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.     

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.     

MECHANISM OF TWO-DIMENSIONAL HEAT AND MASS TRANSFER DURING CONVECTTVE DRYING OF POROUS MXDIA UNDER DIFFERENT DRYING CONDITIONS

ABSTRACT

A numerical investigation was conducted to study two-dimensional heat and mass transfer during convective drying of clay brick. The set of macroscopic equations takes into account the effect of gaseous pressure. The established numerical code has allowed us to determine effects of the surrounding air conditions (temperature, pressure and vapor concentration) on drying Kinetic and on space-time evolution of the state variables (temperature, gaseous pressure, and liquid saturation).     

URTHER DEVELOPMENT OF A COMPUTER PROGRAM SIMULATING HEAT PIPE FUNCTIONING IN CONDEBELT PAPER DRYING

ABSTRACT

A previously developed computer program for depicting the heat and mass transfer behavior of heat pipe conduits, slightly open to a large ambient at their far ends, inside moist paper webs is developed further. The addition consists of accounting for the thermal dynamics of a hot metal slab from which the latent heat of evaporation corresponding to vapor generation in the hot end of the heat pipe is drawn. Values are used for the input parameters representing as closely as possible an approximately 40 % dry (by total weight) printing paper sheet being suddenly pressed against a hot steel or iron slab at l50°C or 200°C. These are conditions that could occur in Condebelt drying. Temperature distributions in the metal and inside the web, as well as the pressure distribution inside the web, are determined as functions of the distance from the hot surface and time. Important parameters are the initial metal and web temperatures, the interface Biot number, the structural geometry of the web, and the metal Fourier number. It is shown that there is a S to 25°C metal surface temperature drop in the first 100 μs after contact with the web. This can be significant in reducing possible web surface damage.     

ANALYSIS OF CONVECTIVE HEAT TRANSFER DURING IMMERSION FRYING

ABSTRACT

Immersion frying was studied as a high temperature drying process and analogies drawn between periods found in drying and similar periods in immersion frying. Analysis of external heat transfer during immersion frying showed a highly complex system of free and forced convection augmented by boiling conditions. Oil flow was found to be driven downward by buoyancy forces due to cooling at the sample surface then upward due to entrainment in vapor bubbles during boiling conditions. Experimental work showed the convective heat transfer coefficient to be a dynamic property ranging from 300 to 1100 W/m²°C and to be strongly coupled with bulk movement of the oil. Heat flux measurements found a peak flux of nearly 30,000 W/m³. Based on analysis of bubble dynamics it is hypothesized that heat flux increases with increased oil degradation through a reduction in vapor bubble size and increase in bubble frequency due to changes in interfacial properties of the oil.     

OPTIMIZATION OF SINGLE-ZONE DRYING OF POLYMER SOLUTION COATINGS TO AVOID BLISTER DEFECTS

ABSTRACT

The optimal conditions for drying polymer-solvent coatings result from a trade-off between minimizing the residual solvent level and creating defects. Blistering defects can be caused by boiling the solvent within the coating. In this paper, we use a detailed drying model with automated constrained optimization to find optimal drying conditions for prototypical coatings that minimize the residual solvent without blistering the coating. The drying oven is assumed to have a single zone with fixed residence time. The optimal drying conditions include the oven air temperature and substrate-side and coating-side heat transfer coefficients The latter are constrained to physically reasonable values. According to our results, the optimal coating-side heat transfer coefficient is always equal to or greater than the optimal substrate-side heat transfer coefficient.     

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.     

VACUUM DRYING OF DISPERSED MATERIALS FROM MULTICOMPONENT LIQUID SYSTEMS: VERIFICATION OF MODEL

ABSTRACT

Experimental data on vacuum drying of chemical and microbial synthesis products under laboratory and industrial conditions are presented. Kinetic relations of vacuum drying of dispersed materials with the removal of a multicomponent liquid system are verified on both laboratory and industrial scale dryers under different operating conditions. The results of the research were generalised and a number of empirical relations needed for drying process calculation are given. The relation between heat transfer coefficient and heat flux and motive force for the vacuum drying process is established.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

ABSTRACT

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.     

MATHEMATICAL MODELLING OF MDF FIBRE DRYING: DRYING OPTIMISATION

ABSTRACT

In the production of MDF, wet resinated fibre must be dried to its target moisture content, normally 9 to 11%, before compaction into a board by hot pressing. Fibre drying can be interpreted as an incorporated process involving gas-solid two phase-flow, inter-component transfer, and heat and mass transfer within the fibre. Based on these mechanisms, a mathematical model has been developed to simulate the MDF fibre drying process. From the model, fibre moisture content, air temperature and air humidity along the dryer length can be predicted and factors affecting the drying rate examined. The model can be employed to optimise drying conditions and to evaluate improvements in dryer design. A case study of drying improvement in reduction of dryer emissions and heat consumption is given to demonstrate the potential application of the developed dryer model.     

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.     

HIGH-INTENSITY DRYING OF PAPER

High-intensity contact drying denotes drying under suf- ficiently intensive heating conditions that, following a brief warmup period, the mist paper web operates at internal tem- peratures in excess of the ambient boiling point. A simplified, two-zone analytical model is first presented. The paper is depicted as having a dry layer, of ever-increasing thickness, adjacent to the hot surface. Heat conduction through this layer (the rate-limiting step) causes evaporation at the interface with the “wet zone.” The vapor is then considered to flow through the wet zone into the ambient. Results of bench-scale experiments are discussed. Drying rates as much as twenty times conventional rates are indicated. The drying rate increases with hot surface/boiling point tem- perature difference and applied mechanical pressure. The instsn- taneous drying rate decreases continuously after a brief warmup period. The vapor pressure at the hot surfacelpaper interface rises quickly to a peak value, followed by a continuously- diminishing level. The heat flux shows a rapid rise to boiling- like conditions, followed by a drop to a range compatible with measured drying rates. The temperature of the open side of the sheet is constant during drying, after its initial rise to the boiling point. The experimental results are compatible with pre- dictions of the model.     

Drying of Wheat Based on the Non-Equilibrium Thermodynamics: A Numerical Study

A new mathematical model to describe simultaneous heat and mass (liquid and vapor) transfer and shrinkage during drying of capillary-porous bodies with particular reference to prolate spheroid solid is presented. As an application, the methodology was used to predict drying of soft red winter wheat (Arthur). The mathematical model was based on the nonequilibrium thermodynamics considering variable transport coefficients and convective boundary conditions at the surface of the solid. All the partial differential equations presented in the model have been written in prolate spheroidal coordinates and solved numerically by a finite-volume method using implicit fully formulation. Results of the drying and heating kinetics and moisture content and temperature distributions in a wheat kernel during drying process are presented and analyzed. The methodology allows verification of the heat, liquid, and vapor fluxes, taking into account the thermal and hydrical gradients inside the grain.     

HIGH-INTENSITY DRYING OF PAPER

High-intensity contact drying denotes drying under suf- ficiently intensive heating conditions that, following a brief warmup period, the mist paper web operates at internal tem- peratures in excess of the ambient boiling point. A simplified, two-zone analytical model is first presented. The paper is depicted as having a dry layer, of ever-increasing thickness, adjacent to the hot surface. Heat conduction through this layer (the rate-limiting step) causes evaporation at the interface with the “wet zone.” The vapor is then considered to flow through the wet zone into the ambient. Results of bench-scale experiments are discussed. Drying rates as much as twenty times conventional rates are indicated. The drying rate increases with hot surface/boiling point tem- perature difference and applied mechanical pressure. The instsn- taneous drying rate decreases continuously after a brief warmup period. The vapor pressure at the hot surfacelpaper interface rises quickly to a peak value, followed by a continuously- diminishing level. The heat flux shows a rapid rise to boiling- like conditions, followed by a drop to a range compatible with measured drying rates. The temperature of the open side of the sheet is constant during drying, after its initial rise to the boiling point. The experimental results are compatible with pre- dictions of the model.     

DRYING OF TOBACCO PARTICLES IN A MOBILISED BED

ABSTRACT

The drying performance of a novel device capable of mobilising a bed of fibrous materials is evaluated. The drying kinetic of the vegetable product used for this work, cut lamina tobacco particles, was determined from fixed bed experiments. A falling-rate period was observed for the entire drying curve. The results showed that the drying rate is controlled by internal mass transfer mechanism for gas superficial velocities above 0.8 m/ s. The proposed model is based on an effective liquid diffusion coefficient that varies with solids temperature according to an Arrhenius-type relationship. Batch drying experiments were carried out in the mobilised bed apparatus under various conditions of inlet air temperature, humidity and flowrate. Assuming perfect mixing and no internal resistance to heat transfer for the solids, the performance of the mobile bed can be predicted using the proposed internal liquid diffusion model     

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

Abstract

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     

高初始含湿多孔介质喷雾干燥过程的热质耦合传递

多孔介质是大量干燥过程的主体,由于实际多孔介质干燥过程的复杂性,建立通用的干燥过程传热传质模型十分困难。通过分析喷雾干燥过程中高初始含湿多孔介质与干燥介质之间的传热传质机理以及各因素对传热传质的影响,根据马歇尔方程探讨了干燥介质与料雾之间的水蒸汽分压差在干燥过程中的变化情况,反映了多孔湿介质在喷雾干燥操作中的传热传质过程的几种特性,为确定实际生产中喷雾干燥器的操作条件指明了新的出路。     

ENERGY SAVING IN INDUSTRIAL DRYING PLANTS BY PARTIAL RECOVERY OF THE LATENT HEAT OF THE EXHAUST AIR

ABSTRACT

Energy saving in industrial drying by recovering part of the latent heat of the vapor exiting the drier is considered in this paper. This heat recovery is accomplished through a two-stage heat exchanger system, wherein the first stage brings the primary circuit to vapor saturation conditions, while the second stage acts as a condenser. Optimal heat recovery is assured by intelligent, fully automated process control.     

DISCONTINUOUS VACUUM DRYING OF OAK WOOD: MODELLING AND EXPERIMENTAL INVESTIGATIONS

Abstract

Vacuum drying and especially discontinuous vacuum drying is a very attractive process for such a wood as oak, because of a reduced drying time and a high quality of the final product. In this paper, a model describing heat, mass and momentum transfer in a capillary porous and hygroscopic medium under vacuum drying with no external heating agent (the material is pre-heated during a convective phase), is presented. The choice of the following three independent unknowns, moisture content, enthalpy and dry air density, leads to a fully well described problem where the effect of gaseous pressure inside the material is taken into account. A new formulation of the boundary conditions and its numerical resolution are validated by experimental results.     

Numerical Investigation on Dielectric Material Assisted Microwave Freeze-Drying of Aqueous Mannitol Solution

Abstract

The dielectric material assisted microwave freeze-drying was investigated theoretically in this study. A coupled heat and mass transfer model was developed considering distributions of the temperature, ice saturation and vapor mass concentration inside the material being dried, as well as the vapor sublimation-desublimation in the frozen region. The effects of temperature and saturation on the effective conductivities were analyzed based on heat and mass flux equations. The model was solved numerically by the variable time-step finite-deference technique with two movable boundaries in an initially unsaturated porous sphere frozen from an aqueous solution of mannitol. The sintered silicon carbide (SiC) was selected as the dielectric material. The results show that dielectric material can significantly enhance microwave freeze-drying process. For case of the dielectric field strength, E = 4000 V/m under typical operating conditions, the drying time is 2081 s, 30.1% shorter and 47.2% longer, respectively, than those for E = 2000V/m and E = 6000 V/m. The heat and mass transfer mechanisms during the drying process were discussed.