Simultaneous Heat and Mass Transfer in Shrinkable Apple Slab During Drying

The goal of the study was to determine the influence of drying shrinkage on the kinetics of convection apple slab drying. The arbitrary Lagrange-Eulerian (ALE) method was used to enter a problem with moving boundaries. It was found that drying shrinkage had a major influence on the both simulated temperature and water content in the material. The lower the moisture content in particles during drying, the more pronounced the effect of shrinkage on simulation of heat and mass transfer. It was found that application of the arbitrary Lagrange-Eulerian method for shrinkage modeling leads to a relatively simple mathematical model of the drying kinetics of shrinkable materials.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

Heat and Mass Transfer in Fry Drying of Wood

This article describes the coupled heat and mass (water, oil) transport phenomena in parallelepiped samples of beech (Fagus sylvatica) fried in peanut oil between 120 and 180°C. The aim was to evaluate the suitability of simultaneous fry drying and oil impregnation as an alternative wood treatment process. Water loss and oil impregnation were continuously assessed during the process. Temperature and pressure were measured at the center of the sample. The water in the peripheral layers of the wood vaporizes at atmospheric pressure. The water at the center of the wood vaporizes at overpressures of the order of 2.8 × 10⁵ Pa. High fluxes of water were recorded of about 0.006 kg/(m²s). The impregnated oil can amount to 20% of the mass of the removed water.     

Heat and Mass Transfer in Fry Drying of Wood

This article describes the coupled heat and mass (water, oil) transport phenomena in parallelepiped samples of beech (Fagus sylvatica) fried in peanut oil between 120 and 180°C. The aim was to evaluate the suitability of simultaneous fry drying and oil impregnation as an alternative wood treatment process. Water loss and oil impregnation were continuously assessed during the process. Temperature and pressure were measured at the center of the sample. The water in the peripheral layers of the wood vaporizes at atmospheric pressure. The water at the center of the wood vaporizes at overpressures of the order of 2.8 × 10⁵ Pa. High fluxes of water were recorded of about 0.006 kg/(m²s). The impregnated oil can amount to 20% of the mass of the removed water.     

Mass and Heat Transfer in a Continuous Plate Dryer

Abstract

A mathematical model for the mass-heat transfer in a continuous plate dryer has been developed. Along with a new mass transfer model, the formulas for several important parameters, such as height, volume of each granular heap and retention time, are provided. According to the penetration model of particle heat transfer, the average drying rate ([mdot]) is predicted together with the mean bulk temperature (T _out) and moisture content (X _out) by a straightforward stepwise calculation procedure. The only empirical parameter N _mix can be predicted by the method, provided that experimental data with various initial moisture contents (X _in) are given. According to the model, the optimization of a plate dryer should aim at the maximizing of the effective covering ratio (μ) and the total area-averaged heat transfer coefficient (α). The model and equations were applied in an experimental plant. In the result, the theoretical predictions are shown to be in satisfactory agreement with experimental data.     

Experimental and Numerical Investigation of the Heat and Mass Transfer for Cut Tobacco During Two-Stage Convective Drying

In this article, a two-stage convective drying strategy was presented for dehydration of flue-cured tobacco. In order to develop the multistage drying method of tobacco, two-stage drying as well as traditional single-stage drying of cut tobacco was experimentally evaluated and accurately simulated by proposed heat and mass transfer models. The experiments were performed in a dual fixed bed dryer. Different air temperature combinations of 120°C/90°C, 110°C/80°C, and 100°C/70°C were employed during two-stage drying. The drying rate and temperature variations of cut tobacco were investigated. The results showed that the average drying rates during two-stage drying were nearly 50% higher than those obtained from lower-temperature single-stage drying. On the other hand, the two-stage drying method, which used high air temperature for the early period and low temperature for the late period, could reduce the exposure of tobacco to high temperature due to the low final temperature of the dried sample. The temperature and moisture evolution of cut tobacco at different air temperature combinations were consistent with simulation results by developed heat and mass transfer models. This indicated that the models had a good prediction precision for two-stage drying of cut tobacco. The model predictions can be useful for the design of a feasible two-stage drying process for flue-cured tobacco.     

Modeling the Heat and Mass Transfer in Microwave Drying of White Oak

A 2D comprehensive heat and mass transfer model was developed to simulate the free liquid, vapor, and bound water movement in microwave drying of white oak specimens. The experimental and model results showed that, for white oak, moisture movement was easily impeded and high gradient of internal vapor pressure occurred. The internal vapor pressure was affected by sample dimension (length and thickness). At the same input power density, the internal pressure generated in the core increased with the sample length and thickness. However, as compared with sample length, sample thickness has less effect on the pressure gradient because of the high ratio of permeability between longitudinal and transverse directions.     

Gaseous Carbon Dioxide as the Heat and Mass Transfer Medium in Drying

Using available correlations for heat transfer, a comparative analysis of drying rates in CO₂ and in air was performed for several basic types of dryers. Higher heat transfer rates were found for dryers with active hydrodynamics, which translates into shorter drying time for materials dried in the first drying period. These results were validated by experiments on drying wheat kernels fluidized by air and by CO₂. Shorter drying times by about 20% were confirmed for CO₂, which offers energy savings of about 3% of the heat input to the dryer. Additional energy savings of 4% of the heat load can be expected for drying at temperatures below 100°C because of the lower wet-bulb temperature for CO₂ than that for air. The potential for CO₂ abatement was evaluated based on a case study for drying of distillers' spent grain.     

Gaseous Carbon Dioxide as the Heat and Mass Transfer Medium in Drying

Using available correlations for heat transfer, a comparative analysis of drying rates in CO₂ and in air was performed for several basic types of dryers. Higher heat transfer rates were found for dryers with active hydrodynamics, which translates into shorter drying time for materials dried in the first drying period. These results were validated by experiments on drying wheat kernels fluidized by air and by CO₂. Shorter drying times by about 20% were confirmed for CO₂, which offers energy savings of about 3% of the heat input to the dryer. Additional energy savings of 4% of the heat load can be expected for drying at temperatures below 100°C because of the lower wet-bulb temperature for CO₂ than that for air. The potential for CO₂ abatement was evaluated based on a case study for drying of distillers' spent grain.     

Mass Transfer Coefficients and Drying Rates in Through Air Drying: Part II

In this study experimental results and analysis are given of convective heat and mass transfer in the drying of tissue and towel products (25 and 50 g/m² basis weight) under commercially realistic conditions under through flow. Parameter effects on drying rate include process variables such as refining, shaping, commercial forming, initial moisture content, and drying temperature. Drying rate curves display initial increase, plateau, and final decrease as the paper dries. Nondimensional Sherwood numbers (versus Peclet number) generally agreed with and augment the available dataset on through drying.     

SMI聚合反应釜传质及传热的研究

提出了SMI耐热改性剂在聚合反应前期的放热曲线,指出该反应的特点。在150 L的聚合反应釜内研究了影响SMI聚合反应的关键参数Pv、Np/Nqd及传热系数K,重现了小试试验的传热、传质结果。借助水运实验验证了经验公式计算传热效果的可靠性,理论计算值与实际值吻合较好,实现了聚合反应的可控性,为进一步放大研究提供了参考依据。     

Analysis of Heat and Mass Transfer in Freeze Drying

The main objective of this work is to build a mathematical model that describes heat and mass transfer in freeze-drying when both plate heating and radiation heating are applied and also to provide further understanding of the mechanism of the drying process. The model, unlike other models, may be used for situations in which sublimation occurs within a temperature range, i.e., the non-existence of a sharp interface and also for cases in which more than one interface may form. The developed model has been tested against experimental measurements of freeze-drying of milk under different operating conditions. Measurements were done using Virtis BT3.3ES freeze dryer with vertical manifolds. The milk was contained in a glassware, specially designed for this project. Four thermocouples were fixed at different positions to track the drying progress. The experimental measurements show no significant shrinkage in the frozen milk when dried, leaving the milk highly porous in structure. In this experimental work, the low thermal conductivity of the dried layer was found to control the process without any significant mass transfer resistance. This includes plate heating where drying was found to progress from the heating surface similar to radiation heating. This is unlike what has been reported in some of literature that drying starts always from the top surface. The model, which was based on heat transfer control, showed a reasonable agreement with the experimental measurements of both plate heating and radiation heating.     

Analysis of the Shrinkage Effect on Mass Transfer During Convective Drying of Sawdust/Sludge Mixtures

Convective drying of wastewater sludges and sawdust/sludge mixtures was studied. The first part of this work was an experimental study performed in a cross-flow convective dryer using 500 g of wet material extruded through a disk with circular dies of 12 mm. The results showed that the sawdust addition has a positive impact on the drying process from a mass ratio of 2/8, on a dry basis, with observed drying rates higher than the original sludge. The second part of this work consisted of developing a drying model in order to identify the internal diffusion coefficient and convective mass transfer coefficient from the experimental data. A comparison was made between fitted drying curves, well represented by the Newton's model, and the analytical solutions of the diffusion equation applied to a finite cylinder. Variations of dimensional characteristics, such as the volume and exchange surface of the sample bed, were obtained by X-ray tomography. This technique allowed us to confirm that shrinkage, which is an important phenomenon occurring during sludge and sawdust/sludge mixture drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by mixing and sawdust addition. The internal diffusion coefficient changed from 7.77 × 10^?9 m²/s for the original sludge to 7.01 × 10^?9 m²/s for the mixed sludge and then increased to 8.35 × 10^?9 m²/s for the mixture of a mass ratio of 4/6. The convective mass transfer coefficient changed from 9.70 × 10^?8 m/s for the original sludge to 8.67 × 10^?8 m/s for the mixed sludge and then increased to 12.09 × 10^?8 m/s for the mixture of a mass ratio of 4/6. These results confirmed that sawdust addition was beneficial to the sludge drying process as the mass transfer efficiency between the air and material increased. Reinforcing the texture of sludge by adding sawdust can increase the drying rate and decrease the drying time, and then the heat energy supply will be reduced significantly. The study also showed that neglecting shrinkage phenomenon resulted in an overestimation for the internal diffusion coefficient for the convective drying of sludges and sawdust/sludge mixtures.     

Convective Heat and Mass Transfer Modeling in Gas‐Fluidized Beds

This review examines selected mechanistic and empirical models reported in the literature to predict convective heat and mass transfer coefficients in gas‐fluidized beds. The role of hydrodynamics in heat and mass transfer is briefly outlined before embarking on the modeling approaches. Both bed to wall and interphase heat transfer, are considered. In bed to wall heat transfer, the main focus of the review is the modeling of particle convective components, based on surface renewal. The concepts of transient and local heat transfer models are also discussed briefly. In the case of mass transfer, only interphase transfer is considered. Emphasis is placed on models based on combustion where mass transfer is seen to occur from a few active particles contained in a fluidized bed of inert particles.     

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.     

Transfer Phenomena During the Drying of a Shrinkable Product: Modeling and Simulation

Drying is an essential step in many production and treatment processes. The control of dry product quality is more and more required in order to insure a good using or handling of the material. Then new mathematical models should integer these requirements and consider the phenomena of shrinkage. This work gives a mathematical formulation of the different transfer phenomena (heat, mass, and momentum) which describe the process. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the distribution of the temperature, the moisture, the strain, and the stress during the process. The product is considered as a two-phase, homogeneous, hygroscopic, isotropic, and highly shrinkable medium. The thickness of the sample is sufficiently small in order to consider the fluxes of heat and mass unidirectional. The principal equations of the model are written in a Lagrangian formulation because of the shrinkage behavior. The model is solved numerically by a finite difference method. A validation of the results is achieved by the comparison of the numerical and experimental data. The simulation allows the derivation of the time and space evolution of several parameters: temperature, moisture, strain, and stress.     

Transfer Phenomena During the Drying of a Shrinkable Product: Modeling and Simulation

Abstract

Drying is an essential step in many production and treatment processes. The control of dry product quality is more and more required in order to insure a good using or handling of the material. Then new mathematical models should integer these requirements and consider the phenomena of shrinkage. This work gives a mathematical formulation of the different transfer phenomena (heat, mass, and momentum) which describe the process. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the distribution of the temperature, the moisture, the strain, and the stress during the process. The product is considered as a two-phase, homogeneous, hygroscopic, isotropic, and highly shrinkable medium. The thickness of the sample is sufficiently small in order to consider the fluxes of heat and mass unidirectional. The principal equations of the model are written in a Lagrangian formulation because of the shrinkage behavior. The model is solved numerically by a finite difference method. A validation of the results is achieved by the comparison of the numerical and experimental data. The simulation allows the derivation of the time and space evolution of several parameters: temperature, moisture, strain, and stress.