RADIATIVE DRYING MODEL OF POROUS MATERIALS

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

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.     

Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4)

In this study, heat transfer and temperature distribution equations for longitudinal convective–radiative porous fins are presented. It is assumed that the thickness of fins varies with length, so four different shapes (rectangular, convex, triangular and exponential) are considered. Temperature-dependent heat generation, convection and radiation are considered and heat transfer through porous media is simulated using passage velocity from Darcy's model. After deriving equation for all geometries, the Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied for predicting the temperature distribution in the porous fins. The selected ceramic porous materials are Al, SiC, and Si₃N₄. Effects of porosity, Darcy number, Rayleigh number, etc. on transferred heat are examined. As a main outcome, exponential section fin with Si₃N₄ material has the most amount of transferred heat among other shapes and materials.     

STUDY OF HEAT AND MASS TRANSFER DURING IR DRYING OF PAPER

ABSTRACT

A mathematical model has been developed to study the drying of paper using a gas-fired IR dryer. The model accounts for various phenomena : water and vapour mass transfer, conduction, convection and radiation heat transfer. The phenomenological equations are solved with a finite difference scheme, including a modified upwind differencing scheme to account for water migration within the paper sheet. The simulation results illustrate the basic underlying phenomena involved in IR paper drying and can be instrumental to the engineer to make the detailed analyses of such a drying process. A sensitivity analysis has shown that the drying rate is most sensitive to parameters governing the IR beat transfer process whereas the paper sheet temperature is most sensitive to parameters governing the mass transfer process with the surroundings.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

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.     

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.     

A Theoretical Model for the Nongray Radiation Drying of Polyvinylalcohol/Water Solutions

Abstract

A theoretical analysis of heat transfer and moisture variation was performed while a PVA solution was exposed to high-intensity nongray irradiation and/or air flow convection. Effective absorption coefficients were incorporated in the radiative transfer analysis. The influence of various radiation and convection parameters on the transfer of heat and moisture variation in the coated layers on an optically thick substrate was investigated. The effects of radiation and convection parameters on the transfer process were presented in terms of the rate of water content removal, heat transfer, and moisture distribution. Results were compared to those of drying when using convective heat. It is evident that the use of thermal radiation combined with convective heat will help in improving the drying rate. Numerical results show that both the radiative energy absorbed by the solution and the substrate and the distribution of water mass fraction in the solution are closely related to the rate of water removal from the solution during the process.     

RADIATION AND NON-DARCY EFFECTS ON CONVECTION IN POROUS MEDIA

Combined conduction, convection and radiation heat transfer in a gray fluid-saturated sparsely packed porous medium is examined analytically for marginal convection using linear stability analysis. The effects of boundary and inertia which were absent in the usual Darcy model are considered. The Milne-Eddington approximation is employed to determine the solutions valid for transparent and opaque media which absorbs and emits thermal radiation. It is shown that the nature of the bounding surfaces and radiation significantly influence the critical Rayleigh and wave numbers. The mechanism for suppressing or augmenting convection is discussed in detail. The results obtained using Galerkin technique are compared with the existing results of Darcy model and of non-radiating systems and agreement is found.     

乙烯气相聚合中颗粒稳态热质传递模型研究

为考察乙烯气相聚合过程中颗粒内部单体浓度及温度分布,建立并求解了颗粒的稳态热质传递模型：等温等浓度模型和变温变浓度模型。等温等浓度模型假设颗粒内单体浓度及温度均匀分布,仅考虑颗粒边界层的对流传质及传热;变温变浓度模型认为颗粒内存在单体扩散及热传导,同时颗粒边界层与本体进行对流传质及传热。模拟结果表明,粒径小的聚合物颗粒内单体浓度低而温度高;随粒径长大,颗粒内浓度升高温度降低,趋于颗粒外的气相浓度和温度;聚合物颗粒内的温度梯度较小,主要温度梯度集中于颗粒表面与气相界面之间。     

Porous frozen material approach to freeze-drying of instant coffee

Abstract

Porous frozen material with a certain initial porosity was prepared to explore its influence on freeze-drying experimentally. Soluble coffee was selected as the solute in aqueous solution and liquid nitrogen ice-cream making method was used to prepare the frozen materials. Results showed that freeze-drying can be significantly enhanced using the initially porous frozen material compared with the traditionally solid one. By keeping the same sample mass and moisture content with sole radiation heating, drying time of the porous frozen sample was about one third shorter than that of the solid one under the same tested operating conditions. SEM images of dried products revealed that the porous material had a loose and tenuous structure that was favorable to the transportation of sublimated vapor and the desorption of bound moisture. Appropriately increasing the chamber surface temperature benefited the freeze-drying process and changing the chamber pressure had little effect on the process. Combined radiation and conduction heating can further promote the freeze-drying process and save as much as 36.4% of the drying time. The porous frozen material was found to have a wider range of operating temperature and result in relatively lower residual moisture content.     

THERMAL CONVECTIVE INSTABILITY IN TRANSLUCENT POROUS MEDIA WITH RADIATIVE HEAT TRANSFER

The onset of thermal convection in a translucent porous layer is considered. Attention is focused on the effect of radiative heat transfer on the critical Rayleigh-Darcy number and the convection cell shape. If we consider the contribution of radiative heat transfer, the basic temperature profile is non-linear and the thermal convective instability is influenced by the ratio of conduction to radiation heat flux, the temperatures at the boundary surfaces, and radiative parameters such as wall emissivity, scattering albedo and extinction coefficient as well as the usual Rayleigh-Darcy number. Effects of these parameters on the onset of convective instability are investigated with the help of linear stability theory employing the Darcy's law and the radiative transport equation simplified by the P₁ approximation. The increased effective thermal conductivity due lo the radiation inhibits the onset of convection and causes increased critical Rayleigh-Darcy number and decreased convection cell size. The results of the present work may be exploited to find out the optimal diameter of aerogel pellets and the air pressure in the double pane window filled with the translucent silica aerogel granules to suppress natural convection.     

Analysis of solar‐driven gasification of biochar trickling through an interconnected porous structure

The efficient transfer of high‐temperature solar heat to the reaction site is crucial for the yield and selectivity of the solar‐driven gasification of biomass. The performance of a gas‐solid trickle‐bed reactor constructed from a high thermal conductivity porous ceramic packing has been investigated. Beech char particles were used as the model feedstock. A two‐dimensional finite‐volume model coupling chemical reaction with conduction, convection, and radiation of heat within the packing was developed and tested against measured temperatures and gasification rates. The sensitivity of the gasification rate and reactor temperatures to variations of the packing's pore diameter, porosity, thermal conductivity, and particle loading was numerically studied. A numerical comparison with a moving bed projected a more uniform temperature distribution and higher gasification rates due to the increased heat transfer via combined radiation and conduction through the trickle bed. © 2014 American Institute of Chemical Engineers AIChE J, 61: 867–879, 2015     

具有初始孔隙的多孔物料冷冻干燥

实验研究了具有一定孔隙的非饱和多孔物料对液体物料冷冻干燥过程的影响。以甘露醇为主要溶质的待干料液采用“液氮制冰激凌法”制备非饱和物料进行冷冻干燥,并与常规饱和的冷冻物料相比较。结果表明,非饱和冷冻物料确实能够显著地强化液体物料的冷冻干燥过程。干燥产品SEM形貌分析显示,初始非饱和冷冻物料具有连续均匀的固体骨架和孔隙,固体基质更加纤细,孔隙空间更大,可以大大减小传质阻力。考察物料内部各点的温度变化发现,初始非饱和物料内部冰晶确实发生整体升华,但仍然存在主要升华区域;非饱和多孔物料的冷冻干燥过程主要是传热控制,而常规饱和物料冷冻干燥主要是传质控制。操作压力对过程的影响可以忽略。采用辐射/导热组合加热方式可改善初始非饱和多孔物料冷冻干燥过程的传热,进一步缩短干燥时间。     

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.     

GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.     

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。     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

HEAT AND MASS TRANSFER WITH POLYCONDENSATION IN RESIN FILM DURING DRYING

ABSTRACT

In a drying process of dielectric resin films coated on electric conductive substances, phenomena such as polymerization of monomers, by-products yield, shrinkage and stress generation lake place simultaneously in addition to heat and mass transfer. For the enhancement of the drying with high efficiency and high quality, it is important to understand the drying mechanism. In this paper, the characteristics of heat and mass transfer in the resin film including polycondensation reaction are presented. The apparent drying rate of polyamideimide varnish films was measured in two different heating modes of radiation and convection. The reaction rate of polycondensation was analyzed both by the thermogravimetry and the differential scanning calorimetry. The apparent drying rate began to drop remarkably when the reaction rate became significant. It implies that the diffusion of the solvent is inhibited by skinning at the surface. Applying the Vrentas/Duda free-volume diffusion model to the prediction of diffusivity, the heat and mass transfer in the resin film were analyzed theoretically with a reasonable accuracy.     

多孔铝内体积对流传热系数的测量

引　言多孔铝 (合金 )作为一种高孔隙率 (孔隙率 >0 9)多孔介质 ,具有明显的多功能性[1] .通孔型多孔铝是指多孔铝的内部孔隙互相连通 ,且外部流体可以通过 ,具有比表面积大、质量轻的特点 ,是开发强化换热装置的优选材料 ,有可能在新型紧凑式换热器、回热器、风冷冷凝器 (或冷却塔 )等换热设备研制过程中获得应用 .但流体流经多孔铝的　对流换热特性实验数据比较缺乏 ,对各种影响因素的研究也欠充分 .Hwang等[2 ] 测量了空气流经70 %、 80 %、 95 %三种孔隙率多孔铝的体积对流传热系数 ,但缺乏对孔隙密度、母材性质等影响的研究 .何德坪…