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

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     

ESTIMATION OF THE EFFECT OF PRODUCT SHRINKAGE ON THE DRYING TIMES,HEAT INPUT AND CONDENSER LOAD OF THE PRIMARY AND SECONDARY DRYING STAGES OF THE LYOPHILIZATION PROCESS IN VIALS

ABSTRACT

The effects of cake shrinkage on the drying times and energy requirements of the primary and secondary drying stages of the freeze drying process involving the drying of a material in a vial, are estimated through the construction and solution of an extended unsteady state and spatially multidimensional model that accounts for the changes introduced by cake shrinkage on the internal and external mass and heat transfer mechanisms of the freeze drying     

BOUND MOISTURE REMOVAL: HEAT AND MASS TRANSFER IN CONTACT DRYING

ABSTRACT

Coupled heat and mass transfer in short-term contact of the moist material and the heating surface (the physical model of drying with agitation) is examined. Technological characteristics of the drying process: heating rate and drying rate, heat transfer coefficient, etc. have been determined based on solutions of the diffusion and diffusion-filtration heat and mass transfer. The usage of non-field method of determination of mass and heat fluxes on the phase interface allows calculation of the drying equipment efficiency without preliminary determination of the fields of required quantities. The results may be used for estimation of the influence of drying conditions and material properties on the moisture removal process.     

AN APPLICATION OF SIMULTANEOUS HEAT AND MASS TRANSFER IN A CYLINDER USING THE FINITE-DIFFERENCE METHOD

ABSTRACT

A study of simultaneous heat and mass transfer during drying an infinite cylinder shape material (twigs of ilex paraguayenais saint hilaire) was carried out. The finite-difference method was used to solve the drying model and a simultaneous heat and mass balance in each node was made. Models with different assumptions were tested and the external mass transfer coefficient was used as a parameter to fit the model to experimental data. The thickness of the node and the time step were selected considering the system stability.

Drying temperature, twig diameter and air velocity were selected as study variables. The models results were in good agreement with experimental measurements giving mass coefficient values between 1.97 10^?4and 9.55 10^?4 Kg/m² s.     

Multiscale and multilayer structural modeling and simulation on drying of grain packing porous media

ABSTRACT

Aiming at the problem of multilayer physical structure for the skeleton of porous media, a multiscale and multilayer structural model of heat and mass transfer processes for drying of grain packing porous media was established by applying the pore network method and multiscale theory. An experimental study on rice drying was conducted in order to validate this model. The simulation and experimental results indicated that the established model could explain the mechanical properties of rice drying well. The rate of heat transfer was faster than the rate of mass transfer and there was a higher moisture gradient inside the rice grain. The diffusion coefficient of rice embryo played an important role in the drying process, and whose effect on drying was larger than the diffusion coefficient of rice hull and chaff. The moisture was imprisoned effectively inside the rice when the diffusion coefficient of rice embryo was very small.     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

MATHEMATICAL AND PHYSICAL FOUNDATIONS OF DRYING THEORIES

ABSTRACT

In this paper a survey is given concerning to the stochastic modelling approaches in transport processes with a special emphasis on application possibilities for simultaneous heat and mass transfer in drying.

First, the mostly used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (state-independent) conductivity coefficients. Powerful discretisation methods are shown for their solution.

Basic principles of variational calculus are discussed then with an attention on direct methods. As a simple application a first-order approximation example is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivity coefficients has a crucial influence on the flow pattern of the coupled heat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefficients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statistical properties of percolative     

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.     

MODEL SELECTI0N IN AIR DRYING OF FOODS

ABSTRACT

The purpose of this investigation is to compare various drying models with respect to (a) the accuracy in calculating the material moisture content and temperature versus time and (b) the computation time required.

Mechanistic as well as phenomenological heat and mass transfer models are considered. The mechanistic models are formulated by considering different combinations of mechanisms between (1) moisture diffusion in the solid towards its external surface (2) vaporization and convective transfer of the vapor into the air stream (3) convective heat transfer from the air to the solid's surface (4) conductive heat transfer within the solid mass. The phenomenological model incorporates the drying constant while the mechanistic models incorporate the mass diffusivity, the mass transfer coefficient in the air boundary layer, the thermal conductivity, and the heat transfer coefficient in the air boundary layer.

The proposed methodology is applied to experimental data of four vegetables, namely, potato, onion, carrot, and green pepper. The experiments involve three thickness levels, five temperatures, three water activities, and three air velocities. The results obtained concern (a) the standard deviations between experimental and calculated values of material moisture content andtemperature, which, in combination with the computation time, are the necessary information for model selection for a special application, and (b) the model parameter estimates which are necessary to use the selected model.     

Experimental Study of the Heat and Mass Transfer During Drying in a Fluidized Bed Dryer

ABSTRACT

Drying curves obtained in a pilot-scale fluidized bed dryer using biological source solids (sawdust, soya and fish meal) were used to estimate the parameters involved in heat and mass transfer phenomenas: heat transfer coefficient and moisture diffusivity coefficient. Parameters involved in mass transfer were estimated from drying models based on diffusional mechanisms and others that in addition consider internal and external resistance to the mass transfer. The estimate ef ective diffusivity coefficient was between 2x10-11 to lx10 (m2/s) for the considered products. Heat transfer coefficient was estimated from drying data points in the constant drying rate period when the external resistance to the mass transfer controls the process.     

MEASUREMENT OF COEFFICIENTS FOB SIMULTANEOUS HEAT AND MASS TRANSFER IN FOOD PRODUCTS

ABSTRACT

Two experimental devices were designed and built to determine four coefficients K_T K_M D_M D (or δ_T = D_T / D_M occurring in simultaneous heat and mass transfer equations, where,K _T and D_M are thermal conductivity and moisture diffcusivity respectively, D_T ( or δ _T is temperature gradient Induced moisture migration coefficient and K_M is moisture gradient Induced heat transfer coefficient. Three food materials, i.e. potato, bread dough and bread, were tested. From this study, it was found that the value of 5 was higher for low density food materials, such as bread, than for high density materials, such as potato. The coefficient & measures moisture migration contribution due to temperature gradient within the material. The average values of δ _T for potato, bread dough and bread were 0.0014, 0.0059 and 0.0127 per °C, respectively. The contribution of temperature gradient to the overall moisture migration is negligible In high density materials. However, this contribution may be important in the moisture migratlon analysls for low density materials. The moisture gradient induced heat transfer coefficient % as found to be negligible for the materials tested in this study     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART II: EXPERIMENTAL RESULTS

ABSTRACT

Experimental measurements of drying rate, moisture distribution, surface moisture content, and temperature distribution are reported for softwood dried in the radial, tangential, and mixed (between radial and tangential) directions. The effects of both the heterogeneous and the anisotropic structure of wood are observed. The drying curves for tangential drying exhibit two distinct transition points - one when the surface reaches the fiber saturation point and one when the surface becomes completely dry. These transitions are not observed consistently for drying in the radial and mixed directions. For mixed drying, as a result of anisotropy, the drying rate is always higher at the side of the sample to which the growth rings point at die surface. Measurements of the surface mass transfer coefficient indicate that the theoretical value which is analogous to the convective heat transfer coefficient agrees well with that measured experimentally at both very high and very low values of the surface moisture content. At intermediate values of the moisture content the ratio of the experimental to the theoretical convective mass transfer coefficient can be as low as 0.20. The model discussed in Part I predicts results that are in good qualitative agreement with the experimental results presented in this paper.     

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.     

DRYING OF CLAY. II RHEOLOGICAL MODELISATION AND SIMULATION OF PHYSICAL PHENOMENA

ABSTRACT

The present study proposes the development of a complete mathematical modelling transfer phenomena involving at the same time heat, mass and momentum transfer during the drying process of clay. Clay is a generic example of colloid materials forming particulate gels. That can be considered as bi-constituent, homogeneous, isotropic, and highly deformable. The model was numerically solved by the finite difference method and validated by comparison of the numerical results with a previous set of experiments data. The simulation has allowed the determination of spatio-temporal evolution within the solid of different variables: temperature fields, moisture contents, displacement, deformation and stresses. The parametric sensibility has been analyzed in the case of thermophysical properties and the external heat transfer coefficient. Various values of external conditions have been analyzed.     

CONVECTTVE HEAT AND MASS TRANSFER AND EVOLUTION OF THE MOISTURE DISTRIBUTION IN COMBINED CONVECTION AND RADIO FREQUENCY DRYING

ABSTRACT

In a previous study (Dostie and Navarri, 1994), experiments indicated that a non-uniform moisture distribution could develop in radio frequency drying depending on the applied power and initial conditions, making the design and scale-up of such a dryer a more difficult task. Consequently, a thorough study of the combined convection and RF drying process was undertaken. Experimental results have shown that the values of the neat and mass transfer coefficients decrease with an increase in evaporation rate caused by RF energy. This effect is adequately taken into account by the boundary layer theory. Furthermore, the usual analogy between heat and mass transfer has been verified to apply in RF drying. Experiments have also shown that a different mass transfer resistance on both sides of the product should not result in non-uniform drying. However, it appears that non-uniform drying is dependent upon the initial moisture distribution and the relative intensity of heal transfer by convection and RF- It was shown that the maximum drying rate occurs at a higher average water content and that the total drying time increases with non-uniformity of the initial moisture distribution.     

Heat and Mass Transfer Coefficients in Computer Simulation of Paper Drying

ABSTRACT

The development of a mathematical model and a computer program to facilitate the study of thc multi-cylinder paper drying process is presented. Experimentally determined values for different heat and mass transfer coefficients are used to ensure the physical validity of the model. A unique feature of the model is its inclusion of a mass transfer coefficient for the dryer fabric. Thus far. the mass transfer mechanisms in the web have not been included. Two heat transfer coefficients are used to tune the model to actual mill data. They areassigned values that are consistent with experimental data. The agreement between predicted and experimental data, obtained hom nine industrial paper dryers, is generally very good. The investigated basis weights range from 48 to 240 g/m2.

Calculations indicate that the condensate and contact heat transfer coefficients have a major influence on the drying process. The thermal conductivity of the paper and cylinder shell, respectively, are relatively important. whereas the influence of the fabric mass transfer coefficient and the cylinder-fabric-paper heat transfer coefficient are less pronounced. Some guidelines on how to obtain corect values are discussed.     

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

ABSTRACT

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

HEAT AND MASS TRANSFER DURING DRYING OF A LIQUID FILM FROM THE SURFACE OF A SINGLE INERT PARTICLE

ABSTRACT

This paper presents the results of theoretical and experimental studies on drying of aqueous suspensions of finely dispersed solids sprayed over the surface of an inert ceramic sphere. The effects of temperature and air velocity on kinetics of heat and mass transfer as well as peeling off the layer of a dry material from the sphere surface are described. The mathematical model of a drying process based on simplified ?gradientless? approach to transfer phenomena is proposed. The adequacy of the model developed for drying of the wet coat from a single sphere to the real drying process taking place in a bed of particulate carrier is confirmed by results of drying of several organic dyestuffs in an industrial spouted bed dryer with inert particles.     

MATHEMATICAL MODELING OF CONTINUOUS DRYERS USING THE HEAT AND MASS TRANSFER PROPERTIES AND PRODUCT-AIR EQUILIBRIUM RELATION

ABSTRACT

In this work a phenomenological mathematical model that describes the continuous drying process is presented. Heat and mass transfer in gas phase, solid phase and gas-solid interface were taking in account in the model. In addition, the equilibrium and interfaces conditions were evaluated using the product sorption isotherm. Model structure is a system of four couple differential equations in conjunction with five algebraicequations. The results shown that this structure is robust with respect to heat or mass transfer controlled mechanisms. Behaviors predicted were similar with other simulators results and with the behavior reported by chemical engineering texts. The proposed mathematical model is able to use in continuous drying operation design involving heat and mass transfer properties and equilibrium relationships.