HIGH INTENSITY DRYING

A mathematical model simulating the heat and mass transfer process during high intensity drying of paper and board has been developed. The model is successful in predicting the vapor pressure developments, pressure driven bulk flow of liquid and vapor, and increased drying rates during high-intensity drying, closely matching the experimental determination.

The model predicts substantial amounts of water removal in the liquid form during high-intensity drying being pushed out of the web by pressurized vapor zone. Water removal by pressure flow of liquid could account for as much as one-third of the total water removed.

Similar to drying under conventional conditions, the existence of a dry zone, wet zone and an intermediate zone with accompanying advancing heat pipe has also been shown for drying under high intensity conditions.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

ABSTRACT

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

Effect of Dielectric Material on Microwave Freeze Drying of Skim Milk

Abstract:

A simultaneous heat and mass transfer model of the dielectric material–assisted microwave freeze drying was derived in this study considering the vapor sublimation-desublimation in the frozen region. The mathematical model was solved numerically by using the finite-difference technique with two moving boundaries. Silicon carbide (SiC) was selected as the dielectric material, and the skim milk was used as the representative solid material in the aqueous solution to be freeze-dried. The results show that the dielectric material can significantly enhance the microwave freeze drying process. The drying time is greatly reduced compared to cases without the aid of the dielectric material. Profiles of the temperature, ice saturation, vapor concentration, and pressure during freeze drying were presented. Mechanisms of the heat and mass transfer inside the material sphere were analyzed. For an initially unsaturated frozen sample of 16 mm in diameter with a 4-mm-diameter dielectric material core, the drying time is 288.2 min, much shorter than 380.1 min of ordinary microwave freeze drying and 455.0 min of conventional vacuum freeze drying, respectively, under typical operating conditions.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Irreversible thermodynamics analysis of ellipsoidal wheat kernel drying,aiming at the evaluation of phenomenological properties

Literature data have revealed that wheat kernel stress–strain relationships, thermal conductivity, and specific heat support the assumption of isotropy. Accepting this premise, we show that drying complexity can be reduced by properly defining the kernel shape and an accurate model. Therefore, we present an irreversible thermodynamics procedure for obtaining transport properties of a wheat kernel. The numerical solution of the associated nonlinear conservation equations was based on the Radial Basis Functions method. Drying behavior of both prolate ellipsoidal and spherical grain kernels is presented and compared. The predicted moisture and temperature profiles correlated favorably with experimental drying profiles, obtained for two temperatures of 47 and 67.5°C.     

吸湿多孔介质冷冻干燥传质传热模型

本研究在作者提出的吸附—解吸平衡关系的基础上,建立了一个全新的考虑吸湿效应的多孔介质冷冻干燥数学模型。模型用有限差分法进行求解,并带有一个移动边界,以模拟介电材料辅助的微波冷冻干燥过程。介电材料选用碳化硅（SiC）,原料液为脱脂奶。模拟结果表明：介电材料能够有效强化微波冷冻干燥过程。在典型操作条件下,介电材料辅助的微波冷冻干燥所用的时间比普通微波冷冻干燥减少33.1%。当料液中固体含量较低或者固体产品的损耗因子较小时,介电材料对微波加热的效果不明显。基于冰饱和度、温度和水蒸气浓度的分布,本文分析了干燥过程中的传质传热机理,并对干燥速率控制因素进行了讨论。     

Optimization Of The Operation Of A Drying Heat Pump Using Superheated Steam

ABSTRACT

A numerical solution of a model which describes the optimal operation of a novel concept of heat pump for drying applications based on the theory of minimum energy cycles is presented. The thermodynamic cycle of the drying heat pump involves vapor condensation in a Laval nozzle, removal of the liquid phase in a separator as well as compression of the working medium, which is superheated vapor.     

Heat and mass transfer model of dielectric-material-assisted microwave freeze-drying of skim milk with hygroscopic effect

A new porous media mathematical model for freeze-drying was developed based on the adsorption-desorption relationship proposed in this paper. A finite difference solution was obtained from a moving boundary problem for the dielectric-material-assisted microwave freeze-drying process. Silicon carbide (SiC) was selected as the dielectric material; and frozen skim milk was used as the aqueous solution to be dried. Simulation results showed that the dielectric material can significantly enhance the microwave freeze-drying process. The drying time was 33.1% shorter than that of ordinary microwave freeze-drying under typical operating conditions. When the solid content of the solution to be freeze-dried was very low, or the solid product had a very small loss factor, microwave heating was less effective without the assistance of dielectric material. The mechanisms of heat and mass transfer during drying were analyzed based on profiles of ice saturation, temperature and vapor concentration. Drying rate-controlling factors were discussed. A comparison was made between the model predictions and the reported experimental data.     

Modeling and simulation of heat and mass transfer during drying of solids with hemispherical shell geometry

A heat and mass transfer model was proposed to describe the moisture and temperature evolution during drying of solid products with hemispherical shell geometry (HSG). The dimensionless form of the model was numerically solved for both several drying conditions and values of a geometrical factor related with the inner radius of the HSG to obtain their moisture and temperature profiles. In addition, average drying kinetics were calculated from the volume integration of local moisture values. A theoretical and numerical approach was used to develop a mass transfer analogy between the proposed HSG and a simpler flat slab-shaped product. These analogies provide simple mathematical expressions for drying process simulation and estimation of diffusion coefficients in solids with the proposed geometry, and may be applicable to other mass and heat transfer operations. Furthermore, the presented procedure may be used to develop similar expressions in other non-traditional or dissection geometries.     

Microwave drying of spheres: Coupled electromagnetics-multiphase transport modeling with experimentation. Part I: Model development and experimental methodology

To understand the effects of shape, size and property changes in a spherical sample during microwave drying, a fundamentals-based coupled electromagnetics and multiphase porous media model is developed and associated experimental details are described. Microwave drying of different sized spheres is carried out in a domestic microwave oven operating at 10% power level. Maxwell's equations for electromagnetics are solved inside a three dimensional (3D) microwave oven to obtain the electric field distribution inside the oven cavity and the spheres. The drying samples are treated as a porous media consisting of three phases: solid (skeleton), liquid (water) and gas (water vapor and air). Modes of transport for the fluid phases include capillary flow, binary diffusion between vapor and air, gas pressure driven flow and phase change between liquid water and vapor which is spatially distributed. An elaborate experimental system comprising of infrared camera, optical fiber probe and digital balance is built to validate the model in terms of temperature distribution, point temperatures, gas pressure generation and moisture loss from the samples at different times during the drying process. Results, validation, sensitivity analysis and “what-if” scenarios are presented in the companion paper. The work together would provide tremendous benefits when designing and developing microwave drying processes and products through a novel synergy between physics-based modeling and detailed experimentation.     

Convective Drying Analysis of a Single Wheat Kernel Based on an Irreversible Thermodynamics Model

The application of irreversible thermodynamics offers a formal treatment for drying analysis that allows the evaluation of intra-particle or intra-medium temperature and moisture profiles, and enthalpy, liquid, and vapor fluxes. However, researchers have claimed that its implementation is complex. This work presents a simple methodology for modeling, solving, and validating the drying equations, as applied to wheat kernels, and for obtaining the inherent and usually unavailable transport coefficients. To clarify and simplify the ensuing physical analysis, a spherical shape and isotropy were assumed. Additionally, solutions obtained with both Dirichlet and convective boundary conditions were analyzed and compared against experimental data. The thermal and hydro-stresses depend heavily on internal vapor and liquid fluxes and on the respective drying evaporation fronts, all of which were evaluated and compared.     

FLOW BOILING HEAT TRANSFER WITH FLUIDIZED SOLID PARTICLES

In order to solve the fouling problems in boiling processes,a boiling system was designedby adding solid particles to the boiling liquid In this paper.both theoretical analyses andexperimental studies on the boiling heat transfer in such a three-phase flow boiling were carried out.Based on the analysis of heat transfer characters of this three-phase flow boiling,a mathematical mod-el for the heat transfer coefficient of flow boiling was developed.The experiments show that,in thepresence of particles the boiling heat transfer is enhanced and is about 2 times that of the vaporliquid two phase one with better flow stability.The fluidized particles rub the heat transfer wall toprevent and to clean the fouling.     

Mathematical Modeling the Drying of Poplar Wood Particles in a Closed-Loop Triple Pass Rotary Dryer

Closed-loop drying systems are an attractive alternative to conventional drying systems because they provide a wide range of potential advantages. Consequently, type of drying process is attracting increased interest. Rotary drying of wood particles can be assumed as an incorporated process involving fluid–solid interactions and simultaneous heat and mass transfer within and between the particles. Understanding these mechanisms during rotary drying processes may result in determination of the optimum drying parameters and improved dryer design. In this study, due to the complexity and nonlinearity of the momentum, heat, and mass transfer equations, a computerized mathematical model of a closed-loop triple-pass concurrent rotary dryer was developed to simulate the drying behavior of poplar wood particles within the dryer drums. Wood particle moisture content and temperature, drying air temperature, and drying air humidity ratio along the drums lengths can be simulated using this model. The model presented in this work has been shown to successfully predict the steady-state behavior of a concurrent rotary dryer and can be used to analyze the effects of various drying process parameters on the performance of the closed-loop triple-pass rotary dryer to determine the optimum drying parameters. The model was also used to simulate the performance of industrial closed-loop rotary dryers under various operating conditions.     

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     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

Multiscale Modeling of Superheated Steam Drying of Particulate Materials

A multiscale model for predicting the superheated steam drying behavior of a packed bed filled with particulate porous material is presented. By using a reaction engineering approach (REA) a semi-empirical model is developed that can describe the heat and mass transfer between a single particle and the surrounding drying agent. By analogy between superheated steam drying and hot air drying, the relative activation energy of the REA model is formulated. Next, the single-particle drying model is fed into a continuum-scale model of a packed bed. The temperature and moisture content of the solid and the vapor temperature are successfully predicted by the bed-scale model. To endow the bed-scale model with predictive capabilities, simulation results are compared with experimental literature data.