RADIATIVE DRYING MODEL OF POROUS MATERIALS

ABSTRACT

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

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.     

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.     

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.     

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.     

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.     

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.     

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。     

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。     

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。     

Natural-convection heat and mass transfer from a vertical cone in porous media filled with nanofluids using the practical ranges of nanofluids thermo-physical properties

The present study aims to analyze the effects of Brownian motion and thermophoresis forces on the natural convection heat transfer of nanofluids around a vertical cone placed in a saturated porous medium. The range of non-dimensional parameters and the definition of two important parameters of heat and mass transfer are discussed. The results show that the range of Lewis number as well as Brownian motion and thermophoresis parameters and also the definition of the reduced Nusselt and Sherwood numbers, used in the previous analyses, should be reconsidered. In the present study, reasonable definitions of reduced Nusselt and Sherwood numbers have been proposed and discussed in details. In contrast with previous researches, the present results show that the heat transfer associated with migration of nanoparticles is negligible compared with heat conduction and convection mechanisms.     

Dynamics of pressurization and blowdown of an adiabatic adsorption bed: 4. Intraparticle diffusion/convection models

The importance of intraparticle mass transfer during pressurization and blowdown steps of PSA processes in an adiabatic adsorption bed was assessed by comparing intraparticle diffusion/ convection and intraparticle diffusion models. Film mass/heat transfer resistances are also considered in the model. The film heat transfer resistance is more important than the heat transfer resistance inside the particle; it can be assumed to be negligible in PSA processes when the temperature variation is not very large, otherwise it leads to serious errors when the adsorption capacity of adsorbents is high and the heat capacity of the system is not high. Intraparticle convection improves the mass transfer inside the particle and leads to faster heat releases into and out of the adsorbents.     

INTERACTION OF SURFACE RADIATION WITH CONJUGATE MIXED CONVECTION FROM A VERTICAL PLATE WITH MULTIPLE NONIDENTICAL DISCRETE HEAT SOURCES

Some of the important results of a numerical investigation into interaction of surface radiation with conjugate mixed convection from a discretely heated vertical plate with three nonidentical heat sources are provided here. The heat sources with identical rate of volumetric heat generation are placed flush-mounted along the plate in the descending order of their height from the bottom to the top ends of the plate. The heat sources are positioned at the leading edge, center, and the trailing edge of the plate, while the cooling medium considered is air, which is assumed to be radiatively transparent. The governing equations for fluid flow and heat transfer are initially converted into vorticity-stream function form and are later solved using the finite volume method coupled with Gauss-Seidel iterative solver. A computer code is written for the purpose. The effects of modified Richardson number, surface emissivity, and thermal conductivity on temperature distribution, peak temperature, drag coefficient, and relative contributions of mixed convection and radiation to heat dissipation are studied.     

水泥窑窑体表面换热系数的计算方法

提出了一种计算水泥窑窑体面换热系数的新方法。这种方法充分考虑了强制对流，自然对流，热辐射和窑体大小对换热系数的影响。推导了窑体表面强制对流与自然对流的换热关系式，通过互相比较得到了可忽略强制对流域自然对流的条件。结果表明，大多数情况下窑体表面的强制流换热数量极相等。因此利用向量总和法建立了混合对流换热关系式。进一步的研究发现，辐射散热所占的比例很大，采用黑度小的材料可显著降低熟料热耗。该方法...     

Effects of porous material on transient natural convection heat transfer of nano-fluids inside a triangular chamber

This study numerically investigates the impact of porous materials, nano-particle types, and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section. The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method, taking into account the Darcy–Brinkman model for porous medium. It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial, transient, and semi-steady. The features of each step are provided in detail. The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper) inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate. In contrast, as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide) inside the chamber increased, convection heat transfer rate improved. At the same time, it was observed that the use of both nano-fluids(single and hybrid) in the porous environment of the aluminum foam could improve convection.     

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.     

Modeling for industrial heat exchanger type steam reformer

In a heat exchanger type steam methane reformer, the temperature profiles and mole fractions along the axial distance from the top of the reformer can be predicted by using the channel model, considering radiation heat transfer. The cross-section of the reformer tube was divided into several channels as concentric circles and then heat transfer and mass transfer at the interfaces between adjacent channels were considered. Because the steam reformer is operated at high temperature, the radiation and convection were combined into one heat transfer coefficient to simplify the transfer analysis. This model predicts the industrial plant data very well; therefore, it may be used with confidence to design the industrial heat exchanger type reformer.     

Characterization of the Thermal Response of Munitions in Storage Exposed to Real and Arbitrary Weather Conditions

The objective of this investigation is to characterize the thermal response of stored munitions exposed to real weather conditions in order to validate current test procedures as well as develop the ability to provide an estimate of the thermal exposure over the lifecycle of a munition. Currently, the thermal history of munitions in storage cannot be determined without continuous monitoring of individual items and there is no method to provide a detailed estimate of the exposure by analyzing existing data when continuous data was not collected. This work describes the experimental and initial numerical investigations of instrumented munitions in storage to characterize their thermal response. The numerical model has the capability to validate broad trends observed from the experimental data. For this investigation, data is being collected through field experiments of inert munitions instrumented with thermocouples that are collocated near a weather station. Data from field experiments are used to develop and validate the numerical model. The numerical model will save time and resources in future investigations of the thermal exposure of munitions in storage as well as advance the understanding of the implications of selecting a long term storage environment. At a fundamental research level, this work contributes to the advances in combined heat transfer by natural convection and radiation inside a 3D enclosure combined with external forced convection and radiation. The numerical model includes several features including heat transfer to the enclosure by solar radiation, conduction, and forced convection, heat transfer between the enclosure container walls and the projectiles by radiation, conduction, and natural convection, heat transfer within the projectile by conduction, distributed thermal energy storage in projectiles, and transient temperature boundary condition at the enclosure walls.     

多孔介质在高温相变蓄热中的强化换热

采用实验方法,验证了金属泡沫、膨胀石墨在高温蓄热系统中强化换热的作用。实验结果表明,在250～290℃之间,金属泡沫多孔材料能够提高纯硝酸钠的换热率2.1倍。由于多孔材料严重抑制了自然对流,在液相加热阶段,硝酸钠与多孔材料混合物的换热率不高于纯硝酸钠的一半。通过比较底部加热和顶部加热两种加热方式下蓄热系统的换热性能,进一步揭示了多孔材料对自然对流的影响。