IDENTIFICATION OF MATHEMATICAL MODEL COEFFICIENTS IN THE ANALYSIS OF THE HEAT AND MASS TRANSPORT IN WOOD

ABSTRACT

A method based on the concept of solving inverse heat and mass transport problems was proposed to identify wood physical properties, with the use of empirical data, a mathematical model corresponding to the direct problem, and an optimization procedure. The computer software was developed to solve transient, three-dimensional, quasi-linear direct and inverse problems of heat and mass transport in wood as an anisotropic body together with initial and boundary conditions of any kind. The software was adapted to data parallel processing environment of high performance computers. Identification of thermal conductivity was performed for beech wood in three principal anatomic directions, and accuracy of temperature distribution predictions was significantly increased (the global relative error of prediction was reduced to 1.0 - 1.9%).     

错流降膜液体干燥剂除湿/再生传热传质数学模型及分析

分析了错流降膜液体干燥剂除湿及再生传热传质过程 ,建立了基于实际除湿系统的描述再生和除湿过程的数学模型 ,考虑到除湿过程中产生的热效应 ,以氯化钙溶液为除湿剂时 ,对气侧和液侧的传热传质系数进行了理论和数值求解 .计算结果表明 ,传热传质系数与气流流动状态、除湿剂的热物理性质等因素有关     

CONVECTTVE HEAT AND MASS TRANSFER IN MOISTURE DESORPTION OF OAK WOOD BY INTRODUCING CHARACTERISTIC TRANSFER COEFFICIENTS

ABSTRACT

This paper presents the effect of forced convective heat and mass transfer coefficients on the predictive ability of a dynamic isothermal set of coupled partial differential equations. The analysis showed that the two coefficient two-dimensional model, resulted in a very good prediction of the experimental data.

The concept of experiment involves: six temperatures, six relative air humidities and three values of circulation velocity. Dimensions of oak (Quercus petraea) wood samples were 250×80×25mm. The experimental installation, designed and constructed for this study, enables the drying process of relatively small samples to be similar to the drying process of real timber.     

CONVECTTVE HEAT AND MASS TRANSFER IN MOISTURE DESORPTION OF OAK WOOD BY INTRODUCING CHARACTERISTIC TRANSFER COEFFICIENTS

This paper presents the effect of forced convective heat and mass transfer coefficients on the predictive ability of a dynamic isothermal set of coupled partial differential equations. The analysis showed that the two coefficient two-dimensional model, resulted in a very good prediction of the experimental data.

The concept of experiment involves: six temperatures, six relative air humidities and three values of circulation velocity. Dimensions of oak (Quercus petraea) wood samples were 250×80×25mm. The experimental installation, designed and constructed for this study, enables the drying process of relatively small samples to be similar to the drying process of real timber.     

ASYMPTOTIC ANALYSIS OF A MODEL HEAT AND MASS TRANSFER PROBLEM

This short communication presents a simple asymptotic analysis of a coupled heat and mass transfer problem which models certain reacting fluid-solid systems. The calculation, which is an extension of earlier work on moving boundary problems, provides an analytical solution to the governing equations. This solution may be useful since it can provide quick analytical estimates of nonisothermal behavior in such systems.     

多孔介质对流干燥机理及其模型

在对现有的多孔介质对流干燥传热、传质模型归类分析的基础上,从介质内部热湿迁移机制出发,建立了能较完善、较准确地描述多孔介质在恒速段及降速段热质传递规律的“三耦合-六场量”混合理论模型.同时针对干燥问题数值模拟中的移动边界问题,提出了一种迭代修正的思想,并发展了相应的数值计算方法.对砖的干燥模拟计算结果表明,本文的模型较其他模型具有更好的精确性.     

MEASUREMENT OF COEFFICIENTS FOB SIMULTANEOUS HEAT AND MASS TRANSFER IN FOOD PRODUCTS

Two experimental devices were designed and built to determine four coefficients K_T K_M D_M D (or δ_T = D_T / D_M occurring in simultaneous heat and mass transfer equations, where,K _T and D_M are thermal conductivity and moisture diffcusivity respectively, D_T ( or δ _T is temperature gradient Induced moisture migration coefficient and K_M is moisture gradient Induced heat transfer coefficient. Three food materials, i.e. potato, bread dough and bread, were tested. From this study, it was found that the value of 5 was higher for low density food materials, such as bread, than for high density materials, such as potato. The coefficient & measures moisture migration contribution due to temperature gradient within the material. The average values of δ _T for potato, bread dough and bread were 0.0014, 0.0059 and 0.0127 per °C, respectively. The contribution of temperature gradient to the overall moisture migration is negligible In high density materials. However, this contribution may be important in the moisture migratlon analysls for low density materials. The moisture gradient induced heat transfer coefficient % as found to be negligible for the materials tested in this study     

MEASUREMENT OF COEFFICIENTS FOB SIMULTANEOUS HEAT AND MASS TRANSFER IN FOOD PRODUCTS

ABSTRACT

Two experimental devices were designed and built to determine four coefficients K_T K_M D_M D (or δ_T = D_T / D_M occurring in simultaneous heat and mass transfer equations, where,K _T and D_M are thermal conductivity and moisture diffcusivity respectively, D_T ( or δ _T is temperature gradient Induced moisture migration coefficient and K_M is moisture gradient Induced heat transfer coefficient. Three food materials, i.e. potato, bread dough and bread, were tested. From this study, it was found that the value of 5 was higher for low density food materials, such as bread, than for high density materials, such as potato. The coefficient & measures moisture migration contribution due to temperature gradient within the material. The average values of δ _T for potato, bread dough and bread were 0.0014, 0.0059 and 0.0127 per °C, respectively. The contribution of temperature gradient to the overall moisture migration is negligible In high density materials. However, this contribution may be important in the moisture migratlon analysls for low density materials. The moisture gradient induced heat transfer coefficient % as found to be negligible for the materials tested in this study     

MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN HOT GAS SPRAY SYSTEMS

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

ABSTRACT

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

INTERRELATION BETWEEN HEAT AND MASS TRANSFER DURING DRYING OF WOOD

Continuous measurement and recording of the core temperature in wood samples during convective drying in an airstream reveals that the temperature difference between the airstream and the core of the wood reflects almost quantitatively the influence of the external conditions and the characteristic features of the drying wood material on the course of the drying velocity. Conclusions concerning the drying practice of timber kiln-drying which arise from the experimental findings are discussed.     

INTERRELATION BETWEEN HEAT AND MASS TRANSFER DURING DRYING OF WOOD

ABSTRACT

Continuous measurement and recording of the core temperature in wood samples during convective drying in an airstream reveals that the temperature difference between the airstream and the core of the wood reflects almost quantitatively the influence of the external conditions and the characteristic features of the drying wood material on the course of the drying velocity. Conclusions concerning the drying practice of timber kiln-drying which arise from the experimental findings are discussed.     

移动散料传热数学模型

探讨了移动散料层与壁面的传热和散料间传热的机理,提出了移动散料层传热的机理模型和二维准均相数学模型.并从机理模型出发,推导出颗粒物料间传热的有效导热系数和散料层与壁面的换热系数公式.在此基础上,对模型进行数值解析,所得移动散料层内温度分布与实验结果一致,证实了本文提出的模型和公式的可用性.     

石墨化电炉传热学模型研究

在分析了炉子电热特性的基础上建立了石墨化炉传热数学模型。应用传热学知识，得到炉内导热方程式，并利用数理方程和傅立叶级数代换，推导出炉内温度分布方程式，并借助于计算机绘制出相关要素的变化曲线。通过分析该变化曲线，对石墨化炉供电制度提出了合理建议。     

A 2-D MICROSCOPIC SIMULATION OF HEAT AND MASS TRANSPORT IN DRY SNOW

The problem of acid deposition and its effects on the environment is receiving increasing attention in North America and Europe. The interaction between

seasonal snowcovers and deposited pollutants is of particular importance because a snowpack accumulates and stores pollutants which can ultimately be released in a rapid pulse with the first melt water in the springtime. As a direct result of an impurity pulse, water quality degrades with deleterious effects on the local environment and aquatic biological species. The timing and severity of an inpurity pulse is dependent upon the redistribution of pollutants in a snowpack which is attributed to a process known as temperature gradient metamorphism.

This work investigates the influence of geometry, density and temperature on the coupled heat and mass transport in idealized, two dimensional ice lattice cells. Mass flux, concentration and temperature distributions, as well as effective diffusion coefficients and thermal conductivities are presented as functions of temperature, geometry, and density. A finite element model of the coupled, heat and mass transport is used to analyze the problem on a microscopic scale in two dimensions. Deforming meshes are used to simulate the growth/decay process which occurs over time in an ice lattice pore.     

A MATHEMATICAL MODEL FOR THE HEAT AND MASS TRANSFER ON A FLAT PLATE UNDER FROSTING CONDITIONS

Processes in which heat is transferred to a cold surface with the simultaneous deposition of frost are important in a variety of refrigeration installations. As the frost layer grows, the heat transfer is affected in part because of the insulating effect of the frost. This can adversely affect the performance of cooling coils and plate freezers in domestic and industrial refrigeration installations. Previous studies indicate that the initial frost deposits are desirable since the rough frost surface acts as fins, thus temporarily increasing the heat transfer rate. The overall process is characterized by its time-dependent nature, especially during the early deposition periods. The work reported here attempts to examine this transient phenomenon by mathematically modeling the frost formation and heat transfer processes on plate freezers held at subfreezing temperatures. This will be achieved by combining three limiting solutions to the unsteady governing equations of the air-frost boundary layer in order to be able to draw an overall picture for the frost formation and heat transfer mechanisms with time.     

SURFACE MASS TRANSFER COEFFICIENTS FOR WOOD

Experimentally determined mass transfer coefficients for wood surfaces are often much lower than theoretically and experimentally determined coefficients for other surfaces. An investigation of this is made by comparing mass transfer coefficients for water and saturated non-wood surfaces, with coefficients measured for wood surfaces. It is found that measurements on wood surfaces are usually evaluated by assuming that Fick's law describes diffusion in wood. As this is not always true, it is proposed that the mass transfer coefficients measured on wood surfaces are low because the internal mass transfer in wood is not well understood. New measurements are presented which support this conclusiou.