability and biological durability at present. However, the quantitative control of the wood color during the HTHT has been a more difficult problem for a long time. To solve the problem of quantitative control of wood color under the thermo-vacuum treatment (TVT) process, the mathematical model of heat and moisture transfer in alder birch wood (Betula alnoides) during the TVT process was built, and its application in the quantitative control of the wood color was also studied. (1) The experimental values and the model values of heat and moisture transfer in wood were found to be in good agreement. (2) The changes of wood temperature and moisture content (MC) were influenced obviously by the heat treatment temperature, the initial MC, and the thickness of specimen as well. The higher the heat treatment temperature was, the more rapid was the rise in the wood temperature and the drop in MC. The higher the initial MC of the wood was and the thicker the wood got, the slower the rise in wood temperature and the drop in MC. (3) Based on the mathematical model of heat and moisture transfer during the TVT process and the wood color index difference regression equations in the function of the temperature and time, the quantitative control of alder birch wood color during the TVT process was achieved. Therefore, it is feasible that heat and mass transfer principle applied during the TVT process guided the wood color quantitative control.     

Moisture Changes in Grain During Aeration Under Warm Humid Conditions

ABSTRACT

Two mathematical models (an equilibrium model and a combined model) were evaluated, which described the moisture and heat transfer in low temperature drying and aeration. The predicted moisture contents from both models were compared with the experimental data. Comparisons indicated that the combined model was more accurate than the equilibrium model. The combined model is based on the idea that the partial pressure difference is the driving force in moisture transfer. A series of simulation was performed using the combined model to evaluate the effect of air temperature, air relative humidity, and the temperature difference between grain and air on the moisture changes in stored rough rice. The simulation results proved the concept of using the partial pressure difference to describe the moisture transfer in stored grain. A minimum of 5.6°C in     

Heat and mass transfer in granular potash fertilizer with a surface dissolution reaction

Potash is a widely used granular fertilizer and when exposed to high humidities it readily adsorbs water vapour forming a liquid electrolyte solution on each particle. Heat and mass transfer due to air flow through granular potash beds is studied experimentally and numerically. A one dimensional experimental setup is used to measure the temperature and air humidity response and mass gain of a potash bed subjected to a change in air flow. A porous media mathematical model is developed to predict the transient temperature and moisture content distributions. The processes are modelled as nonequilibrium heat and mass transfers between the porous solid and air flow gaseous phases. The state of the surface electrolyte solution is modelled by the thermodynamics of electrolyte solutions. Experimental and numerical results show non‐equilibrium internal moisture and heat transfer processes exist with significant differences in the pore air and particle temperature and surface relative humidity.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

Numerical Simulation of the Drying of a Deformable Material : Evaluation of the Diffusion Coefficient

ABSTRACT

We are interested in the simulation of heat and mass transfer processes accompanying the drying of a deformable agricultural product. We have used an implicit method with classical finite differences to resolve the set of equations. The identification of the diffusion coefficient within a thin carrot layer is carried by trial and error on two analytical forms. These two forms take into account moisture content, temperature and shrinkage of the product.

The drying rates of thin layer of carrot pieces are measured in a laboratory tunnel dryer. These drying curves are established by varying some airflow parameters such as velocity, temperature and relative humidity. The internal and surface temperature of the slab were recorded by means of therrnosensors. The simulated solutions are in agreement with the experimental results.     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

Modelling the Bulk Cooling of Alfalfa Pellets

ABSTRACT

Cooling of alfalfa pellets after being made is one o f the unit operations in the pelleting of alfalfa. Using the thermal properties and drying diffusion coeficient together with other properties reported in refereed journals. a combined heat and mass transfer model was developed for the cooling of alfalfa pellets in deep beds. The model utilized the distributed heat and mass transfer equations to describe the temperature and moisture of the pellets. The distributed model interacts with the cooling air through a convective boundary condition for the temperature and a time–varying exponential surface condition for the moisture. Coupling o f the heat and mass transfer processes was carried out at the surface of the pellet using evaporative surface condition. The model was validated with field experimental data from a double–deck crossflow cooler. The simulated pellet and air temperatures were within 5⁰C of the collected field data while predicted moisture from the model was within 0.3% o f the experimental data.     

HEAT AND MASS TRANSFER RELATIONS FOR CROP DRYING

ABSTRACT

In present communication, an attempt has been made to study the heat and mass transfer for crops namely wheat and gram. The removal of moisture from the crop was determined under simulated conditions and it was used to develop heat and mass transfer relation using linear as well as multiple regression analysis. The observations were recorded for relative humidity, temperature of crop and air and for moisture evaporated. Experimental error in terms of per cent uncertainty was calculated for recorded data which is in the range of 20 - 30 per cent for forced convection and natural cooling, respectively.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

EFFECT OF CREEP AND MECHANO-SORPTIVE EFFECT ON STRESS DEVELOPMENT DURING DRYING

ABSTRACT

Constitutive equations to quantify wood deformation under combined mechanical loading and moisture content change (1] were coupled with the moisture distribution developed during drying to predict stress and strain in 50 by 190-mm Douglas-fir heartwood lumber.

Two combinations of temperature and relative humidity were used to dry the wood. The overall board shrinkage and the immediately released and set strains were measured as a function of time. Those strains were compared with analytic results, which showed good agreement.

The roles that four strain components played in the development of stress-both at board surface and center were compared for different drying conditions. The significance of creep and mechano-sorptive strain in relieving the stress was demonstrated by varying the model parameters.     

Three-Dimensional Modeling and Simulation of Heat and Mass Transfer Processes in Porous Media: An Application for Maize Stored in a Flat Bin

If the relative humidity and temperature of the air inside a granular mass of stored grain exceeds a certain threshold value, microorganism activity is likely to increase. Lower relative humidity and temperature, when uniformly distributed inside the grain mass, prevent moisture migration and an increase in microorganism activity. To cool down or maintain the temperature of the grain mass below a threshold value, forced ventilation with an appropriate airflow can be used to remove excess moisture or heat generated by grain or microorganism respiration. The objective of this work was to solve the equations that describe the conservation of heat, mass, and momentum in order to predict heat and mass transfer processes in the environment inside a grain mass of maize, stored in a flat bin. Three-dimensional computational fluid dynamics was used to solve the equations. The analysis of heat and mass transfer was performed considering the geometry of a two-ton-capacity bin prototype using a hexahedral mesh for the finite volume analysis. The numerical grid was defined to discretize the physical flow domain of interest to calculate velocity, temperature, and moisture distribution in the bulk of stored grain. The predicted results were compared with experimental data, and the agreement between them was very good.     

Simulation of Liquid Diffusion-Controlled Drying of Shrinking Thin Slabs Subjected to Multiple Heat Sources

Abstract

Although a detailed mathematical model incorporating all physical mechanisms of moisture and heat transfer in the material would yield valuable design information, it is not feasible to do this on a routine basis for the design of dryers. A simple liquid diffusion model was developed in the present study to quantitatively assess the influence of various operating parameters of engineering interest in drying of heat-sensitive materials. Heat of wetting, temperature, and moisture dependent effective diffusivity and thermal conductivity, changes in product density and drying-induced ideal shrinkage of the product are considered in this model. The effects of combining convection with conduction, radiation, and volumetric heating using a microwave field are simulated in view of the increasing interest in multimode heat input drying processes. Numerical results are reported on drying of potato slices to demonstrate how the moisture and temperature profiles as well as drying performance are affected by multi-mode heat input. Effects of key parameters e.g., drying air velocity, temperature, relative humidity, and product thickness are computed and discussed.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART II: EXPERIMENTAL RESULTS

ABSTRACT

Experimental measurements of drying rate, moisture distribution, surface moisture content, and temperature distribution are reported for softwood dried in the radial, tangential, and mixed (between radial and tangential) directions. The effects of both the heterogeneous and the anisotropic structure of wood are observed. The drying curves for tangential drying exhibit two distinct transition points - one when the surface reaches the fiber saturation point and one when the surface becomes completely dry. These transitions are not observed consistently for drying in the radial and mixed directions. For mixed drying, as a result of anisotropy, the drying rate is always higher at the side of the sample to which the growth rings point at die surface. Measurements of the surface mass transfer coefficient indicate that the theoretical value which is analogous to the convective heat transfer coefficient agrees well with that measured experimentally at both very high and very low values of the surface moisture content. At intermediate values of the moisture content the ratio of the experimental to the theoretical convective mass transfer coefficient can be as low as 0.20. The model discussed in Part I predicts results that are in good qualitative agreement with the experimental results presented in this paper.     

Letter to the Editor

Abstract

The water sorption isotherms of the Erythrina fusca Lour bark at 30 and 40°C were determined over relative humidity ranging from 55 to 85%. The equilibrium moisture content was determined gravimetrically. The moisture sorption isotherms showed that the equilibrium moisture decreases with increase of temperature. Six models were used for to fit the experimental curves of equilibrium humidity. Parameters of each equation were determined by nonlinear regression analysis. The isosteric heat of moisture sorption was calculated using the Claussius-Clapeyron equation.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE CONVECTIVE DRYING OF AUSTRALIAN PINUS RADIATA TIMBER

ABSTRACT

A series of experiments on the convective drying of Pinus radiata has been undertaken at the CSIRO Division of Forest Products in Australia. This paper uses the experimental results to compare predictions from both a comprehensive mathematical model, which includes wood temperature, moisture content and pressure distributions, and a simplified model (two versions) which assumes constant total pressure. From the- simulations, it is seen that both models adequately predict the overall kinetics of the wood drying process. For a complete understanding of the heat and mass transfer phenomena that occur in wood during drying the comprehensive model is necessary. However, it is computationally long and expensive, and as such, does not suit the practical drying needs of the timber industry in Australia. Consequently, the simplified model, which has acceptable computation time and sufficient accuracy for engineering purposes, enables die wood drying process to be optimised from both performance and economic perspectives.     

寒冷地区湿传递对多层墙体热湿性能的影响

墙体的传热传湿对建筑围护结构的热工性能、建筑能耗和室内环境有十分重要的影响。以相对湿度和温度为驱动势建立多层墙体一维非稳态热、湿和空气耦合传递模型（HAM模型）,并利用有限元法进行数值求解,重点关注湿传递对传热的影响机理。结果表明：考虑传湿时墙体交界面处湿度梯度大,相变速率大;墙体内部会产生湿积累,缩短墙体的使用年限;墙体内部温度上升幅度和上升速率大,墙体交界面处局部Nusselt数变化受湿传递的影响大;相变潜热量占总传热量的26.1%,计算空调负荷时不可忽略。     

Optimization of Rubber Wood Drying by Response Surface Method and Multiple Contour Plots

Abstract

By adopting the central-composite experiment design, the response surface methodology was used to optimize operating conditions of rubber wood drying. The independent variables are initial moisture content of rubber wood, and three drying environment parameters namely, temperature, relative humidity, and air velocity. The investigating responses are final moisture content, drying time, and energy consumption. The restriction of the optimization is the designated final moisture content, which is not greater than 16%. The third-order polynomial models with transformed responses were developed from experiment data to generate 3-D response surfaces and contour plots. The analysis of variance (ANOVA) was performed to identify the significant parameters affecting the rubber wood drying. Drying temperature and holding relative humidity are those two influential operating parameters that significantly control the final moisture of rubber wood and affect the drying time and energy. The multiple contour plots of drying responses show that the optimum operating regions are located mainly at high temperature drying zone. The high temperature drying practice can save energy and drying time by 44 and 25% respectively, in comparison to the conventional temperature drying.