Natural convection heat and moisture transfer with thermal radiation in a cavity partially filled with hygroscopic porous medium

This article deals with natural convection heat and moisture transfer with thermal radiation in a cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous medium and moisture content transfer in hygroscopic porous medium were solved by the finite element method. The radiative heat transfer is calculated by making use of the radiosity of the surfaces that are assumed to be grey. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation and Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and porous medium. The mean temperature at the interface decreases, the temperature and moisture content gradients are created on the upper two corners of the porous medium region, and the moisture content in the porous medium decreases in the porous medium as Ra increases.     

表面辐射对部分填充吸湿性多孔介质的封闭腔体内热湿耦合传递的影响

根据多孔介质热质传递原理, 基于有限元的方法数值分析了具有表面热辐射的部分填充吸湿性多孔介质的封闭腔体内部自然对流流动及热湿耦合传递过程, 探讨了表面发射率、Rayleigh数和Darcy数等参数对封闭腔体内部自然对流流动及热湿耦合传递过程的影响, 研究结果表明, 壁面热辐射的作用可以提高多孔介质内部的温度, 而且随着表面发射率的增大, 多孔介质内部的水分逐步向其右上角迁移和聚集。另外, Darcy数、多孔介质与空气的热导率比对方腔内部多孔介质的热量传递和水分迁移影响较小。     

Modeling conventional drying of wood: Inclusion of a moving evaporation interface

A one-dimensional mathematical model is presented that accounts for a moving evaporation interface in simulating the coupled heat and mass transfer during convective drying of wood. In the model proposed, the only mechanism considered in water transport within wood is diffusion. Additionally, the transport of moisture is dominated by the gradient of the moisture content. The controlling equations were established from Whitaker’s volume averaging laws and solved numerically with the finite volume method. The simulation results for the density of vapor and the volume rate of evaporation indicate that the migrating moisture was mainly in the form of gas under conditions of lower moisture content. The evaporation interface moved at approximately constant speed and the evaporation rate of the interface decreased with time. Finally, the core temperature and average moisture content in wood were successfully simulated.     

DRYING LIGHT-WEIGHT CONCRETE SLABS

To study unsteady state problems of heat and mass transfer in concrete pavements, which are generally considered to be fine porous media, both relevant material characteristics and transport properties must be considered simultaneously. A system of nondimensional differential equations for heat and mass transfer in porous media is derived and used to investigate the drying history of moisture content in a particular light-weight concrete slab. An implicit finite difference numerical scheme is employed for obtaining the numerical results. The results show that the Lewis number Le, Bi_h number Bi_m play an essential role in the simultaneous mass and heat transfer.     

DIRECT CONTACT DRYING OF A MOVING POROUS STRIP

Combined heat transfer and evaporation dynamics are analyzed during drying of a continuously moving, porous strip which is in direct contact with a heated plate. A transient, quasi-two-dimensional model of conjugate heat transfer between a hot massive externally /internally heated plate and wet porous strip moving along the plate is developed by accounting for evaporation dynamics. The model consists of four conjugate energy conservation equations with proper boundary/interface conditions which describe the heat transfer in four distinct zones (1-electrically or indirectly heated massive metal plate, 2-thin superheated vapor film resulting from vaporization of water in the porous strip that separates hot plate and porous strip, 3-dry region of the porous strip, and 4-wet region of the porous strip). The relevant dimensiouless parameters governing the problem are identified, and results of parametric calculations are reported to gain fundamental understanding of the process.     

盐水液滴降压蒸发析盐过程传热传质特性

针对单个盐水(NaCl溶液)液滴在降压环境下蒸发析盐的传热传质过程建立了数学模型。模型考虑了多孔盐壳在液滴表面的形成过程,降压过程引起的气流运动,液核通过多孔介质的传质扩散,以及液滴表面的蒸发换热和对流换热。将实验数据与计算结果对比,验证了模型的有效性。通过模型计算获得了液滴表面温度及液滴质量随时间的变化。结果表明盐水液滴在降压环境下蒸发析盐过程的温度变化分为4个阶段:温度骤降阶段、温度回升阶段、平衡温度阶段和温度上升阶段。平衡温度阶段,盐壳界面运动较慢,随蒸发进行,液核尺寸逐渐减小,盐壳界面运动速度加快。理论分析了环境压力对盐水液滴蒸发析盐过程的影响,环境压力越低,平衡温度越低,盐分完全析出时间越短。     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

HEAT AND MASS TRANSFER IN THE PLANT-SOIL-AIR SYSTEM

ABSTRACT

Combined heat transfer and evaporation dynamics are analyzed during drying of a continuously moving, porous strip which is in direct contact with a heated plate. A transient, quasi-two-dimensional model of conjugate heat transfer between a hot massive externally /internally heated plate and wet porous strip moving along the plate is developed by accounting for evaporation dynamics. The model consists of four conjugate energy conservation equations with proper boundary/interface conditions which describe the heat transfer in four distinct zones (1-electrically or indirectly heated massive metal plate, 2-thin superheated vapor film resulting from vaporization of water in the porous strip that separates hot plate and porous strip, 3-dry region of the porous strip, and 4-wet region of the porous strip). The relevant dimensiouless parameters governing the problem are identified, and results of parametric calculations are reported to gain fundamental understanding of the process.     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

ABSTRACT

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

Effect of Pressure on Moisture Transfer During Moisture Adsorption

ABSTRACT

A set of coupled heat, mass, and pressure transfer equations was used to describe the moisture adsorption process in gmn kernels. The finite element method was used to solve the system of equations. The technique was applied to analyze the temperature, moisture, and pressure distribution in a barley kernel during soaking with steep water. The temperature and moisture distributions with (heat, mass, and pressure transfer model) and without (heat and mass uansfer) the effect of pressure were simulated for assumed conditions. The results obtained from the heat, mass, and pressure transfer model show a marked difference from the results obtained from the heat and mass transfer model. This indicated that a pressure gradient exists during the transfer Process, causing additional moisture movement due to filtration effect. Hence. the pressure tern cannot be assumed constant during the moisture adsorption process. The simulated temperature, moisture and pressure profiles and gradients can be used for determining the optimum time required for solking kernels with sleep water to produce barley malt.     

NONLINEAR FINITE ELEMENT ANALYSIS OF COUPLED HEAT AND MASS TRANSFER PROBLEMS WITH AN APPLICATION TO TIMBER DRYING*

A finite element formulation and solution of a set of nonlinear coupled heat and mass transfer equations for porous capillary media is presented. The model considers temperature and moisture dependent material properties and can accomodate diffusion of moisture as either a liquid or a vapor. Application was made to drying of timber and predicted results agreed well with the experimental data.     

NONLINEAR FINITE ELEMENT ANALYSIS OF COUPLED HEAT AND MASS TRANSFER PROBLEMS WITH AN APPLICATION TO TIMBER DRYING*

A finite element formulation and solution of a set of nonlinear coupled heat and mass transfer equations for porous capillary media is presented. The model considers temperature and moisture dependent material properties and can accomodate diffusion of moisture as either a liquid or a vapor. Application was made to drying of timber and predicted results agreed well with the experimental data.     

HD低温蒸发系统中填料蒸发器传质传热的分析

通过研究系统中填料蒸发器的蒸发传质传热过程以及两相流动特性，采用计算流体力学（computational fluid dynamics，CFD）中离散相与连续相耦合的方法来模拟规整填料内部通道的蒸发传质传热过程，实现了填料蒸发器中两相传质传热的过程以及液滴流动的可视化，为研究气液两相在规整填料内的流动提供了一种模拟方法。通过与实验结果的比较，最终选用RNG k-ε湍流模型来分析规整填料内部气液两相传质传热以及流动情况。数值模拟研究了规整填料板间距对填料内部气液两相传质传热以及液滴运动影响，发现随着板间距的增大，填料内部压力降逐渐降低，出口空气中水蒸气的含量不断减小，液滴蒸发速率降低，液滴进出口质量差减小，气相出口温度逐渐降低，蒸发传质传热效率降低。随着气速的增大，出口空气中水蒸气的含量不断减小，液滴蒸发速率增加，气相出口温度降低，气液两相传质传热效率降低。     

Analysis of Multiphase Flow and Heat Transfer: Pressure Buildup in an Unsaturated Porous Slab Exposed to Hot Gas

This study develops a mathematical model for coupled heat and mass transfer in an unsaturated porous slab exposed to a flowing hot gas. Effects of the initial saturation conditions on associated variables, i.e., total pressure, temperature, moisture content, and multiphase flow, are studied. The Newton-Raphson method based on a finite volume technique is applied. This study emphasizes the influence of initial saturation level and gravitational effect in heat and multiphase flow phenomena associated with this system. Gravity enhances the downward flow of liquid within the porous slab. Pressure buildup occurs near the interface between the wet and the dry zone. However, it appears that the order of magnitude to the total pressure is small. This study explains the fundamental mechanism of multiphase flow that involves heat and mass transfer in a heated unsaturated porous slab.     

Analysis of Multiphase Flow and Heat Transfer: Pressure Buildup in an Unsaturated Porous Slab Exposed to Hot Gas

This study develops a mathematical model for coupled heat and mass transfer in an unsaturated porous slab exposed to a flowing hot gas. Effects of the initial saturation conditions on associated variables, i.e., total pressure, temperature, moisture content, and multiphase flow, are studied. The Newton-Raphson method based on a finite volume technique is applied. This study emphasizes the influence of initial saturation level and gravitational effect in heat and multiphase flow phenomena associated with this system. Gravity enhances the downward flow of liquid within the porous slab. Pressure buildup occurs near the interface between the wet and the dry zone. However, it appears that the order of magnitude to the total pressure is small. This study explains the fundamental mechanism of multiphase flow that involves heat and mass transfer in a heated unsaturated porous slab.     

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     

CROSS-EFFECT OF HEAT AND MASS TRANSFER OF LU1KOV EQUATION: MEASUREMENT AND ANALYSIS

This paper mainly focuses on cross-effect of heat and mass transfer of capillary porous media which A.B.Luikov set up on irreversible thermodynamics principle. On the basis of perfecting the equations of heat and mass transfer, the heat and mass transfer parameters are determined during drying processes, and thermal gradient coefficient δ and moisture gradient coefficient ξ are obtained which show the cross-effect of heat and mass transfer. Thus the fundamentals are provided for quantitative analysis of cross-effect of heat and mass transfer. The convective drying mathematical model under the first unsteady boundary condition is therefore proposed. By the application of Henry transform, the theoretical solution of unsteady drying process is given and its validity is verified     

Analysis of moving boundary problem of growth of Bismuth germanate crystal by heat exchanger method

Transient two-dimensional model of the growth of BGO crystal by heat exchanger method has been developed. A finite element method with nonorthogonal mapping technique for the solution of the moving boundary problem is developed where the melt/solid interface shape changes from hemispherical to planar. The moving boundary problems for the melt/solid interface location and the temperature field were solved by two mapping rule method which enables the computation of interface shape changing from hemispherical to planar. The maximum deflection of interface is shown when the melt/solid interface meets the corner of crucible. As the excess heating temperature and the heat exchanger temperature were increased, more growth time for whole process is required but the quality of BGO crystal may be improved. The ratio of the height to the radius of crucible hardly affects the deflection of BGO melt/solid interface when it is greater than 1.5. As the cooling zone radius is decreased, maximum deflection is decreased. The heat transfer between the crucible and the heating element should be suppressed to maximize planarity of the interface shape.     

Drying of Coarse Particles in a Vertical Pneumatic Conveyor

In the present work, one-dimensional two-phase continuum models were applied to simulate the pneumatic drying of porous alumina and solid glass particles. Pressure profiles, gas and solid temperature, and gas and solids moisture profiles were obtained in a 53.4-mm conveying tube. For both particles, maximum values of gas-to-particle heat transfer coefficients were obtained at air velocities close to the minimum pressure gradient velocity. Experimental temperature and moisture profiles of gas and solids were compared to simulated predictions, showing that models based on the two-phase flow approach fail to predict all the observed physical phenomena in simultaneous momentum, heat, and mass transfer for pneumatic drying of coarse particles. However, using adequate correlations and constitutive equations to predict interaction forces and transport parameters, it was possible to obtain good predictions of gas and solid temperature profiles and of moisture content.     

FUNDAMENTALS OF GRANULATION TECHNIQUES

In the present work, one-dimensional two-phase continuum models were applied to simulate the pneumatic drying of porous alumina and solid glass particles. Pressure profiles, gas and solid temperature, and gas and solids moisture profiles were obtained in a 53.4-mm conveying tube. For both particles, maximum values of gas-to-particle heat transfer coefficients were obtained at air velocities close to the minimum pressure gradient velocity. Experimental temperature and moisture profiles of gas and solids were compared to simulated predictions, showing that models based on the two-phase flow approach fail to predict all the observed physical phenomena in simultaneous momentum, heat, and mass transfer for pneumatic drying of coarse particles. However, using adequate correlations and constitutive equations to predict interaction forces and transport parameters, it was possible to obtain good predictions of gas and solid temperature profiles and of moisture content.